Merged Past Papers Mathematics_4024.pdf

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/11

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2013

Qu 1

2

3

4

Answers

Mark

(a)

100

1

(b)

475

1

(a)

0.06 oe

1

(b)

50

1

(a)

3.556

1

(b)

12000

1

(a)

<

1

(b)

(0) . 07

1

16

2

5

Syllabus 4024 Part Marks

B1 for PX or XQ = 8 or M1 for PX2 = 102 – 62 oe

8+5 oe seen 20

6

7 oe isw 20

2

B1 for

7

1 : 60 000

2

C1 for 1 : figs 6 or M1 for 4.5 : 270 000 oe

8

9

(a)

148 soi

1

(b)

−

12 13

1

(a)

18

1

(b)

90

2

M1 for x B1 for figs

10 (a) (b)

55

1

ma − b oe m

2

10 x = 81 or better or 100 81 seen 9

M1 for b = ma – mc or

b =a–c m

B1 ft for their c after M0 square

1

(b)

trapezium

1

(c)

kite

1

11 (a)

© Cambridge International Examinations 2013

Paper 11

Page 3

Mark Scheme GCE O LEVEL – May/June 2013

Syllabus 4024

12 (a)

619

1

(b)

196

1

(c)

169, 196 or 961

1

25

2

M1 for a correct area

1.25 oe

1

Accept

14 (a)

32˚

1

(b)

26˚

1

Accept 90 – ( (a) + 32

(c)

58˚

1

Accept 90 –

13 (a) (b)

)

(ii) Arc radius 5 centre B.

16 (a) (b)

(a ) ft 20

1 ( (a) + 32) 2

1

15 (a) (i) Bisector of ADC

(b)

Paper 11

1

Correct region shaded.

1

44

1

5400

2

C1 for figs 54 M1 for 23 : 33 seen in any form.

6.24×103

1

8×10-2

2

18 (a)

30

1

(b)

66

1

(c)

30

2

M1 for an attempt at 78 – 48.

19 (a)

7π 9

2

M1 for

17 (a) (b)

(b) (i)

(ii)

6

2 π 3

11 15

C1 for figs 8 or for any correct value however expressed.

40 πr 2 360

1

1

© Cambridge International Examinations 2013

Page 4

Mark Scheme GCE O LEVEL – May/June 2013

20 (a) (i) 26

1

(iii) 16

1

–2

1

(R =) 3p3 seen

1

(b)

4

2

(c)

(Diagram) 2

1

22 (a)

Correct triangle C

1

(b)

Correct triangle D

2

(c)

1 0    0 3

1

23 (a) (i)

4 oe 6

1

21 (a)

(ii)

e.g. y =

4 x + 3 oe 6

M1 for 192 = 3p3 oe

C1 for two vertices correct or for triangle of the correct size and orientation.

1

(iii) y = 3x + 2

1

y≥2

2

6 9    1 3

1

(b)

C1 for one of these.

4 y≤ x+2 6

24 (a) (i)

(ii)

1 5

Paper 11

1

(ii) 6

(b)

Syllabus 4024

 1 3    −1 2

2

B1 for det = 5 soi or  1 3   −1 2

for k  (b)

1, 2, 3,4,6,8,12

2

(c)

M ′∩ N

1

B1 for 5 correct with no extras

© Cambridge International Examinations 2013

Page 5

25 (a) (b) (c) (d)

Mark Scheme GCE O LEVEL – May/June 2013 5xy(2x + 3y)

1

(5a – b)(5a + b)

1

1 − 2x ( x + 1) ab 6

2

Final Answer

Syllabus 4024

3 − 2( x + 1)

2

M1 for

2

C1 for any 2 terms correct

M1 for

( x + 1) 2

oe

3a 2 5b 2 c × soi 10bc 9a

© Cambridge International Examinations 2013

Paper 11

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/12

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2013

Qu 1

2

3

4

5

6

7

8

9

Answers

Mark

(a)

6 35

1

(b)

15 16

1

(a)

8 Final ans. 23

1

(b)

11 : 12

1

(a)

5 cm, 500 mm, 500 m, 50 km

1

(b)

4160

1

(a)

−

1 3

1

(b)

–1

1

(a)

F

1

(b)

E

1

(a)

Correct reflection

1

(b)

Correct rotation

1

(a)

– 1.3

1

(b)

3.2

1

(c)

– 1.5

1

(a)

64

1

(b)

13

1

(c)

Any irrational number in range 1
1

(a)

0.0041

1

(b)

11 ( < 131 < ) 12

1

(c)

(3 × 2 + 1 )2 = 49

1

© Cambridge International Examinations 2013

Syllabus 4024

Part Marks

Paper 12

Page 3

Mark Scheme GCE O LEVEL – May/June 2013

10 (a)

2

A

1 7 5

4

8

3 9

10

B

6

6

1

(c)

1, 5, 7.

1

12

1

1.44 : 1

2

Perpendicular bisector of AB.

1

Correct region shaded

2

(b) 12 (a) (b)

Paper 12

1

(b)

11 (a)

Syllabus 4024

B1 for 1.22 seen or 62 : 52 soi.

B1 for arc radius 6 cm, centre C After 0 for (a) and (b), Allow 1 for an accurate bisector of any side.

13 (a)

(b)

 4 − 1    1 − 1 1 6

 0 − 3   2 2 

1

oe isw

2

B1 for determinant = 6 soi or  0 − 3   soi 2 2 

14 (a)

62.7(0)

2

C1 for 66.5(0) or B1 for 8.25 soi

(b) 15 (a)

(b)

35 (P = )

1 1 2 Q oe seen 4

10, – 10

1

2

B1 for 25 =

1 2 Q oe 4

© Cambridge International Examinations 2013

Page 4

16 (a)

(b)

Mark Scheme GCE O LEVEL – May/June 2013 1 16

1

3y 2 x

2

Syllabus 4024

Paper 12

C1 for 2 out of 3 terms correct.

B1 for

for

1 3x 2 3 x2

(9) y 4 soi or x2 y3

soi

y

5π cao 8

2

3

1

4.8×107 cao

1

(b)

9.3×106

oe

2

M1 for 1.85×107 – 9.2×106 oe

(c)

5.1×108

cao

1

After 0 in (a) and (c), Allow 1 for a correct (c) in any form.

17 (a) (b) 18 (a)

19 (a) (i) 1 (ii) 2.1 r 2 (b) 20 (a)

M1 for

1

1 only. 10

2

34

1

2

2

M1 for

7x + 3 Final answer ( x + 4)( x − 1)

2

Σfx 20

M1 for 3x + 2(2x – 1) = 12 or better soi or

for

(b)

45 πr2 360

3x 2x 1 + =3+ 4 2 2

M1 for

5( x − 1) + 2( x + 4) soi ( x + 4)( x − 1)

© Cambridge International Examinations 2013

Page 5

Mark Scheme GCE O LEVEL – May/June 2013

Syllabus 4024

4 16 30 52 70 80

1

(b)

Correct ft curve

2

B1 for at least 5 correct ft points

(c)

16 to 18

2

B1 for their CF at m = 45 ft

21 (a)

Paper 12

After 0, allow B1 for 80 – their CF at m = 44 Line from (13 10,12) to (13 55,0)

2

(b)

6.9 to 7.4

1

(c)

18

1

(d)

Correct graph

2

B1 for final speed 20 km/h soi or for first two lines of the graph correct.

Congruency shown

3

Maximum of 2 independent B marks for

22 (a)

23 (a)

B1 for start of line correct or for a line with the correct gradient. Or for a line from (13 10,0) to (13 55, 12)

) ) AB0 = AD O = 90˚ or

AB = AD or BO = DO or AO is common (b)

Kite or Cyclic Quadrilateral

1

(c)

44

2

t2 – 2t – 15

seen

1

(b)

(8x – 3y)(8x + 3y)

1

(c)

(3a + 2)(2b – a)

2

24 (a)

(d) (i) (x – 3)2 – 6 (ii)

3± 6

)

B1 for BOD = 136˚

B1 for any factorisation of any two terms, at any stage.

1 1ft

FT from (d)(i)

© Cambridge International Examinations 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/21

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2013

Syllabus 4024

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied SECTION A Qu. 1

3

Mark

Part Marks

(a)

x=3

2

M1 for ± 5x = ± 15 =

(b)

x = 4, y = –1

3

B2 for one correct value www

(c) (i)

–1, 0, 1

1

y > –2 final answer

2

B1 for –2 seen

(a)

24

2

B1 for 15 seen

(b) (i) (a)

180 – q cao

1

(i) (b)

p – q cao

1

(ii) (a)

8 cm

1

(ii) (b)

4.9 cm

1

(a) (i)

10, 12

1

(ii)

2m oe

1

(b) (i)

25, 36

1

(ii)

n2

1

(iii)

18

1

t2 + 2t oe

1

675

1

(ii) 2

Answers

(c) (i) (ii)

© Cambridge International Examinations 2013

Paper 21

Page 3

4

5

10 1 9 1 10 0 oe , , , , , 11 11 10 10 10 10 correctly placed

2

(ii) (a)

6 oe 11

1

(ii) (b)

9 22

2

(b) (i)

1

1

(ii)

2

1

€ 216

1

($1 = €) 0.68

1

Profit $43.3(0)

3

(a) (i)

(a) (i) (ii) (b) (i)

(ii) 6

36 to 36.1%

Syllabus 4024

Paper 21

B1 for 3 correct values correctly placed

M1 for 3 ×

B2 for Loss $43.40 or M1 for two of 87.50, 48.60 and $27.20 and M1 for attempt at adding any three prices and then subtracting 120

1 ft

18 7 18 M1 for tan 55 = DE A1 for DE = 12.6 to 12.61 cm 1 M1 for (9 + 7 + their 12.6) × 18 or for a 2 complete alternative method M1 for tan A =

68.7°

2

257 to 257.5

4

(b)

26°

2

M1 for 41.5 or 112.5 used

(a)

0.01 m/s cao

2

M1 for 200/19.94 or 100/9.98

(b) (i)

120 120 or x x+3 120 120 6 oe − = x x + 3 60 Correct eqn with denominator removed

3

B1

(ii)

x = 58.5 or – 61.5

3

(iii)

123 – 123.1 minutes

2

(a) (i) (ii)

7

Mark Scheme GCE O LEVEL – May/June 2013

B1

B2 for 1 correct answer Or for 58 – 59 AND –61 – –62 − 3 ± 14409 B1 for 2 C1 for –58.5 AND 61.5 M1 for 120/their positive 58.5

© Cambridge International Examinations 2013

Page 4

Mark Scheme GCE O LEVEL – May/June 2013

Syllabus 4024

Paper 21

SECTION B

8

(a) (i) (ii) (iii) (b) (i)

9

–5.5 or –5

1 2

1

2x + 3 4 1 g = 0.5 or 2

f–1(x) =

2 2

Enlargement Scale factor –3, Centre A

5

2

2x − 3 2y + 3 or oe 4 4 8g − 3 M1 for =g 2

C1 for

B1 B1

1

(ii)

2.2 to 2.24 or

(iii)

 0    − 7

2

B1 for 0 B1 for –7

(iv)

10    1

2

 or AF =   M1 for use of DF =   4   − 2

h = 29.8 to 29.85

2

M1 for π × 4 2 × h (= 1500)

100

1

(b)

x = 2.5

2

(c) (i)

(2y – 3)(2y + 11)

1

(ii)

y = 1.5 or –5.5

1

(iii)

67.5 cm2

1 ft

(iv)

495 cm2

3

9 cao 25

1

(a) (i) (ii)

(d)

 − 2

M1 for

 1 

1 × 12 x × 5 x or better for cross section 2

B1 2 × their (iii) B1 240 × their 1.5

© Cambridge International Examinations 2013

Page 5

10 (a) (i)

Mark Scheme GCE O LEVEL – May/June 2013

2 2 , oe 3 3

Syllabus 4024

1

(ii)

8 points correctly plotted and one set of 5 joined with a curve

2 ft

B1 for at least 6 correct plots

(iii)

1.7 to 1.8 AND –1.7 to –1.8

1 ft

(iv)

–2.5 to –5 (dep on M1)

M1 for tangent to curve at –1.5 soi After M0, SC1 for 3 to 4 M1 for x + y = 2 drawn

(v)

–1.3 to –1.4 (dep on M1)

2 2 ft

a = 3, b = 405 (cao)

2

(ii)

(0, 5) cao

1

(iii)

20

(b) (i)

One mark for each

1 ft

510 – 520 m

1

(ii)

C positioned 7 cm from A and 6 cm from B with both construction arcs drawn

2

(iii)

146° ± 2

(iv)

D positioned 10.3 cm ± 0.8 from A and DAˆ C = 34° ± 2°

2

B1 for DAC = 34 ( ± 2°)

164 to 164.11° www

4

B3 for QPR = 110 to 110.11

11 (a) (i)

(b) (i)

B1 for c positioned 7 cm from A and/or 6 cm from B

1 ft

Or B2 for

− 2750 or –0.343 to 0.344 80000

Or B1 for (cos P =)

160 2 + 250 2 − 340 2 (2×) 160 × 250

And

(ii)

Paper 21

18780 – 18800

2ft

M1 for their P + 54° 1 M1 for × 250 × 160 × sin 110.1 2

© Cambridge International Examinations 2013

Page 6

Mark Scheme GCE O LEVEL – May/June 2013

Syllabus 4024

Paper 21

14.8 kg www

3

M1 for 15×3+14×8+20×12+24×15+31×17+24×20+12 ×26 (= 2076) M1 for dividing by 140 (indep)

(ii)

Correct histogram

3

M2 for 5 correct bars or M1 for 3 correct bars or all correct heights seen

(iii)

11 oe 35

2

M1 for 15 + 14 + 15 ( = 44) used

9

1

(ii)

35%

1

(iii)

96°

2

12 (a) (i)

(b) (i)

M1 for (15 + 2) ÷ 64 (× 360)

© Cambridge International Examinations 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/22

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2013

Syllabus 4024

Paper 22

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Qu. 1

Answers (a) (i)

Mark

$720.7 – $721.1

2

(ii) $1.45

1

(b) (i) $8272

2

(ii) 8560 - 8562

3

(b)

n2

1

(c)

32

2

(d)

3 2

1

(a)

n(n+1) oe

360

or better

B1 for (T =) 1024 seen

1ft

(n + 1)(n + 2) oe

x = – 4 cao

(b) (i) y ≤ 4.25 oe final answer (ii) 3,4

4

72 2.06

B1 for 2 correct

2

1 2

3.4 100

or

or C1 for Simone’s 8560 seen or C1 for Simone by $8.28 final answer

25, 21, 45

(f)

M1 for 8000 ×

2.06 72

2

(a)

(e)

M1 for 25200 ÷ 72 (=350) or

1ft

(iii) Lydia by $1.52, final answer, cao 2

Part Marks

1 2

(n − 1)(n − 2) oe

2

or C1 for

2

M1 ± 2x = or ±8 =

2

C1 for 4.25 oe seen

1

(c)

x = 1.5, y = – 3

3

B2 for 1 correct value www Or B1 for pair of values satisfying either eqn

(a)

7

2

M1 for (AF + 16) × 6 = 138 or equiv seen

(b) (i) EG = 5.75

2

C1 for 11.5 seen or for 5.7 or 5.8 seen

2

B1 for (their 5.75) : (16 – their 5.75) C1 for 41k : 23k

(ii) 23k : 41k where k is an integer

© Cambridge International Examinations 2013

Page 3

5

Mark Scheme GCE O LEVEL – May/June 2013

No and 799.5 cm (or 7.995 m)

(a)

(b) (i) $27 (ii) $1210 – 1211

6

Syllabus 4024

2

M1 for 180.5 and 15.5 seen

2

M1 for 130% ≡ 35.10 soi

3

M1 for 50.70×4 + 35.10×5 (378.30) M1 for their 378.30×2.2 (=832.26) Or their 202.80 × 2.2

(a)

35o

1

(b)

286.7 to 287

2

M1 for sin their 35 =

(c)

(0) 31 to (0)31.2

3

M1 for Tan θ =

335 500

x 500

or

Paper 22

or better

500 335

^

B1 for SPQ = 33.8 – 34 7

(a) (i) Bar height 1.4 between 100 – 120

1

(ii) p = 48 q = 42 (iii)

57 200

2

B1 for p = 48 or B1 for q = 42

1

or 0.285 or 28.5%

(b) (i) 40 < y ≤ 60

1

(ii) 39.9

3

M1 for 34 × 10+57 × 30+85 × 50+24×70 (= 7980) i.e. 340 + 1710 + 4250 + 1680 M1 for dividing by 200 (indep)

SECTION B 8

(a)

150 m

1

(b)

C due east of B (±2°) and C 12 cm (±2mm) from A

2

B1 for due E of B , B1 for 12 cm from A

(c)

994.9 to 995 m

2

M1 for 18002 – 15002 (= 990000) Or 122 – 102 (= 44)

(d)

1800 1500 or x x +1 1800 1500 – = 60 oe x x +1 Correct eqn with both denominators removed

B1 B1 3

© Cambridge International Examinations 2013

Page 4

9

Mark Scheme GCE O LEVEL – May/June 2013

(e)

x = 7.83, – 3.83

(f)

229 – 230 s

(a) (i)

5    2

3

Paper 22

B2 for one correct answer Or for 7.8 – 7.85 AND -3.8 – -3.85 4 ± 136 OR B1 for or better. 2 Or C1 for -7.83 AND 3.83

1ft 1

45 or 6.7 to 6.71

2

(iii) (a) Enlargement Scale Factor 3 Centre B

2

(ii)

Syllabus 4024

 7.5  (b)    3 

2ft

 − 3  3  B1 for   or   seen. Must be in  6   − 6 vector form.

B1 for Enl, B1 for SF3 and Cent B oe

B1 for 7.5 B1 for 3.

(b) (i) f (– 4) = – 2

1

(ii) g = 11

2

M1 for

3g + 2 =7 5

2

C1 for

5x + 2 5y − 2 or oe 3 3

(iii) f-1 (x) =

10 (a) (i)

5x − 2 oe 3

n 24

B1

24 − n oe 24 (ii) (a)

2

n(25 − n) oe final answer 25 × 24

B1

1 1 p

2

B1 for their (a) =

(iii) n = 15 or 10

2

M1 for (n – 15)(n – 10) or

3 oe 20

2

C1 for

(b) p = 4

(iv)

7 20

oe

© Cambridge International Examinations 2013

25 ± 25 seen 2

Page 5

Mark Scheme GCE O LEVEL – May/June 2013

(b) (i) 300

Paper 22

1

1 12

1

(iii) 25

1

(ii)

Syllabus 4024

11 (a) (i) – 8.5

1

(ii) 8 points correctly plotted and joined with a smooth curve on correct axes

3

B1 for correct scale (condone rev axes) B1 for 6 or 7 given table points correctly plotted on their axes B1 for smooth curve through all 8 points on their consistent axes

(iii) 2.5 – 6.5 (dep on tangent soi)

2

M1 for tangent at x = 1.5 soi

(iv) – 0.85 to – 0.95

2

M1 for y = 1 soi

2

B1 for p = 1.2 , B1 for q = 0.5 ft

4 oe 5

2

M1 for

r = 22 cao

3

B1 for 70000 soi M1 for π × r2 × figs46 (only term)

(b) (i) 18(.0) to 18.03 cm2

2

M1 for

(b) (i) p = 1.2 q = 0.5 (ii)

12 (a)

−

−2 oe 3 − theirq

1 2

× 4 × 11 × sin125

(ii) 360 to 360.6 cm3

1ft

(iii) x =13.69 to 13.7

4

M1 for 42 + 112 ± (2) × 4 × 11 × cos125 M1 for x2 = 42 + 112 - 2×4 × 11 × cos125 or better A1 for 187.4 – 187.5

(iv) 609.8 to 610.1 cm2

2

M1 for at least 4 correct areas

© Cambridge International Examinations 2013

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 3 9 0 6 7 5 5 8 0 8 *

MATHEMATICS (SYLLABUS D)

4024/11 May/June 2013

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (SLM/CGW) 64207/3 © UCLES 2013

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

In this shape all the lengths are in centimetres. 5

20

10

12 25 5

Work out (a) the perimeter,



Answer

...................................... cm [1]

Answer

.....................................cm2 [1]

Answer

............................................ [1]

Answer

............................................ [1]

(b) the area.

2

Evaluate (a) 0.3 × 0.2,

(b) 3.5 ÷ 0.07 .



© UCLES 2013

4024/11/M/J/13

For Examiner’s Use

3 3

(a) A bag containing fruit has mass 3.813 kilograms. When the bag is empty its mass is 257 grams.

For Examiner’s Use

Find, in kilograms, the mass of the fruit.



Answer

....................................... kg [1]

Answer

.....................................cm2 [1]

(b) The area of a shape is 1.2 m2. Convert this area to cm2.

4

(a) Complete the statement in the answer space using one of these symbols.

G

1

=



2

H

Answer 0.65 ...............................

27 [1] 40

(b) Express 7% as a decimal.



© UCLES 2013

Answer

4024/11/M/J/13

............................................ [1]

[Turn over

4 5

For Examiner’s Use

O 6

Q

X P



PQ is a chord of the circle, centre O. X is the midpoint of PQ. OX = 6 cm and the radius of the circle is 10 cm. Calculate PQ.



© UCLES 2013

Answer

4024/11/M/J/13

...................................... cm [2]

5 6

A bag contains red, yellow and green sweets. 2 1 of the sweets are red and of the sweets are yellow. 5 4

For Examiner’s Use

What fraction of the sweets are green?

7

Answer

............................................ [2]

On a map the length of a lake is 4.5 centimetres. The actual length of the lake is 2.7 kilometres. Write the scale of the map as a ratio in the form 1 : n.



© UCLES 2013

Answer 1 : ....................................... [2]

4024/11/M/J/13

[Turn over

6 8

(a) One approximate solution of the equation sin x° = 0.53 is x = 32. Use this value of x to find the solution of the equation that lies between 90° and 180°.



Answer (b)

A 13

D





............................................ [1]

C

5

B

12

Triangle ABC is right-angled at B and BC is produced to D. AB = 5 cm, BC = 12 cm and AC = 13 cm. t . Write down the value of cos ACD



© UCLES 2013

Answer

4024/11/M/J/13

t = .......................... [1] cos ACD

For Examiner’s Use

7 9

Ahmed pays a total of $81 for wood, paint and a hammer.

For Examiner’s Use

(a) The amounts he pays for the wood, paint and hammer are in the ratio 4 : 3 : 2. Calculate how much Ahmed pays for the hammer.



Answer $ .......................................... [1] (b) When Ahmed paid $81 he had received a 10% discount on the normal price. Calculate the normal price.

10

Answer $ .......................................... [2] b = m (a – c) (a) Evaluate b when m = 5, a = 8 and c = –3.



Answer b = ....................................... [1] (b) Rearrange the formula to make c the subject.



© UCLES 2013

Answer c = ....................................... [2]

4024/11/M/J/13

[Turn over

8 11

Choose a quadrilateral from the list to complete each statement. Kite



Parallelogram

Rectangle

Rhombus

For Examiner’s Use

Square

Trapezium

(a) A ......................................................... has four equal sides and four angles of 90°.

[1]

(b) A ......................................................... has just one pair of parallel sides.

[1]

(c) A ......................................................... has just one pair of opposite angles equal and its diagonals bisect at 90°.

[1]

12

6

9

1

The three cards above can be rearranged to make three-digit numbers, for example 916. Arrange the three cards to make (a) the three-digit number that is closest to 650,

Answer

............................................ [1]

Answer

............................................ [1]

Answer

............................................ [1]

(b) the three-digit number that is a multiple of 7,

(c) a three-digit number that is a square number.

© UCLES 2013

4024/11/M/J/13

9 13

For Examiner’s Use

v

Speed (m/s)

0

10

20

30 40 50 Time (t seconds)

60

70

The diagram shows the speed-time graph for 70 seconds of a car’s journey. After 20 seconds the car reaches a speed of v m/s. During the 70 seconds the car travels 1375 m. (a) Calculate v.



Answer v = ....................................... [2] (b) Calculate the acceleration of the car during the first 20 seconds.



© UCLES 2013

Answer

4024/11/M/J/13

....................................m/s2 [1]

[Turn over

10 14

For Examiner’s Use

T

A

32°

D

O

B

A, B and T are points on a circle, centre O. AOD is a straight line and DT is a tangent to the circle at T. t = 32° TAO Find t , (a) ATO



Answer

t = ................................ [1] ATO

Answer

t = ................................ [1] TDO

Answer

t = ............................... [1] ABT

t , (b) TDO

(c)

t . ABT

© UCLES 2013

4024/11/M/J/13

11 15

For Examiner’s Use

A B

D

C

(a) Construct the locus of all points, inside the quadrilateral ABCD, which are (i) equidistant from DA and DC,

[1]

(ii) 5 cm from B.

[1]

(b) On the diagram, shade the region inside the quadrilateral containing the points that are nearer to DA than DC and more than 5 cm from B.

© UCLES 2013

[1]

4024/11/M/J/13

[Turn over

12

16 Maryam makes two geometrically similar cakes. The heights of the cakes are 6 cm and 9 cm.

For Examiner’s Use

(a) Maryam decorates each cake with a ribbon around the outside. The length of the ribbon for the larger cake is 66 cm.

Find the length of the ribbon for the smaller cake.



Answer

...................................... cm [1]

(b) Maryam uses 1600 m3 of cake mixture to make the smaller cake. Find the volume of cake mixture she uses to make the larger cake.

17

p = 2.4 × 102

Answer

.....................................cm3 [2]

Answer

............................................ [1]

Answer

............................................ [2]

q = 6 × 103

Giving your answers in standard form, find (a) p + q,

(b) 2p ÷ q.

© UCLES 2013

4024/11/M/J/13

13 18 Eighty cyclists were each asked the distance (in kilometres) they cycled last week.

For Examiner’s Use

80 70 60 50 Cumulative frequency 40 30 20 10 0

0

20

40

60

80

100

120

Distance (kilometres)

The cumulative frequency diagram represents the results. Use the graph to estimate (a) the number of cyclists who cycled between 60 and 80 kilometres,



Answer

............................................ [1]

Answer

...................................... km [1]

Answer

...................................... km [2]

(b) the median distance cycled,

(c) the interquartile range for the distance cycled.



© UCLES 2013

4024/11/M/J/13

[Turn over

14 19 The diagram shows the metal cover for a circular drain. Water drains out through the shaded sections.

For Examiner’s Use

B A

O

D

C

O is the centre of circles with radii 1 cm, 2 cm, 3 cm, 4 cm and 5 cm. t = 40°. The cover has rotational symmetry of order 6 and BOC (a) Calculate the area of the shaded section ABCD, giving your answer in terms of π.

Answer .....................................cm2 [2]



© UCLES 2013

4024/11/M/J/13

15 (b) The total area of the metal (unshaded) sections of the cover is

55 π cm2. 3

For Examiner’s Use

(i) Calculate the total area of the shaded sections, giving your answer in terms of π.

Answer .....................................cm2 [1]



(ii) Calculate the fraction of the total area of the cover that is metal (unshaded). Give your answer in its simplest form.



Answer

............................................ [1]

Answer

............................................ [1]

Answer

............................................ [1]

20 (a) Evaluate (i) 50 + 52,

1

(ii)

36 2 ,

^2 3h . 2

(iii)

6



Answer ............................................ [1] k

1 (b) c m = 9 3 Find the value of k.

Answer k = ...................................... [1]



© UCLES 2013

4024/11/M/J/13

[Turn over

16 21 R is directly proportional to the cube of p. When p = 2, R = 24.

For Examiner’s Use

(a) Find the formula for R in terms of p.



Answer R = ..................................... [1] (b) Find the value of p when R = 192.



Answer p = ....................................... [2] (c) Which of the diagrams below represents the graph of R against p? R

R

R

p Diagram 1

R

p Diagram 2

p Diagram 3



© UCLES 2013

R

p Diagram 4

p Diagram 5

Answer Diagram ...................... [1]

4024/11/M/J/13

17 22

For Examiner’s Use

y

7 6 5

B

4 3 2

A

1 –7

–6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

8

x

–1 –2 –3 –4 –5

The diagram shows triangles A and B.

(a) The translation c

-4 m maps triangle A onto triangle C. 3

On the diagram, draw and label triangle C.

[1]

(b) The rotation 90° clockwise, centre (1, 1), maps triangle A onto triangle D. On the diagram, draw and label triangle D.

[2]

(c) Find the matrix of the transformation that maps triangle A onto triangle B.



© UCLES 2013

Answer

4024/11/M/J/13





[1]

[Turn over

18 23

For Examiner’s Use

y 7 T

6 5 4 3 2 S

R

1 0

1

2

3

4

5

6

7

8

x

The diagram shows a triangle RST. (a) Write down (i) the gradient of the line ST,



Answer

............................................ [1]

Answer

............................................ [1]

(ii) the equation of a line that is parallel to ST,



(iii) the equation of the line with gradient 3 that passes through S.



Answer

............................................ [1]

(b) One of the inequalities that defines the shaded region RST is x G 6 . Write down the other two inequalities that define this region.



Answer



© UCLES 2013

................................................. ............................................ [2]

4024/11/M/J/13

19 24 (a) A = e



3 o 2

4 1

B=e

2 -3 o 1 1

For Examiner’s Use

(i) Find 2A – B.



Answer





[1]

Answer





[2]

(ii) Find B –1.





(b)  = {natural numbers} P = {factors of 8} Q = {factors of 12} List the elements of the set P Q.



Answer ................................................................ [2] (c)  M

N

Use set notation to describe the shaded subset in the Venn diagram.

© UCLES 2013

Answer ............................................ [1] 4024/11/M/J/13

[Turn over

20 25 (a) Factorise fully

10x2y + 15xy2.

For Examiner’s Use



Answer (b) Factorise

............................................ [1]

25a2 – b2.



Answer ............................................ [1] (c) Simplify

3 2 . 2 (x + 1) x+1

(d) Simplify

Answer

............................................ [2]

Answer

............................................ [2]

3a 2 9a . ' 10bc 5b 2 c



Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

4024/11/M/J/13

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 0 2 1 5 8 3 0 0 9 3 *

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2013

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (SLM/SW) 64206/2 © UCLES 2013

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

Evaluate (a)

4 2 - , 7 5



Answer (b)

5 2 ' � 8 3

2

�������������������������������������������� [1]

Answer �������������������������������������������� [1] A bag contains red counters and blue counters� On each counter there is either an odd or an even number� The table shows the number of counters of each type� Odd

Even

Red

6

9

Blue

5

3

(a) Find the fraction of the counters that are blue�



Answer �������������������������������������������� [1] (b) Find the ratio of odd to even numbers�



© UCLES 2013

Answer ������������������� : �������������������� [1]

4024/12/M/J/13

For Examiner’s Use

3 3

(a) Write these lengths in order of size, starting with the shortest� 500 m

Answer ������������������������ shortest

5 cm

50 km

500 mm

������������������������

������������������������

������������������������

For Examiner’s Use

[1]

(b) Convert 41�6 cm2 to mm2�

Answer ����������������������������������� mm2 [1]

4

A line has equation 3y = 2 – x � (a) Find the gradient of the line�



Answer �������������������������������������������� [1] (b) The line passes through the point (5, k)� Find the value of k�



© UCLES 2013

Answer k = �������������������������������������� [1]

4024/12/M/J/13

[Turn over

4 5

The diagram shows the regions A to I�

For Examiner’s Use

y 5 4 C

3 2 1 0

B

A

D E

G

F 1

2

I

H 3

4

5 x

Give the letter of the region defined by each set of inequalities� (a) x > 0, y > 0, y < 1 and y < 4 – 2x



Answer �������������������������������������������� [1] (b) y > 1, y < x – 2 and y < 5 – x



© UCLES 2013

Answer �������������������������������������������� [1]

4024/12/M/J/13

5 6

The diagram shows triangle A�

For Examiner’s Use

y 7 6 5 4 3

A

2 1 –7

–6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

7 x

–1 –2 –3 –4

(a) Reflect triangle A in the line x = 1� Label the image B�

[1]

(b) Rotate triangle A through 90° clockwise about the point (–1, 3)� Label the image C�

[1]

© UCLES 2013

4024/12/M/J/13

[Turn over

6 7

The diagram shows a scale used to measure the water level in a river�

m 2.0 1.5 1.0 0.5 0 –0.5 –1.0 –1.5 –2.0 –2.5

For Examiner’s Use

June

The table shows the reading, in metres, at the beginning of each month� Month

January

February

March

April

May

Reading (m)

0�8

1�2

1�3

0�5

–0�1

June

July –1�9

(a) The diagram shows the water level at the beginning of June� Complete the table with the June reading�

[1]

(b) Work out the difference between the highest and lowest levels shown in the table�



Answer ����������������������������������������m [1] (c) The August reading was 0�4 m higher than the July reading� Work out the reading in August�



© UCLES 2013

Answer ����������������������������������������m [1]

4024/12/M/J/13

7 8

(a) James thinks of a two-digit number� It is a cube number� It is an even number�

For Examiner’s Use

What is his number?



Answer �������������������������������������������� [1] (b) Omar thinks of a two-digit number� It is a factor of 78� It is a prime number� What is his number?



Answer �������������������������������������������� [1] (c) Write down an irrational number between 1 and 2�

9

Answer �������������������������������������������� [1] (a) Write 0�004 075 1 correct to two significant figures�



Answer �������������������������������������������� [1] (b)

131 lies between two consecutive integers� Complete the inequality below with these integers�



Answer ������������ 1 131 1 ������������� [1] (c) Add brackets to the statement below to make it correct�

3 × 2 + 1 2 = 49

© UCLES 2013

[1]

4024/12/M/J/13

[Turn over

8 10  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {odd numbers} B = {multiples of 3}

For Examiner’s Use

(a) Complete the Venn diagram to illustrate this information�  A

B

[1] (b) Find the value of n (A B)�



Answer �������������������������������������������� [1] (c) List the elements of the set A B9�

11

Answer �������������������������������������������� [1] A photo is 10 cm long� It is enlarged so that all dimensions are increased by 20%� (a) Find the length of the enlarged photo�



Answer �������������������������������������� cm [1] (b) Find the ratio of the area of the enlarged photo to the area of the original photo� Give your answer in the form k : 1�

© UCLES 2013

Answer ����������������������������������� : 1 [2] 4024/12/M/J/13

9 12 The diagram below shows triangle ABC� (a) Construct the perpendicular bisector of AB�

[1]

(b) Shade the region inside the triangle containing points that are closer to A than to B and more than 6 cm from C�

[2]

For Examiner’s Use

A

B

© UCLES 2013

C

4024/12/M/J/13

[Turn over

10 13

A=e

2 3 o -2 0

B=e

-2 -3

4 o 1

For Examiner’s Use

(a) Find A – B �



Answer





[1]

Answer





[2]

(b) Find A–1 �



© UCLES 2013

4024/12/M/J/13

11 14 (a) Sofia earns $7�60 for each hour she works� She starts work at 7�45 a�m� and finishes at 4�30 p�m� She stops work for half an hour for lunch�

For Examiner’s Use

How much does she earn for the day?



Answer $ ������������������������������������������ [2] (b) Marlon earns $1500 each month� He pays rent of $525 each month� Find the amount he pays in rent as a percentage of his earnings�



© UCLES 2013

Answer ����������������������������������������% [1]

4024/12/M/J/13

[Turn over

12 15 P is directly proportional to the square of Q� When P = 9, Q = 6�

For Examiner’s Use

(a) Find the formula for P in terms of Q�



Answer P = �������������������������������������� [1] (b) Find the values of Q when P = 25�



Answer Q = �������������� or ������������������ [2]

16 (a) Evaluate 4–2 �



Answer �������������������������������������������� [1] (b) Simplify

e

1 2

9xy o � x3y2 6



© UCLES 2013

Answer �������������������������������������������� [2]

4024/12/M/J/13

13 17

For Examiner’s Use

45° 45° 3 2

The diagram shows part of an earring� It is in the shape of a sector of a circle of radius 3 cm and angle 45°, from which a sector of radius 2 cm and angle 45° has been removed� (a) Calculate the shaded area� Give your answer in the form

aπ , where a and b are integers and as small as possible� b

Answer �������������������������������������cm2 [2]

(b) The earring is cut from a sheet of silver� The mass of 1 cm2 of the silver sheet is 1�6 g�

By taking the value of π to be 3, estimate the mass of the earring�



© UCLES 2013

Answer ����������������������������������������� g [1]

4024/12/M/J/13

[Turn over

14 18 The table shows information about the annual coffee production of some countries in 2010� Country

For Examiner’s Use

Number of bags per year

Brazil Vietnam

1.85 × 107

Colombia

9.2 × 106

Indonesia

8.5 × 106

(a) In 2010, Brazil produced 48 million bags of coffee� Complete the table with the coffee production for Brazil, using standard form�

[1]

(b) How many more bags of coffee were produced in Vietnam than in Colombia?



Answer

�������������������������������������������� [2]

(c) The mass of a bag of coffee is 60 kg� Work out the number of kilograms of coffee produced in Indonesia� Give your answer in standard form�



© UCLES 2013

Answer

4024/12/M/J/13

��������������������������������������� kg [1]

15 19 (a) Keith records the number of letters he receives each day for 20 days� His results are shown in the table� Number of letters

Frequency

0

4

1

6

2

3

3

2

4

1

5

4

For Examiner’s Use

(i) Write down the mode�

Answer �������������������������������������������� [1] (ii) Work out the mean�



Answer �������������������������������������������� [2] (b) Over the same 20 days, Emma received a mean of 1�7 letters each day� How many letters did Emma receive altogether?



© UCLES 2013

Answer �������������������������������������������� [1]

4024/12/M/J/13

[Turn over

16 20 (a) Solve

3x 2x - 1 + = 3� 4 2

For Examiner’s Use



Answer x = �������������������������������������� [2] (b) Write as a single fraction in its simplest form 5 2 . + x+4 x-1



© UCLES 2013

Answer �������������������������������������������� [2]

4024/12/M/J/13

17 21 A group of 80 students took a Physics test� This table shows the distribution of their marks� Mark (m)

For Examiner’s Use

0 1 m G 10 10 1 m G 20 20 1 m G 30 30 1 m G 40 40 1 m G 50 50 1 m G 60

Frequency

4

12

14

22

18

10

m G 40

m G 50

m G 60

(a) Complete the cumulative frequency table� Mark (m)

m G 10

m G 20

m G 30

Cumulative frequency [1] (b) Draw a cumulative frequency curve for this information� 80 70 60 50 Cumulative frequency 40 30 20 10 0

0

10

20

30

40

50

60

Mark

[2]

(c) The pass mark for the test is 45� Use your cumulative frequency curve to estimate the number of students who passed�



© UCLES 2013

Answer �������������������������������������������� [2]

4024/12/M/J/13

[Turn over

18 22 Varun leaves home at 13 00 and cycles 12 km to college� The distance-time graph below shows Varun’s journey�

For Examiner’s Use

His sister Kiran leaves college at 13 10 and cycles home on the same road at a constant speed of 16 km/h� (a) On the same grid, draw the distance-time graph for Kiran’s journey� College 12 10 8 Distance from home (km)

6 4 2

Home 0 13 00

13 10

13 20

13 30

13 40

13 50

14 00

Time of day

[2]

(b) How far was Kiran from home when she passed Varun?

Answer

��������������������������������������km [1]

(c) Find Varun’s speed for the first 20 minutes of his journey� Give your answer in kilometres per hour�



Answer �����������������������������������km/h [1] (d) On the grid below, draw the speed-time graph for Varun’s journey� 25 20 Speed 15 (km/h) 10 5 0 13 00

13 10

13 20

13 30 Time of day

© UCLES 2013

4024/12/M/J/13

13 40

13 50

14 00

[2]

19 23

B 68°

For Examiner’s Use

C

O

A

D

B, C and D are points on the circle, centre O� BA and DA are tangents to the circle at B and D� (a) Show that triangles ABO and ADO are congruent�

��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ���������������������������������������������������������������������������������������������������������������������������������������������� [3] (b) What type of special quadrilateral is ABOD?

Answer �������������������������������������������� [1] (c) Angle BCD = 68°� Find angle BAD�



Answer Angle BAD = ��������������������� [2]

Question 24 is printed on the following page.

© UCLES 2013

4024/12/M/J/13

[Turn over

20 24 (a) Expand and simplify (t – 5)(t + 3)�

For Examiner’s Use



Answer �������������������������������������������� [1] (b) Factorise 64x2 – 9y2 �



Answer �������������������������������������������� [1] (c) Factorise 6ab – 2a – 3a2 + 4b �



Answer �������������������������������������������� [2] (d) (i) Write x2 – 6x + 3 in the form (x – a)2 + b �



Answer �������������������������������������������� [1] (ii) Hence solve x2 – 6x + 3 = 0 leaving your answer in the form p ! q �



Answer x = ��������������������������������������� [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

4024/12/M/J/13

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 0 5 1 0 3 4 8 7 8 5 *

4024/21

MATHEMATICS (SYLLABUS D)

May/June 2013

Paper 2 

2 hours 30 minutes

Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 24 printed pages. DC (KN/SW) 64205/3 © UCLES 2013

[Turn over

2









Section A [52marks]











Answerallquestionsinthissection.

1

(a) Solve4(x–2)=7–x.

For Examiner’s Use

Answer x=......................................... [2]   

(b)   

Solvethesimultaneousequations.    2x+y=7   4x–3y=19

Answer  x=.........................................



 y=......................................... [3]

(c) (i) Writedowntheintegervaluesthatsatisfy–1<n <2.

Answer  ............................................... [1]



(ii) Solve2–3y<8.

 ©UCLES2013

Answer  ............................................... [2] 4024/21/M/J/13

3 2

(a) Theinteriorangleofaregularpolygonis165o.





For Examiner’s Use

Howmanysideshasthepolygon?

Answer  ............................................... [2]

(b)

B

D

p° A

F

q° E

C

G

FAECG andADBarestraightlines.DEisparalleltoBC.







t =p°and AED t =q°. (i) FAD Findanexpressionintermsofpand/orqfor t , (a) BCG

Answer  ............................................... [1]

t . (b) DBC



Answer  ............................................... [1]







(ii) AE=7cm,EC=3cm,DE=5.6cmandDB=2.1cm. (a) FindBC.

Answer  ......................................... cm[1]



(b) FindAD.

Answer  ......................................... cm[1] ©UCLES2013

4024/21/M/J/13

[Turn over

4 3

(a) Thediagramsshowparallelogramsmadefromsmalltriangles.

Parallelogram





1

4

3

2

For Examiner’s Use

5

(i) Completethetablebelow. Parallelogramm

1

2

3

4

Numberofsmalltriangles

2

4

6

8

5

6

[1]





(ii) Find an expression, in terms of m, for the number of small triangles used to make Parallelogramm.

Answer  ............................................... [1]

(b) Thediagramsshowtrianglesmadefromthesamesmalltriangles.

Triangle





1

2

3

4

(i) Completethetablebelow. Trianglen

1

2

3

4

Numberofsmalltriangles

1

4

9

16





5

5

6

[1]

(ii) Find an expression, in terms of n, for the number of small triangles used to make Trianglen. Answer  ............................................... [1]





(iii) Triangleqismadefrom324smalltriangles. Findq.

Answer  ............................................... [1] ©UCLES2013

4024/21/M/J/13

5



(c) Thediagramsshowtrapeziumsmadefromthesamesmalltriangles.



Trapezium

1

Trapezium

4

2

For Examiner’s Use

3

5

(i) Bycomparingthediagramswiththoseinparts(a)and(b),findanexpression,interms oft,forthenumberofsmalltrianglesusedtomakeTrapeziumt.

Answer  ............................................... [1]



(ii) HowmanysmalltrianglesareusedtomakeTrapezium25?

Answer  ............................................... [1]

©UCLES2013

4024/21/M/J/13

[Turn over

6 4

(a) Aboxofchocolatescontains10milkchocolatesand2plainchocolates. Sachaeats3chocolateschosenatrandomfromthebox. Thetreediagramshowsthepossibleoutcomesandtheirprobabilities. First chocolate

Second chocolate

9 11

10 12

Third chocolate

milk

milk 2 11

plain

8 10

milk

2 10

plain

9 10

milk

1 10

plain

........ 2 12

........

milk

milk ........

plain ........

For Examiner’s Use

plain

........

........

plain milk

plain





(i) Completethetreediagram.





(ii) Expressingeachanswerasafractioninitslowestterms,findtheprobabilitythatSacha





[2]

(a) eats3milkchocolates,

Answer  ............................................... [1]



(b) eats2milkchocolatesand1plainchocolateinanyorder.

Answer  ............................................... [2] ©UCLES2013

4024/21/M/J/13

7

(b) Thefrequencydiagramshowsthedistributionofthenumberoflettersreceivedbyafamily eachdayovera31dayperiod.

For Examiner’s Use

9 8 7 6 Number of days

5 4 3 2 1 0





Forthisdistribution,find





(i) themode,

0

1

2 3 4 Number of letters

5

6

Answer  ............................................... [1]



(ii) themedian.

Answer  ............................................... [1]

©UCLES2013

4024/21/M/J/13

[Turn over

8 5

(a) (i)

For Examiner’s Use

Exchangerate $1=€0.72



EddietravelsfromtheUSAtoGermany. Hechanges$300intoeuros(€).





Howmanyeurosdoeshereceive?

Answer  €............................................. [1]







(ii) WhenEddiereturnstotheUSAhehas€51leftthatheexchangesfor$75. Whatexchangeratehasbeenusedinthiscase?

Answer  $1=€.................................... [1]

©UCLES2013

4024/21/M/J/13

9

(b) Gregbuys60gardenplantsatacostpriceof$2.00eachtosellinhisshop. Hesells25ofthemataprofitof75%and18ofthemataprofitof35%. Hesellstherestoftheplantsfor 45 ofthecostprice.





For Examiner’s Use

(i) Calculatetheprofitorlosshemakesfromsellingthese60plants,statingifitisaprofit orloss.

Answer  Gregmakesa...........................of$.....................[3]



(ii) Findthepercentageprofitorloss.

Answer  ...........................................%[1]

©UCLES2013

4024/21/M/J/13

[Turn over

10 6

(a) ABCDisatrapeziumwithBCparalleltoAD. 9

B

For Examiner’s Use

C

18

A

55° 7

E





EisthepointonADsuchthatBEisperpendiculartoAD. t =55°,AE=7cm,BE=18cmandBC =9cm. BDA





Calculate





t , (i) BAE

D

Answer  ............................................... [2]



(ii) theareaofthetrapeziumABCD.

Answer  .........................................cm2[4] ©UCLES2013

4024/21/M/J/13

11

(b) P

For Examiner’s Use

Q 112°

41°

S

PQRSisanothertrapezium. t =112°and PRS t =41°,eachmeasuredcorrecttothenearestdegree. PQR



R



t . Findthesmallestpossiblevalueof QRP

Answer  ............................................... [2]

©UCLES2013

4024/21/M/J/13

[Turn over

12 7

(a) InanathleticsmatchBenwonthe100mracein9.98sandCalvinwonthe200mracein 19.94s.





For Examiner’s Use

Whatisthedifferenceintheiraveragespeeds? Giveyouranswerinmetrespersecond,correcttotwodecimalplaces.

Answer  ......................................... m/s[2]

(b)

Twocarseachcompleteajourneyof120km. Thefirstcarisdrivenatanaveragespeedofx km/h. Thesecondcarisdrivenatanaveragespeed3km/hfasterthanthefirstcar. Thefirstcartakes6minuteslongertocompletethejourney.





(i) Writedownanequationinxandshowthatitsimplifiestox2+3x–3600=0.





©UCLES2013



[3] 4024/21/M/J/13

13



(ii) Solvetheequationx2+3x–3600=0,givingeachanswercorrectto onedecimalplace.

For Examiner’s Use

Answer x=..................or..................[3]



(iii) Howmanyminutesdoesthefirstcartaketotravelthe120km?

Answer  ................................. minutes[2]

©UCLES2013

4024/21/M/J/13

[Turn over

14 









Section B[48marks]











Answerfourquestionsinthissection.











Eachquestioninthissectioncarries12marks.

8

(a) 





Find





(i) f(–2),







f (x) =

4x - 3 2

Answer f(–2)=................................. [1]



(ii) f–1(x),

Answer f–1(x)=................................ [2]



(iii) thevalueofgsuchthatf(2g)=g.

Answer  g=........................................ [2]

©UCLES2013

4024/21/M/J/13

For Examiner’s Use

15

(b)

For Examiner’s Use

B C

A

E D





BADandCAEarestraightlinesandBCisparalleltoED.





BA = c





(i) DescribefullythesingletransformationthatmapstriangleABContotriangleADE.

1 12 m, ED = c m and BA = 1 BD . -2 -3 4

Answer.............................................................................................................................. ...................................................................................................................................... [2]



(ii) Calculate BA .

Answer  ............................................... [1]







(iii) FindCD.

Answer

 

[2]

Answer

 

[2]

(iv) FisthemidpointofBD. Find EF .

©UCLES2013

4024/21/M/J/13

[Turn over

16 9

(a) Shape Iisacylinderwithradius4cmandheighthcm. ThevolumeofShape Iis1500cm3.





For Examiner’s Use

4

(i) Findh. h

Shape I

Answer  ............................................... [2]



(ii) Shape Iismadebypouringliquidintoamouldatarateof0.9litresperminute. Findthenumberofsecondsittakestopourthisliquidintothemould.

Answer  ................................. seconds[1]

(b) Shape IIisaprismoflength8cmwithatriangularcross-section, shownshaded. Twosidesoftheshadedtriangleareatrightanglestoeachotherand havelengths5xcmand12xcm.

12x

GiventhatShape IIalsohasavolumeof1500cm3,findx. 5x

8

Shape II

Answer  ............................................... [2] ©UCLES2013

4024/21/M/J/13

17



(c) Shape IIIisalsoaprismoflength8cmwithatriangularcross-section, shownshaded. Twosidesoftheshadedtriangleareatrightanglestoeachotherand havelengths5ycmand12ycm.Thethirdsideisoflength13y cm. 12y y satisfiestheequation4y2+16y–33=0.







For Examiner’s Use

13y

(i) Factorise4y2+16y–33.

8

5y Shape III

Answer  ............................................... [1]



(ii) Hencesolvetheequation4y2+16y–33=0.

Answer  y=..................or..................[1]



(iii) Findtheareaoftheshadedtriangle.

Answer  ........................................cm2[1]



(iv) FindthetotalsurfaceareaofShape III.

Answer  ........................................cm2[3]

(d) Find

Volume of Shape III asafractioninitssimplestform. Volume of Shape II

Answer  ............................................... [1] ©UCLES2013

4024/21/M/J/13

[Turn over

18 10 (a) Thetableshowssomevaluesofxandthecorrespondingvaluesofyfor y = x

–3

y

–2.5

–2

–1.5

–1

1

1.5

2

2.5

0.96

1.5

2.67

6

6

2.67

1.5

0.96





(i) Completethetable.





(ii) Onthegriddrawthegraphof y =

6. x2

For Examiner’s Use

3

[1] 6 for–3GxG3. x2

y 8 7 6 5 4 3 2 1 –3

–2

–1

0

1

2

3



x

[2]

(iii) Useyourgraphtofindthevaluesofxwheny=2.

Answer x=..................or..................[1]



(iv) Bydrawingatangent,findthegradientofthecurvewhenx=1.5.

Answer  ............................................... [2]



(v) Bydrawingasuitablelineonthegrid,solvetheequation

6 = 2 - x. x2

Answer  x=......................................... [2] ©UCLES2013

4024/21/M/J/13

19

(b) Thegraphshowsasketchofy=5a x.

For Examiner’s Use

y (4, b)

(2, 45) P x

O





Twopointsonthecurveare(2,45)and(4,b).





(i) Findthevaluesofaandb.

Answer  a=.........................................



 b=......................................... [2]



(ii) Findthecoordinatesofthepoint,P,wherethegraphcrossesthey-axis.

Answer (.....................,.....................) [1]



(iii) FindthegradientofthestraightlinejoiningthepointsPand(2,45).

Answer  ............................................... [1] ©UCLES2013

4024/21/M/J/13

[Turn over

20 11 (a) Thescalediagramshowsthepositions,AandB,oftwoboats.

For Examiner’s Use

North

A

Scale: 1 cm to 50 m

B





(i) Findtheactualdistancebetweenthetwoboats.

Answer  ............................................m[1]











(ii) AthirdboatispositionedatC,suchthatAC=350mandBC=300m. CiseastofthelineAB. UserulerandcompassestofindC.

[2]

(iii) MeasurethebearingofCfromA. Answer  ............................................... [1]









(iv) AfourthboatispositionedatD,suchthatACisthelineofsymmetryofthe quadrilateralABCD.

©UCLES2013

CompletethequadrilateralABCD.

4024/21/M/J/13

[2]

21

(b) Thediagramshowsthepositions,P,QandR,ofthreebuoys. ThebearingofQfromPis054o,PQ=250m,QR=340mandPR=160m.

For Examiner’s Use

Q North

250

54° P 340 160

R





(i) CalculatethebearingofRfromP.

Answer  ............................................... [4]



(ii) CalculatetheareaoftrianglePQR.

Answer  .......................................... m2[2] ©UCLES2013

4024/21/M/J/13

[Turn over

22 12 (a) Thedistributionoftheweightsofluggagefor140passengersisshowninthetable. Weightof luggage (wkg)

01wG6 61wG10 101wG14 141wG16 161wG18 181wG22 221wG30

Frequency





For Examiner’s Use

15

14

20

24

31

24

12

(i) Calculateanestimateofthemeanweightofluggage.

Answer  ........................................... kg[3]



(ii) Onthegridopposite,drawahistogramtorepresentthisdata.





(iii) Estimatetheprobabilitythatapassenger,chosenatrandom,hasluggageweighingless than13kg.

[3]

Answer  ............................................... [2]

©UCLES2013

4024/21/M/J/13

23 For Examiner’s Use

0

2

4

6

8

10

12 14 16 18 Weight of luggage (kg)

20

22

24

26

28

30 w

TURN OVER FOR THE REST OF THE QUESTION

©UCLES2013

4024/21/M/J/13

[Turn over

24

(b) Thepiechartrepresentsthedistributionofthebirthplacesofagroupof60students.

Do not write in this margin

Singapore

South Africa

48° 126°

Pakistan

54° 42° Australia





United Kingdom

(i) FindthenumberofstudentsinthegroupwhowereborninAustralia.

Answer  ............................................... [1]



(ii) CalculatethepercentageofstudentsinthegroupwhowereborninSouthAfrica.

Answer  ............................................%[1]



(iii) Fourmorestudentsjointhegroup. Ofthese,twostudentswereborninPakistan,oneinSingaporeandoneinChina. Anewpiechartistobedrawnusingtheinformationaboutthewhole groupofstudents.









Forthenewpiechart,calculatetheangleofthesectorthatrepresentsthestudentsborn inPakistan. Giveyouranswercorrecttothenearestdegree.

Answer  ............................................... [2] Permissiontoreproduceitemswherethird-partyownedmaterialprotectedbycopyrightisincludedhasbeensoughtandclearedwherepossible.Everyreasonableefforthasbeen madebythepublisher(UCLES)totracecopyrightholders,butifanyitemsrequiringclearancehaveunwittinglybeenincluded,thepublisherwillbepleasedtomakeamendsat theearliestpossibleopportunity. UniversityofCambridgeInternationalExaminationsispartoftheCambridgeAssessmentGroup.CambridgeAssessmentisthebrandnameofUniversityofCambridgeLocal ExaminationsSyndicate(UCLES),whichisitselfadepartmentoftheUniversityofCambridge.

©UCLES2013

4024/21/M/J/13

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 8 4 6 1 5 4 2 5 0 3 *

4024/22

MATHEMATICS (SYLLABUS D)

May/June 2013

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (CW/CGW) 64204/3 © UCLES 2013

[Turn over

2 Section A [52 marks] Answer all questions in this section. 1

(a) (i)

Exchange rate £1 = $2.06 £1 = 72 rupees Manraj changes 25 200 rupees into dollars ($). Calculate how many dollars he receives.



Answer $.............................................. [2] (ii) Misja changes 380 euros into dollars ($). He receives $551. How many dollars does he receive for each euro?



© UCLES 2013

Answer 1 euro = $ ............................... [1]

4024/22/M/J/13

For Examiner’s Use

3 (b) Account

Simple interest per year

Super Saver

3.4%

Extra Saver

3.5%

For Examiner’s Use

On 31 March 2011, Lydia and Simone each had $8000 in an account. Lydia’s money is in a Super Saver Account. Simone’s money is in an Extra Saver Account. (i) How much money did Lydia have in her account on 31 March 2012 after the interest had been added?



Answer $.............................................. [2] (ii) On 31 March 2012, Lydia transferred this money to an Extra Saver Account. How much money did she have in this account on 31 March 2013 after the interest had been added?



Answer $.............................................. [1] (iii) Simone kept her money for the two years in the Extra Saver Account, which earned simple interest of 3.5% per year. After all interest had been added, who had more money in their account on 31 March 2013 and by how much?

Answer

© UCLES 2013

................................... had $ ................................... more [2]

4024/22/M/J/13

[Turn over

4 2

Small triangles are formed by placing rods between dots as shown in the diagrams.

Diagram 1

Diagram 2

Diagram 3

For Examiner’s Use

Diagram 4

(a) Complete the table. Diagram n

1

2

3

4

Number of small triangles (T  )

1

4

9

16

Number of dots (D)

3

6

10

15

Number of rods (R)

3

9

18

30

5

[2] (b) Find an expression, in terms of n, for the number of small triangles (T  ) formed in Diagram n.



Answer ................................................ [1] (c) Given that R = D + T – 1,



© UCLES 2013

find the value of n when D = 561 and R = 1584.

Answer n = ......................................... [2]

4024/22/M/J/13

5 (d)

1, 3, 6, 10, 15, ....

For Examiner’s Use

1 n (n + 1) . 2

The nth term of the above sequence is

Hence find an expression for R in terms of n.



Answer ................................................ [1] (e) How many rods are there in Diagram 15?



Answer ................................................ [1] (f) Find an expression for D in terms of n.



© UCLES 2013

Answer ................................................ [2]

4024/22/M/J/13

[Turn over

6 3

(a) Solve 3(x – 5) = 5x – 7.

For Examiner’s Use



Answer x = .......................................... [2] (b) (i) Solve

4y - 3 G 7. 2



Answer ................................................ [2] (ii) State the integers that satisfy both



4y - 3 G 7 and y 2 2 . 2

Answer ................................................ [1] (c) Solve the simultaneous equations. 2x – y = 6 4x + 3y = –3



Answer x = ..........................................



© UCLES 2013

y = .......................................... [3]

4024/22/M/J/13

7 4

ABCDEF is a hexagon with BE as its only line of symmetry. A

For Examiner’s Use

B

C F 6

G

16

6 D E

AF is parallel to CD and DF intersects BE at G. BE = 16 cm and DG = GF = 6 cm. The area of the hexagon ABCDEF is 138 cm2. (a) Calculate AF.



Answer .......................................... cm [2] (b) The area of the hexagon ABCDEF is four times the area of the triangle DEF. (i) Find EG.



Answer .......................................... cm [2] (ii) Find EG : GB, giving your answer in the form m : n where m and n are integers.

© UCLES 2013

Answer ......................  : ...................... [2] 4024/22/M/J/13

[Turn over

8 5

For Examiner’s Use

15

180

Mr Chan wants a fence along the side of his garden which is 8 metres long. He buys 4 fence panels and 5 posts. Each fence panel is 180 cm wide, correct to the nearest centimetre. Each post is 15 cm wide, correct to the nearest centimetre. (a) If there are no gaps between the panels and the posts, is it possible for the fence to be longer than 8 metres? Show your working.

[2] (b) A shop buys the posts from a manufacturer and sells them at a profit of 30%. The shop sells each post for $35.10. (i) How much does each post cost from the manufacturer?

© UCLES 2013

Answer $............................................. [2] 4024/22/M/J/13

9 (ii)

Fence panels Posts

For Examiner’s Use

$50.70 each $35.10 each

Mr Chan buys 4 fence panels and 5 posts. He hires a builder to put up the fence. The builder charges 220% of the total cost of the fence panels and posts to do the work. What is the total amount Mr Chan pays for his fence?



© UCLES 2013

Answer $.............................................. [3]

4024/22/M/J/13

[Turn over

10 6

The diagram shows the positions, P, Q, R and S, of four hotels. S North 335

Q 210° North 500

65° P

R

The bearing of Q from P is 065° and the bearing of R from Q is 210°. t = 90°. PQ = 500 m, SQ = 335 m and PQS t . (a) Calculate PQR



Answer ................................................ [1] (b) Calculate the shortest distance from P to QR.

© UCLES 2013

Answer ............................................ m [2] 4024/22/M/J/13

For Examiner’s Use

11 (c) Calculate the bearing of S from P.



© UCLES 2013

For Examiner’s Use

Answer ................................................ [3]

4024/22/M/J/13

[Turn over

12 7

(a) The distribution of the times spent by 200 customers at a restaurant one evening is shown in the table. Time (t minutes) Frequency

30 G t < 60

60 G t < 80

80 G t < 90

90 G t < 100

100 G t < 120

24

p

q

58

28

The diagram shows part of the histogram that represents this data. 6

5

4

Frequency 3 density

2

1

0

30

40

50

60

70

80

90

100

110

120

Time (t minutes)

(i) Complete the histogram.

[1]

(ii) Find p and q.

Answer p = .........................................



q = ......................................... [2] (iii) Estimate the probability that a customer, chosen at random, spent more than 95 minutes in the restaurant.

© UCLES 2013

Answer ................................................ [1] 4024/22/M/J/13

For Examiner’s Use

13 (b) The table below shows the distribution of the ages of these customers. Age (y years)

0 < y G 20

20 < y G 40

40 < y G 60

60 < y G 80

34

57

85

24

Frequency

For Examiner’s Use

(i) State the modal class.

Answer ................................................ [1] (ii) Calculate an estimate of the mean age of these customers.



© UCLES 2013

Answer ...................................... years [3]

4024/22/M/J/13

[Turn over

14 Section B [48 marks]

For Examiner’s Use

Answer four questions in this section. Each question in this section carries 12 marks. 8

The scale diagram shows the positions, A and B, of two buoys. B is due South of A and AB = 1500 m. A

B

(a) Write down the scale of the diagram.



Answer 1 cm to ...............................m [1] (b) A third buoy is positioned at C which is due East of B and 1800 m from A. Mark the position of C on the diagram.

[2]

(c) Calculate the actual distance BC. Give your answer correct to the nearest metre.



© UCLES 2013

Answer ............................................ m [2]

4024/22/M/J/13

15 (d) A boat travels from C to A at an average speed of x m/s. A second boat travels from B to A at an average speed 1 m/s faster than the first boat. It takes the first boat 1 minute longer to reach A than the second boat.

For Examiner’s Use

Write down an equation in x and show that it simplifies to x2 – 4x – 30 = 0.

[3] (e) Solve x2 – 4x – 30 = 0, giving each answer correct to two decimal places.



Answer x = ................... or ..................[3] (f) How long did it take the first boat to reach A? Give your answer in seconds.



© UCLES 2013

Answer .................................. seconds [1]

4024/22/M/J/13

[Turn over

16 9

(a) ABCD is a parallelogram.

For Examiner’s Use

C D B A

J1N J- 4N AB = K O and BC = K O . L4P L 2P (i) Find BD.



Answer (ii) Calculate AC .



 

[1]

Answer ................................................ [2] (iii) The parallelogram ABCD is mapped onto the parallelogram PBQR. J 3N J- 12N O and BQ = K O . PB = K L12P L 6P (a) Describe fully the single transformation that maps the parallelogram ABCD onto the parallelogram PBQR. Answer ...................................................................................................................... .............................................................................................................................. [2]

© UCLES 2013

4024/22/M/J/13

17 (b) S is the midpoint of PQ.

For Examiner’s Use

Find SR.

 

Answer (b)

f (x) =

[2]

3x + 2 5

Find (i) f (–4),



Answer f (–4) = .................................. [1] (ii) the value of g such that f(g) = 7,



Answer g = ......................................... [2] (iii) f –1 (x).



© UCLES 2013

Answer f –1 (x) = ................................. [2]

4024/22/M/J/13

[Turn over

18 10 (a) A bag contains red and blue pegs. Altogether there are 25 pegs of which n are red. Rashid picks two pegs without replacement. The tree diagram shows the possible outcomes and their probabilities. First peg

For Examiner’s Use

Second peg n–1 24 red

red

25 – n 24

n 25

blue 25 – n 25

red

blue

blue

(i) Complete the tree diagram.

[2]

(ii) (a) Write an expression, as a single fraction in terms of n, for the probability that Rashid picks a red peg then a blue peg in that order.



Answer ................................................ [1] (b) The probability that Rashid picks a red peg then a blue peg in that order is

1 . p

Given that the number of red pegs, n, satisfies the equation n2 – 25n + 150 = 0, find p.

© UCLES 2013

Answer p = ......................................... [2] 4024/22/M/J/13

19 (iii) Solve n2 – 25n + 150 = 0 to find the possible values of n.



For Examiner’s Use

Answer n = .................. or ..................[2] (iv) Given that at the start there are more blue pegs than red pegs in the bag, find the probability that Rashid picks two red pegs.



Answer ................................................ [2] (b) Each member of a group of children was asked their favourite colour. The pie chart represents the results. red

yellow 108° 30° 78°

54° pink

green blue

(i) The number of children whose favourite colour is red is 75. Find the number of children in the group.



Answer ................................................ [1] (ii) Find, in its simplest form, the fraction of children whose favourite colour is green.



Answer ................................................ [1] (iii) How many more children answered yellow than answered blue?

© UCLES 2013

Answer ................................................ [1] 4024/22/M/J/13

[Turn over

20 11

(a) The table shows some values of x and the corresponding values of y for y = 2x3 – 3x2 + 5. x y

–1.5

–1

–0.5

0

0.5

1

1.5

2

0

4

5

4.5

4

5

9

(i) Complete the table.

[1]

(ii) Using a scale of 4 cm to represent 1 unit, draw a horizontal x-axis for - 1.5 G x G 2 . Using a scale of 2 cm to represent 5 units, draw a vertical y-axis for - 10 G y G 10 . Draw the graph of y = 2x3 – 3x2 + 5 for - 1.5 G x G 2 .

[3]

(iii) Use your graph to estimate the gradient of the curve when x = 1.5.



Answer ................................................ [2] (iv) By drawing a suitable line on your graph, find the solution of the equation 2x3 – 3x2 + 4 = 0.

© UCLES 2013

Answer x = .......................................... [2] 4024/22/M/J/13

For Examiner’s Use

21 (b)

For Examiner’s Use

y (q , 2.4)

(3 , 0.4) x

O

p . x Two points on the curve are (3, 0.4) and (q, 2.4).

The graph shows a sketch of the curve y = (i) Find p and q.



Answer p = .........................................



q = ......................................... [2] (ii) Calculate the gradient of the straight line joining the points (3, 0.4) and (q, 2.4).



© UCLES 2013

Answer ................................................ [2]

4024/22/M/J/13

[Turn over

22 12 (a)

For Examiner’s Use

r 46

A cylindrical tank of height 46 cm and radius r cm has a capacity of 70 litres. Find the radius correct to the nearest centimetre.



Answer .......................................... cm [3] (b)

4

x 20

125° 11

A triangular prism has length 20 cm. The sides of the shaded cross-section are 4 cm, 11 cm and x cm. The angle between the sides of length 4 cm and 11 cm is 125°. (i) Calculate the area of the shaded cross-section.



© UCLES 2013

Answer .........................................cm2 [2]

4024/22/M/J/13

23 (ii) Calculate the volume of the prism.

For Examiner’s Use

Answer .........................................cm3 [1]

(iii) Calculate x.



Answer x = .......................................... [4] (iv) Calculate the surface area of the prism.



© UCLES 2013

Answer .........................................cm2 [2]

4024/22/M/J/13

24 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

4024/22/M/J/13

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/11

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2014

Question 1

(a)

Answers

Mark

correct shape

Part Marks

1

(a)

5.3

1

(b)

90

1

(a)

29.2

1

(b)

38.7

1

obtuse angled

2

(a)

[ 5 oe

1

(b)

–2, –1, 0, 1

1

(a)

45 (°)

1

(b)

27

1

a = 10.05 b = 14 / 3 oe

2

B1 for either 280 × 2π × 3 or M1 for 360

(a)

8

2

M1 for two of 30, 50, 0.5, 20 seen

(b)

(0).32

1

9

3y + 4 y +1

3

10 (a)

–4

1

[0]8 18

1

33

1

3

4 5

6

7

8

Paper 11

1

(b)

2

Syllabus 4024

(b) (i) (ii) 11 (a)

180 [°]

1

(b)

220 [°]

1

(c)

285 [°] cao

1

M1 for 5² + 7² (= 74)

M1 for M1 for

y(3 – a) = a – 4 soi and a further 3y + 4 = a + ay soi

© Cambridge International Examinations 2014

Page 3

12 (a)

Mark Scheme GCE O LEVEL – May/June 2014 4n + 3 oe

1

5 29

2

3

1

(b) (i)

x5

1

(ii)

2 3a

1

14 (a) (i)

15

1

(ii)

12

1

Column, F.D. 1.2 width 50 to 65

1

10 etc.

1

0

1

(b) 13 (a)

(b) 15 (a) (b)

50 etc.

(c)

Syllabus 4024

Paper 11

B1 for either

1

16 (a)

38 [°]

1

(b)

57 [°]

1

(c)

85 [°]

1 ft

17 (a) (i)

8t + 17

1

2p + 13q

1

5 x 2 y (5 xy − 3)

1

[0].12

1

Blue 36

3

M2 for the difference between ½60 × 8 and [½30 × 6 + 20 × 6 +½10(6 + 7.2) oe or M1 for using area under graph.

2 × 10−5

2

B1 for 2000 × 10–8 6 or M1 for figs soi 3

2.99 × 10−23

2

B1 for figs 299 or better

(ii) (b) 18 (a) (b)

19 (a)

(b)

© Cambridge International Examinations 2014

Page 4

20 (a)

Mark Scheme GCE O LEVEL – May/June 2014 7 –9

2 3

(b) 21 (a) (i)

(ii) (b) 22 (a) (b) (i) (ii) (c) 23 (a) (b)

–3

(0, 3) (2, 0)

B1 for either or M1 for using x2 – 2ax + a2 + b or (x – 7)2 + k seen.

2

M1 for framework (3x + h)(x + k) seen.

2

B1 for either or M1 for substituting 0 for either x or y

1

(–1, 9)

1

Correct triangle

1

Perpendicular bisector of AC

1

Arc centre A radius 4 cm

1

Correct region shaded

1

17

2

M1 for (1 : 3)2 soi

72 oe 125

3

M1 for y =

2

B1 for three correct

oe

k and x3 A1 for k = 72

(b) (i)

12 oe 90

1FT

FT from their tree diagram

(ii)

48 oe 90

2FT

FT from their tree diagram 24 oe FT seen B1 for 90 4 6 6 4 × + × oe FT or M1 for 10 9 10 9

25 (a)

(b)

Paper 11

2

3 oe 2

−

3 6 4 5 , , 9 9 9 9

24 (a)

Syllabus 4024

 4 − 6    − 6 14 

2

B1 for three elements correct.

 11 − 7     − 14 18 

2

B1 for three elements correct

© Cambridge International Examinations 2014

Page 5

(c)

Mark Scheme GCE O LEVEL – May/June 2014

1  4 1   10  2 3 

2

Syllabus 4024

Paper 11

B1 for (det A =) 10 seen or implied or  4 1  seen For   2 3 or M1 for 4 × 3 – (–2 × –1)

© Cambridge International Examinations 2014

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2014 series

4024 MATHEMATICS 4024/12

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2014

Question 1

2

3

4

5

6

9

Mark

(a)

14

1

(b)

0.3oe

1

(a)

9

1

(b)

–2.5

1

(a)

Decimal between 0.75 and 0.875

1

(b)

Fraction between

(a)

47

1

(b)

11 03

1

(a)

8.52 × 10–5 final answer

1

(b)

5 × 106

1

(a)

Rotational symmetry of order 3 0 lines of symmetry

1

(b)

Pattern completed correctly

1

54

2

(a)

Isosceles

1

(b)

128°

1

(a)

25 oe final answer 28

1

(b)

3

7

8

Answers

10 (a) (b)

1 final answer 3

3 7 and 4 8

Syllabus 4024

1

2

406 000 000 oe

1

5

2

Paper 12

Part Marks

E.g.

13 4 or 16 5

Both correct

C1 for answer 36 C 60 2 3 = oe or for Or B1 for k = 200 24 40 2

B1 for

10 16 5 oe or for × 3 3 8

B1 for two of 40, 10 and 0.8 seen

© Cambridge International Examinations 2014

Page 3

Mark Scheme GCE O LEVEL – May/June 2014

11 (a)

ε

Syllabus 4024

Paper 12

1 Q

P

R

12

2

B1 for 8 seen

 172    oe  206 

2

B1 for one value correct

Amount taken on Monday and Tuesday

1

17

1

2−x oe 3

2

14 (a)

35.5

1

(b)

118

2

15 (a)

0.5

1

x[1 y [ 0.5x + 1oe

2

40

1

(b)

56.25

1

(c) (i)

225

1

(ii)

400

1

 3   1

1

(b)

 − 1 0    0 1

1

(c)

Correct enlargement, vertices (–1, 2), (1, 2), (1, 6)

(b) 12 (a) (b) 13 (a) (b)

(b)

16 (a)

17 (a)

2

x−2 oe 3 2− y B1 for 3 Or M1 for x = 2 – 3y soi

C1 for

B1 for use of 34.5 and 24.5

FT their gradient in y [ mx + 1 B1 for one correct Or B1 for both x = 1 and y = 0.5x + 1 soi

B1 for two vertices corrector for correct size and correct orientation

© Cambridge International Examinations 2014

Page 4

18 (a) (b) (i)

Mark Scheme GCE O LEVEL – May/June 2014 135

1

165

1FT

24 cao

2

19 (a) (i)

6

1

(ii)

3

1

16b 6 or 16b6a-2 2 a

2

20 (a)

v 25

1

(b)

10

2

(c)

108

1 FT

(ii)

(b)

7 7 3 6 , , , correctly completed 10 9 9 9

21 (a)

(ii)

22 (a) (b) 23 (a) (b) (c)

FT 300 – their (a) M1 for 360 ÷ (180 – their 165)

B1 for answer with 16 in numerator or for two out of three terms algebraically correct (1)a or better seen Or B1 for 4b 3

B1 for any correct expression for one area

1

7 FT 15

2

B1 for

9

2

B1 for 15 2 − 12 2

279

2FT

2x2 + 9x + 4

21 oe FT 90 3 7 7 3 Or M1 for × + × 10 9 10 9

B1 for 0.5 × their 9 × 12 B1 for (their 9)2+122

1

7x + 6 final answer x( x + 2) 2 or –5

Paper 12

1

1 15

(b) (i)

Syllabus 4024

1 3

B2 for (x – 2)(x + 5)( = 0) − 3 ± 49 Or 2 B1 for x2 + 3x – 10 = 0 oe 3 term equation or x2 + 3x – 10

© Cambridge International Examinations 2014

Page 5

Mark Scheme GCE O LEVEL – May/June 2014 Correct frequency polygons drawn

3

(b)

1 < t Y 1.5

1

(c)

Correct comment(s) making a comparison of times between girls and boys.

1

(2y + x) + (3y + x) + (2y + 10) + (3x + 5) = 360

1

x = 20, y = 35

3

24 (a)

25 (a) (b)

Syllabus 4024

Paper 12

Consisting of these marks which can be awarded singly: B1 for linear scale up to 8 on frequency axis B1 for plots at correct heights B1 for plotting their points at centre of interval and joined with ruled lines

E.g. The mode for the boys is higher than the mode for the girls The range of times was longer for boys than for girls. Most girls spent between 1 and 2 hours, but boys times more evenly spread between 0 and 3 hours

B2 for one correct with supporting working Or M1 for correct method to eliminate one variable, condoning one arithmetic slip , Or correct substitution to obtain an equation in one variable and A1ft for correct evaluation to find the other variable Or SC1 After 0 scored, for correct substitution and evaluation to find the other variable

(c)

65 cao

1

© Cambridge International Examinations 2014

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/21

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2014

Question 1

2

Answers

Syllabus 4024

Mark

Paper 21

Part marks x − 2( x − 4) or better ( x − 4) 2

(a)

8− x ( x − 4) 2

2

M1 for

(b)

x = 2.5 o.e., y = –3

3

B2 for one correct with supporting working Or B1 for pair of values satisfying one equation

(c)

x = 6 or –1

3

M1 for x2 – 5x – 6 = 0 M1 for (x – 6)(x + 1) = 0 5 ± 49 Or M2 for 2 Or M1 for 5 and 2 correct or

(d)

y+3 final answer 2y + 5

3

(a) (i)

0 or none

1

7, 8, 11, 13, 14

1

(iii)

3 or 0.27 or better 11

1

(iv)

5

1

(b) (i)

3

1

(ii)

11

1

(iii)

18

1

(ii)

M1 for (y + 3)(y – 3) seen M1 for (2y + 5)(y – 3) seen

All correct

© Cambridge International Examinations 2014

49

Page 3

3

Syllabus 4024

Paper 21

37.5[%]

2

M1 for 5.5 ÷ (240 ÷ 60) soi by 1.375 Or B1 for either 150 seen and 90 seen

(ii)

73.5[0]

2

M1 for 45 × 5.5 + (60 – 45) × 5.5 × 0.8 oe Or B1 for 247.5 seen or for 66 seen

(iii)

208.7[0]

2

M1 for 240 ÷ 1.15 oe

(iv)

2837.5[0]

2

M1 for 2500 × 0.045 × 3 oe soi by 337.5

160

1

1.21875 to 1.22

2

(a) (i)

24U

1

(ii)

18U=

1

(iii)

42U

1

(iv)

108U=

1

14.56 to 14.6

2

M1 for cos 72 =

13.3 to 13.304…

2

M1 for

(a) (i)

(b) (i) (ii) 4

Mark Scheme GCE O LEVEL – May/June 2014

(b) (i)

(ii)

M1 for 0.78 ÷ 0.64

4.5 AD

DE 4.5 = sin 66 sin 18

Or for ‘their (b)(i)’ × cos(‘their (a)(i)’) 5

(a) (i) (ii)

(b) (i) (ii)

n + 6, n + 7

1

(n + 1)(n + 6) – n(n + 7) = n2 + 7n + 6 – n2 – 7n = 6

2

M1 for (n + 1)(n + 6) – n(n + 7) or reversed Or B1 for n 2 + 7 n + 6

5n + 50 or 5(n + 10)

2

M1 for [n], n + 9, n + 10, n + 11, n + 20 seen

56, 65, 66, 67, 76 completed in cross

2

M1 for n = 56 Or for 66 in centre of cross

© Cambridge International Examinations 2014

Page 4

6

(a) (i)

60.28 to 60.35

Syllabus 4024

2

M1 for π × 1.62 × 7.5

Paper 21

(a)

length 9.6, width 6.4

1

Condone reversed

(b)

98.7 to 99.2

2

M1 for ‘their 9.6 × 6.4’ × 7.5 – 6 × ‘their 60.3’ Or B1 for 460.8, or 361.68 to 362.1

224.5[375]

2

M1 for 17.75 and 12.65 seen

No, frame could measure 17.5 cm by 12.5 cm

1

Accept statement involving lower bound of either length or width

(a)

–3.5, 5.5

2

B1 for each

(b)

7 correct plots joined with smooth curve

2

P1 for at least 5 correct plots

(c)

x = –2.7 to –2.6, 0.3 to 0.4, 2.2 to 2.3

2

FT their curve B1 for 2 correct solutions

(d)

Tangent drawn at x = –2 2 to 3

(e) (i)

y = 5 – 4x oe

2

M1 for y = –4x + k or y = mx + 5 or –4x + 5

C = 1, D = –4

2

M1 for

(ii)

(b) (i) (ii) 7

Mark Scheme GCE O LEVEL – May/June 2014

(ii)

M1 A1

On their curve

x3 − 3 x + 1 = 5 − 4 x FT 2

© Cambridge International Examinations 2014

Page 5

8

9

Mark Scheme GCE O LEVEL – May/June 2014

Syllabus 4024

(a)

32.25 or 32.75

3

(b) (i)

[4], 16, 32, 55, 75, 80

1

(ii)

6 correct plots joined with smooth curve using correct axes

3

(iii)

(a)

33 to 35

1

(b)

18 to 20

2

B1 for 41 to 43 or 21.5 to 23.5

Paper 21

M1 for (4×5 + 12×15 + 16×25 + 23×35 + 20×45 + 5×55) [= 2580] M1 for ÷ 80

B2 for 6 correct plots Or B1 for 4 correct plots

(c)

1 30

2

M1 for

5 4 × 25 24

(a)

248.6 to 249

3

M1 for 130 2 + 164 2 + or − [2] × 130 × 164 × cos 115 And M1 for AC 2 = 130 2 + 164 2 − 2 × 130 × 164 × cos 115

(b)

9660 or 9661.2(…)

2

M1 for

1 × 130 × 164 × sin115 2

(c)

7

2

M1 for

their 9660 × 3.25 or 6(.2) or 6.3 5000

(d)

43.49 to 43.5

2

M1 for 130 tan 18.5

(e)

148.6 to 149

3

B1 for 65U or 25U seen M1 for 164 × sin ‘65’ or 164 × cos ‘25’ soi

© Cambridge International Examinations 2014

Page 6

Paper 21

1

(ii)

 3 vector   drawn  − 3

2

B1 for two correct movement without arrow Or one correct movement with arrow

(iii)

a = 2, b = 3

2

B1 for each Or SC1 a = –2 and b = –3

(b) (i)

(ii)

(b)

Syllabus 4024

3.16 to 3.163 or 10

10 (a) (i)

11 (a)

Mark Scheme GCE O LEVEL – May/June 2014

Enlargement Scale factor –2 Centre (3, 1)

B1 B1 B1

(a)

(5, 4), (7, 4), (5, 6)

(b)

Stretch Factor 2 x-axis invariant

2

B0 for question if second transformation mentioned

B1 for 2 correct

B1 B1

100 x

1

x2 – 77x + 200 = 0 derived www

4

80 seen x−5 100 80 + = 2.5 oe M1 for x x−5 B1 for

M1 for 100(x – 5) + 80x = 2.5x(x – 5) (c)

74.31 and 2.69 final answer

4

B3 for one correct root seen or for 74 to 74.31 and 2.69 to 2.7 p ± (or + or −) q r B1 for p = 77 and r = 2 And B1 for q = 5129 or q = 71.6...

If in the form

(d)

74.31, because 2.69 would give negative speed for second part

1

(e)

11

2

M1 for

100 80 − or 0.191 [hours] 74.31 74.31 − 5

© Cambridge International Examinations 2014

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the May/June 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/22

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – May/June 2014

Question 1

Mark

Paper 22

Part marks

(a)

138 to 140

1

(b)

D marked at intersection of correct arcs

2

B1 for a correctly positioned D with one correct construction arc or no correct arcs Or, provided D to the west of AB B1 for D on one correct arc or radii 5 cm and 6 cm reversed with arcs Or, provided D to the east of AB B1 for D on intersection of two correct construction arcs

(c)

103°

1

Tolerance ± 2°

(d) (i)

P and Q marked at intersection of perpendicular bisector and circle

3

B1 for perpendicular bisector of AC minimum 3 cm long B1 for arcs radius 4.5 cm centre B, minimum 3 cm long cumulatively B1 for P and Q at correct positions

249°

1

Tolerance ± 2°

97

1

(ii) 2

Answers

Syllabus 4024

(a) (i) (ii)

(c = ± )

4f +d 6

2

M1 for 4f = 6c2 – d or better

(b)

x ≥ 2 cao

2

B1 for final answer {+ or –} x * {+ or –} 2, where * can be wrong inequality or equals

(c)

(3 + 5x)(3 – 5x) oe

1

Must be integers

(d)

(8p – 3q)(x – 2y) oe seen isw

2

M1 for x(8p – 3q) oe or – 2y(8p – 3q) oe Or 8p(x – 2y) oe or – 3q(x – 2y) oe

© Cambridge International Examinations 2014

Page 3

Mark Scheme GCE O LEVEL – May/June 2014

Question

Answers 1.12 and –2.32 final answer

(e)

Syllabus 4024

Mark 4

Paper 22

Part marks B3 for one correct solution or x = 1.1 to 1.121 and -2.321 to -2.3 p ± (or + or −) q r B1 for p = –6 and r = 10

If in the form

And B1 for q = 296 or 3

533.9(0) to 534

2

M1 for 32 × 5.20 + 0.15 × 2450

(ii)

1760

3

M1 for 409.6 – 28 × 5.20 [= 264] M1 for ‘their 264’ ÷ 0.15

(b) (i)

3.75

2

SC1 for an answer of 28.75, 28.7, 28.8, 15, 3.7, 3.8 or 0.0375

402.5[0] or 403 or 402

2

M1 for

(a) (i)

1 3

1

(ii)

2 3

1

25 numbers completed correctly

1

(a) (i)

(ii)

4

(b) (i) (ii)

5

q = 17.2...

920 ×7 ( 4 + 5 + 7)

After 0+0 allow B1 for 2/6 and 4/6 Or 0.33 and 0.66 or better

(a)

18 oe isw 30

1

(b)

8 oe isw 30

1

After 0+0+0 for (b), If all 36 used B1 for 18/36 and 10/36 If 35 used, B1 for 18/35 and 9/35 64 or better AB

(a)

78.1 to 78.13

2

M1 for cos 35 =

(b)

127.9 to 128

3

M1 for 642 + 802 + or – (2) × 64 × 80 cos 125 M1 for AD2 = 642 + 802 – 2 × 64 × 80 cos 125

(c)

24.1 to 24.2°

3

M1 for

sin ADC sin 125 oe = 64 their128

M1 for sin ADC = (d)

2900

2

64 × sin 125 their128

M1 for 0.5 × (80 + 65) × 40

© Cambridge International Examinations 2014

Page 4

Mark Scheme GCE O LEVEL – May/June 2014

Question 6

7

Mark

Paper 22

Part marks

(a)

23 – 6n cao

2

B1 for –6n soi

(b) (i)

4, 10, 18, 28

2

B1 for 3 correct terms seen

(ii)

3 and 24

4

M1 for

(a) (i)

9600 cao

2

M1 for

360 × 1600 oe 60

(ii)

11 cao 60

1

(iii)

1440 cao

2

M1 for

(144 − 90) × their 9600 oe 360

40.1

3

M1 for 12 × 17.5 + 36 × 25 + 45 × 35 + 33 × 50 + 24 × 70 M1 for division by their (12 + 36 + … + 24)

(ii)

Correct histogram

3

B1 for 5 bars correct width and position B1 for at least 3 correct heights k × (2.4, 3.6, 4.5, 1.65, 1.2) B1 for 5 correct heights

(iii)

38 or 39 or 40 or 41

1

 4    − 5

1

(b) (i)

8

Answers

Syllabus 4024

(a) (i)

41 cao

n 2 + 3n = 6 or better 5n − 12 M1 for n2 – 27n + 72 = 0 B1 for either 3 or 24

(ii)

6.4(0) to 6.41 or

(iii)

y = –1.25x + 7 oe

2

B1 for gradient = –1.25 or y-intercept = +7 soi in a final equation

(iv)

(12, –8)

2

B1 for one value correct

(b) (i)

(ii)

(a)

b–a

1

1

(b) 3a cao

1

(c) 4(b – a)

2

(a)

1:4

(b) 1 : 15

B1 for correct unsimplified CD or for 3(b – a)

1 1

© Cambridge International Examinations 2014

Page 5

Mark Scheme GCE O LEVEL – May/June 2014

Question 9

Answers 15 2 + 6 2 = 16.15(5...)

(a)

Syllabus 4024

Mark

Paper 22

Part marks

1

Must be shown to at least 2 d.p.

(b)

417 to 419

3

M1 for π × 6 × 16.2 soi by 305.4 M1 for π × 62 soi by 113.1

(c)

565 to 566

2

M1 for

(d)

316 to 317

2FT

(e) (i)

18.89 to 18.9

2

M1 for

662 to 665

2

M1 for  3 2  or 1.58… seen oe  

2

B1 for

1 × π × 6 2 × 15 or better 3

FT their (c) × 0.56 evaluated B1 for figs 316(…) or 317(…) or their (c) × figs 56 evaluated 3

2 or 1.25… seen oe 2

(ii)

50 50 ) or 2x + 2 x x 50 50 or x + x + + x x

[L =]

10 (a)

2(x +

50 seen x

(b)

41.5 to 41.6, 45

2

B1 for one correct

(c)

Correct smooth curve through the eight given points correctly plotted on correctly scaled axes

3

± half a small square B2 for seven or eight of the given points correctly plotted on their axes or B1 for six of the given points correctly plotted on their axes

(d)

2.8 to 3.2 < x < 16.8 to 17.2

B1 B1

M1 for attempt to read off two x values at y = 40

(e) (i)

27.5 < answer < 28.5

1

7, 7 cao

1

10, 10 cao

1

(ii) (f)

© Cambridge International Examinations 2014

Page 6

Mark Scheme GCE O LEVEL – May/June 2014

Question 11 (a) (i)

Answers EC = BE or AC = FE and ∠AEC = ∠FBE or ∠ECA = ∠BEF Two correct reasons for their choices

Third statement, leading to correct congruence condition i.e. RHS, SAS, SSA (ii)

BFD

(iii)

∠EBF = ∠DFB = 90° Cointerior/interior/supplementary/allied angles [sum to 180] OR ∠BEF = ∠EFD = 60° Alternate angles [are equal]

(iv) (b) (i)

Syllabus 4024

Mark B1 B1

Part marks

Statements and reasons: EC = BE; radii AC = FE; diameters ∠AEC = ∠FBE [= 90°]; angle in semicircle ∠ECA = ∠BEF [= 60°]; equilateral triangle

B1 1 1 1dep OR 1 1dep

Both 90° could be marked on diagram

Both 60° could be marked on diagram

120°

1

120° could be marked on diagram

6.126 to 6.13

2

M1 for Or

(ii)

Paper 22

38.2 to 38.3

3

1 × 4 × 4 × sin 130 2

1 PQ × perpendicular height (numerical) 2

M1 for

(360 − 130) × π × 4 2 soi by 32.11 360

130 × π × 4 2 soi by 18.15 360 And M1 for ‘their major sector area’ + ‘their triangle area’ Or for ‘their circle area’ – ‘their minor sector area’ + ‘their triangle area’

or

© Cambridge International Examinations 2014

Cambridge International Examinations Cambridge Ordinary Level

* 4 3 3 8 1 5 0 9 2 8 *

MATHEMATICS (SYLLABUS D)

4024/11 May/June 2014

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (RW/KN) 81743/3 © UCLES 2014

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Complete the pattern so that AB is the only line of symmetry. A

B

[1] (b) Shade four more small triangles in the shape below to make a pattern with rotational symmetry of order 3.

[1] 2

(a) Evaluate 5 + 1 # 0.3 .



Answer

.......................................................... [1]

Answer

.......................................................... [1]

(b) Evaluate 18 ' 0.2 .



© UCLES 2014

4024/11/M/J/14

3 3 9

4.3

5.6

The diagram shows a parallelogram with lengths as marked. All the lengths are in centimetres. (a) Calculate the perimeter of the parallelogram.



Answer

....................................................cm [1]

Answer

.................................................. cm2 [1]

(b) Calculate the area of the parallelogram.

4

In the triangle PQR, PQ = 5 cm, QR = 7 cm and PR = 9 cm. Decide whether the triangle is acute angled or obtuse angled. Show calculations to support your decision.



© UCLES 2014

Answer Triangle PQR is .......................................................... [2]

4024/11/M/J/14

[Turn over

4 5

(a) Solve 4 G 3y - 11.



Answer y ........................................................ [1] (b) Write down all the integers that satisfy the inequality - 4 G 2x 1 4 .

6

Answer

.......................................................... [1]

(a) The angles of a triangle are in the ratio 3 : 4 : 5. Calculate the smallest angle in the triangle.



Answer

.......................................................... [1]

(b) The ratio of boys to girls in a class is 4 : 5. There are 3 more girls than boys. Calculate the total number of students in the class.



© UCLES 2014

Answer

4024/11/M/J/14

.......................................................... [1]

5 7

A thin piece of wire is shaped into a figure five as shown. 5.25

4.8

3 280°

The shape has two straight sections of length 5.25 cm and 4.8 cm. The curved part is the arc of the major sector of a circle, radius 3 cm. The angle of the major sector is 280°. The total length of wire needed to make the figure is ^a + brh cm. Find the values of a and b.



Answer a = ....................................................



© UCLES 2014

b = .................................................... [2]

4024/11/M/J/14

[Turn over

6 8

(a) By writing each number correct to one significant figure, estimate the value of 28.6 + 47.7 . 0.47 # 21.4

(b) Write

Make a the subject of the formula y =



© UCLES 2014

.......................................................... [2]

Answer

.......................................................... [1]

8 as a decimal. 25

9

Answer

a-4 . 3-a

Answer a = .................................................... [3]

4024/11/M/J/14

7 10 (a) One morning the temperature was 5 °C. By the evening the temperature had dropped 9 °C. Write down the temperature in the evening.



Answer

.................................................... °C [1]

(b) The times of some buses from Aytown to Deetown are shown. Aytown

07 04

08 04

08 56

09 00

09 32

10 56

Beetown

-

-

09 05

-

09 41

11 05

Ceetown

07 18

08 18

09 14

-

-

11 14

Deetown

07 35

08 35

09 31

09 28

10 05

11 31

(i) Maryam lives in Ceetown and has to be in Deetown by 09 30. What time is the latest bus from Ceetown that she can catch?

Answer

.......................................................... [1]

(ii) Aadil catches the 09 32 from Aytown to Deetown. How long does his journey take?



© UCLES 2014

Answer

4024/11/M/J/14

............................................minutes [1]

[Turn over

8 11 North

A

North

C

B

The diagram shows a map of a lake. Three points A, B and C are on the edge of the lake. (a) A ship sails due south from A to B. Write down the bearing of B from A.

Answer

.......................................................... [1]

(b) A yacht sails from A to C. Measure and write down the bearing of C from A.

Answer

.......................................................... [1]

(c) A cruiser sails from C to D on a bearing of 105°. Work out the bearing of C from D.

© UCLES 2014

Answer 4024/11/M/J/14

.......................................................... [1]

9 12 (a) Here are the first four terms of a sequence. 7

11

15

19

Write down an expression, in terms of n, for the nth term of this sequence.



Answer

.......................................................... [1]

(b) un is the nth term of another sequence. Here is the formula connecting the nth and ^n + 1hth terms of this sequence. 3un - 4 = un + 1 The value of u3 is 11. Find u2 and u4.



Answer u2 = ..................................................



u4 = .................................................. [2]

13 (a) Solve 2 ^5 ph = 250 .



Answer p = .................................................... [1] (b) Simplify (i) 1 ' x - 5 ,

(ii)



© UCLES 2014

Answer

.......................................................... [1]

Answer

.......................................................... [1]

3a 9a 2 ' . 4 8

4024/11/M/J/14

[Turn over

10 14 The table shows the ages of guests at a party. Age (y years) Frequency

10 G y 1 20

20 G y 1 40

40 G y 1 45

45 G y 1 50

50 G y 1 65

p

20

8

q

18

The histogram represents some of this information. 3

2 Frequency density 1

0 10

20

30

40 Age (y years)

50

60

70

(a) Use the histogram to find the value of (i) p,



Answer p = .................................................... [1] (ii) q.



Answer q = .................................................... [1] (b) Complete the histogram.

© UCLES 2014

[1]

4024/11/M/J/14

11 15 (a) Find an integer r such that r 2 5 and 5r - 1 is a square number.



Answer r = .................................................... [1] (b) Find the value of s which makes 8s + 2 a prime number.



Answer s = .................................................... [1] (c) Write down an irrational number between 7 and 8.



© UCLES 2014

Answer

4024/11/M/J/14

.......................................................... [1]

[Turn over

12 16 A

38°

D

66°

E

B

C

F

In the diagram AB = AC and AD is parallel to BC. A line from D intersects AC at E and BC at F. t = 66°. t = 38° and BAC ADE Find t , (a) DFC



Answer

t = ............................................. [1] DFC

Answer

t = ............................................. [1] ABC

Answer

t = ............................................. [1] AED

t , (b) ABC

(c)

t . AED



© UCLES 2014

4024/11/M/J/14

13 17 (a) Expand and simplify (i)

4 ^2t + 3h + 5,

(ii)

Answer

.......................................................... [1]

Answer

.......................................................... [1]

Answer

.......................................................... [1]

6p + 3q - 2 ^2p - 5qh.

(b) Factorise completely 25x 3 y 2 - 15x 2 y .



© UCLES 2014

4024/11/M/J/14

[Turn over

14 18 8

6 Speed (m/s)

blue boat

4

red boat 2

0

0

10

20

30

40

50

60

Time (seconds)

Two boats, one red and one blue, leave a harbour at the same time. They travel in the same direction. The speed-time graphs for the boats are shown, for the first minute of their journey. (a) Find the acceleration of the blue boat in the last 10 seconds.



Answer

................................................. m/s2 [1]

(b) Find which boat is ahead after one minute and by what distance.



© UCLES 2014

Answer

........................................ is ahead by ........................................ m [3]

4024/11/M/J/14

15 19 (a) Light travels at a speed of 3 # 10 8 m/s. Calculate the time it takes for light to travel 6 km. Give your answer in standard form.



Answer

.......................................................s [2]

(b) One molecule of water is made up of two atoms of hydrogen and one atom of oxygen. The mass of one atom of hydrogen is 1.67 # 10 - 24 g. The mass of one atom of oxygen is 2.66 # 10 - 23 g. Calculate the mass of one molecule of water. Give your answer in standard form.



Answer

20 (a) Given that



...................................................... g [2]

x 2 - 14x + 40 = ^x - ah2 + b , find the values of a and b.

Answer a = ....................................................



b = .................................................... [2] (b) Solve the equation 3x 2 + 7x - 6 = 0 by factorisation.



© UCLES 2014

Answer x = ....................... or ....................... [2]

4024/11/M/J/14

[Turn over

16 21 (a) The line 2y = 6 - 3x meets the y-axis at A and the x-axis at B. Write down (i) the coordinates of A and B,



Answer

A = ( ................ , ................)





B = ( ................ , ................ ) [2]

Answer

.......................................................... [1]

(ii) the gradient of the line.



(b) Another straight line cuts the x-axis at P ^- 4, 0h and passes through Q ^2, 18h. Find the coordinates of the midpoint of PQ.



© UCLES 2014

Answer ( .......................... , ......................... ) [1]

4024/11/M/J/14

17 22 (a) Construct, using ruler and compasses only, an equilateral triangle ABC. The side AB has been drawn for you.

A

B

[1] (b) Construct the locus of points, inside triangle ABC, which are (i) equidistant from A and C,

[1]

(ii) 4 cm from A.

[1]

(c) A point X lies within triangle ABC, is nearer to A than to C and is less than 4 cm from A. On your diagram shade the region in which X must lie.

© UCLES 2014

4024/11/M/J/14

[1]

[Turn over

18 23 (a) A spherical tennis ball and a spherical beach ball have diameters in the ratio 1 : 3. The surface area of the beach ball is 153 cm2. Calculate the surface area of the tennis ball.



Answer

.................................................. cm2 [2]

(b) y is inversely proportional to the cube of x. When x = 2 , y = 9 . Find y when x = 5.



© UCLES 2014

Answer y = .................................................... [3]

4024/11/M/J/14

19 24 On a plate there are ten biscuits. Four of the biscuits are round and six of the biscuits are square. Sabah chooses a biscuit at random from the plate and eats it. She then chooses another biscuit at random from the plate. The tree diagram shows the possible outcomes and some of their probabilities. First biscuit

Second biscuit

............ 4 10

round

............ ............ 6 10

round

square

round

square

............

(a) Complete the tree diagram.

square

[2]

(b) Calculate the probability that Sabah chooses (i) two round biscuits,



Answer

.......................................................... [1]

Answer

.......................................................... [2]

(ii) one round biscuit and one square biscuit.



© UCLES 2014

4024/11/M/J/14

[Turn over

20 25

A=c

3 -1 m -2 4

B=c

5 0

3 m -2

(a) Find 3A - B .



Answer

f

p

[2]

Answer

f

p

[2]

Answer

f

p

[2]

(b) Find A2.



(c) Find the 2 # 2 matrix X, where AX = c



1 0 m. 0 1

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/11/M/J/14

Cambridge International Examinations Cambridge Ordinary Level

* 5 4 5 6 0 0 5 3 9 8 *

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2014

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (RW/KN) 81742/2 © UCLES 2014

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate 12 + 8 ' ^9 - 5h.

Answer .............................................................. [1] (b) Evaluate 0.018 ' 0.06 .

Answer .............................................................. [1] 2

Tasnim records the temperature, in °C, at 6 a.m. every day for 10 days. -6

-3

0

-2

-1

-7

-5

2

-1

-3

(a) Find the difference between the highest and the lowest temperatures.

Answer ........................................................ °C [1] (b) Find the median temperature.

Answer ........................................................ °C [1] 3

It is given that

3 7 1n1 . 4 8

(a) Write down a decimal value of n that satisfies this inequality.

Answer .............................................................. [1] (b) Write down a fractional value of n that satisfies this inequality.

Answer .............................................................. [1]

© UCLES 2014

4024/12/M/J/14

3 4

Here is part of a bus timetable. Bus station

09 56

10 26

10 56

11 26

11 56

City Hall

10 03

10 33

11 03

11 33

12 03

Railway station

10 17

10 47

11 17

11 47

12 17

Hospital

10 28

10 58

11 28

11 58

12 28

Airport

10 43

11 13

11 43

12 13

12 43

(a) How long does the bus take to get from the bus station to the airport?

Answer ............................................... minutes [1] (b) Chris has a flight from the airport at 14 05. He must check in at the airport 2 hours before the flight. He will take a bus to the airport from the City Hall. Write down the latest time that Chris can take a bus from the City Hall to be at the airport in time.

Answer .............................................................. [1] 5

(a) Express 0.000 085 2 in standard form.

Answer .............................................................. [1] (b) Calculate ^3 # 10 5h ' ^6 # 10 - 2h, giving your answer in standard form.

Answer .............................................................. [1]

© UCLES 2014

4024/12/M/J/14

[Turn over

4 6

(a) Complete the description of the pattern below.

The pattern has rotational symmetry of order ............... and ............... lines of symmetry.

[1]

(b) Shade in two more small squares in this shape to make a pattern with exactly 2 lines of symmetry.

[1] 7

The cost of a mirror is directly proportional to the square of its width. A mirror of width 40 cm costs $24. Work out the cost of a mirror of width 60 cm.

Answer $ .......................................................... [2]

© UCLES 2014

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5 8

A and B are points on the circle, centre O. TA and TB are tangents to the circle. t = 64° . BAT

A 64° O T B

(a) What special type of triangle is triangle ABT ? Answer .............................................................. [1] (b) Work out AÔB.

Answer AÔB = ............................................... [1]

© UCLES 2014

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6 9

(a) Evaluate

1 3 + . 7 4

Answer .............................................................. [1] 1 3 (b) Evaluate 5 ' 1 , giving your answer as a mixed number in its lowest terms. 5 3

Answer .............................................................. [2] 10 (a) Write 405 917 628 correct to three significant figures.

Answer .............................................................. [1] (b) By writing each number correct to one significant figure, estimate the value of 41.3 . 9.79 # 0.765

Answer .............................................................. [2]

© UCLES 2014

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7 11

(a) On the Venn diagram, shade the set P l + ^Q , Rh. 

P

Q

R

[1] (b) A group of 40 children are asked what pets they own. Of these children, 13 own a cat, 5 own both a cat and a dog and 15 own neither a cat nor a dog. Using a Venn diagram, or otherwise, find the number of children who own a dog, but not a cat.

Answer .............................................................. [2]

© UCLES 2014

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8 12 A café sells hot drinks. On Monday it sells 80 teas, 60 coffees and 40 hot chocolates. On Tuesday it sells 70 teas, 90 coffees and 50 hot chocolates. A cup of tea costs $0.80, a cup of coffee costs $1 and a cup of hot chocolate costs $1.20. This information can be represented by the matrices M and N below. J80 M=K L70

60 90

40N O 50P

J0.8N K O N=K 1 O K O L1.2P

(a) Work out MN.

Answer

[2]

(b) Explain what the numbers in your answer represent.

Answer ............................................................................................................................................... ............................................................................................................................................................ ....................................................................................................................................................... [1]

© UCLES 2014

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9 13

f ^xh = 2 - 3x Find (a) f ^- 5h,

Answer f ^- 5h = ............................................. [1] (b) f -1 ^xh.

Answer f -1 ^xh = ............................................. [2] 14 A rectangular garden has length 35 metres and width 25 metres. These distances are measured correct to the nearest metre. (a) Write down the upper bound of the length of the garden.

Answer ......................................................... m [1] (b) Work out the lower bound of the perimeter of the garden.

Answer ......................................................... m [2]

© UCLES 2014

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10 15

y 5 4

L

3 2 1 0

1

2

3

4

5

x

(a) Find the gradient of the line L.

Answer .............................................................. [1] (b) The shaded region on the diagram is defined by three inequalities. One of these is x + y G 4 . Write down the other two inequalities.

Answer ................................................................... .............................................................. [2]

© UCLES 2014

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11 16 (a) Dwayne buys a camera for $90. He sells the camera for $126. Calculate his percentage profit.

Answer ......................................................... % [1] (b) The price of a computer was $375. In a sale, the price was reduced by 15%. Calculate the reduction in the price of the computer.

Answer $ .......................................................... [1] (c) The exchange rate between euros and dollars is €1 = $1.25 . (i) Convert €180 to dollars.

Answer $ .......................................................... [1] (ii) Convert $500 to euros.

Answer € .......................................................... [1]

© UCLES 2014

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[Turn over

12 17 The diagram shows triangles A, B and C.

y 7 6 5 4 3 B

2 C

–7

–6

–5

–4

–3

A

1 –2

–1

0

1

2

3

4

5

6

7

x

(a) Triangle A can be mapped onto triangle B by a translation. Write down the column vector for the translation. Answer

f

p

[1]

(b) Find the matrix representing the transformation that maps triangle A onto triangle C.

Answer

f

p

[1]

(c) Triangle A is mapped onto triangle D by an enlargement, scale factor 2, centre ^5, 0h. Draw and label triangle D.

© UCLES 2014

[2]

4024/12/M/J/14

13 18 (a) Find the size of the interior angle of a regular octagon.

Answer .............................................................. [1] (b) A regular octagon, an equilateral triangle and a regular n-sided polygon fit together at a point.

octagon a°

(i) An interior angle of the regular n-sided polygon is a°. Find a.

Answer

a = .................................................... [1]

Answer

n = .................................................... [2]

(ii) Find the value of n.

© UCLES 2014

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[Turn over

14 19 (a) Evaluate (i)

3

216 ,

Answer .............................................................. [1] 1

(ii) 16 2 - 16 0 .

Answer .............................................................. [1] J 3a 2 b N- 2 O . (b) Simplify K 4 L12ab P

Answer .............................................................. [2]

© UCLES 2014

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15 20 The diagram shows the speed-time graph for 100 seconds of a car’s journey. The car accelerates uniformly from a speed of v m/s to a speed of 3v m/s in 50 seconds. It then continues at a constant speed.

3v Speed (m/s) v 0

0

50 Time (t seconds)

100

(a) Find, in terms of v, the acceleration of the car in the first 50 seconds.

Answer ..................................................... m/s2 [1] (b) The car travels 2500 metres during the 100 seconds. Find v.

Answer

v = .................................................... [2]

(c) Find the speed of the car, in kilometres per hour, when t = 75.

Answer .................................................... km/h [1]

© UCLES 2014

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[Turn over

16 21 Luis has 3 black pens and 7 red pens in a case. He takes two pens from the case at random without replacement. (a) Complete the tree diagram to show the possible outcomes and their probabilities. First pen

Second pen

2 9 3 10

black

............ ............ ............

black

red

black

red

............

red

[1] (b) Find, as a fraction in its lowest terms, the probability that (i) Luis takes two black pens,

Answer .............................................................. [1] (ii) Luis takes two different coloured pens.

Answer .............................................................. [2]

© UCLES 2014

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17 22 Shape ABCDEFG is made from two squares and a right-angled triangle. AB = 15 cm and BC = 12 cm. 12

B

C

15 A

G

D

E

F

(a) Find the length AG.

Answer ........................................................cm [2] (b) Find the total area of the shape.

Answer ...................................................... cm2 [2]

© UCLES 2014

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[Turn over

18 23 (a) Expand and simplify ^2x + 1h^x + 4h .

Answer .............................................................. [1] (b) Write

3 4 + as a single fraction in its simplest form. x x+2

Answer .............................................................. [1] (c) Solve

10 = x+3. x

Answer

© UCLES 2014

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x = ....................... or ....................... [3]

19 24 Some students were asked how long they had each spent doing homework the day before. The results are summarised in the table. Time (t hours)

0 1 t G 0.5

0.5 1 t G 1 1 1 t G 1.5

1.5 1 t G 2

2 1 t G 2.5

2.5 1 t G 3

Girls

0

5

8

6

0

1

Boys

3

3

4

5

3

2

(a) On the grid, draw a frequency polygon to represent this information for the girls and another frequency polygon for the boys.

Frequency

0

0.5

1

1.5

2

2.5

3

Time (t hours)

[3] (b) Write down the modal group for the girls. Answer .............................................................. [1] (c) Make a comment comparing the distribution of the times spent by the girls with the times spent by the boys. Answer ............................................................................................................................................................ ....................................................................................................................................................... [1]

© UCLES 2014

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[Turn over

20 25 In quadrilateral ABCD angle A = ^2y + xh ° angle B = ^3y + xh ° angle C = ^2y + 10h ° angle D = ^3x + 5h ° (a) By finding the sum of the angles in the quadrilateral, show that 7y + 5x = 345.

[1] (b) Given that angle A = 90° then 2y + x = 90 . Solve the simultaneous equations to find x and y. 7y + 5x = 345 2y + x = 90

Answer

x = ......................................................... y = .................................................... [3]

(c) Find the size of the smallest angle in the quadrilateral.

Answer .............................................................. [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/12/M/J/14

Cambridge International Examinations Cambridge Ordinary Level

* 9 7 0 7 7 9 1 0 5 4 *

4024/21

MATHEMATICS (SYLLABUS D)

May/June 2014

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (NF/KN) 93827/2 R © UCLES 2014

[Turn over

2 Section A [52 marks] Answer all questions in this section. 1

(a) Express as a single fraction in its simplest form

x 2 . 2^x - 4h x-4



Answer (b) Solve the simultaneous equations.

2x - 3y = 14 6x + 4y = 3



Answer x = ..............................................



© UCLES 2014

.................................................... [2]

y = .............................................. [3]

4024/21/M/J/14

3 (c) Solve x ^x - 4h = 6 + x .



Answer x = .................... or ..................... [3] (d) Simplify

y2 - 9 . 2y 2 - y - 15



© UCLES 2014

Answer

4024/21/M/J/14

.................................................... [3]

[Turn over

4 2

(a)  = {x: x is an integer and 5 G x G 15} A = {x : x is a multiple of 3} B = {x : x is a factor of 60} C = {x : x is a prime number}

(i) Find n ^A + B + Ch.



Answer

.................................................... [1]

Answer

.................................................... [1]

Answer

.................................................... [1]

Answer

.................................................... [1]

(ii) Find ^A , Bhl .

(iii) A number, r, is chosen at random from . Find the probability that r ! A + B .

(iv) Given that D 1 B and D 1 C , find D.



© UCLES 2014

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5 (b) An activity camp offers 3 sports: tennis, cricket and volleyball. One day, 50 children took part in these sports. 19 children played tennis, 34 children played cricket and 23 children played volleyball. 2 children played all three sports. 5 children played tennis and cricket. 10 children played tennis and volleyball.

By drawing a Venn diagram, or otherwise, find the number of children who played (i) tennis and cricket but not volleyball,

Answer

.................................................... [1]

Answer

.................................................... [1]

Answer

.................................................... [1]

(ii) cricket and volleyball but not tennis, (iii) cricket only.

© UCLES 2014

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[Turn over

6 3

(a) Zara owns a hairdressing salon. She buys a pack of 60 bottles of shampoo from a warehouse for $240. She plans to sell the bottles of shampoo to her customers for $5.50 each. (i) Calculate the percentage profit Zara makes on each bottle she sells for $5.50 .



Answer

.................................................... [2]

(ii) Zara sells 45 bottles at the full price then sells the rest with a 20% discount. Calculate the total profit she makes selling all 60 bottles.



Answer $ .................................................. [2] (iii) When the warehouse sells a pack of shampoo for $240 it makes a profit of 15%. Calculate the price paid for the pack of shampoo by the warehouse.



Answer $ .................................................. [2] (iv) Zara borrows $2500 from a bank to make improvements to her salon. She is charged 4.5% per year simple interest. She pays the money back after 3 years. Calculate the total amount Zara must pay to the bank.



© UCLES 2014

Answer $ .................................................. [2]

4024/21/M/J/14

7 (b) The exchange rate between dollars ($) and pounds (£) is $1 = £0.64 . The exchange rate between dollars ($) and euros (€) is $1 = €0.78 . (i) Luke changes $250 into pounds. Calculate how many pounds he receives.



Answer £ .................................................. [1] (ii) Complete the statement to show the exchange rate between pounds and euros.

Exchange rate £1 = € .................. [2]

© UCLES 2014

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[Turn over

8 4 B

A

C

24° O

F 72°

D

E

A, B, C, D and E are points on a circle with centre O. AD is a diameter of the circle and F is the point of intersection of AD and CE. t = 24° and ADC t = 72°. ACE (a) Find (i)

t , ADE

(ii)

.................................................... [1]

Answer

.................................................... [1]

Answer

.................................................... [1]

t . ABC



© UCLES 2014

Answer t , CFD

(iv)

.................................................... [1]

t , CED

(iii)

Answer

4024/21/M/J/14

9 (b) Given that DC = 4.5 cm, calculate (i) the diameter of the circle,



Answer

............................................. cm [2]

Answer

............................................. cm [2]

(ii) DE.



© UCLES 2014

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[Turn over

10 5

(a) Here is part of a number grid. A square can be placed anywhere on the grid outlining four numbers. The numbers in opposite corners of the square are multiplied together and the difference between the products is found. 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

1

9 × 14 − 8 × 15 = 126 − 120 =6

(i) The grid is continued downwards. If n represents the number of the top left of the square, complete this square with expressions for the other numbers.

n

n+1

[1] (ii) Use your answer to part (a)(i) to prove that the difference between the products of the opposite corners is always 6.

[2]

© UCLES 2014

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11 (b) Here is part of a different number grid. A cross can be placed anywhere on the grid outlining five numbers. The numbers in the cross are added together. 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

41

42

43

(i) Find and simplify an expression, in terms of n, for the sum of the numbers in the cross below. n



Answer

.................................................... [2]

(ii) The sum of the numbers in the cross below is 330. Complete the cross with the correct numbers.

[2] © UCLES 2014

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[Turn over

12 6

(a) A candle is in the shape of a cylinder of radius 1.6 cm and height 7.5 cm. (i) Calculate the volume of the candle.



Answer

............................................ cm3 [2]

(ii) Six of these candles are packed into a box of height 7.5 cm as shown.

7.5

(a) Find the length and width of the box.



Answer length = ................................ cm



width = ............................... cm [1] (b) Calculate the volume of empty space in the box.



© UCLES 2014

Answer

4024/21/M/J/14

............................................ cm3 [2]

13 (b) The length of a rectangular photo is 17.8 cm, correct to the nearest millimetre. The width of the photo is 12.7 cm, correct to the nearest millimetre. (i) Calculate the lower bound of the area of the photo.



Answer

............................................ cm2 [2]

(ii) Kate has a rectangular frame with length 18 cm and width 13 cm, both measured correct to the nearest centimetre. Will the photo definitely fit into the frame? Explain your answer.

Answer ........................ because ................................................................................................ .............................................................................................................................................. [1]

© UCLES 2014

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[Turn over

14 Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks.

7

The variables x and y are connected by the equation y =

x3 - 3x + 1 . 2

Some corresponding values of x and y are given in the table below. x

−3

y

−2 3

−1 3.5

0

1

2

1

−1.5

−1

3

(a) Complete the table.

[2]

(b) On the grid below, plot the points from the table and join them with a smooth curve. y 6

4

2

–3

–2

–1

0

1

2

3

x

–2

–4

[2] © UCLES 2014

4024/21/M/J/14

15 (c) Use your graph to solve the equation

x3 - 3x + 1 = 0 . 2 Answer

........................................................................ [2]

(d) By drawing a tangent, find the gradient of the curve at the point (−2, 3).



Answer

.................................................... [2]

Answer

.................................................... [2]

(e) The line AB intersects the curve at point P. The coordinates of point A are (0, 5). The coordinates of point B are (2, −3). (i) Find the equation of line AB.



(ii) The x-coordinate of point P is a solution of the equation

x3 + Cx + D = 0 . 2

Find C and D.



Answer C = .............................................



© UCLES 2014

D = ............................................. [2]

4024/21/M/J/14

[Turn over

16 8

A group of 80 students enters a science quiz. The table shows the distribution of their scores. Score (s) Frequency

0 1 s G 10 4

10 1 s G 20 20 1 s G 30 30 1 s G 40 40 1 s G 50 50 1 s G 60 12

16

23

20

5

(a) Calculate an estimate of the mean score.



Answer

.................................................... [3]

(b) (i) Complete the cumulative frequency table for their scores. Score (s) Cumulative frequency

s G 10

s G 20

s G 30

s G 40

s G 50

4

s G 60 80

[1] (ii) On the grid below, draw a horizontal s-axis for 0 G s G 60 using a scale of 2 cm to represent 10 points and a vertical axis from 0 to 80 using a scale of 2 cm to represent 20 students. Draw a smooth cumulative frequency curve to represent this information.

[3] © UCLES 2014

4024/21/M/J/14

17 (iii) Use your graph to estimate (a) the median score,

Answer

.................................................... [1]

Answer

.................................................... [2]

(b) the interquartile range of the scores.



(c) Students who scored more than 40 points can enter the next round of the quiz. Two of these students are selected at random. Work out the probability that both students scored more than 50 points.



© UCLES 2014

Answer

4024/21/M/J/14

.................................................... [2]

[Turn over

18 9

The diagram shows a field on horizontal ground. The side AB is next to a straight road XY. t = 115°. AB = 130 m, BC = 164 m and ABC Y B 130

115°

A X

164

C

(a) Calculate AC.



Answer

................................................ m [3]

Answer

............................................. m2 [2]

(b) Work out the area of the field.



© UCLES 2014

4024/21/M/J/14

19 (c) The field is to be sown with grass seed. Each square metre of the field is sown with 3.25 g of seed. The seed is only sold in 5 kg bags. How many bags of grass seed must be bought?



Answer

.................................................... [2]

Answer

................................................ m [2]

(d) A bird is hovering directly above B. The angle of elevation of the bird from A is 18.5°. Calculate the height of the bird above B.



(e) Calculate the shortest distance from C to the road XY.



© UCLES 2014

Answer

4024/21/M/J/14

................................................ m [3]

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20 10 (a) p = c

1 m -3

q =c

-2 m 0

(i) Find p .



Answer

.................................................... [1]

(ii) On the unit grid below, draw and label the vector p − q.

[2] (iii) The vector r is shown on the unit grid below.

r

It is given that r = ap + bq . Find the values of a and b.



Answer a = ..............................................



© UCLES 2014

b = .............................................. [2]

4024/21/M/J/14

21 (b) The diagram shows triangles A and B. y 6 4 A

2

–6

–4

–2

0 B

2

4

6

8

x

–2 –4

(i) Describe fully the single transformation that maps triangle A onto triangle B.

Answer ...................................................................................................................................... .............................................................................................................................................. [3] (ii) The transformation represented by the matrix c

1 0

0 m maps triangle A onto triangle C. 2

(a) Find the coordinates of the vertices of triangle C.

Answer (............ , ............) , (............ , ............) , (............ , ............) [2] (b) Describe fully the single transformation that maps triangle A onto triangle C.

Answer .............................................................................................................................. ...................................................................................................................................... [2]

© UCLES 2014

4024/21/M/J/14

[Turn over

22 11

Imran drives a distance of 180 km on a business trip. He drives the first 100 km at an average speed of x km / h. He drives at an average speed 5 km / h slower than this for the remainder of the journey. (a) Find, in terms of x, an expression for the time taken, in hours, for the first 100 km.



Answer

......................................... hours [1]

(b) Given that the journey takes a total of 2 hours 30 minutes, form an equation in x and show that it simplifies to x 2 - 77x + 200 = 0 .

[4] (c) Solve the equation x 2 - 77x + 200 = 0 , giving each answer correct to 2 decimal places.

© UCLES 2014

Answer x = .................... or ..................... [4] 4024/21/M/J/14

23 (d) Which of the solutions in part (c) represents the speed for the first 100 km of Imran’s trip? Give a reason for rejecting the other solution.

Answer ………… km / h because .................................................................................................... ...................................................................................................................................................... [1] (e) Find the difference between the times taken for the first and second parts of the journey. Give your answer in minutes, correct to the nearest minute.



© UCLES 2014

Answer

4024/21/M/J/14

...................................... minutes [2]

24 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/21/M/J/14

Cambridge International Examinations Cambridge Ordinary Level

* 5 2 2 0 9 3 7 1 3 2 *

4024/22

MATHEMATICS (SYLLABUS D)

May/June 2014

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 19 printed pages and 1 blank page. DC (NF/KN) 81755/1 © UCLES 2014

[Turn over

2 Section A [52 marks] Answer all questions in this section. 1

The scale drawing shows three airfields, A, B and C, with B due north of A. The scale is 1 cm to 20 km. North

B

C

A

(a) Find the actual distance between A and B.



© UCLES 2014

Answer

4024/22/M/J/14

.............................................. km [1]

3 (b) A beacon, D, is to the west of the line AB. It is 100 km from A and 120 km from B. Construct the position of D on the scale drawing.

[2]

(c) Measure the bearing of C from B.

Answer

.................................................... [1]

(d) An aircraft is •

equidistant from A and C,

•

90 km from B.

(i) By constructing suitable loci, mark on the diagram the two possible positions, P and Q, of the aircraft.

[3]

(ii) Given that the aircraft is east of the line AB, find, by measuring, its bearing from C.



© UCLES 2014

Answer

4024/22/M/J/14

.................................................... [1]

[Turn over

4 2

(a)

f=

6c 2 - d 4

(i) Find f when c = 8 and d =- 4 .



Answer

.................................................... [1]

Answer

.................................................... [2]

Answer

.................................................... [2]

Answer

.................................................... [1]

(ii) Express c in terms of d and f.

(b) Solve 17 - 5x G 2x + 3 .

(c) Factorise 9 - 25x 2 .



© UCLES 2014

4024/22/M/J/14

5 (d) Factorise completely 8px + 6qy - 3qx - 16py .



Answer

.................................................... [2]

(e) Solve 5x 2 + 6x - 13 = 0 . Give your answers correct to two decimal places.



© UCLES 2014

Answer x = ..................... or .................... [4]

4024/22/M/J/14

[Turn over

6 3

(a) Mariam works in a shop. She earns $5.20 per hour. She also earns a bonus of 15% of the value of the items she sells in a week. (i) In one week she works for 32 hours and sells items with a value of £2450. Calculate Mariam’s total earnings for the week.



Answer $ .................................................. [2] (ii) In another week, Mariam worked for 28 hours and earned a total of $409.60 . Calculate the value of the items she sold that week.



Answer $ .................................................. [3] (b) (i) Jack opens a bank account paying simple interest. He pays in $800 and leaves it in the account for 4 years. At the end of 4 years he closes the account and receives $920. Calculate the percentage rate of simple interest paid per year.



Answer

................................................ % [2]

(ii) Jack uses some of the $920 to pay for a holiday and a computer. He saves the remainder. The money is divided between the holiday, computer and savings in the ratio 4 : 5 : 7 . Calculate the amount he saves.

© UCLES 2014

Answer $ .................................................. [2] 4024/22/M/J/14

7 4

A bag contains six identical balls numbered 2, 3, 4, 5, 6 and 7. (a) A ball is taken from the bag at random. Find, as a fraction in its lowest terms, the probability that the number on the ball is (i) a multiple of 3,



Answer

.................................................... [1]

Answer

.................................................... [1]

(ii) prime.



(b) All six balls are replaced in the bag. Two balls are taken from the bag, one after the other, without replacement. The numbers on the two balls are added together. (i) Complete this possibility diagram to show all the outcomes. + 2

2

3

4

5

6

7

5

6

7

8

9

3 4 5 6 7

[1] (ii) Find the probability that the sum of the numbers is (a) odd,



Answer

.................................................... [1]

Answer

.................................................... [1]

(b) less than 8.



© UCLES 2014

4024/22/M/J/14

[Turn over

8 5 A 35° 64 125°

80

C

D

B F

65

E

The diagram shows a framework ABCD supporting a shop sign. The framework is fixed to a vertical wall AB with CD horizontal. AC = 64 cm and CD = 80 cm. t = 35° , BCA t = 90° and ACD t = 125° . BAC (a) Calculate AB.



Answer

............................................... cm [2]

Answer

............................................... cm [3]

Answer

.................................................... [3]

(b) Calculate AD.

t . (c) Calculate ADC



© UCLES 2014

4024/22/M/J/14

9 (d) On the sign CDEF, FE is parallel to CD and is 40 cm below it. FE = 65 cm. Calculate the area of the sign CDEF.



6

Answer

(a) The first five terms of a sequence are

............................................ cm2 [2]

17, 11, 5, −1, −7.

Find, in terms of n, an expression for the nth term of this sequence.



Answer

.................................................... [2]

(b) The nth term, Sn , of a different sequence is found using the formula Sn = n 2 + 3n . (i) Work out the first four terms of this sequence.



Answer

........... , ........... , ........... , ........... [2]

(ii) The nth term, Tn , of another sequence is found using the formula Tn = 5n – 12 . S There are two values of n for which n = 6 . Tn Form and solve an equation in n to find these two values.

© UCLES 2014

Answer n = ................... and ................... [4] 4024/22/M/J/14

[Turn over

10 Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a) The pie chart summarises the results of a local election.

Candidate D

Candidate A

144° 60° Candidate C

Candidate B

(i) Candidate B received 1600 votes. Work out the total number of people who voted in the election.



Answer

.................................................... [2]

(ii) What fraction of the vote did candidate D receive? Give your answer in its lowest terms.



Answer

.................................................... [1]

(iii) How many more votes than candidate A did candidate C receive?



© UCLES 2014

Answer

4024/22/M/J/14

.................................................... [2]

11 (b) The table summarises the ages of the members of a film club. Age (a years) 15 G a 1 20 20 G a 1 30 30 G a 1 40 40 G a 1 60 60 G a 1 80 Frequency

12

36

45

33

24

(i) Calculate an estimate of the mean age of the members.



Answer

.................................................... [3]

(ii) On the grid below, draw a histogram to represent this data.

10

20

30

40

50

60

70

80

Age (a years)

[3] (iii) Find an estimate for the number of members of the film club who are over 50.



© UCLES 2014

Answer

4024/22/M/J/14

.................................................... [1]

[Turn over

12 8

(a) In this question you may use the grid below to help you. J4N J 8N The point P has position vector KK OO and the point Q has position vector KK OO . 2 -3 L P L P (i) Find PQ.

Answer (ii) Find PQ .



J K K KK L

N O O OO P

[1]

Answer

.................................................... [1]

Answer

.................................................... [2]

(iii) Find the equation of the line PQ.



(iv) Given that Q is the midpoint of the line PR, find the coordinates of R.



© UCLES 2014

Answer ( ...................... , ...................... ) [2]

4024/22/M/J/14

13 (b)

D

B b O

a

C

A

In the diagram triangles OAB and OCD are similar. OA = a , OB = b and BC = 4a - b . (i) Express, as simply as possible, in terms of a and/or b (a) AB,

Answer

.................................................... [1]

Answer

.................................................... [1]

Answer

.................................................... [2]

(b) AC , (c) CD. (ii) Find, in its simplest form, the ratio (a) perimeter of triangle OAB : perimeter of triangle OCD,



Answer

......................... : ........................ [1]

(b) area of triangle OAB : area of trapezium ABDC.



© UCLES 2014

Answer

4024/22/M/J/14

......................... : ........................ [1]

[Turn over

14 9

1 2 rr h ] 3 [Curved surface area of a cone = πrl] [Volume of a cone =

15

6

The diagram shows a solid cone of height 15 cm and base radius 6 cm. (a) Show that the slant height of the cone is 16.2 cm, correct to one decimal place.

[1] (b) Calculate the total surface area of the cone.



Answer

............................................ cm2 [3]

Answer

............................................ cm3 [2]

(c) Calculate the volume of the cone.



© UCLES 2014

4024/22/M/J/14

15 (d) The cone is made from wood. The mass of 1 m3 of the wood is 560 kg. Calculate the mass of the cone in grams.



Answer

................................................. g [2]

(e) Another cone is made of the same material and is geometrically similar to the first. The mass of the second cone is double the mass of the first. (i) Calculate the height of the second cone.



Answer

.............................................. cm [2]

(ii) Calculate the total surface area of the second cone.



© UCLES 2014

Answer

4024/22/M/J/14

............................................ cm2 [2]

[Turn over

16 10 Adil wants to fence off some land as an enclosure for his chickens. The enclosure will be a rectangle with an area of 50 m2. 50 m2 x (a) The enclosure is x m long. Show that the total length of fencing, L m, required for the enclosure is given by L = 2x +

100 . x

[2] (b) The table below shows some values of x and the corresponding values of L, correct to one decimal place where appropriate, for L = 2x +

100 . x

x

2

4

6

8

10

12

14

16

L

54

33

28.7

28.5

30

32.3

35.1

38.3

18

20

Complete the table.

[2]

(c) On the grid opposite draw a horizontal x-axis for 0 G x G 20 using a scale of 1 cm to represent 2 m and a vertical L-axis for 0 G L G 60 using a scale of 2 cm to represent 10 m. On the grid, plot the points given in the table and join them with a smooth curve.

[3]

(d) Adil only has 40 m of fencing. Use your graph to find the range of values of x that he can choose.

Answer

..................... G x G .................... [2]

(e) (i) Find the minimum length of fencing Adil could use for the enclosure.

Answer

................................................ m [1]

(ii) Find the length and width of the enclosure using this minimum length of fencing. Give your answers correct to the nearest metre.

© UCLES 2014

Answer Length = .................... m Width = .................... m [1] 4024/22/M/J/14

17 (f) Suggest a suitable length and width for an enclosure of area 100 m2, that uses the minimum possible length of fencing.

© UCLES 2014

Answer Length = .................... m Width = .................... m [1]

4024/22/M/J/14

[Turn over

18 11

(a) The diagram shows two circles with equal radii. A, E and C are points on the circle, centre B. B, E, D and F are points on the circle, centre C. ABCD is a straight line. E

A

D

C

B

F

(i) Show that triangles AEC and FBE are congruent.

[3] (ii) State another triangle that is congruent to triangle AEC.



Answer Triangle ...................................... [1] (iii) Explain why EB is parallel to DF. Answer ....................................................................................................................................... .............................................................................................................................................. [2] t . (iv) Work out ABE

© UCLES 2014

Answer 4024/22/M/J/14

.................................................... [1]

19 (b) P and Q are points on the circle centre O with radius 4 cm. t = 130° . POQ

P 130°

O 4

Q

(i) Calculate the area of triangle POQ.



Answer

............................................ cm2 [2]

(ii) Calculate the area of the major segment, shown unshaded in the diagram.



© UCLES 2014

Answer

4024/22/M/J/14

............................................ cm2 [3]

20 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/22/M/J/14

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the May/June 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/11

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – May/June 2015

Qu 1

2

Answers

17 41 , oe 24 24

(a)

1

(b)

3.2 oe

(a)

Syllabus 4024

Mark

Paper 11

Part Marks

1 1

X

1

(b)

Correct centre marked and order = 3

1

(a)

3 cao 80

1

(b)

3 4

(a)

( 0).0044(00….)

1

(b)

(±) 5

1

(a)

1.6 × 10 11

1

(b)

7.4 × 10 6

1

6

2.2, or 2 15 , only

2

7

Correct frequency polygon

2

B1 for linear vertical scale and 5 or 6 correct heights. B1 for plots at the midpoints of the intervals, and joined by straight lines. After B0, allow SC1 for 4 or 5 correct plots (i.e. correct midpoints and heights).

8

6

2

B1 for n < 8... , or for n > 5... or B1 for 2 correct integers only or for 3 correct integers and one incorrect

9

12 oe 25

2*

10

(1 8)

2

3

4

5

31 40

7

4 5

8

1

M1 for figs 22, or

figs 11 figs 5

B1 for “k” = 12 or M1 for 3 × 22 = y × 52 oe or (their k) / 52 oe C1 for one correct element in a 1 × 2 matrix

© Cambridge International Examinations 2015

Page 3

Mark Scheme Cambridge O Level – May/June 2015

11

2x2 + 1 2 x2 + 1 , or 2 x( x + 1) x +x

12 (a)

1 9

1

(b)

(±) 3

1

(c)

10

1

4.5, or any equiv.

1

22.5, or any equiv.

2

Acceptable line

1

(b)

2:3:4

1

(c)

54

1

( 6, 2 )

1

(b)

square cao

1

(c)

25 cao

1

13 (a) (b)

14 (a)

15 (a)

Final answer

3

Syllabus 4024

Paper 11

B1 for denom. = x(x + 1) oe and B1 for num. = 1(x + 1) + 2x(x + 1) –3x oe soi

2

a M1 for 10 ×   , where a and b are b corresponding sides, possibly cancelled down, with a > b.

© Cambridge International Examinations 2015

Page 4

Mark Scheme Cambridge O Level – May/June 2015  − 2 − 1    −1 5 

16 (a)

 83  − 5  8

(b)

17 (a) (b)

1  8 1 8

or

1  3 1   8  − 5 1

2

2*

B1 for 3( 1 – 4a2 ) or (1-2a)(1+ 2a) seen

( x – 3 )( x + 2y )

2*

B1 for any (partial) factorisation of x2 + 2xy ; x2 – 3x ; –6y + 2xy ; –6y – 3x

42, 48

1

smallest = 11 largest = 19

2

19 (a)

47

1

(b)

34

1

(c)

22

1

(d)

77

1

20 (a) (i)

220°

1

(ii)

130°

1

(iii)

(0)40°

1

7

1

Correct region identified

2

Line parallel to L, through top left hand point of R

1

(b)

(b) 21 (a)

(b) (i) (ii) 22 (a) (b) (i) (ii)

 3 1  seen B1 for   − 5 1 or B1 for (determinant =) 8 seen

3( 1 – 2a )( 1 + 2a )

1

(ii)

Paper 11

1

3

18 (a) (i)

Syllabus 4024

3.5 to 4 (inclusive)

1dep

Acceptable D and completion of quad ABCD

1

Perpendicular bisector of BC

1

Bisector of angle ABC

1

M1 for Venn diagram with n –11, 11 and 6 correctly placed or n – 11+ 11+ x + 6 =25 soi Or B1 for either answer correct Or C1 for reversed answers

Ft from (a) and (b) ie 111 – y or 158 – (x + y)

B1 for the lines x = 1 and x = 5 the lines y = 2 and y = 4

or

Mark dep on 1 mark scored in b)i)

© Cambridge International Examinations 2015

Page 5

Mark Scheme Cambridge O Level – May/June 2015

Syllabus 4024

Paper 11

DP = 5.4 to 5.9 cm (inclusive)

1

1450

1

(b)

2.2 (minutes) oe

1

(c) (i)

Line from (3, 2000) to (13, 0)

1

12

1

scale factor = –2 and centre = ( 0, 2 ) soi

2

B1 for either

triangle with vertices (3, 1), (4, 1), (7, 3)

2

C1 for two correct vertices, or for triangle with vertices (1, 3), (1, 5), (2, 5)

Correct third ball branches with 13 and 23 and correct fourth ball branch(es) with(0 and) 1

2

B1 for either

(c) 23 (a)

(ii) 24 (a) (b) 25 (a)

3 oe 10

1

1 oe 2

2

1 1 1 = − 10 × 11 10 11

1

1 1 1 1 1 1 4 + + + = − = 1× 2 2 × 3 3 × 4 4 × 5 1 5 5

1

19 20

1

(b) 109

1

(b) (i)

(ii)

26 (a)

(b) (i)

(ii) (a)

(c)

n oe n +1

Dependent on two acceptable intersecting loci

B1 for

1

© Cambridge International Examinations 2015

3 2 2 × × their  seen 5 4 3

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the May/June 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/12

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme GCE O LEVEL – May/June 2015

Question

Answers

Mark

(a)

21

1

(b)

9 oe 20

1

2

7 5 13 0.64 0.7 12 8 20

2

3

4

2

1

Syllabus 4024 Part Marks

B1 for 3 correct Or completely reversed answer Or SC1 for 0.65, 0.583, 0.625 seen M1 for

1 × 12 × (b + 4b) oe 2

Or B1 for correct use of 11

4

2

3 hours 30 minutes

2

1 ( a + b) h 2

B1 for answer 11 60 Or

5

Paper 12

5 2 × 60 and × 60 soi 12 5

B1 for 20 55 oe seen Or M1 for 12 25 – (05 25 – 5) Or (12 25 + 5) – 05 25 soi

6

500

2

B1 for two from 30, 2 and 0.9 seen

7

96 oe isw 64

2

B1 for k = 96 soi Or M1 for 24 × 22 = y × 82 Or y = (their k)/82

8

9

10

(a)

p, q, r, s, t, u

1

(b)

s, v

1

(a)

5.21 × 10–6

1

(b)

3 × 105

1

p = 3.8

2

B1 for one correct

q = 77°

© Cambridge International Examinations 2015

Page 3

Mark Scheme GCE O LEVEL – May/June 2015

11

(1, 6) (1, 5) (1, 4)

2

12 (a)

–2

1

(b) (i) –3

1

(ii) –8, 8

1

22 × 3 × 5

1

(b)

15

1

(c)

9

1

Correct triangle with arcs

2

128 to 133°

1

6

1

13 (a)

14 (a)

(b) 15 (a)

b=

(b)

8a − c 2 oe 3

2

16 (a) (i) 9

1

1 3

1

1 16 x 4

1

(ii)

(b) 17 (a)

(b) 18 (a)

Stretch y-axis invariant/parallel to x-axis and factor 4

2

x 4

1

pq(p – 1)

1

(b) (i) (5x – 4)(x + 1)

1

(ii) 0.8 oe , –1

1

Syllabus 4024

Paper 12

B1 for 2 correct no extras Or 3 correct no more than 5 extras After B0 allow SC1 for lines x = 2 and y = 7 drawn on the diagram

Both correct

B1 for correct triangle with no arcs or 1 arc After B0 allow SC1 for triangle with arcs with 5 cm and 6 cm reversed

M1 for c2 = 8a – 3b

B1 for Stretch

Or FT their factorisation

© Cambridge International Examinations 2015

Page 4

Mark Scheme GCE O LEVEL – May/June 2015

1240

19 (a)

2

Syllabus 4024

M1 for 8 × 140 + 10 × (8 +

Paper 12

50 × 8) isw 100

After B0 allow SC1 for answer of 1160 or 1280 276

(b)

2

20 (a) (i) 27 cao

1

(ii) 5 cao (b) 21 (a)

2

B1 for 30 ± 0.2 and 25 ± 0.2 seen

Median 28, IQR = 5

1

FT their (a)(i) + 1 and their (a)(ii)

 −1 9     − 5 13 

2

B1 for 2 or 3 correct elements

(b) (i) 2.5 oe (ii)

B1 for 240 × 0.03 × 5 oe seen

1

 − 1 2  isw oe 0.5  − 2.5 3 

1

FT their (b)(i) If 0 scored in (b)(i) and (b)(ii) SC1 for correct FT adjoint matrix

−1 2    isw  − their (bi) 3  22 (a)

0.25

1

(b)

32

1FT

FT 8 ÷ their (a) soi

(c)

1.9

2FT

FT 7.6 × their (a) M1 for figs their (a) × figs 76 soi

© Cambridge International Examinations 2015

Page 5

23 (a)

(b)

24 (a)

Mark Scheme GCE O LEVEL – May/June 2015

Syllabus 4024

Paper 12

1 2 Or for 2x < 12 and 2x [ 1 1 Or for x = 6 and x = 2

1 Y x < 6 isw 2

2

x = 5, y = –3

3

B2 for either x or y correct with supporting working Or M1 for correct method to eliminate one variable. And A1FT for correct evaluation to find the other variable Or after B0 scored, allow SC1 for 2 correct values but no working shown or correct substitution and evaluation to find the other variable using one of the original equations

h = 4r

2

Answer only is 0. M1 for either version of the full method, that can be accepted in the form

B1 for x < 6 or x [

2×

2 3 1 2 4 1 πr = πr h or πr 3 = πr 2 h 3 3 3 3

After B0, allow SC1 for h= r (b)

17

2FT

M1 for (their h)2 + r2

(c)

πr 2 (2 + 17 ) oe

1FT

FT πr 2 (2 + their17 )

25 (a) (i) b – a (ii) 3b – 2a (b) (i)

4 a 3

1 1 2FT

M1 for such as BO + OC + CE Or BD – ED or –b + a + AE Or B1 for ( CE ) = ± Or ( DE ) = ±

(ii) trapezium

1 their (a)(ii) 3

2 their (a)(ii) 3

1

26 (a) (i) 95 – 6n oe isw

2

(ii) 16 cao

1

(b) (i) 2n – 3

2

(ii) 39 cao

1

B1 for – 6n seen

M1 for (n + 1)2 – 4(n + 1) seen

© Cambridge International Examinations 2015

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the May/June 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/21

Paper 2 (Paper 2), maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – May/June 2015

Qu 1

Answers

(a) (i)

Syllabus 4024

Mark

Part Marks

22 78 or × 36 200 or 7964 100 100

28 236

2

B1 for

(ii)

140 000

3

M1 for

(iii)

30

2

M1 for figs

600

3

B1 for 0.135 soi

(b)

8 x = 36 200 – 25 000 100 36 200 − 25 000 or figs 8 Or B1 for figs (36 200 – 25 000) ÷8 or 11 200 1080 − 756 1080

M1 for figs 2

3

681 113.5 or 104.5

(−1 − 3) 2 + (2 − 10) 2

(a)

8.94

2

M1 for

(b)

– 0.447

2

M1 for

(c)

x + 2y = 13 oe correctly obtained

2

M1 for ( x − (1)) 2 + ( y − 2) 2 = ( x − 3) 2 + ( y − 10) 2

(d)

( – 1, 7 )

1

(a) (i)

Convincing proof

1

HFG

1

HEF + HFK = HEF + HFG

1

(vertically) opposite same segment

2

B1 for either

(ii)

PLˆ M = 180 – y PRˆ M = 180 – (180 – y) = y

2

B1 for either

(iii)

Similar justified

3

B1 for Similar B1 for both MSˆQ and PMˆ R

(a)

63.6 to 63.62

2

M1 for π r 2

(b)

352 to 353

2

B1 for 161(.2) or 190.9 or 191

(c)

10

2

M1 for

(ii) (a) (b) (b) (i)

4

Paper 21

4 80

1 2 2 π 5 h or π 5 3 3 3

© Cambridge International Examinations 2015

Page 3

5

Mark Scheme Cambridge O Level – May/June 2015

(a)

Correctly shown

2

(b)

Complete explanation

1

(c)

4.256 to 4.26(0)

3

M1 for tan x =

55.8 to 55.9

4ft

Paper 21

4 11

BCˆ A = CDˆ F corresponding and y + BCˆ A = 90 = x + CDˆ F

M2 for ( AC =) Or M1 for

(d)

Syllabus 4024

M3 for

4 cos y

4 = cosy AC

1 (their (c) + their FD)×7 2

Or B2 for (FD =) 11.7 or 137 or

42 + 112

Or B1 for ( DF 2 ) = 42 + 112 6

7

(a)

x3 – 1

2

M1 for x3 + x2 + x – x2 – x – 1

(b)

0.4

3

M1 for

(c)

(x = ) –0.5

4

B3 for one correct value with supporting working Or B2 for a pair of values satisfying one equation Or M1 for attempt to equate coefficients

(a) (i)

20.9 to 21(.0)

1

(ii)

4.6(0) to 4.61

1

3x2 + 9x – 247 (= 0) correctly obtained

4

(b) (i)

(y = ) – 2

3 x ( x − 2) − 4( x + 2) (= 3) ( x + 2)( x − 2) B1 for 3x2 – 6x – 4x – 8 or x2 – 4 soi

B3 for 162 = x 2 + 4 x 2 + 12 x + 9 − 2 x 2 − 3x Or M2 for 162 = x 2 + (2 x + 3) 2 − 2 x(2 x + 3) cos 60 Or M1 for (162 =) x 2 + (2 x + 3) 2 ± (2) x(2 x + 3) cos 60

8

(ii)

7.70 and –10.70

(iii)

7.70

(iv)

61.3 to 62(.0)

2ft

M1 for

1 × their 7.70 × their 18.40 × sin60 2

42.18 to 42.22

2

M1 for

260 or 2π × 9.3 360

(a) (i)

3

18.40

B2 for one correct solution Or 7.69 to 7.70 and –10.69 to –10.70 p± q , B1 for p = – 9 and r = 6 or Or if in the form r for q = 3045 (55.18)

1ft

© Cambridge International Examinations 2015

Page 4

Mark Scheme Cambridge O Level – May/June 2015

Paper 21

260 × π × 9.32 360

196 to 196.32

2

M1 for

194 to 195

2

M1 for subtraction of two areas

0.578 confirmed

2

M1 for (2πr =)

(b)

18.1 to 18.2

2

M1 for 2π × 0.578 × 5

(c)

5.24 to 5.25

2

M1 for π × 0.5782 × 5

(a)

–27 –8 – 1 0 1 8 27

1

(b)

7 correct plots and smooth curve

2

(c) (i)

– 2.4 to – 2.6

1

(ii)

4 to 6

1

(iii)

t = u3

1

(iv)

10 to 13

2

M1 for a tangent at x = 2

Correct line

2

B1 for correct intercept (0, 3) or gradient 5

(–1.95 to –1.7) (– 0.8 to –0.5) (2.4 to 2.6)

2

B1 for one correct

(ii) (b) (i) (ii) (a)

9

Syllabus 4024

(d) (i) (ii)

10 (a) (i)

(ii)

1 oe 3

1

48 oe 1495

2

260 × 2π × 0.8 360

B1 for 5 plots

M1 for (2 ×)

60 24 × 300 299

After 0, allow SC1 for 2 × (b)

50.8

3

(c) (i)

100 148 220 276

1

7 correct plots and smooth curve

2

50 to 50.5

1

7.25 to 8.00

2

(ii) (d) (i) (ii)

60 24 × 300 300

M1 for 15240, or 2640 + 1880 + 2352 + 3744 + 3136 + 1488 , or 44 × 60 + 47 × 40 + 49 × 48 + 52 × 72 + 56 × 56 + 62 × 24 B1 for division by 300

B1 for 5 correct plots

B1 for 46.5 to 47.0 or 54.25 to 54.50 seen or their reading at 225, or 75 seen

© Cambridge International Examinations 2015

Page 5

Mark Scheme Cambridge O Level – May/June 2015

Syllabus 4024

b

1

(ii)

2b correctly obtained

2

M1 for GB + BA + AE + ED soi

(iii) (a)

8 8 a– b 5 5

2

B1 for DC = 2c – 2b

8 oe 5

1

11 (a) (i)

(b) (b) (i) (a) (b)

1 :

Reflection in y = x

2

B1 for reflection

0 1   1 0

2

M1 for either column

(ii)

Vertices (–3, 6) (–3, 0) (0, –2)

1

(iii)

90

1

© Cambridge International Examinations 2015

Paper 21

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the May/June 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/22

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – May/June 2015

Qu. 1

3

Mark

Paper 22

Part Marks

(a)

17 x + 13 cao final answer 6

2

(b) (i)

1 or 0.5 cao 2

1

(ii)

y = 1 final answer

1

(iii)

Line from (6, 1) to (4, 3)

1

(iv)

y = –x + 7 final answer

2

B1 for any equation with grad –1 and/or intercept 7

(0, 6)

2

B1 for line from (2, 2) with y-intercept between 5 and 7 soi Or for correct (unsimplified) equation (y = –2x + 6)

(a)

27

1

(b)

Constant speed

1

(c)

0.08 or

(d)

3 to 3.5

1

(e)

1500

2

M1 for

(f)

27 cao

2

M1 for their (total distance ÷ total time) soi

(a) (i)

67.8

3

M1 for

(v)

2

Answers

Syllabus 4024

2 final answer 25

M1 for

2(4 x − 1) 3(3x + 5) + or better oe 6 6

1

1 ( 200 + 50)12 2 Or B1 for ∆ = 900 or rectangle = 600 After 0, allow SC1 for 1750

15×10+45×15+75×11+105×7+135×5+165×2

i.e. 150+675+825+735+675+330 (=3390) B1 for ÷ 50 (independent of M mark) 90 ø t < 120

1

Or clear equivalent

100 and 76 and 48

2

B1 for 100 and 76, or for 48

Completed pie chart with at least one sector correctly labelled

1

(a) (i)

72

1

(ii)

83

1

(iii)

108

1

(iv)

83

1FT

(ii) (b) (i) (ii) 4

Their (ii)

© Cambridge International Examinations 2015

Page 3

(b) (i)

5

Mark Scheme Cambridge O Level – May/June 2015

4 (π) cao

(ii)

12 +

(iii)

8

4 π final answer 3

Syllabus 4024

Paper 22

40 360

2

B1 for π × 62 or for

2

B1 for (a =) 12, or for (b =)

4 3

1ft

(a)

(±) 9.3(0) to 9.31

4

M2 for BC2 = 82 + 112 – 2 × 8 × 11 cos 56 Or M1 for 82 + 112 ± (2) × 8 × 11 cos 56 B1 for 86.5 to 86.6

(b)

122.2 to 122.3

3

M2 for (sin ADC =)

11sin 30 , or 57.7 to 6.5

57.8, or 58 Or M1 for

6

sin ADC sin 30 oe = 11 6.5

(c)

45.7 to 45.71

4

B1 for 27.7 to 27.8 seen 1 M1 for × 11 × 8 × sin 56 (= 36.478...) 2 or for 8 × sin 56 if using heights their stated area M1 for × 100 their areaABC their height ADC × 100 or their height ABC

(a)

325

2

M1 for

(b)

465 and 2.56 to 2.57

3

B2 for 465 or 2.56 to 2.57 seen Or M1 for 400 × 1.17 (468)

(c)

170

3

B2 for 420 or 144.5(0) Or M1 for 357 ÷ 0.85 or 357 – (250 × 0.85)

250 26650 or 20500 20500 Or B1 for 82 seen

© Cambridge International Examinations 2015

Page 4

Mark Scheme Cambridge O Level – May/June 2015

Syllabus 4024

Paper 22

SECTION B Qu. 7

Answers

Mark

3x − 7 oe final answer 2

2

M1 for 3y = 2x + 7 or 3x = 2y + 7 oe

m = –14

2

M1 for

4, 4 and smooth correct graph drawn

3

B1 for 4 and 4 B1 for 7 correct plots

(ii)

(y =) 6.2 to 6.4

1

(iii)

line drawn and x = –0.7 to –0.8 x = 2.7 to 2.8

2

M1 for correct line drawn

(iv)

line drawn and x = –2.3 to -2.7

2

M1 for horizontal line crossing curve at intersection of x = 3.5 and their curve or for the line y = –2.75

(a)

321

1

(b)

9.43 to 9.44

2

M1 for sin 39 =

y oe 15

(c)

19.3 to 19.31

2

B1 for cos 39 =

15 oe x

(d) (i)

X marked 12cm from A on bearing of 141o

2

B1 for either a correct distance or bearing

Correct region shaded

3

B1 for arc, min length 3 cm, radius 6 cm, centre A B1 for bisector of ∠ABC, min length 3 cm

(a) (i)

(ii) (b) (i)

8

(ii)

f–1(x) =

Part Marks

2m + 7 m = oe 3 2

B1 for shading (iii) 9

(a) (i) (ii)

17.6 to 18.4 dependent on an acceptable X and Y

2

2x(2x2 – 5y) final answer

1

(3a + b)(3a – b) final answer

1

(b)

m=

(c) (i)

(ii)

5 , 0.625 8

M1 for Y established at northern end of shading

7 = 3 − 2m 4

2

M1 for 7 = 12 – 8m or

h2 + (h + 7)2 = 232 leading to correct rearrangement

2

M1 for h2 + (h + 7)2 = 232

h (h + 7) oe isw 2

1

© Cambridge International Examinations 2015

Page 5

Mark Scheme Cambridge O Level – May/June 2015

(iii)

120 cao

1

(iv)

12.4, –19.4

3

(v)

54.76 to 54.8

1FT

Syllabus 4024

Paper 22

B2 for one correct solution, or for 12.38 to 12.40 and –19.38 to –19.40 p± q Or if in form , B1 for p = –7 r and r = 2 and B1 for q = 1009 or q = 31.7 to 31.8

Rotation 90° anticlockwise about (1,1)

2

B1 for Rotation B1 for 90° anticlockwise and about (1,1)

(ii)

Correct triangle

2

B1 for two correct vertices

(iii)

Correct triangle

2

B1 for two correct vertices

(iv)

24

2

B1 for 42 soi or M1 for

(b)

2

1

(c)

4

1

(d)

Rectangle, Rhombus

2

7 or 0.23… or better 30

1

(ii)

11 cao 15

1

(iii) (a)

All probabilities correctly placed

2

B1 for at least 8 correct

308 154 or or 0.354 870 435

2

M1 for 7 6   15 14    their × their  +  × their  30 29   30 29  

10 (a) (i)

11 (a) (i)

(b)

1 × 12 × 4 2

B1 for one correct

7   8 +  × their  29   30 Correct histogram

3

B2 for at least 3 correct bars Or B1 for at least 1 correct bar or correct frequency densities seen

(ii)

61 or 62

2

B1 for 6 or 7 seen

(iii)

10

1

(b) (i)

© Cambridge International Examinations 2015

Cambridge International Examinations Cambridge Ordinary Level

* 5 7 6 3 3 8 7 0 6 1 *

MATHEMATICS (SYLLABUS D)

4024/11 May/June 2015

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (AC/CGW) 100473/3 © UCLES 2015

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Evaluate

3 1 +1 . 8 3



Answer .............................................. [1] (b) Evaluate 5 – 3(2 – 1.4).



2

Answer ............................................... [1] (a) In the diagram, six small triangles are shaded. Shade one more small triangle, so that the diagram will then have one line of symmetry.

[1] (b) The diagram below has rotational symmetry. Mark the centre of rotational symmetry with a dot, and write down the order of rotational symmetry.



© UCLES 2015

Answer Order of rotational symmetry = .............................................. [1]

4024/11/M/J/15

3

3

3 (a) Express 3 % as a fraction in its simplest form. 4



Answer ............................................... [1] (b) Arrange these fractions in order, beginning with the smallest. 4 5

31 40

Answer .................... , .................... , .................... [1] smallest

4

3 4

1 10 = 3.162 278 , 3 = 3.166 667 . 6 1 Find the difference between 3 and 10. 6

(a) Correct to 6 decimal places,

Give your answer correct to 2 significant figures.



Answer .............................................. [1] (b) Estimate, correct to the nearest whole number, the value of



© UCLES 2015

2.986 2 + 4.002 2 .

Answer .............................................. [1]

4024/11/M/J/15

[Turn over

4

5

p = 4 # 10 5

q = 7 # 10 6

Expressing each answer in standard form, find (a)

p2 ,



Answer .............................................. [1] (b) p + q .

6

Answer .............................................. [1] A car manufacturer states that a particular car •

uses 5 litres of fuel in travelling 100 km,

•

produces 110 grams of CO2 for each kilometre travelled.

Use this information to calculate the mass of CO2 produced by 1 litre of fuel. Give your answer in kilograms.



© UCLES 2015

Answer ........................................ kg [2]

4024/11/M/J/15

5

7

The times taken by each member of a group of people to run one kilometre were recorded. The results are shown in the table. Time (t minutes) Frequency

21tG3

31tG4

41tG5

51tG6

61tG7

71tG8

0

4

5

3

1

0

On the grid below, draw a frequency polygon to represent these results.

0

1

2

3

4 5 6 Time (t minutes)

7

8

9

[2] 8

Find the integers n that satisfy 20 1 4n - 3 1 30 .



© UCLES 2015

Answer .............................................. [2]

4024/11/M/J/15

[Turn over

6

9

y is inversely proportional to the square of x. Given that y = 3 when x = 2, find y when x = 5.



Answer y = ........................................ [2]

10

P = (3



4 –5)

J- 1 1N K O 0O Q=K 1 K O L 0 - 1P

Evaluate PQ.



© UCLES 2015

Answer

4024/11/M/J/15

[2]

7

11

Express

3 1 +2as a single fraction in its simplest form. x x+1



Answer .............................................. [3]

12 Given that 6 x = 9 , write down the value of (a) 6 -x ,



Answer .............................................. [1] x

(b) 6 2 ,



Answer .............................................. [1] (c) 6 0 + 6 x .



© UCLES 2015

Answer .............................................. [1]

4024/11/M/J/15

[Turn over

8

13 15

Z

A

X

12

3 B

8

Y

C

In the diagram, triangle ABC is similar to triangle XYZ. AB = 3 cm, BC = 8 cm, YZ = 12 cm and ZX = 15 cm. (a) Calculate XY.



Answer ........................................ cm [1] (b) Given that the area of triangle ABC is 10 cm2, calculate the area of triangle XYZ.

Answer ...................................... cm2 [2]



© UCLES 2015

4024/11/M/J/15

9

14

Adults Boys

Girls

A pie chart is used to illustrate the numbers of adults, girls and boys in a group of people. The angles for the adults and girls are 80° and 120° respectively. The diagram shows part of the pie chart. (a) Complete the pie chart.

[1]

(b) Express the ratio of numbers of adults : girls : boys a, b and c are the smallest possible whole numbers.

in the form a : b : c , where

Answer .................... : .................... : .................... [1] (c) There are 6 more girls than adults. Calculate the number of people in the whole group.



© UCLES 2015

Answer .............................................. [1]

4024/11/M/J/15

[Turn over

10

15 y A

B

O

x

A is the point (1, 7)

B is the point (6, 7) J 0N The line AB is mapped onto the line PQ by the translation K O . L- 5P (a) Find the coordinates of Q.



Answer ( ................... , ................... ) [1] (b) What special type of quadrilateral is ABQP?



Answer .............................................. [1]

(c) Find the area of the quadrilateral ABQP.

Answer ................................... units2 [1]



© UCLES 2015

4024/11/M/J/15

11

J- 1 - 3N J1 O-K 16 (a) Express as a single matrix K 1 0 L P L2



J1 (b) Find the inverse of K L5

- 2N O. - 5P

Answer .............................................. [1]

- 1N O. 3P



Answer .............................................. [2]

17 (a) Factorise completely 3 - 12a 2 .



Answer .............................................. [2] (b) Factorise x 2 - 6y + 2xy - 3x .



© UCLES 2015

Answer .............................................. [2]

4024/11/M/J/15

[Turn over

12

18 (a)  = { x : x is an integer, 40 G x G 50 } P = { x : x is a prime number } Q = { x : x is a multiple of 6 } (i) Find n( P ).



Answer .............................................. [1] (ii) List the members of Q.



Answer .............................................. [1] (b) In a group of 25 people, 11 people own both a bicycle and a skateboard, 6 people own neither a bicycle nor a skateboard, n people own a bicycle. Find the smallest and the largest possible values of n.



Answer smallest .............................................. [1]



largest .............................................. [1]

© UCLES 2015

4024/11/M/J/15

13

19 B

T

z°

A

43°

y°

t°

68°

O

C

x°

D

In the diagram, A, B, C and D lie on the circle, centre O. AD is a diameter. The tangent to the circle at B meets the line DA produced at T.

t = 68° and CAO t = 43°. AOB (a) Find x.



Answer x = ........................................ [1] (b) Find y.



Answer y = ........................................ [1] (c) Find z.



Answer z = ........................................ [1] (d) Find t.



© UCLES 2015

Answer t = ......................................... [1]

4024/11/M/J/15

[Turn over

14

20 North

B

North

C 40° A D

Four oil-rigs are positioned at the vertices of a rectangle ABCD . The bearing of B from A is 040°. (a) Find the bearing of (i) A from B,

Answer .............................................. [1] (ii) C from B,



Answer .............................................. [1] (iii) C from D.



Answer .............................................. [1] (b) A supply helicopter is due to arrive at D at 8.15 a.m. It leaves its base at 7.33 a.m. and takes 49 minutes to fly to D. How many minutes late does it arrive at D?



© UCLES 2015

Answer .............................................. [1]

4024/11/M/J/15

15

21 y 6 5 4 3 L

2 1 0

1

2

3

4

5

6

x

(a) On the grid, shade the region, R, given by these inequalities. 1GxG5 2GyG4 (b) The line L, with equation y =

[2]

1 x , is drawn on the grid. 3

1 (i) Draw the line y = x + k so that it passes through a point belonging to R such that k is as 3 large as possible. [1] (ii) Write down this largest value of k.

© UCLES 2015

Answer k = ........................................ [1]

4024/11/M/J/15

[Turn over

16

22 The diagram shows the lines AB and BC. (a) The point D is 11 cm from A and 9 cm from C. On the diagram, construct the quadrilateral ABCD.

[1]

(b) On the diagram, construct the locus of points, inside quadrilateral ABCD, that are (i) equidistant from B and C,

[1]

(ii) equidistant from AB and BC.

[1]

(c) These two loci meet at the point P. Label the point P on the diagram and measure DP. A

B

C



© UCLES 2015

Answer DP = ..................................... cm [1]

4024/11/M/J/15

17

23 Kim and Lee run a 2000 metre cross-country course that starts at P and ends at Q. Lee starts 1 minute after Kim. Their distance-time graphs are shown in the diagram.

2000

1500

Distance from P 1000 (metres)

500

0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

Time (minutes)



(a) Find the distance Lee has run when he overtakes Kim.



Answer ......................................... m [1] (b) Find how much longer Kim takes to complete the course than Lee.



Answer ................................ minutes [1] (c) Melvin starts 3 minutes after Kim. He runs the course in the opposite direction to that taken by Kim and Lee. He runs at a constant speed and takes 10 minutes to reach P. (i) On the diagram, draw the distance-time graph for Melvin.

[1]

(ii) Express Melvin’s speed in km/h.

© UCLES 2015

Answer .................................... km/h [1] 4024/11/M/J/15

[Turn over

18

24 y 7 6 5 4 3

B

2

A

1 –5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

8

x

–1

The diagram shows triangles A and B. (a) Triangle A is mapped onto triangle B by an enlargement. Find the scale factor, and the centre, of this enlargement. Answer scale factor = .................... centre = .................... [2] (b) Triangle A is mapped onto triangle C by a shear, with invariant line the x-axis and shear factor 2. On the diagram, draw triangle C.

© UCLES 2015

[2]

4024/11/M/J/15

19

25 A bag contains 5 balls, of which 3 are red and 2 are blue. One ball is taken, at random, from the bag and is not replaced. If this ball is red, another ball is taken, at random, from the bag and is not replaced. This process is repeated until a blue ball is taken from the bag. Part of the tree diagram that represents these outcomes is drawn below. First ball

Second ball

3– 5

2– 4

2– 5

red

2– 4

blue

red

blue

(a) Complete the tree diagram.

[2]

(b) Expressing each answer as a fraction, find the probability that (i) the second ball taken is blue,



Answer .............................................. [1] (ii) a blue ball is the second, or the third, ball taken.



Answer .............................................. [2]

Question 26 is printed on the next page.

© UCLES 2015

4024/11/M/J/15

[Turn over

20

26 A pattern of numbers is given below. Row 1

1 1 1 = 1#2 1 2

Row 2

1 1 1 = 2#3 2 3

Row 3

1 1 1 = 3#4 3 4

Row 4

1 1 1 = 4#5 4 5

(a) Write down Row 10. Answer ........................................................................................................................................... [1] (b) Adding the first two rows gives the result Adding the first three rows gives the result

1 1 1 1 2 + = - = . 1#2 2#3 1 3 3 1 1 1 1 1 3 + + = - = . 1#2 2#3 3#4 1 4 4

(i) Write down the result of adding the first four rows. Answer ................................................................................................................................. [1] (ii) Use the pattern to write down (a) the value of

1 1 1 1 + + + ... + , 1#2 2#3 3#4 19 # 20



Answer .............................................. [1]

(b) the number of rows that add up to

109 , 110



Answer .............................................. [1]

(c) an expression, in terms of n, for the result of adding the first n rows.



Answer .............................................. [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/11/M/J/15

Cambridge International Examinations Cambridge Ordinary Level

* 4 4 6 4 8 3 0 8 9 1 *

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2015

Paper 1 

2 hours

Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 19 printed pages and 1 blank page. DC (AC/FD) 97054/2 © UCLES 2015

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate

1.3 + 2.9 . 0.2

Answer............................................. [1]

 1 1 (b) Evaluate2 # . 4 5

Answer���������������������������������������������� [1]

 2

Writethesenumbersinorderofsize,startingwiththesmallest.





©UCLES2015



13 7 5 0.7 0.64 20 12 8

Answer...............,...............,...............,...............,...............[2] smallest

4024/12/M/J/15

3 3

b

12

4b

 

Thediagramshowsatrapeziumwithlengthsincentimetres. Theareaofthetrapeziumis120cm2.



Findthevalueofb.

Answerb=...................................... [2]

 4 

Abagcontainsredcounters,bluecountersandyellowcounters. Thereare60countersinthebag.



Theprobabilitythatacountertakenatrandomfromthebagisredis

 

2 . 5 5 . Theprobabilitythatacountertakenatrandomfromthebagisblueis 12 

Howmanyyellowcountersareinthebag?

Answer��������������������������������������������� [2]



©UCLES2015

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4 5  

FarizatravelsfromLondontoAstana. ThetimeinAstanais5hoursaheadofthetimeinLondon,sowhenitis1000inLondon thelocaltimeinAstanais1500.

 

ShefliesfromLondontoMoscowandthenfromMoscowtoAstana. TheflightleavesLondonat1225andtakes4hourstoreachMoscow.



1 Farizawaits4 hoursinMoscowfortheflighttoAstana. 2



ShearrivesinAstanaat0525localtime.



HowlongdidtheflightfromMoscowtoAstanatake?

Answer...............hours...............minutes[2] 6

Bywritingeachnumbercorrecttoonesignificantfigure,estimatethevalueof 29.3 2 . 2.04 # 0.874

Answer��������������������������������������������� [2]



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5 7

yisinverselyproportionaltothesquareofx.



Giventhaty=24whenx=2,findywhenx=8.

Answery=..................................... [2]

 8

TheVenndiagramshowsthesetsA,BandC.  A

B q

p s

t

r u

v C







Listtheelementsof



(a) A∪B,

w

Answer............................................ [1]

 

(b) B′∩C. Answer............................................ [1]



©UCLES2015

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6 9

(a) Write0.00000521instandardform. Answer��������������������������������������������� [1]

 

(b) Givingyouranswerinstandardform,evaluate(6 # 10 7) # (5 # 10 -3) .

Answer��������������������������������������������� [1]

 10 Thesetwotrianglesarecongruent.  Thelengthsareincentimetres,correcttothenearest0.1cm. q°

5.6

p 62°

3.8

5.6



41°

5.1

Findpandq.



Answerp=...........................................



    q=..................................... [2]

©UCLES2015

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7 11

y 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

x



Thediagramshowstheline y = 2x + 1.

 

ThepointPhascoordinates(a,b)whereaandbarebothpositiveintegers. Thevaluesofaandbsatisfytheinequalitiesa 1 2 ,b 1 7 andb 2 2a + 1.



WritedownallthepossiblecoordinatesofP.

Answer................................................................................................................................................. [2]

©UCLES2015

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[Turn over

8 12 Omarhasapackofnumbercards.  Hepicksthesefivecards. _2

_4

_2

4

1







(a) Writedownthemodeofthefivenumbers. Answer���������������������������������������������� [1]

 

(b) Hetakesanothercardfromthepack.





(i) Ifthemeanofthesixnumbersis -1 ,whatnumberdidhepick?

Answer���������������������������������������������� [1]

  

 

(ii) I fthedifferencebetweenthehighestandlowestofthesixnumbersis12,  whatarethetwopossiblenumbershecouldhavepicked?

Answer�������������������� or....................[1]

 13 (a) Express60asaproductofitsprimefactors.

Answer��������������������������������������������� [1]

 

(b) Findthesmallestpossibleintegermsuchthat60misasquarenumber.

Answerm=.................................... [1]

 

(c) Thelowestnumberthatisamultipleofboth60andtheintegernis180.





Findthesmallestpossiblevalueofn.

Answern=..................................... [1]



©UCLES2015

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9 14 IntriangleABC,AB=5cmandAC=6cm.   (a) ConstructtriangleABC.   LineBCisdrawnforyou. 





B

C



[2] (b) Measure BAtC inyourtriangle. Answer�������������������������������������������� [1]



©UCLES2015

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10 15  



c = 8a - 3b

(a) Findcwhena = 3andb = - 4 . Answerc=�������������������������������������� [1]

 

(b) Rearrangetheformulatomakebthesubject.

Answerb=..................................... [2]

 16 (a) Evaluate 



(i) 2 0 + 2 3 ,



J1N 2 (ii) K O . L9P

 

Answer�������������������������������������������� [1]

1

Answer�������������������������������������������� [1]

 

-2

(b) Simplify ^4x 2h .

Answer�������������������������������������������� [1]



©UCLES2015

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11 J4 0N O representsthetransformationT. 17 Thematrix K 0 1 L P (a) DescribefullythetransformationT.   Youmayusethegridbelowtohelpyouanswerthisquestion.





Answer............................................................................................................................................... ....................................................................................................................................................... [2]  

(b) ThetransformationTmapstriangleAontotriangleB.  TheareaoftriangleBisxcm2.





Find,intermsofx,theareaoftriangleA.

Answer������������������������������������ cm2[1]



©UCLES2015

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12 18 (a) Factorisecompletely p 2 q - pq .

Answer�������������������������������������������� [1]

 

(b) (i) Factorise 5x 2 + x - 4 .

Answer�������������������������������������������� [1]

 



(ii) Hencesolve 5x 2 + x - 4 = 0 .

Answerx=................ or................[1]

 19   

(a)   

Luisworksinanoffice. Fornormaltimeheispaid$8perhour. Forovertimeheispaidthesamerateasnormaltimeplusanextra50%. Onemonthheworks140hoursnormaltimeand10hoursovertime.





Workouthowmuchheispaidforthatmonth’swork.

Answer$........................................ [2]

  

(b) Sarainvests$240inanaccountthatpays3%peryearsimpleinterest.  Sheleavesthemoneyintheaccountfor5years.





WorkouthowmuchmoneySarahasattheendof5years.

Answer$........................................ [2]



©UCLES2015

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13 20 Thetimestakenfor200peopletocompletea5kmracewererecorded.  Theresultsaresummarisedinthecumulativefrequencydiagram. 200 180 160 140 120

Cumulative frequency 100 80 60 40 20 0 16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

Time (minutes)



(a) Usethediagramtoestimate





(i) themediantime, Answer������������������������������minutes[1]

 



(ii) theinterquartilerangeofthetimes.

Answer������������������������������minutes[2]

  

(b) Itwasfoundthattherecordingofthetimeswasinaccurate.  Thecorrecttimeswerealloneminutemorethanrecorded.





Writedownthemedianandinterquartilerangeofthecorrecttimes.





AnswerMedian=........................minutesInterquartilerange=........................minutes[1]

©UCLES2015

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14 J 1 21 (a) Expressasasinglematrix 3 K L-2

3N J 4 O-K 5P L-1

0N O. 2P 

Answer            [2]







J3 - 2N O A= K L p - 1P ThedeterminantofAis2.





(i) Findp.

(b) 

Answerp=..................................... [1]

 



(ii) FindA–1.

Answer           [1]



©UCLES2015

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15 22 Thescaleofamapis1:25000. 

(a) Thescalecanbewrittenas1cm:dkm.





Findd.

Answerd=..................................... [1]

 

(b) Thedistancebetweentwovillagesis8km.





Findthedistance,incentimetres,betweenthetwovillagesonthemap.

Answer���������������������������������������cm[1]

 

(c) Thedistancebetweenthepeaksoftwomountainsismeasuredonthemapas76mm.





Calculatethedistance,inkilometres,betweenthetwopeaks.

Answer������������������������������������� km[2]



©UCLES2015

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16 23 (a) Solvetheinequalities. - 4 G 2x - 5 1 7

Answer�������������������������������������������� [2]

 

(b) Solvethesimultaneousequations. 3x+4y=3 2x–y=13



Answerx=...........................................



    y=..................................... [3]

©UCLES2015

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17 1 24 [Volume of a cone = rr 2 h , curved surface area of a cone = rrl ] 3 4 [Volume of a sphere = rr 3 , surface area of a sphere = 4rr 2 ] 3

h r

 

Thesolidisformedfromahemisphereofradiusrcmfixedtoaconeofradiusrcmandheighthcm. Thevolumeofthehemisphereisonethirdofthevolumeofthesolid.



(a) Findhintermsofr.

Answerh=..................................... [2]

 

(b) Theslantheightoftheconecanbewrittenasr k cm,wherekisaninteger.





Findthevalueofk.

Answerk=..................................... [2]

  

(c) Findanexpression,intermsofrandπ,forthetotalsurfacearea,incm2,ofthesolid. 

Answer������������������������������������ cm2[1]



©UCLES2015

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18 25

C A a O

b

D

B



1 Inthediagram,AisthemidpointofOCandBisthepointonODwhereOB = OD. 3



OA = a andOB = b .



(a) Express,assimplyaspossible,intermsof aandb





(i) AB, Answer�������������������������������������������� [1]

 



(ii) CD. Answer............................................ [1]

 

(b) EisthepointonCDwhereCE:ED=1:2.





(i) Express BE ,assimplyaspossible,intermsofaand/orb.

Answer�������������������������������������������� [2]

 



(ii) WhatspecialtypeofquadrilateralisABEC? Answer�������������������������������������������� [1]



©UCLES2015

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19 26 (a) Thefirstfourtermsofasequence,S,are89,83,77,71. 



(i) FindanexpressionforSn,thenthtermofthissequence.

AnswerSn=.................................... [2]

 



(ii) FindthesmallestvalueofnforwhichSn<0.

Answern=...................................... [1]

 

(b) Thenthtermofadifferentsequence,T,isgivenbyTn = n 2 - 4n .





(i) FindandsimplifyanexpressionforTn + 1 - Tn .

Answer............................................ [2]

 



(ii) ThedifferencebetweenTp + 1 andTp is75.







Findthevalueofp.

Answerp=..................................... [1]



©UCLES2015

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20 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

©UCLES2015

4024/12/M/J/15

Cambridge International Examinations Cambridge Ordinary Level

* 9 9 9 2 7 9 5 5 0 8 *

MATHEMATICS (SYLLABUS D)

4024/21 May/June 2015

Paper 2 

2 hours 30 minutes

Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (NH/CGW) 100477/2 © UCLES 2015

[Turn over

2 Section A [52marks] Answerallquestionsinthissection. 1

(a) Afurnituresalesmanearned$36200lastyear. (i) Hehadtopay22%ofthisamountastax.







Howmuchwasleftafterpayingtax?

Answer $ .......................................... [2]



(ii) Hisearningsof$36200weremadeupof$25000basicsalaryplus8%ofthevalueofthe furniturethathesold. Calculatethevalueofthefurniturethathesold.



© UCLES 2015

Answer $.......................................... [3]

4024/21/M/J/15

3 (iii) Heboughtabookcasefromtheshopwhereheworked. Itsmarkedpricewas$1080butbecauseheworkedthere,heonlypaid$756. Calculatethepercentagediscountonthemarkedpricethathehadbeengiven.



Answer ........................................ %[2] (b) George opened an account and invested a sum of money at 4.5% simple interest per year for3years.Attheendofthe3yearsheclosedtheaccount,withdrawingatotalof$681. CalculatetheamountthatGeorgeinvested.



© UCLES 2015

Answer $......................................... [3]

4024/21/M/J/15

[Turn over

4 2

Qisthepoint(–1,2),Risthepoint(3,10)andSisthepoint(–4,2). (a) Calculatethelengthof QR.



Answer ....................................units [2] t . (b) Calculatethevalueof cosSQR



© UCLES 2015

Answer ............................................ [2]

4024/21/M/J/15

5 (c) ApointP(x, y)issuchthat PQ=PR. (i) Showthat x +2y = 13.



[2] (ii) P isontheline y=7. FindthecoordinatesofP.



© UCLES 2015

Answer

4024/21/M/J/15

(...................,...................)[1]

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6 3

(a) (i)

D

C

A

B

IntrapeziumABCD,ABisparalleltoDC.DBandACarestraightlines. Explainwhy theareaoftriangle ACB=theareaoftriangle ADB.



[1] (ii)

G H

E





K

F

Thediagramshowsthequadrilateral EHGK. HF isparalleltoGKandEFK isastraightline. (a) Nameatriangleequalinareatotriangle HFK.



Answer ............................................ [1]

(b) Henceshowthat theareaoftriangleHEK = theareaofquadrilateralHEFG.



© UCLES 2015

[1]

4024/21/M/J/15

7 (b) P

S L

x°

y°

R

Q

M





TwocirclesintersectatLandM. R and P are on the circumference of one circle. S and Q are on the circumference of the other circle. PLQ andRLSarestraightlines. t =x°andMLQ t = y°. PLR t =x°. (i) Completetheproofthat SMQ Statement

Reason

t =SLQ t  x°= PLR

.............................................................................................

t =SMQ t =x° SLQ

............................................................................................. 

[2]

t =y°. (ii) Provethat PRM Statement

Reason



[2] (iii) Completethefollowingstatement,givingyourreasons.





ThetrianglesPRM andQSM are............................................. Reasons...................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ............................................................................................................................................... [3]

© UCLES 2015

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8 4

[The volume of a cone =

1 2 4 πr h] [The volume of a sphere = πr3] 3 3

7.6

4.5

Asolidisformedbyjoiningaconeofradius4.5cmandheight7.6cmtoahemisphereofradius4.5cm asshown. (a) Calculatetheareaofthecirclewheretheyarejoined.

Answer .....................................cm2[2]

(b) Calculatethetotalvolumeofthesolid.

Answer .....................................cm3[2]



© UCLES 2015

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9 (c) Another solid of the same type is made by joining a cone of radius 5cm and height h cm to a hemisphereofradius5cm. Theconeandhemispherehaveequalvolumes. Calculatetheheightofthecone.



© UCLES 2015

Answer ...................................... cm[2]

4024/21/M/J/15

[Turn over

10 5

B

C

D

4 y° A

x° 7

11

F

 

4

E

IntheframeworkABCDEF,BCDisastraightline,andCAisparalleltoDF. t , BDE t and DEF t arerightangles. ABD AB=4m,DE=11mandEF=4m. t =x°. (a) FDE





Showthat x=20.0 correctto3significantfigures.



[2] t = y°. (b) BAC Statingyourreasons,explainwhy y=x.



© UCLES 2015

[1]

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11 (c) CalculateAC.



Answer ........................................ m[3] (d) TheperpendiculardistancebetweentheparallellinesCA andDFis7m. CalculatetheareaofACDF.

Answer .......................................m2[4]



© UCLES 2015

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12 6

(a) Expandthebracketsandsimplify  (x–1)(x2+x+1).



Answer ............................................ [2] (b) Solvetheequation 

3x 4 = 3. x+2 x-2



© UCLES 2015

Answer ............................................ [3]

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13 (c) Solvethesesimultaneousequations.

4x–3y=4 4y–3x=–6.5



Answer x = ......................................  y=...................................... [4]



© UCLES 2015

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[Turn over

14 Section B[48marks] Answerfourquestionsinthissection. Eachquestioninthissectioncarries12marks. 7

(a) (i)

Evaluate

8 sin 54° . sin 18°



Answer ............................................ [1] (ii) Evaluate 4.73 2 - 1.65 sin 43° .



Answer ............................................ [1] (b)

B x A

60° 16 2x + 3

C





t =60°. InthetriangleABC,BC = 16cm and BAC AB =xcm and AC=2x+3cm. (i) Formanequationinxandshowthatitsimplifiesto 3x 2 + 9x - 247 = 0 .



© UCLES 2015

[4]

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15 (ii) Solvetheequation   3x 2 + 9x - 247 = 0 ,   givingyouranswerscorrectto2decimalplaces.



Answer

x=.............................or.............................[3]

(iii) HencewritedownthelengthsofABandAC.



Answer

AB =....................cmAC = ....................cm[1]

(iv) FindtheareaoftriangleABC.

Answer .....................................cm2[2]



© UCLES 2015

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16 8

ThediagramshowsasectorAOBofacirclewithcentreOandradius9.3cm. Theangleofthesectoris260°. A (a) (i) CalculatethelengthofthemajorarcAB. 9.3

B

O 260°



Answer ...................................... cm[2] (ii) CalculatetheareaofthemajorsectorAOB.

Answer .....................................cm2[2]



(b) Asectorofradius0.8cm,centreO,isremovedfromthesectorAOB asshowninDiagramI. Theshadedshapeisusedtomakepartofaconicalfunnel. AD isjoinedtoBC as showninDiagramII. B

A D Diagram I

0.8

A,B

C O

D,C Diagram II

ThecircumferenceofthetopoftheconicalfunnelisthemajorarcAB,andthecircumferenceof thebottomoftheconicalfunnelisthemajorarcCD. (i) Calculatetheexternalsurfaceareaofthispartofthefunnel.

Answer .................................... cm2 [2]



© UCLES 2015

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17 (ii) Thefunneliscompletedbyattachinganopencylinderofheight5cm tothebottomoftheconicalpart. (a) Showthattheradiusofthecylinderis0.578cm,  correctto3significantfigures.

5



[2] (b) Calculatetheexternalcurvedsurfaceareaofthiscylinder.

Answer .....................................cm2[2]

(c) Calculatethevolumeofthiscylinder.

Answer .....................................cm3[2]



© UCLES 2015

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18 9 



f(x)= x 3

(a) Completethefollowingtable. x

–3

–2

–1

0

1

2

3

f(x)   

[1] (b) Usingascaleof2cmtorepresent1unit,drawahorizontalx-axisfor –3 G x G 3.  Usingascaleof2cmtorepresent10units,drawaverticaly-axisfor –30 G y G 30 .  Usingyouraxes,plotthepointsinthetableandjointhemwithasmoothcurve. Answer



[2] (c) (i) Useyourgraphtosolve f(x)=–15.



© UCLES 2015

Answer ............................................ [1]

4024/21/M/J/15

19 (ii) Useyourgraphtofindasuchthat f - 1 ^ah = 1.7 .



Answer ............................................ [1] (iii) Giventhat f - 1 ^ t h = u ,expresstintermsofu.



Answer t =....................................... [1] (iv) Bydrawingatangentto y = f ^xh, estimatethegradientofthecurvewhenx=2.



Answer ............................................ [2] (d) (i)

Usingthesameaxesdrawthelinethatrepresentsthefunction g ^xh = 5x + 3.



[2] (ii) Hencefindthethreesolutionsoftheequation f ^xh = g ^xh.



© UCLES 2015

Answer

4024/21/M/J/15

x =............or............or............[2]

[Turn over

20 10 Onedayafarmercollected300eggsfromhischickens. Thetablebelowshowsthedistributionofthemassesoftheeggs. Mass (m grams) Frequency

42<m G 46 46<m G 48 48<m G 50 50<m G 54 54<m G 58 58<m G 66 60

40

48

72

56

24

(a) (i) Aneggischosenatrandom. Calculatetheprobabilitythatthemassofthiseggisnotgreaterthan48grams.



Answer ........................................... [1] (ii) Aneggischosenatrandomfromthe300eggs. Anothereggischosenatrandomfromthosethatremain. Calculatetheprobabilitythatthemassofoneeggisatmost46grams,andthemassofthe otherismorethan58grams.



Answer ............................................ [2] (b) Calculateanestimateofthemeanmassofanegg.



© UCLES 2015

Answer ......................................... g[3]

4024/21/M/J/15

21 (c) (i) Completethecumulativefrequencytable. Mass (m grams)

m G 42

m G 46

Cumulative Frequency

0

60

m G 48

m G 50

m G 54

m G 58

m G 66 300



[1] (ii) Onthegrid,drawasmoothcumulativefrequencycurvetoillustratethisinformation.

300

250

200 Cumulative frequency 150

100

50

0

40

45

50

55

60

65

70

Mass (m grams)



[2] (d) (i)

Useyourgraphtofindthemedianmassoftheeggs.



Answer ......................................... g[1] (ii) Useyourgraphtofindtheinterquartilerange.

© UCLES 2015

Answer ......................................... g[2] 4024/21/M/J/15

[Turn over

22 11

(a)

ABCDE isapentagon. AFB,AHEandBGC arestraightlines. FisthemidpointofAB. HisthemidpointofAE. G dividesBCintheratio1:2.





AH = a, AF = a - b, BG = ED = c .

c

B

C

F

a-b

A



G

E a

c

D

H

(i) Find FH .



Answer ............................................ [1] (ii) Usingvectors,showthatGD isparalleltoFH.



[2] (iii) Itisgiventhat c =

4 1 a + b . 5 5

(a) Express DC intermsofaandb.

Answer ............................................ [2]

 (b) Find

AF : DC . 

Answer ..................... :.....................[1]



© UCLES 2015

4024/21/M/J/15

23 y

(b)

8 A

4 B

–4

C

A

8 x

B 4

0 C –4

(i) ThetransformationTmapstriangleABC ontotriangle AlBlC l . (a) DescribefullythetransformationT.   Answer........................................................................................................................... [2] (b) ThematrixMrepresentsthetransformationT. 

FindthematrixM.

J K Answer K K L



N O OO  P

[2]

(ii) Triangle AlBlC l ismappedontotriangle AmB mC m byareflectioninthey-axis. Drawandlabeltriangle AmB mC m .

[1]

(iii) TriangleABCismappedontotriangle AmB mC m byananticlockwiserotationabouttheorigin. Statetheangleofrotation.

© UCLES 2015

Answer ............................................ [1]

4024/21/M/J/15

24 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/21/M/J/15

Cambridge International Examinations Cambridge Ordinary Level

* 5 4 5 9 2 0 9 1 8 5 *

4024/22

MATHEMATICS (SYLLABUS D)

May/June 2015

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (CW/FD) 97070/2 © UCLES 2015

[Turn over

2 Section A [52 marks] Answer all questions in this section. 1

(a) Simplify

4x - 1 3x + 5 + . 3 2



Answer ............................................ [2] (b)

y 10 9 8 7 J

6 5 4 3 2

K

1 0

1

2

3

4

5

6

7

8

9

10

x

(i) Find the gradient of line J.



Answer ............................................ [1] (ii) Write down the equation of line K.

© UCLES 2015

Answer ............................................ [1] 4024/22/M/J/15

3 (iii) Draw a line, L, through (6, 1) such that the area enclosed between J, K and L is 6 cm2.

[1] (iv) Find the equation of line L.



Answer ............................................ [2] (v) The line N is perpendicular to line J at (2, 2) . Find the coordinates of the point where line N crosses the y-axis.



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Answer ............................................ [2]

4024/22/M/J/15

[Turn over

4 2

The diagram is a speed-time graph of a train’s journey between two stations. 30

25

20

Speed (m/s) 15

10

5

0

0

100

200

400 300 Time (seconds)

500

600

(a) What was the maximum speed of the train?

Answer ......................................m/s [1] (b) Circle the statement that describes the train’s motion 350 seconds after it left the first station. Accelerating

Decelerating

Constant speed

Stopped at a station

[1]

(c) Calculate the acceleration of the train during the first 150 seconds of its journey.

Answer .................................... m/s2 [1]

© UCLES 2015

4024/22/M/J/15

5 (d) What was the speed of the train 20 seconds before it completed its journey?

Answer ......................................m/s [1] (e) How far did the train travel during the first 200 seconds?



Answer ........................................ m [2] (f) Calculate the average speed of the train in kilometres per hour during the first 200 seconds.



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Answer ................................... km/h [2]

4024/22/M/J/15

[Turn over

6 3

(a) In a survey, 50 students were asked how long they spent exercising during one particular week. The results are summarised in the table. Time (t minutes)

Frequency

0 G t 1 30

10

30 G t 1 60

15

60 G t 1 90

11

90 G t 1 120

7

120 G t 1 150

5

150 G t 1 180

2

(i) Calculate an estimate of the mean time each student spent exercising that week.



Answer .............................. minutes [3] (ii) During that week, the time Simon spent exercising is shown below. Tuesday Thursday

12.37 p.m. until 1.24 p.m. 8.57 a.m. until 9.42 a.m.

Which interval is his time recorded in?



© UCLES 2015

Answer ............................................ [1]

4024/22/M/J/15

7 (b) A gym has four different types of machines. Carol is going to draw a pie chart to show how many times the machines are used in one day. She has started to make a table. Machine

Frequency

Angle of sector

Running

90

120°

Rowing

75

Cycling

57

Weights

64°

(i) Complete the table.

[2]

(ii) Complete the pie chart.

Weights

Running

[1]

© UCLES 2015

4024/22/M/J/15

[Turn over

8 4

(a) A 72°

B X

25° C

E

D

A, B, C, D and E are five points on the circumference of a circle. t = 72° and AEB t = 25° . EB is parallel to DC, EAC X is the intersection of AC and EB. Find (i)

t , EBC



Answer ............................................ [1] (ii)

t , CXB



Answer ............................................ [1] (iii)

t , EDC



Answer ............................................ [1] (iv)

t . ACD



© UCLES 2015

Answer ............................................ [1]

4024/22/M/J/15

9 (b) 40° 6

The angle of a sector of a circle, radius 6 cm, is 40°. (i) The area of the sector is kπ cm2. Find the value of k.



Answer ............................................ [2] (ii) Find an expression, in terms of π, for the perimeter of the sector. Give your answer in the form (a + bπ) centimetres.



Answer ...................................... cm [2] (iii) A geometrically similar sector has perimeter (72 + nπ) centimetres. Find the value of n.



© UCLES 2015

Answer ............................................ [1]

4024/22/M/J/15

[Turn over

10 5

In the diagram, AB = 8 cm, AC = 11 cm and DC = 6.5 cm. t = 26° and DAC t = 30° . BAD

B

8 D

A

6.5

26° 30° 11

C

(a) Calculate BC.



Answer ...................................... cm [4] (b) Calculate the obtuse angle ADC.



Answer ............................................ [3] (c) Find the percentage of triangle ABC that has been shaded.

© UCLES 2015

Answer ........................................ % [4] 4024/22/M/J/15

11 6

(a) Yuvraj and Sachin travel to England. Yuvraj exchanges 20 500 rupees and receives £250 . Sachin exchanges 26 650 rupees into pounds (£) at the same exchange rate. How many pounds does Sachin receive?



Answer £ .......................................... [2] (b) Dan goes to a bank to exchange some pounds (£) for euros (€). He has £400 which he wants to exchange. The bank only gives euros in multiples of 5 euros. The exchange rate is £1 = €1.17 . Find the number of euros he receives and his change from £400 .



Answer Dan receives € .....................



His change is £ .................... [3] (c) Kristianne buys a fridge and a freezer in a sale. The sale offers 15% off everything and she pays a total of $357 . Before the sale, the freezer cost $250 . What was the cost of the fridge before the sale?

© UCLES 2015

Answer $ .......................................... [3] 4024/22/M/J/15

[Turn over

12 Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a)

f (x) =

2x + 7 3

(i) Find f -1(x) .

Answer f -1(x) = ............................. [2]

(ii) Given that f (m) =

m , find m. 2



Answer ............................................ [2] (b) (i) Complete the table of values for y = 6 + x - x 2 , and hence draw the graph of y = 6 + x - x 2 on the grid opposite.

© UCLES 2015

x

-3

-2

y

-6

0

-1

0

1

6

6

4024/22/M/J/15

2

3

4

0

-6

13 y 7 6 5 4 3 2 1 –3

–2

–1

0

1

2

3

4

x

–1 –2 –3 –4 –5 –6 –7

[3]

(ii) Use your graph to estimate the maximum value of 6 + x - x 2 .

Answer ............................................ [1] (iii) By drawing the line x + y = 4 , find the approximate solutions to the equation 2 + 2x - x 2 = 0 .



Answer x = ................. or ................. [2] (iv) The equation x - x 2 = k has a solution x = 3.5 . By drawing a suitable line on the grid, find the other solution. Label your line with the letter L.

© UCLES 2015

Answer ............................................ [2] 4024/22/M/J/15

[Turn over

14 8

Two ports, A and B, are 15 km apart and B is due south of A. A boat sails from A on a bearing of 141°. North

A

141°

15

B

(a) State the bearing of A from the boat.

Answer ............................................ [1] (b) Calculate the shortest distance between the boat and B.



Answer ...................................... km [2] (c) When the boat is due east of B, calculate its distance from A.



© UCLES 2015

Answer ...................................... km [2]

4024/22/M/J/15

15 (d) The scale drawing, drawn to a scale of 1 cm to 2 km, shows A, B and a third port, C. North A

C

B

(i) When the boat has travelled 24 km, it stops at the point X. Mark and label X on the diagram.

[2]

(ii) A second boat is located I II

less than 12 km from A nearer to BC than to BA.

Shade the region in which this second boat must lie.

[3]

(iii) The point Y is the position of the second boat when it is as far as possible from X. Mark and label Y on the diagram and hence find the maximum possible distance between the two boats.



© UCLES 2015

Answer ...................................... km [2]

4024/22/M/J/15

[Turn over

16 9

(a) Factorise completely (i)

4x 3 - 10xy ,



Answer ............................................ [1] (ii)

9a 2 - b 2 .



Answer ............................................ [1] (b) Solve

7 = 4. 3 - 2m



Answer ............................................ [2] (c)

23

h

A right-angled triangle has a base that is 7 cm longer than its height, h cm. The hypotenuse of the triangle is 23 cm. (i) Show that h satisfies the equation h 2 + 7h - 240 = 0 .

[2] © UCLES 2015

4024/22/M/J/15

17 (ii) Write down an expression, in terms of h, for the area of the triangle.

Answer ..................................... cm2 [1]

(iii) Hence state the exact area of the triangle.

Answer ..................................... cm2 [1]



(iv) Solve h 2 + 7h - 240 = 0 , giving your answers correct to 1 decimal place.



Answer h = ................. or ................. [3] (v) Calculate the perimeter of the triangle.



© UCLES 2015

Answer ...................................... cm [1]

4024/22/M/J/15

[Turn over

18 10 (a) y 6 5

A

4 3 B

2 1

–7

–6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

x

–1 –2 –3 –4 –5 –6

(i) Describe fully the single transformation that maps triangle A onto triangle B. Answer ....................................................................................................................................... ............................................................................................................................................... [2] J- 2N (ii) Triangle B is mapped onto triangle C by a translation, vector K O . L- 3P Draw and label triangle C. [2] (iii) Triangle A is mapped onto triangle D by a reflection in the line y = x . Draw and label triangle D.

[2]

(iv) Triangle E is geometrically similar to triangle A and its longest side is 12 cm. Calculate the area of triangle E.

Answer ..................................... cm2 [2]

© UCLES 2015

4024/22/M/J/15

19 (b)

State the number of lines of symmetry of the octagon above.

Answer ............................................ [1] (c) The cross-section of a prism is an equilateral triangle. State the number of planes of symmetry of the prism.



Answer ............................................ [1] (d) Name two special quadrilaterals that have exactly 2 lines of symmetry and also rotational symmetry of order 2.

Answer ............................. and ............................. [2]

© UCLES 2015

4024/22/M/J/15

[Turn over

20 11

(a) Some people were asked which continent they visited on their last holiday. The results are shown in the table below. Continent

Number of people

North America (NA)

7

Europe (E)

15

Asia (A)

8

(i) Find the probability that one of these people, chosen at random, visited North America.

Answer ............................................ [1] (ii) Find the probability that one of these people, chosen at random, did not go to Asia. Give your answer as a fraction in its lowest terms.



Answer ............................................ [1] (iii) Two of these people are chosen at random. The tree diagram opposite shows the possible outcomes and some of their probabilities. (a) Complete the tree diagram.

[2]

(b) What is the probability that the two people went to the same continent?



© UCLES 2015

Answer ............................................ [2]

4024/22/M/J/15

21 First Person

Second Person

.......

NA

.......

.......

.......

....... 15 30

E

.......

....... 8 30

....... A

.......

.......

NA

E

A NA

E

A NA

E

A

TURN OVER FOR THE REST OF THIS QUESTION

© UCLES 2015

4024/22/M/J/15

[Turn over

22 (b) The table shows the distribution of the total cost per person for holidays in 2014 for another group of people. Total cost per person ($c) Frequency

0 G c 1 250

250 G c 1 500

35

20

500 G c 1 1000 1000 G c 1 2000 2000 G c 1 3500 15

8

6

(i) Draw a histogram to represent this data. 0.14

0.12

0.10

0.08 Frequency density 0.06

0.04

0.02

0

0

500

1000

1500

2000

2500

3000

3500

Total cost ($)

[3]

© UCLES 2015

4024/22/M/J/15

23 (ii) Estimate the number of people who spent less than $700 on holidays in 2014.



Answer ............................................ [2] (iii) Of the people who spent less than $250 on holidays in 2014,

2 did not go on holiday. 7

How many people did not go on holiday in 2014?



© UCLES 2015

Answer ............................................ [1]

4024/22/M/J/15

24 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/22/M/J/15

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/11 May/June 2016

Paper 1 MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 5 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – May/June 2016

Question

Answers

Syllabus 4024

Mark

Paper 11

Part marks

(a)

14

1

(b)

(0).45(0)

1

(a)

1 oe 24

1

(b)

3 cao 7

1

(a)

02 25

1

(b)

3150

1

4

530

2*

B1 for (1800 and 1270); or for 370 or 530 seen

5

88

2*

M1 for (4 × 80 + 120), or better.

1

2

3

6

–5

(a)

3.4 × 10

(b)

0.42 × 10

–5

1 33.7 × 10

–6

30; 8; 0.4 all three

0.034 × 10

–3

1

Accept correct equivs.

M1*

B1 for two of 30; 8; 0.4

600

A1

Ans. 600 ww, award C1

(a)

Acceptable kite

1

(b)

Acceptable parallelogram

1

9

y ⩽ 3 oe y ⩾ –x oe

1 1

C1 for y ... 3 oe and y ... –x oe, where ‘...’ is the wrong inequality or =

10

(x – 4)(3y + 5)

2*

B1 for 5(x – 4), or 3y(x – 4), or x(3y + 5), or 4(3y + 5).

11 (a)

– 10 12 oe

1

7

8

(b)

6

2*

B1 for 3 = 2 ‘x’ – 9 or for

y+9 2 3.6 oe

1

(b)

25

1

(c)

1:250 000

1

12 (a)

© Cambridge International Examinations 2016

x+9 or 2

Page 3

Mark Scheme Cambridge O Level – May/June 2016

Question 13

Answers

Syllabus 4024

Mark

A correct method to eliminate one variable.

* M1

Both x = –2 and y = –1.5 www;

A2

Paper 11

Part marks

Or A1 for one correct or ft their value of x or y correctly evaluated in one equation 3 For y, accept –1.5, or −1 12 , or − , 2 only. If [0] earned, then C1 for a pair of values that satisfy either equation

Vol. of hemisphere =

14

Vol. of cone = k = 12 15 (a)

2 × π × 33 oe or 18π 3

1 × π × 32 × 2 or 6π 3

M1* M1* A1

4.5 oe

2*

7.5 or any equiv.

1

16 (a)

10°

1

(b)

20°

1

(c)

60°

1

17 (a)

10, 12

1

(b)

2n + 2

1

(c)

99

(b)

18 (a) (b)

2*

Vertical axis label should be ‘Frequency density’ or heights should be 3, 8, 10, 2. Rectangles with same bases as in (a), with heights 3, 8, 10, 2. Vertical label ‘Frequency density’ and a suitable scale.

M1 for 8 = k42 oe or 8 ÷ 42 = y ÷ 32 oe

M1 for their (b) = 200

1 3*

C2 for 4 bars correct, with no label or incorrect scale on vertical axis or for 3 bars correct with ‘Frequency density’ label and numbered linear scale. C1 for numbers 3, 8, 10, 2; or ‘Frequency density’ label or for 3 bars correct

19 (a) (b)

40°

1

140°

1 © Cambridge International Examinations 2016

Page 4

Mark Scheme Cambridge O Level – May/June 2016

Question

Answers

Mark

(c)

50°

1

(d)

40°

1

20 (a)

0

1

(b)

1

1

(c)

1.6 oe

2*

21 (a)

22 × 53

1

p = 5 and q = 4

1

(ii)

p = –3 and q = 0

1

(iii)

p = 8 and q = 4

1

101° to 103°

1

Circular arc, centre B, radius 4 cm.

1

Line parallel to AC, 2 cm away.

1

AP = 6.2 to 6.6 cm

1

(b) (i)

22 (a) (b) (i) (ii) (c) 23 (a)

Q

P

Syllabus 4024 Part marks

M1 for (11 × 1 + 9 × 2 + 7 × 3 + 6 × 4 + 1 × 6) / 50

1

R

24

1

(ii)

8

1

(iii)

22 or 26 or 30

1

20 oe T

1

5

1

15

1

Curve, concave down, from (0, 0) to (T, 150)

1

p–q

1

3p – 4q

1

(b) (i)

24 (a) (i) (ii) (b) (i) (ii) 25 (a) (i) (ii)

Paper 11

© Cambridge International Examinations 2016

Page 5

Mark Scheme Cambridge O Level – May/June 2016

Question (iii)

Answers 9p – 9q

Paper 11

Mark

Part marks

2*

B1 ft for a correct unsimplified form seen or correct route seen

1:8

1

26 (a) (i)

0

1

(ii)

3 7

1

(b)

2 oe 7

1

(c)

11 oe 14

2*

(b)

Syllabus 4024

M1 for

© Cambridge International Examinations 2016

1 1 4 ×1 + × 2 2 7

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2016

Paper 1 MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 5 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – May/June 2016

Question 1

2

Answers

Mark

(a)

0.69

1

(b)

8 oe 15

1

(a)

… 2 ... 2

1

(a)

Ruled straight line through (0, 0) and (100, 56)

1

(b)

35 to 37

1

… = 0.15 = 15[%]

2

4

Paper 12

Part marks

1

(b)

3

Syllabus 4024

C1 for two or three correct

5 = 0.625 = … 8

5

6

7

(a)

9

1

(b)

–18

1

(a)

25 × 3

1*

(b)

72

1

(a)

1.5 [hours] or 90 [minutes] oe

1

(b)

20 35

1 36 oe 5

20 y = 2 oe 2 10 6

2*

M1 for 20 = 102k oe or

16

2*

B1 for 15, 8 and 11 correctly placed and 26 not placed in Venn diagram or for x + 26 + 8 = 50 oe or for 50 – 26 – 8 oe leading to answer

10

x = 0.5 oe y = –2

2*

C1 for either x or y correct or for two values that fit one equation

11 (a)

x4 3 y3

1

v2 2t

1

8

7.2 or

9

(b)

© Cambridge International Examinations 2016

Page 3

Mark Scheme Cambridge O Level – May/June 2016

Question 12 (a) (i) (ii) (b) 13 (a) (b) (i) (ii) 14 (a) (b)

15 (a)

Answers

Syllabus 4024

Mark

Paper 12

Part marks

arc radius 3.5 cm, centre A

1

bisector of angle ACB

1

Correct region shaded

1

270, 3 1000 , 52, 25

1

any value in range 4 < x < 9

1

any value in range –1 < x < 0

1

(–4, 2)

(6, 2)

1

Both correct

(–3, –1) (5, 5)

2

C1 for one correct or for two x-values or two y-values correct or for both (4, 6) and (–2, –2)

x + y ⩽ 8 oe

2

C1 for two correct

2y ⩾ x + 4 oe x⩾0 3

1

16 (a)

595

1

(b)

340

2*

M1 for 10 × 25.5 soi

17

280, 295, 310

3*

C2 for two correct values OR B2 for two from 70°, 40° and 55° seen OR B1 for 70° seen or for 10° or 120° correctly positioned on diagram

18 (a)

16

1

(b)

(b)

160 or 10 × their (a)

2ft*

M1 for 0.5 × their v × (8 + 12) oe or 0.5 × their v × 4 + their v × 8 oe

© Cambridge International Examinations 2016

Page 4

Mark Scheme Cambridge O Level – May/June 2016

Question

Answers ∠POA = ∠QOB vertically opposite AO = OB equal radii ∠PAO = ∠QBO = 90° tangent perpendicular to radius

19

Syllabus 4024

Mark 3*

Paper 12

Part marks B1 for two pairs of equal angles: ∠POA = ∠QOB and ∠PAO = ∠QBO or for one pair of angles and pair of sides: ∠POA = ∠QOB or ∠PAO = ∠QBO and AO = OB AND B1 for a correct reason linked with a correct pair of angles / sides

2 2 8 1 , , , correctly positioned 10 9 9 9

1

(b) (i)

56 oe 90

1*

(ii)

32 oe 90

2ft*

20 (a)

8 2 2 8 × + × 10 9 10 9 ft their tree diagram with fractions < 1

M1 for

2x + 3 oe

1

7

1

8 − 2x oe final answer 3

2*

B1 for 3x = 8 – 2y or 3y = 8 – 2x or 2x = 8 – 3y or 2y = 8 – 3x or 1.5x = 4 – y or 1.5y = 4 – x 8 − 2x 8 − 2y or oe seen or oe 3 3 seen

1.8 × 108 cao

2

C1 for 1.7[…] × 108 or answer figs 18

(b)

5

1

(c)

20 cao

2*

C1 for answer figs 2 or answer 18 OR B1 for 4 × 107 oe and 2 × 106 oe seen

Two correct bars drawn

2

C1 for rectangle base 0 to 10 height 2.8 or for rectangle base 30 to 60 height 0.6

(b)

12

1

(c)

30 18 + m oe or oe evaluated 150 138 + m

21 (a) (b) (i) (ii)

22 (a)

23 (a)

2ft*

B1 FT for fraction with numerator or denominator correct or for answer 20% or 0.2

© Cambridge International Examinations 2016

Page 5

Mark Scheme Cambridge O Level – May/June 2016

Question

Answers 320

24 (a)

Syllabus 4024

Mark 3*

Paper 12

Part marks M2 for

a × π × (3r ) 2 = 8π r 2 oe 360

OR a × π × (3r ) 2 oe seen 360 or for 8π r2 seen

M1 for

6r +

(b)

16π r final answer 3

2*

C1 for kr +

16π r , where k ⩾ 0 3

OR their 320 × 2π × 3r oe 360 their 320 or for 6r + × nπ r oe 360 where n is a positive integer

M1 FT for

25 (a) (i)

–6

1

(ii)

15

2*

C1 for 152 – 5 × 15 or for 15, –10 OR M1 for (p + 10)(p – 15) [= 0]

4

2*

B1 for 3 × 52 – 5k = 55 oe

3 + 4t oe t −1

3*

C2 for

(b) 26 (a)

7 3 − 4t or t −1 t −1

OR M1 for t(p – 4) = p + 3 or pt – 4t = p + 3 AND M1 for isolating p terms after fraction eliminated e.g. pt – p = 3 + 4t or p(t – 1) = 3 + 4t (b)

2x −1 final answer x−5

3*

B1 for (2x + 1)(2x – 1) seen AND B1 for (2x + 1)(x – 5) seen

© Cambridge International Examinations 2016

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/21 May/June 2016

Paper 2 MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 6 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – May/June 2016

Question 1

Answers 7.5(0)

(a)

Syllabus 4024

Mark 2

Paper 21

Part Marks M1 for x +

60 x = 12 soi or 100

B1 for ÷ by 160 (b)

45

2

M1 for

17.40 − 12 × 100 12

(c)

35

2

M1 for

17.4 − 11.31 × 100 17.4

(d)

25

3

M1 for 60 × 17.4 + x × 11.31(⩾ 1320) or B1 276 A1 for 24.4(03...)

2

(a)

6

2

M1 for p − 1 = 5(7 − p) soi

(b)

3b 2 a

2

M1 for

9b 4 oe a2

1

3a 2 b3 3 a 2b

oe

or B1 for 3b² as numerator or

(c)

q2 3

2

B1 for q 2 (1 − q) or 3(1 − q )

(d) (i)

(4t − 1)(t + 9)

2

B1 for (at + c)(bt + d ) with ab = 4 or cd = −9

(ii) 3

1 − 9 or ft 4

1ft

(a)

Correct graph

(b) (i)

−2.3 ± 0.5

1.3 ± 0.5

1

(ii)

−2.8 ± 0.5

1.8 ± 0.5

2

M1 for x 2 + x − 3 = 2 soi

2

B1 for correct scales and 4 points or wrong scales and all points.

(c)

2.4 to 3.6

2

M1 for tangent at x =1

(d) (i)

y = 2x − 2

2

B1 for 2x or −2

2

Dependent on line drawn

(ii)

−0.6

k a

1.6

B1 for their line having FT gradient or FT intercept

© Cambridge International Examinations 2016

Page 3

Mark Scheme Cambridge O Level – May/June 2016

Question 4

Answers Complete proof

(a)

Syllabus 4024

Mark 3

Paper 21

Part Marks B2 for 2 pairs of equal angles 1 pair with reason. B1 for 1 pair of equal angles.

5

B1 for NM : BL = 2 : 3 oe or NM = LC

(b) (i)

2:5

2

(ii)

4:9

1

(iii)

1:3

2

B1 for such as 4 ∆ANM = or ∆ABC 25 ∆NBL 9 = ∆ABC 25

15.1 or 15.08(…..

3

M1 for tan θ =

(a)

31 115 or tan θ = 115 31

A1for θ = 15.1 or θ = 74.9 (b) (i) (ii) 6

18.8 or 18.77…… 251 or 251.2(…….

2 1ft

M1 for sin θ =

354 1100


270 − their LJK final ans.

(a)

 6 −2     −5 11 

2

B1 for at least 2 elements correct in a 2 x 2 matrix

(b)

15 −7    7 8

2

B1 for at least 2 elements correct or  4 −1   4 −1  M1 for    soi 1 3  1 3 

(c)

−

1  −5 0    oe 10  −7 2 

2

isw (d)

0 0   0 0

1

(e)

0 0     7 −7 

2

B1 for det B = −10 soi or  −5 0     −7 2 

1 0 B1 for   soi 0 1

© Cambridge International Examinations 2016

Page 4

Mark Scheme Cambridge O Level – May/June 2016

Question 7

Answers 4.53 to 4.54

(a)

Syllabus 4024

Mark 4

Paper 21

Part Marks B2 for BOC = 52 or after B0 ˆ = 90 or B1 for ABC triangle OBC isosceles or
BAC = 26

M1 for (b) (i) (ii)

52 × 2π 5 ft 360

101 or 32π or 100 to 100.6

2

M1 for π(16.52 ) or 15.52

0.87 to 0.871

3

B1 for π15.52 or 44πr2 and M1 for r 2 =

7

(iii)

3

π 15.52 − 650 44π

M1 for π15.52d = 500 A1 for 0.66 to 0.663

8

(a) (i) (ii) (b) (i)

(ii)

−1.92 (3……

1

8 p+5

2

M1 for

H and h correctly derived

2

M1 for correct substitution in the formula for the area of a trapezium.

75 correctly ( x − 1)(2 x + 3) derived

3

M1 for

8 8 = p + 5 or pq = 8 − 5q or p = − 5 q q

15(2 x + 3) − 30( x − 1) soi ( x − 1)(2 x + 3)

B1 for 30 x + 45 − 30 x + 30 (iii) (a)

(b)

soi

75 = 1.5 ( x − 1)(2 x + 3)

Equation correctly derived.

2

B1 for

4.90

2

B1 for 12 − 4 × 2 × (−53) soi or B1 for

−1 ± their 425 2× 2

© Cambridge International Examinations 2016

soi

Page 5

Mark Scheme Cambridge O Level – May/June 2016

Question 9

Answers

Syllabus 4024

Mark

Paper 21

Part Marks

5.38 to 5.39 or √29

2

M1 for ( AC 2 ) = 22 + 52

(ii)

0.517 to 0.518

2

M1 for

(iii)

68.8 to 68.9

4

AF = cos15 oe or BC²=BE²+ (their CE)² or 2 any complete alternative method

(a) (i)

CE = sin15 oe 2

M1 for

A1 for 1.932 and

ˆ = M1 for tan FAE (b) (i)

80.9(4…. Or 81

3

5 5 oe or 2cos15 their ( AF )

B1 for 102 = 62 + 92 − 2×6×9×cos θ or B2 for cosθ =

92 + 62 − 102 2×9×6

>

1

(2) (4) 14 54 84 98 (100)

1

(b)

Correct curve

2

(c) (i)

195 ft 190 ⩽ and < 200

1

50 –75

2

B1 for one quartile correct in ranges 225 to 235 or 160 to 175

Correct curve

4

P3 for at least 4 correct plots or

(ii) 10 (a)

(ii) (d)

P1 for at least 5 correct plots

B1 + B1 for any two correct points soi. (e)

92 ft

(f)

B 15 ft A

1 1ft

Their 90 – 75

© Cambridge International Examinations 2016

Page 6

Mark Scheme Cambridge O Level – May/June 2016

Question

Answers

Syllabus 4024

Mark

Part Marks

 −6     2

1

8    4

2

(ii)

 −8    ft  −4 

1

(iii)

8.94 or 8.94 to 8.95 or √80 oe

2

M1 for

Triangle vertices (5,4), (13,0), (9,8)

2

B1 for 2 correct

(ii)

Triangle F (5,4), (7,3), (6,5)

1

(iii)

Rotation 180 Centre (5,4)

3

11 (a)

(b) (i)

(c) (i)

Paper 21

8  B1 for   or k 

k    4

(−8) 2 + (−4) 2 oe

ft

B2 for Rotation with either centre or angle. B1 for Rotation.

© Cambridge International Examinations 2016

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/22 May/June 2016

Paper 2 MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 6 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – May/June 2016

Question 1

2

Answers

Part marks

41 472 or 41 470 or 41 500 cao

1

(b)

$65 ( not from 64.84 rounded )

2

M1 for 1.05x = 68.25 soi

(c)

7.50 – 7.60

3

[M2 for 1.05 × 1.024 oe] or M1 for 40500 × their 65 [=2 632 500] and M1 their 41 472 × 68.25[= 2 830 464]

(a) (i)

5   6

1

4.47 – 4.473 or 4.5 or √20 or 2√5

2

1 1 b – a or (b – 2a) or 2 2 equivalent two term answers

1

(b) (i)

(a)

(ii) (a) (i)

1

3 : 1 cao

1

1.64 or 1

16 25

2

(ii)

2

1

(iii)

0

1

(b)

appropriate reason

1

(c)

1 cao 30

2

(d)

Correct bar chart with axes labelled

2

(e)

00134

1

(a) (i)

Correct triangle with arcs shown

2

104 to 108

1

(ii)

M1 for √((±4)2 + (±2)2)

final answer

3 1 3b − 6a b – 3a or 3( b – a) or or 2 2 2 equivalent two term answers final answer

(b)

4

Mark

Paper 22

(a)

(ii)

3

Syllabus 4024

Dependent on correct (b)(i)(a) and (b)(i)(b) M1 for

0 × 7 + 1× 5 + 2 × 6 + 3 × 4 + 4 × 3 7+5+6+4+3

M1 for

5 4 × oe 25 24

B1 if only one error (eg incorrect height, scales missing / incorrect, inconsistent bar widths, or 4 correct bars)

B1 for correct triangle with no arcs or triangle with one side correct length with arcs or triangle with BC = 7 and AC = 12 with arcs (reflection)

© Cambridge International Examinations 2016

Page 3

Mark Scheme Cambridge O Level – May/June 2016

Question

Answers

Mark

(b)

150o

2

(c) (i)

110o

1

(ii)

165o

2ft

27 2 x final answer 4

(d)

Syllabus 4024

3

Paper 22

Part marks M1 for 180 – (360 ÷ 12) or (180 × (12–2)) ÷ 12

3 × their p provided p < 120 and p ≠ 90 2 B1 for 30, 15 or 75 seen ft

EITHER 1 3x B2 for (6 x + 3 x) oe 2 2 or B1 for PQ = 3x OR B1 for 3x2 (area of small trapezium) 2 3 B1 for their 3x2 ×   oe 2 OR If AB = x used 27 2 27 SC2 for x or SC1 for 16 16

5

(a)

4 x 2 (2 y − 3x3 ) final answer

(b)

x = 6.5 or

(c)

y > –2.6 or y > –

or y > – 2 (d) (i)

13 1 or 6 2 2 13 5

2

M1 for 4 x − 2 x − 10 = 3 or better

2

M1 for – 5y < 20 – 7 oe or better Or SC1 for 2.6 or – 2.6 oe seen

3 final answer 5 OR

EITHER

18 − 4 x Width = 2

oe

18 − 4 x × 2x = 10 oe 2 (ii)

1

3.85 and 0.65 cao

Width =

4x +

10 oe 2x

20 = 18 oe 2x

M1

isw

A1 3

B2 for 3.850 to 3.851 and 0.649 to 0.650 or one correct answer or 3.9 and 0.6 p± q p+ q or or Or if in form r r p− q r B1 for p = 9 and r = 4 or q = 41

© Cambridge International Examinations 2016

Page 4

Mark Scheme Cambridge O Level – May/June 2016

Question (iii) 6

(a) (i)

(ii)

(b) (i)

(ii)

Answers

Syllabus 4024

Mark

6.35 to 6.45 or – 6.45 to – 6.35 oe

1

(a) 10

1

(b) 9

1

(c) 3,5,7,11

1

4 oe isw 11

1ft

Paper 22

Part marks

ft from their (a)(i)(c)

8 0   final answer 3 1

2

B1 for 3 correct elements

1  1 −2    oe isw 2 4 1

2

 1 −2  1a B1 for k   or  2 4c 1

b  d

SECTION B 7

8

(a)

58, 88, 104, 113, 118

1

(b)

Correct cumulative frequency graph 1 Tolerance small square for plots 2

3

(c) (i)

30 < their answer ⩽ 31

1ft

(ii)

53 ⩽ their answer ⩽ 55

1ft

(d)

Correct graph through (10, 6) (25, 30) (34, 60) (44, 90) (60, 120)

(e)

garage A 44 to 48 104/2.6 = 40 garage B at 38 to 44

3 B1 B1 B1

B2 for at least 6 correct plots B1 for at least 3 correct plots If 0 SC2 for consistent horizontal translation to the left of all points or SC1 for consistent horizontal translation to the left of all points with one slip

B2 for at least 4 correct points plotted B1 for at least 2 correct points plotted

Dep on 2nd B1; an answer of 40 needs to be confirmed by checking graph

(a)

0.5

1

(b)

Correct graph with smooth curve

2

B1 for at least 4 correct points

(c)

Tangent drawn and gradient = 2.3 to 3.0

2

B1 for tangent drawn at x = 4 or B1 for gradient 2.3 to 3.0

(d) (i)

Correct method to eliminate y and reaching the given equation without error including at least one intermediate line

1

© Cambridge International Examinations 2016

Page 5

Mark Scheme Cambridge O Level – May/June 2016

Question

9

Answers

Mark

(ii)

2.3 to 2.4 dep on line drawn

2

(e) (i)

1 or 0.33.. 3

1

(ii)

Tangent gradient roughly

(iii)

y=

1 3

1 x + k oe where 0 < k < 0.25 3

Syllabus 4024

Paper 22

Part marks B1 for 2x + y = 6 drawn

1

2ft

Ft from their e(i) 1 B1 for x + k oe where 0 < k < 0.25 3 1 or y = x + k oe (any k outside range) 3

(a)

173.8 to 174 m

3

B1 for 9 and 115 soi AB 30 or better M1 for = sin 115 sin 9

(b)

51.4 to 51.5

4

B3 for 38.5 to 38.6 or 752 + 1802 − 1302 or M2 for cos DFE = 2 × 75 × 180 M1 for 1302 = 752 +1802– 2×75×180 cos F

(c) (i)

188 to 189

1

(ii)

169 to 170.2 km / h

2

M1 for 15 × their 188 seen

(iii)

15.67 to 16.0

2

M1 for

a=3b=5

2

B1 for one correct

(b)

 −6   −2    or 3    3  1

1

(c)

Reflection , y = x

2

B1 for reflection or B1 for y = x only

(d)

Enlargement, Scale factor – 2, centre (– 4, 2)

3

B1 for enlargement / negative enlargement B1 for scale factor – 2 B1 for centre (– 4, 2)

(e)

 1 − 2   0  

1

10 (a)

 0  oe 1 −  2

© Cambridge International Examinations 2016

90 (= 14.3) 2π

Page 6

Mark Scheme Cambridge O Level – May/June 2016

Question (f)

Answers

Syllabus 4024

Mark

Paper 22

Part marks

(i)

(– h, – g)

1

(ii)

Reflection y = – x

2

B1 for reflection or B1 for y = – x only

5.06 to 5.08

4

B1 for r + 3.5 seen B1 for π(r + 3.5)2 – πr2 or 20π(r + 3.5)2 – 20πr2 B1 for 20π(r + 3.5)2 – 20πr2 = 3000 or better

Solid II by 2.5 – 2.6

4

B3 11.25 to 11.3 cm

11 (a) (i)

(ii)

or M1 for

1 × π r2×2r = 3000 or better 3

and M1 for r3 =

(b)

630 to 632

4

M1 for

3000 × 3 ( = 1432) 2×π

1 1 × 8 × 8 × sin 60 or × 8 × 48 2 2

oe M1 for 8 × 24 soi or 192 soi M1 for 3 × 8 × 24 + 2 × their (triangle area)

© Cambridge International Examinations 2016

Cambridge International Examinations Cambridge Ordinary Level

* 6 4 2 1 2 2 7 5 3 1 *

MATHEMATICS (SYLLABUS D) Paper 1

4024/11 May/June 2016 2 hours

Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (LK/SG) 115720/3 © UCLES 2016

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2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate 12 - 6 ' 3 + 4 .

Answer ............................................. [1] (b) Evaluate 0.3 # 1.5 .

Answer ............................................. [1] 2

(a) Evaluate

2 5 - . 3 8

Answer ............................................. [1] (b) Evaluate

1 7 ' , giving your answer as a fraction in its lowest terms. 3 9

Answer ............................................. [1]

© UCLES 2016

4024/11/M/J/16

3

3

(a) An aircraft leaves at 22 35 on a flight that takes 3 hours and 50 minutes. Find the time when the aircraft arrives.

Answer ............................................. [1] (b) The aircraft flies a distance of 3200 km, correct to the nearest 100 km. Write down the lower bound for the distance.

Answer ...................................... km [1] 4

A bottle full of liquid has a total mass of 1.27 kg. When the bottle is half-full of liquid the total mass is 900 grams. Calculate the mass of the bottle.

Answer .................................. grams [2]

© UCLES 2016

4024/11/M/J/16

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4

5

Stella walks to a park. For 4 minutes she walks at a rate of 80 steps per minute. For 1 minute she walks at a rate of 120 steps per minute. Find the mean number of steps per minute she takes.

Answer ............................................. [2] 6

(a) Write the number

0.034 # 10 -3 in standard form. Answer ........................................... [1]

(b) Arrange the following numbers in order, starting with the smallest. 0.034 # 10 -3

33.7 # 10 -6

0.42 # 10 -5

Answer ........................................ , ........................................ , ....................................... [1] smallest

© UCLES 2016

4024/11/M/J/16

5

7

By writing each number correct to 1 significant figure, estimate the value of 29.2 # 8.17 . 0.396

Answer ............................................. [2] 8

(a) Complete the diagram to make a quadrilateral ABCD which has AC as its line of symmetry. A

B

C

[1] (b) Complete the diagram to make a quadrilateral PQRS which has rotational symmetry of order 2. P

Q

R

[1]

© UCLES 2016

4024/11/M/J/16

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6

9 y 4 3 2 1 –5

–4

–3

–2

–1

0

1

2 x

The shaded region in the diagram is defined by three inequalities. 1 One of these is y H x + 2  . 2 Write down the other two inequalities. Answer  ............................................. ............................................. [2] 10 Factorise completely

3xy - 20 + 5x - 12y .

Answer ............................................. [2]

© UCLES 2016

4024/11/M/J/16

7

11

f (x) = 2x - 9 (a) Find f c- m. 3 4

Answer ............................................. [1] (b) Find f –1(3).

Answer ............................................. [2] 12 A map is drawn to a scale of 2 cm to 5 km. (a) Two towers are 9 km apart. Calculate the distance between them on the map.

Answer ....................................... cm [1] (b) On the map, a town covers an area of 4 cm2 . Calculate its actual area.

Answer ..................................... km2 [1] (c) Express the scale of the map in the form 1 : n.

Answer

© UCLES 2016

4024/11/M/J/16

1 : ............................................. [1]

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8

13 Solve the simultaneous equations. 3x = 4y 1 + 5x = 6 y

Answer  x = ............................................. y = ............................................. [3]

© UCLES 2016

4024/11/M/J/16

9

14 [The volume of a sphere is

4 3 1 rr ] [The volume of a cone is rr 2 h ] 3 3

A cone is removed from a solid wooden hemisphere of radius 3 cm.

3

The cone has radius 3 cm and height 2 cm.

2

The volume of wood remaining is kr cm 3 . Find k.

Answer  k = ............................................. [3] 15 (a) y is directly proportional to the square of x. Given that y = 8 when x = 4, find y when x = 3.

 

Answer  y = ............................................. [2] (b) p is inversely proportional to q. It is known that p = 15 for a particular value of q. Write down the value of p when this value of q is doubled. Answer  p = ............................................. [1]

© UCLES 2016

4024/11/M/J/16

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10

16 E

D

C A

160° B

P

Q

R

In the diagram, AB, BC, CD and DE are four sides of a regular polygon. Each interior angle of the polygon is 160°. ABPQR, DCP and EDQ are straight lines. t . (a) Find CAB

t = ............................................. [1] Answer CAB

  t . (b) Find CBP

t = ............................................. [1] Answer CBP

  t R. (c) Find DQ

 

© UCLES 2016

t R = ............................................. [1] Answer DQ

4024/11/M/J/16

11

17 A sequence of diagrams is made using counters.

Diagram 1

Diagram 2

Diagram 3

Diagram 4

(a) Complete the table. Diagram number

1

2

3

Number of counters

4

6

8

4

5

[1] (b) Find an expression, in terms of n, for the number of counters in Diagram n.

Answer  ............................................. [1] (c) In this sequence, Diagram p has 200 counters. Find the value of p.

Answer p = ............................................. [2]

© UCLES 2016

4024/11/M/J/16

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12

18 Henri did a survey of the lengths of the leaves on a plant. The results are summarised in the table. Length (x cm)

11xG3

31xG4

41xG5

51xG8

Frequency

6

8

10

6

(a) When asked to draw a histogram to illustrate the results, Henri drew the following diagram. 10 8 Frequency

6 4 2 0

0

1

2

3

4

5

6

7

8

9

Length (x cm)

Explain why this diagram is incorrect. ................................................................................................................................................................... .............................................................................................................................................................. [1]

(b) On the grid below, draw a correct histogram for Henri’s results.

0

1

2

3

4

5

6

7

8

9

Length (x cm)

[3] © UCLES 2016

4024/11/M/J/16

13

19 B 40°

A P

R

Q

C

D

In the diagram, the two circles intersect at P and Q. The line AB is a tangent to the circles at A and B. AD and BC are diameters. BD intersects the larger circle at R. t = 40° . DBC t . (a) Find CPR

t = ............................................. [1] Answer CPR

  t . (b) Find CQR

t = ............................................. [1] Answer CQR

  t . (c) Find ABD

t = ............................................. [1] Answer ABD

  t . (d) Find ADB

 

© UCLES 2016

t = ............................................. [1] Answer ADB

4024/11/M/J/16

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14

20 The number of goals scored in each of 50 football matches was recorded. The results are given in the table. Number of goals scored

0

1

2

3

4

5

6

Frequency

16

11

9

7

6

0

1

For these results, find (a) the mode,

Answer ............................................. [1] (b) the median,

Answer ............................................. [1] (c) the mean.

Answer ............................................. [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/11/M/J/16

15

21 (a) Express 500 as the product of its prime factors.

Answer ............................................. [1] (b)

M = 2 # 32

N = 24 # 32

Find the values of p and q when (i)

M # N = 2 p # 3q ,

Answer  p = ............... q = ................ [1] (ii)

M ' N = 2 p # 3 q  ,

Answer  p = ............... q = ................ [1] (iii)

N 2 = 2 p # 3 q  .

Answer  p = ............... q = ................ [1]

© UCLES 2016

4024/11/M/J/16

[Turn over

16

22 The diagram shows triangle ABC. C

A

B

t . (a) Measure ABC t = ............................................. [1] Answer  ABC

 

(b) On the diagram, construct the locus of points, inside triangle ABC, that are (i) 4 cm from B,

[1]

(ii) 2 cm from AC.

[1]

(c) The point P is 4 cm from B, 2 cm from AC, and nearer to A than to C. Label the position of P on the diagram and find the length of AP. Answer AP = ....................................... cm [1]

© UCLES 2016

4024/11/M/J/16

17

23 (a) In the Venn diagram, shade the region which represents the subset (P , Q)l + R . 

P

Q

R

[1] (b)  = { x : x is an integer and 22 G x G 33 } E = { x : x is an even number } T = { x : x is a multiple of 3 } F = { x : x is a multiple of 4 } (i) List the members of T + F .

Answer ............................................. [1] (ii) Find n (E , T ) .

Answer ............................................. [1] (iii) Given that y ! F l + E  , find one possible value of y.

 

© UCLES 2016

Answer y  = ............................................. [1]

4024/11/M/J/16

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18

24 The diagram shows the speed-time graph of a train which slows down from 20 m/s to a stop in T seconds.

20 Speed (m/s) 0 0

Time (t seconds)

T

(a) (i) Find an expression, in terms of T, for the retardation of the train. Answer .................................... m/s2 [1] 3 (ii) Find the speed of the train when t = T  . 4

Answer ...................................... m/s [1] (b) The distance travelled by the train between t = 0 and t = T is 150 m. (i) Find T.

Answer T  = ............................................. [1] (ii) On the diagram, sketch the distance–time graph of the train.

150 Distance (metres) 0

0

Time (t seconds)

T

[1]

© UCLES 2016

4024/11/M/J/16

19

25 A p Y

Z

C

q X

B

In the diagram, 1 X is the point on AB where AX = AB , 4 1 Y is the point on AC where AY = AC , 3 Z is the point on BC produced where CZ = 2BC. AY = p and AX = q . (a) Express, as simply as possible, in terms of p and q, (i)

XY , Answer XY = ............................................. [1]

(ii)

BC ,

Answer BC = ............................................. [1] (iii)

XZ .

Answer XZ = ............................................. [2] (b) Hence find XY : YZ.

Answer ................ : ............... [1]

Question 26 is printed on the next page

© UCLES 2016

4024/11/M/J/16

[Turn over

20

26

Box 1

Box 2

Box 1 contains 2 white balls. Box 2 contains 4 white balls and 3 black balls. (a) Ann chooses, at random, one ball from each box. (i) Find the probability that these balls are both black. Answer ............................................. [1] (ii) Find the probability that these balls have different colours.

Answer ............................................. [1] (b) From the original contents of Box 2, Belle chooses, at random, two balls without replacement. Find the probability that these balls are both white.

Answer ............................................. [1] (c) Carla chooses one of the boxes at random. With the original box contents, she then chooses, at random, one ball from this box. Find the probability that the ball is white.

Answer ............................................. [2]

© UCLES 2016

4024/11/M/J/16

Cambridge International Examinations Cambridge Ordinary Level

* 5 9 3 6 5 8 7 8 5 0 *

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2016

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (RW/AR) 115690/2 © UCLES 2016

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate ^2.05 + 1.4h # 0.2 .



Answer ........................................... [1] (b) Evaluate

1 13 - 45 .

2

Answer ������������������������������������������� [1] (a) Complete this description. A rectangle has rotational symmetry of order ……… and ……… lines of symmetry.

[1]

(b) Shade 4 more small squares in the shape below to make a pattern with rotational symmetry of order 4.

[1]

© UCLES 2016

4024/12/M/J/16

3

3

It is given that 100 dollars ($) is equivalent to 56 pounds (£). (a) Use this information to draw a conversion graph between pounds and dollars on the grid below. 100

80

60 Pounds (£) 40

20

0

0

20

40

60

80

100

120

Dollars ($)

140

160 180

200

[1]

(b) Use your graph to convert $64 to pounds.



© UCLES 2016

Answer £ ......................................... [1]

4024/12/M/J/16

[Turn over

4

4

Complete the table. Fraction

Decimal

Percentage

1 2

=

0.5

=

50%

3 20

=

..........................

=

..........................

=

..........................

=

62.5%

..........................

[2] 5

The table shows some information about the temperatures in a city. Date

Maximum temperature

Minimum temperature

1 February

–10 °C

T °C

1 March

4 °C

–5 °C

(a) Find the difference between the maximum and minimum temperatures on 1 March.



Answer ...................................... °C [1] (b) The minimum temperature, T °C, on 1 February was 13 degrees lower than the minimum temperature on 1 March. Find T.



© UCLES 2016

Answer T = ..................................... [1]

4024/12/M/J/16

5

6

(a) Express 96 as a product of its prime factors.



Answer ........................................... [1] (b) 24 is a common factor of 96 and the integer n. Given that n is less than 96, find the largest possible value of n.

7

Answer ........................................... [1] The table shows information about some flights from Dubai to Mumbai. Departs Dubai (local time)

03 30

Arrives Mumbai (local time)

08 10

Flight duration

16 10

21 55 02 30

3 hours 10 minutes 2 hours 55 minutes

3 hours 5 minutes

(a) Work out the time difference between Dubai and Mumbai.



Answer ........................................... [1] (b) Work out the local time in Mumbai when the 16 10 flight arrives.

© UCLES 2016

Answer ........................................... [1] 4024/12/M/J/16

[Turn over

6

8

y is directly proportional to the square of x. When x = 10, y = 20. Find the value of y when x = 6.

9

Answer y = ..................................... [2] 50 students are asked what type of movie they like to watch. Of these students, • • •

26 like comedy, 15 like both action and comedy and 8 like neither action nor comedy.

Using a Venn diagram, or otherwise, find the number of students who like action but not comedy.



© UCLES 2016

Answer ........................................... [2]

4024/12/M/J/16

7

10 Solve the simultaneous equations. 6x + y = 1 4x - y = 4



Answer x = .....................................

11

y = ..................................... [2] Simplify (a)

5x 7 y , 15x 3 y 4



Answer ........................................... [1] (b) c

1 2 -2

4t m . v4



© UCLES 2016

Answer ........................................... [1]

4024/12/M/J/16

[Turn over

8

12 The diagram below shows triangle ABC.

C

A

B

(a) On the diagram construct the locus of points inside the triangle that are (i) 3.5 cm from A,

[1]

(ii) equidistant from AC and BC.

[1]

(b) On the diagram, shade the region inside the triangle containing the points that are more than 3.5 cm from A and closer to AC than to BC.

© UCLES 2016

4024/12/M/J/16

[1]

9

13 (a) Write these values in order of size, starting with the smallest. 25

52

3

1000

270

Answer ............... , ............... , ............... , ............... [1] smallest (b) Write down one possible value of x that satisfies each inequality. (i)

21

x13



Answer x = ..................................... [1] (ii)

-1 1 x 3 1 0



Answer x = ..................................... [1]

14 The coordinates of the midpoint of the line AB are (1, 2). The length of the line AB is 10 units. (a) If the gradient of AB is 0, find the coordinates of A and B.



Answer A = (............ , ............)



B = (............ , ............) (b) If the gradient of AB is

3 , find the coordinates of A and B. 4



Answer A = (............ , ............)



B = (............ , ............)

© UCLES 2016

[1]

4024/12/M/J/16

[2]

[Turn over

10

15 The diagram shows the lines x + y = 8 and 2y = x + 4 . y 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

x

(a) The shaded region on the diagram is defined by three inequalities. Write down these three inequalities.

Answer ...........................................



...........................................



........................................... [2] (b) Another region, R, is defined by the inequalities x + y G 8 , 2y G x + 4 and y H a , where a is an integer. This region contains 5 points with integer coordinates. Write down the value of a.



© UCLES 2016

Answer a = ..................................... [1]

4024/12/M/J/16

11

16 Anil has some sweets with a mass of 600 g, correct to the nearest 10 grams. (a) Write down the lower bound of the mass of sweets.



Answer ........................................ g [1] (b) Anil sells the sweets in small portions. Each portion has a mass of 25 g, correct to the nearest gram. He sells 10 portions of the sweets. Calculate the lower bound of the mass of sweets remaining.



Answer ........................................ g [2]

17 In the diagram, the bearing of B from A is 170°. The bearing of A from C is 060°. The bearing of C from B is x°.

North

North A 170° 060° C

North

B

x°

Given that triangle ABC is isosceles, find the three possible values of x.

Answer x = .................. or .................. or .................. [3]

© UCLES 2016

4024/12/M/J/16

[Turn over

12

18 The diagram is the speed-time graph for part of a car’s journey.

v Speed (m/s) 0

0

8 Time (t seconds)

12

The retardation of the car between t = 8 and t = 12 is 4 m/s2. (a) Find v.



Answer v = ..................................... [1] (b) Find the total distance travelled by the car in the 12 seconds.



© UCLES 2016

Answer ....................................... m [2]

4024/12/M/J/16

13

19 A

P

O

Q

B

AB is a diameter of the circle, centre O. PA and QB are tangents to the circle at A and B respectively. Prove that triangle PAO is congruent to triangle QBO. Give a reason for each statement you make.

.................................................................................................................................................................... .................................................................................................................................................................... .................................................................................................................................................................... ............................................................................................................................................................... [3]

© UCLES 2016

4024/12/M/J/16

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14

20 A bag contains 10 counters of which 8 are blue and 2 are white. Two counters are taken from the bag at random without replacement. (a) Complete the tree diagram to show the possible outcomes and their probabilities. First counter

8 10

Second counter 7 9

Blue

.............

White

Blue

............. .............

Blue

White .............

White

[1]

(b) Find, as a fraction, the probability that (i) both counters are blue,



Answer ........................................... [1] (ii) one counter is blue and the other is white.



© UCLES 2016

Answer ........................................... [2]

4024/12/M/J/16

15

21 (a) The table shows the values of the function f ^xh for some values of x. x

1

2

3

4

5

f ^xh

5

7

9

11

13

Express the function f ^xh in terms of x.

Answer f ^xh = ................................ [1]



(b)

g ^xh =

8 - 3x 2

(i) Evaluate g ^- 2h.



Answer ........................................... [1] (ii) Find g -1 ^xh.



© UCLES 2016

Answer g -1 ^xh = ........................... [2]

4024/12/M/J/16

[Turn over

16

22 The table shows the populations, correct to 2 significant figures, of some African countries in 2014. Country

Population

Nigeria Sudan

3.6 × 107

Chad

1.1 × 107

Namibia

2.2 × 106

(a) In 2014, the population of Nigeria was 177 156 000. Complete the table with the population of Nigeria using standard form, correct to 2 significant figures.

[2]

(b) Complete the following. The population of Chad was ............... times the population of Namibia.

[1]

(c) The population density of a country is measured as the number of people per square kilometre. It can be found by dividing the population of the country by its area in km2. The area of Sudan is 1.86 × 106 square kilometres. Estimate the population density of Sudan. Give your answer correct to 1 significant figure.

Answer ...................... people / km2 [2]



© UCLES 2016

4024/12/M/J/16

17

23 The table and histogram show some information about the times taken by a group of students to travel to school one day. Time (t minutes)

0 1 t G 10

10 1 t G 20

20 1 t G 30

30 1 t G 60

60 1 t G 120

28

40

52

18

m

Frequency

6 5 Frequency 4 density 3 2 1 0

0

10

20

30

40

50 60 70 Time (t minutes)

80

90

100

110

120

(a) Complete the histogram.

[2]

(b) Find the value of m.



Answer m = .................................... [1] (c) Work out the fraction of students who took more than half an hour to travel to school.



© UCLES 2016

Answer ........................................... [2]

4024/12/M/J/16

[Turn over

18

24

r

a° 3r

The diagram shows a sector of a circle with radius 3r cm and angle a° and a circle with radius r cm. The ratio of the area of the sector to the area of the circle with radius r cm is 8 : 1. (a) Find the value of a.



Answer a = ..................................... [3] (b) Find an expression, in terms of r and r, for the perimeter of the sector.



© UCLES 2016

Answer ..................................... cm [2]

4024/12/M/J/16

19

25 (a) The nth term of a sequence is given by n 2 - 5n . (i) Find the 2nd term in the sequence.



Answer ........................................... [1] (ii) The pth term in the sequence is 150. Find the value of p.



Answer p = ..................................... [2] (b) The nth term of another sequence is given by 3n 2 - kn . The 5th term in this sequence is 55. Find the value of k.



Answer k = ..................................... [2]

Question 26 is printed on the next page

© UCLES 2016

4024/12/M/J/16

[Turn over

20

26 (a) Make p the subject of the formula t =

p+3 . p-4



Answer p = ..................................... [3] (b) Simplify fully

4x - 1 . 2x 2 - 9x - 5 2



Answer ........................................... [3]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/12/M/J/16

Cambridge International Examinations Cambridge Ordinary Level

* 9 6 5 3 7 3 0 2 7 7 *

4024/21

MATHEMATICS (SYLLABUS D)

May/June 2016

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (KN/SG) 115632/3 © UCLES 2016

[Turn over

2 Section A[52marks] Answerallquestionsinthissection. 1

Ashopkeeperbuyssomeplatesfromamanufacturerfor$12each. (a) Themanufacturermakesaprofitof60%. Calculatethecostofmanufacturingeachplate.



Answer $........................................ [2] (b) Theshopkeepersellseachplatefor$17.40. Calculatethepercentageprofitmadebytheshopkeeper.



Answer ....................................... %[2] (c) Inasale,eachplateisreducedfrom$17.40to$11.31. Calculatethepercentagediscountgiven.



© UCLES 2016

Answer ....................................... %[2]

4024/21/M/J/16

3 (d) Theshopkeeperbuys100platesat$12each. Hesells60platesat$17.40eachandxplatesat$11.31each. Theshopkeepermakesaprofitofatleast10%. 



Findtheleastpossiblevalueofx.



© UCLES 2016

Answer ........................................... [3]

4024/21/M/J/16

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4 2



(a) Solvetheequation

p-1 = 5. 7-p

Answer ........................................... [2]

1

J9ab 6N2 (b) Simplify K 3 2 O . La b P



© UCLES 2016

Answer ........................................... [2]

4024/21/M/J/16

5 q2 - q3 (c) Simplify . 3 - 3q



Answer ........................................... [2] (d) (i) Factorise 4t 2 + 35t - 9 .



Answer ........................................... [2] (ii) Hencesolvetheequation 4t 2 + 35t - 9 = 0 .



© UCLES 2016

Answer ........................................... [1]

4024/21/M/J/16

[Turn over

6 3

Thetablebelowisfor y = x 2 + x - 3. x

–3

–2

–1

0

1

2

y

3

–1

–3

–3

–1

3

(a) Usingascaleof2cmto1unitonthex-axisfor - 3 G x G 2  andascaleof1cmto1unitonthey-axisfor - 4 G y G 4 , plotthepointsfromthetableandjointhemwithasmoothcurve. y

x



[2] (b) (i) Useyourgraphtoestimatethesolutionsoftheequation x 2 + x - 3 = 0 .



Answer x=................or................ [1] (ii) Useyourgraphtoestimatethesolutionsoftheequation x 2 + x - 5 = 0 .

© UCLES 2016

Answer x=................or................ [2] 4024/21/M/J/16

7 (c) Bydrawingatangent,estimatethegradientofthecurveat^1, –1h.



Answer ........................................... [2] (d) Theequation x 2 - x - 1 = 0 canbesolvedbydrawingastraightlineonthegraphof y = x 2 + x - 3. (i) Findtheequationofthisstraightline.



Answer ........................................... [2] (ii) Drawthisstraightlineandhencesolve x 2 - x - 1 = 0 .



© UCLES 2016

Answer x=................or................ [2]

4024/21/M/J/16

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8 4

A

N

M

B

L

C

ANB,BLCandCMAarestraightlines.NMisparalleltoBCand LNisparalleltoCA. (a) ProvethattriangleANMissimilartotriangleNBL. Giveareasonforeachstatementyoumake.

............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ....................................................................................................................................................... [3]

© UCLES 2016

4024/21/M/J/16

9 (b) AN:NB=2:3 (i) FindNM:BC.



Answer ................... :....................[2] (ii) FindareaANM:areaNBL.



Answer ................... :....................[1]

(iii) FindareaANM:areaNMCL.



© UCLES 2016

Answer ................... :....................[2]

4024/21/M/J/16

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10 5

(a) A 31 C

115

B

ABisverticalandCBishorizontal. AB=31mandCB=115m. 



CalculatetheangleofdepressionofCfromA.



© UCLES 2016

Answer ........................................... [3]

4024/21/M/J/16

11 (b)

L

J

354 1100 K

JandKaretwopositionsatsea. ThebaseofalighthouseisatL. JisdueEastofLandKisdueSouthofL. KL=354mandKJ=1100m. t . (i) Calculate LJK



Answer ........................................... [2] (ii) HencefindthebearingofKfromJ.



© UCLES 2016

Answer ........................................... [1]

4024/21/M/J/16

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12 6

J4 - 1N J2 0N K O K O  B = A=  1 3 7 5 L P L P (a) Evaluate2A–B.



Answer 

J K KK L

N O OO [2] P

Answer 

J K KK L

N O OO [2] P

2

(b) FindA .



© UCLES 2016

4024/21/M/J/16

13 (c) FindB–1.



Answer 

J K KK L

N O OO [2] P

Answer 

J K KK L

N O OO [1] P

Answer 

J K KK L

N O OO [2] P

(d) A+Z=A FindZ.

(e) M+2I=B,whereIisthe2 # 2 identitymatrix. FindM.



© UCLES 2016

4024/21/M/J/16

[Turn over

14 Section B[48marks] Answerfourquestionsinthissection. Eachquestioninthissectioncarries12marks. 7 

(a) ACisadiameterofthecircle,centreO,radius5cm. t =64°. ACB 

B

Calculatethelengthoftheminorarc BC. A



64° 5

O

C

Answer ..................................... cm[4] (b)

16.5

rim 15.5

Abakingtrayisanopencylinderofradius15.5cmwitharim. Theouteredgeoftherimisacircleofradius16.5cm.

© UCLES 2016

4024/21/M/J/16

15 (i) Calculatetheareaofthetopsurfaceoftherim.

Answer ....................................cm2[2]



(ii) 44identicalcircularholesarecutoutofthebottomofthebakingtray. Theareaofthebottomthatremainsis650cm2. Calculatetheradiusofeachcircularhole.



Answer ..................................... cm[3] (iii) d mm 15.5 cm

Tomakeapizza,thebakingtrayiscompletelyfilledwithdoughtoadepthofdmm. Theopencylinderholds500cm3ofdough. Calculatethedepthofthedough,dmm,givingyouranswercorrecttothenearestmillimetre.



© UCLES 2016

Answer .................................... mm[3]

4024/21/M/J/16

[Turn over

16 8

(a) 

p=

8 - 5q q

(i) Findpwhenq=2.6.



Answer ........................................... [1] (ii) Expressqintermsofp.



Answer ........................................... [2] (b)

x–2

x+3

H Trapezium A

h

x

Trapezium B x

ThelengthsoftheparallelsidesoftrapeziumAarexcmand^x - 2hcm. ThelengthsoftheparallelsidesoftrapeziumBarexcmand^x + 3hcm. TheheightoftrapeziumAisHcmandtheheightoftrapeziumBishcm. Theareaofeachtrapeziumis15cm2. (i) Showthat H =

15 30 andh = . x-1 2x + 3



© UCLES 2016

[2]

4024/21/M/J/16

17 (ii) Findanexpressionintermsofxforthedifferenceinheight,H–h,betweentrapeziumAand 75 trapeziumB,andshowthatitsimplifiesto . ^x - 1h^2x + 3h



[3] (iii) Thedifferenceinheightis1.5cm. (a) Showthat 2x 2 + x - 53 = 0 .



[2] (b) Findx,givingyouranswercorrectto2decimalplaces.



© UCLES 2016

Answer x=...................................... [2]

4024/21/M/J/16

[Turn over

18 9

(a)

D 2

5 F

C

A 15°

E

B

ABCDrepresentstherectangularslopingsurfaceofatriangularprism. ABEFisahorizontalrectangle.CEandDFarevertical. t =15°,DC=5mandAD=2m. CBE (i) CalculateAC.



Answer ....................................... m[2] (ii) CalculateCE.



© UCLES 2016

Answer ....................................... m[2]

4024/21/M/J/16

19 t . (iii) Calculate FAE



Answer ........................................... [4] (b) (i) θ° 9

6

10

Atrianglehassidesof10cm,9cmand6cm,andanangleofθ °,asshowninthediagram. Calculateθ.



Answer ........................................... [3] (ii) ThetriangleKGHhassidesofacm,bcmandccm asshowninthediagram. t isanobtuseangle. Itisgiventhat KGH

G

a K

c

b H

Completethestatementbelowusingoneofthesymbols1 G = H 2. 

© UCLES 2016

c2……^a 2 + b 2h

[1]

4024/21/M/J/16

[Turn over

20 10 100electriclightbulbsofBrandAweretestedtofindhowlongeachbulblasted. Theresultsaresummarisedinthetablebelow. Time (thours)

tG50

Number ofbulbs

2

501 tG100 1001tG150 1501tG200 2001tG250 2501tG300 3001tG350 2

10

40

30

14

2

tG200

tG250

tG300

tG350

(a) Completethecumulativefrequencytable. Time (thours)

tG50

tG100

Cumulative frequency

2

4

tG150

100



[1] (b) Onthegrid,drawasmoothcumulativefrequencycurvetorepresentthisinformation. LabelthiscurveBrandA.

100

80 Cumulative frequency 60

40

20

0

0

50

100

150

200

250

300

350

Time (t hours)



© UCLES 2016

[2]

4024/21/M/J/16

21 (c) (i) Useyourgraphtoestimatethemedian.

Answer ................................. hours[1] (ii) Useyourgraphtoestimatetheinterquartilerange.



Answer ................................. hours[2] (d) 100BrandBbulbsgavethefollowingresults. 4bulbslasted50hoursorless. Thelongesttimeanybulblastedwas300hours. Themedianis250hours. Theupperquartileis275hours. Theinterquartilerangeis75hours.

Onthegrid,drawandlabelthecumulativefrequencycurvefortheBrandBbulbs.

[4]

(e) Usingyourgraph,estimatethenumberofBrandAbulbsthatlasted275hoursorless.

Answer ........................................... [1]

(f) Completethestatementbelow.





Brand............had............morebulbsthatlastedlongerthan275hoursthanBrand.............. [1]

© UCLES 2016

4024/21/M/J/16

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22 11

(a) TriangleABChasverticesA(2,2),B(3,5)andC(4,1). Triangle AlBlC l hasvertices Al (–4,4), Bl (–3,7)andC l (–2,3).





WritedownthecolumnvectorofthetranslationthatmapstriangleABContotriangle AlBlC l . J N K O O [1] Answer  K KK OO L P (b) PQRSisaparallelogram. J- 4N ThepositionvectorofPrelativetoOisgivenbyOP = K O . L 2P Q J4N ThepositionvectorofQrelativetoOisgivenbyOQ= K O . L6P P

R O

(i) Express PQasacolumnvector.

S

(ii) Find RS .

J K Answer  K KK L

N O O [2] OO P

(iii) Find RS .

J K Answer  K KK L

N O O [1] OO P

© UCLES 2016

Answer ...................................units[2] 4024/21/M/J/16

23 (c) y 10

5 D

0

0

5

10

15

x

ThediagramshowstriangleD. (i) Anenlargementwithcentre(5,4),scalefactor2,mapstriangleDontotriangleE. DrawandlabeltriangleE.

[2]

(ii) Anenlargementwithcentre(5,4),scalefactor0.5,mapstriangleDontotriangleF. DrawandlabeltriangleF.

[1]

(iii) TriangleGhasvertices(5,4),(4,3)and(3,5). TriangleFcanbemappedontotriangleGusingasingleenlargement. TriangleFcanalsobemappedontotriangleGusingadifferent singletransformationT. DescribefullythesingletransformationT.

Answer....................................................................................................................................... .................................................................................................................................................... ............................................................................................................................................... [3]

© UCLES 2016

4024/21/M/J/16

24 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/21/M/J/16

Cambridge International Examinations Cambridge Ordinary Level

* 6 7 8 3 2 6 8 5 2 3 *

4024/22

MATHEMATICS (SYLLABUS D)

May/June 2016

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 19 printed pages and 1 blank page. DC (NF/SW) 115721/2 © UCLES 2016

[Turn over

2

Section A [52 marks] Answer all questions in this section. 1

(a) Each year the Reds play the Blues in a baseball match. In 2014, there were 40 500 tickets sold for the match. In 2015, the number of tickets sold was 2.4% more than in 2014. Calculate the number of tickets sold for the match in 2015.



Answer .......................................... [1] (b) In 2015, the cost per ticket for the match was $68.25. The cost per ticket for the match increased by 5% from 2014 to 2015. Calculate the cost per ticket for the match in 2014.



Answer $ ....................................... [2] (c) Calculate the percentage increase, from 2014 to 2015, in the total money taken for the match.

© UCLES 2016

Answer ...................................... % [3] 4024/22/M/J/16

3

2

J 4N KL = K O L- 2P

J2N (a) JK = K O L5P

J- 1N LM = K O L 3P

(i) Find JM .



Answer (ii) Calculate

[1]

KL .



Answer .......................................... [2] (b) O

a A

E

D b C B

In the diagram, OA = a and OB = b . C is the point such that OAC is a straight line and AC = 2OA. D is the midpoint of OB. E is the point such that EC = OD . (i) Express, as simply as possible, in terms of a and b, (a) AD,

Answer .......................................... [1] (b) EB.



Answer .......................................... [1] (ii) Find EB : AD .



© UCLES 2016

Answer .................... : ................... [1]

4024/22/M/J/16

[Turn over

4

3

Steven asked 25 women how many children they have. The results are summarised in the table below. Number of children

Frequency

0

7

1

5

2

6

3

4

4

3

(a) Find (i) the mean,



Answer .......................................... [2] (ii) the median,



Answer .......................................... [1] (iii) the mode.



Answer .......................................... [1] (b) Steven says that the mode is the average that best represents the data. Explain why Steven is wrong.





Answer ....................................................................................................................................... [1]

(c) Steven chooses two women at random from the group. Calculate the probability that both of them have just one child. Give your answer as a fraction in its simplest form.

© UCLES 2016

Answer .......................................... [2] 4024/22/M/J/16

5

(d) Draw a bar chart to represent this data.

Frequency

Number of children

[2] (e) Steven shows Frank the paper on which he recorded the data from his survey. Part of the paper has been torn. 1

4

2

2

3

0

1

0

3

2

2

0

4

1

3

1

0

0

2

2

Which five numbers are missing from the paper?

© UCLES 2016

Answer ...... , ...... , ...... , ...... , ...... [1]

4024/22/M/J/16

[Turn over

6

4

(a) Triangle ABC has sides AB = 8 cm, AC = 7 cm and BC = 12 cm. (i) Use a ruler and compasses to construct triangle ABC. Side AB has been drawn for you.

A

B

[2] t . (ii) Measure BAC

Answer .......................................... [1] (b) Calculate the interior angle of a regular 12-sided polygon.



© UCLES 2016

Answer .......................................... [2]

4024/22/M/J/16

7

(c) 125° 3p°

p° q°

The diagram shows a hexagon with two parallel sides and one horizontal line of symmetry. (i) Calculate p .



Answer .......................................... [1] (ii) Calculate q .



Answer .......................................... [2] (d) A D



P

B C

S

Q

R

Trapezium PQRS is similar to trapezium ABCD. t = 90°. AB is parallel to DC and ABC 1 DC = 2AB, BC = 2 AB and PQ = 34 DC . Given that BC = x cm, find an expression, in terms of x, for the area of PQRS.

Answer ................................... cm2 [3]



© UCLES 2016

4024/22/M/J/16

[Turn over

8

5

(a) Factorise fully 8x2y − 12x5 .



Answer .......................................... [1] (b) Solve 4x − 2(x + 5) = 3 .



Answer .......................................... [2] (c) Solve 7 − 5y < 20 .



Answer y ........................................ [2] (d) A rectangle has length 2x cm, perimeter 18 cm and area 10 cm2. (i) Show that 2x2 − 9x + 5 = 0. 2x

[2] (ii) Solve 2x2 − 9x + 5 = 0 , giving your answers correct to 2 decimal places.



Answer x = .................... or .................... [3] (iii) Find the difference between the length and the width of the rectangle.

© UCLES 2016

Answer .................................... cm [1] 4024/22/M/J/16

9

6

(a)  = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } A = { x : x is a prime number } B = { x : x is an even number } C = { x : x is a multiple of 5 } (i) List the members of the subsets (a) B + C ,



Answer .......................................... [1] (b) ^A , B , Ch ' ,



Answer .......................................... [1] (c)

A + B' .



Answer .......................................... [1] (ii) A number q is chosen at random from . Find the probability that q ! A + B' .

(b) Find

J3 - 1N X=K O 0P L2

J 2 Y=K L- 1

2N O 1P

Answer .......................................... [1]

(i) 2X + Y ,



Answer

J K KK L

N O OO P

[2]

Answer

J K KK L

N O OO P

[2]

(ii) Y –1 .



© UCLES 2016

4024/22/M/J/16

[Turn over

10

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

One day, garage A records the amount of petrol bought by the first 120 customers. The results are summarised in the table below.

Petrol (k litres)

0 < k  10 10 < k  20 20 < k  30 30 < k  40 40 < k  50 50 < k  60 60 < k  70 70 < k  80

Number of customers

9

13

36

30

16

9

5

2

k  50

k  60

k  70

k  80

(a) Complete the cumulative frequency table below. Petrol (k litres)

k  10

k  20

9

22

Cumulative frequency

k  30

k  40

120 [1]

(b) On the grid below, draw a cumulative frequency curve to represent this data. 120 110 100 90 Cumulative frequency

80 70 60 50 40 30 20 10 0

0

10

20

30

40 Petrol (k litres)

50

60

70

80

[3] © UCLES 2016

4024/22/M/J/16

11

(c) Use your graph to estimate (i) the median,

Answer ................................ litres [1] (ii) the 90th percentile of the distribution.



Answer ................................ litres [1] (d) On the same day, garage B also recorded the amount of petrol bought by its first 120 customers. The results are summarised below. 6 customers bought 10 litres or less. The most petrol bought by any customer was 60 litres. The median amount of petrol bought was 34 litres. The lower quartile of the distribution was 25 litres. The interquartile range of the distribution was 19 litres. Draw the cumulative frequency curve for garage B on the grid on the previous page.

[3]

(e) Petrol is priced at $2.60 per litre at both garages. Garage A offers a gift to customers who buy over 35 litres. Garage B offers a gift to customers who spend over $104. Use your graphs to estimate the number of these customers offered a gift at each garage and complete the sentence below. Show your working.



© UCLES 2016

Answer Garage ............. offers a gift to .............. more customers than garage .............. [3]

4024/22/M/J/16

[Turn over

12

8

The table below shows some values of x and the corresponding values of y for y = x

0

y

1 4

1

1 x #2 . 4

2

3

4

5

1

2

4

8

(a) Complete the table.

[1]

(b) On the grid below, draw the graph of y =

1 x #2 . 4

y 8

7

6

5

4

3

2

1

0

1

2

3

4

5 x

[2]

© UCLES 2016

4024/22/M/J/16

13

(c) By drawing a suitable line, find the gradient of your graph where x = 4.



Answer .......................................... [2] 1 (d) (i) Show that the line 2x + y = 6 , together with the graph of y = # 2 x , can be used to solve 4 the equation 2x + 8x − 24 = 0 .

[1] (ii) Hence solve 2x + 8x − 24 = 0 .



Answer x = .................................... [2] (e) The points P and Q are (2, 3) and (5, 4) respectively. (i) Find the gradient of PQ .



Answer .......................................... [1] (ii) On the grid, draw the line l, parallel to PQ, that touches the curve y =

1 x #2 . 4

[1]

(iii) Write down the equation of l.



© UCLES 2016

Answer .......................................... [2]

4024/22/M/J/16

[Turn over

14

9

(a)

A 30

C

B

The diagram shows a vertical wind turbine with blades 30 m long. The blades are stationary with the point A being the maximum distance possible from the horizontal ground. The point B is such that the angle of elevation of A from B is 34° and the angle of elevation of the centre of the blades, C, from B is 25°. Calculate the distance AB.



Answer ...................................... m [3] (b) A different wind turbine, shown in the diagram on the next page, has the centre of its blades, F, 75 m from the base of the turbine, D. Point E is on sloping ground, 180 m from F and 130 m from D. Calculate the angle of depression of E from F.

© UCLES 2016

Answer .......................................... [4] 4024/22/M/J/16

15

F

75 180 D 130 E

(c) P is the point on a blade which is furthest from the centre of the blades. Each blade is 30 m long. (i) Calculate the distance travelled by P as the blade completes one revolution.



Answer ...................................... m [1] (ii) The blade completes 15 revolutions per minute. Calculate the speed of P, giving your answer in kilometres per hour.



Answer ................................ km / h [2] (iii) A point Q lies on the straight line between P and the centre of the blades. Q travels 90 m as the blade completes one revolution. Calculate PQ.

© UCLES 2016

Answer ...................................... m [2] 4024/22/M/J/16

[Turn over

16

10 Triangles A, B, C and D are drawn on a centimetre square grid. y 6 5 4

B

3 2 1 –6

–5

–4 D

–3

–2

–1

0

A 1

2

3

4

5

6x

–1 –2 –3 –4

C

–5 –6

(a) The perimeter of triangle A is ^a + bh cm, where a and b are integers. Find a and b.



Answer a = ............... b = .............. [2] (b) Triangle A is mapped onto triangle B by the translation T. Write down the column vector that represents T.



Answer

J K KK L

N O OO P

[1]

(c) Describe fully the single transformation that maps triangle B onto triangle C.





Answer .............................................................................................................................................





....................................................................................................................................... [2]

© UCLES 2016

4024/22/M/J/16

17

(d) Describe fully the single transformation that maps triangle B onto triangle D.





Answer .............................................................................................................................................





....................................................................................................................................... [3]

(e) Write down the matrix that represents the transformation which maps triangle D onto triangle A.



Answer

[1]

(f) The transformation V is a reflection in the line y = 0. The transformation W is a rotation 90° clockwise about (0, 0). The single transformation X is equivalent to the transformation V followed by the transformation W. (i) The point (g, h) is mapped onto the point P by the transformation X. Find the coordinates of P.



Answer ( ............. , ............. ) [1] (ii) Describe fully the single transformation X.





Answer .............................................................................................................................................





....................................................................................................................................... [2]

© UCLES 2016

4024/22/M/J/16

[Turn over

18

11

[ Volume of a cone =

1 2 πr h ] 3

(a) r

3.5

20

Solid I

Solid I is a cylinder with a small cylinder removed from its centre, as shown in the diagram. The height of each cylinder is 20 cm and the radius of the small cylinder is r cm. The radius of the large cylinder is 3.5 cm greater than the radius of the small cylinder. The volume of Solid I is 3000 cm3. (i) Calculate r.



© UCLES 2016

Answer r = .................................... [4]

4024/22/M/J/16

19

(ii) Solid II is a cone with volume of 3000 cm3. The perpendicular height of the cone is twice its radius.

Which solid is the taller and by how much?

Solid II



Answer Solid ............ is the taller by

.............................. cm [4]

(b) The diagram shows a triangular prism of length 24 cm. Its cross-section is an equilateral triangle with sides 8 cm.

24

Calculate the total surface area of the prism.

8

Answer ................................... cm2 [4]

© UCLES 2016

4024/22/M/J/16

20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/22/M/J/16

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/11

Paper 1

May/June 2017

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 6 printed pages. © UCLES 2017

[Turn over

4024/11

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

Part Marks

1(a)

(0).016 oe

1

1(b)

2 × ( 3 + 4 ) × 5 cao

1

2(a)

22

1

2(b)

Any trapezium of area 18 with height 4 cm and other parallel side 3 cm long

1

20

2 B1 for 135 seen or ∠BDC=25 or ∠DAE = 45 or ∠DEA = 45

4(a)

2 × 2 × 3 × 3 oe

1

4(b)

2,13

1 In either order

3

5

t + 3t = 140 or 4t = 140

B1

[ t ] = 35

B1

6(a)

kite

1

6(b)

parallelogram

1

77

2 B1 for 66 or 37 or 24 or 53 seen

8(a)

1400

1

8(b)

12.25

1

9(a)

16

1

9(b)

80

2 B1 for 120 or 96 seen 24 1 16 + x 4 or M1 for = or = oe 40 + x 5 40 + x 5

7

© UCLES 2017

Page 2 of 6

4024/11

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

10(a)(i)

248.37

1

10(a)(ii)

250

1

6

1

10(b) 11

Part Marks

Correct method to eliminate one variable reaching ax = b or cy = d

M1

x = −2 y=3

A2 A1 for either x = −2 or y = 3 Or after A0, C1 for a pair of values which satisfy either equation or for correct answers with no working

12(a)(i)

5

1

12(a)(ii)

16

1

12(b)

Histogram completed correctly

1 Column 20-30, height 1.4

13(a)

19 40

1

13(b)

14 15

1

13(c)

31 oe 48

1 Must be integers

14(a)

1.86 × 10–4

1

14(b)(i)

6.4 × 1017

1

14(b)(ii)

7.87 × 108

2 B1 for figs 787 seen

© UCLES 2017

Page 3 of 6

4024/11

Question 15(a)

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED Answer

Marks

1080

1

15(b)(i)

1 oe 27

1

15(b)(ii)

1040

2

16(a)(i)

13

1

16(a)(ii)

58

1

16(b)

[ r ] = [±]

2

A−5 2

Part Marks

M1 for their 1080 × their

M1 for r² =

1 or 40 27

A−5 or √(2r²) = √(A – 5) 2

17(a)

B drawn with vertices (2,–3) (3,–3 )(3,–5)

1

17(b)(i)

C drawn with vertices (4,1 (6,1) (6,3)

2 B1 for correct size triangle drawn but in wrong position or B1 for C drawn using stretch, sf 2 with x-axis invariant, vertices (2,2) (3,2) (3,6)

17(b)(ii)

 2 0   0 1

1

18(a)(i)

1 9

1

18(a)(ii)

25

1

18(b)

b2 3a

2 B1 for b² or 3a in final answer or b4 M1 for 9a 2

© UCLES 2017

Page 4 of 6

4024/11

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

Part Marks

19(a)

430

1

19(b)

300

1

19(c)

12

2

20(a)

11

1

20(b)

30

1

20(c)(i)

line joining (1125, 25) to (1155, 0)

1

20(c)(ii)

1136 – 1137

1 Ft their line with negative gradient

21(a)(i)

Correct Venn diagram

2 B1 if 1 or 2 errors in the numbers

21(a)(ii)

55

1

21(b)(i)

40

1

21(b)(ii)

39

1

© UCLES 2017

Page 5 of 6

M1 for

2.4 × 20 4

4024/11

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

22(a)

1 1 (3 , 3 ) 2 2

1

22(b)

(–1, 4)

1

22(c)

(1, 0)

1

22(d)

23(a)(i) 23(a)(ii)

y=

2

1 7 x + oe 3 3

q–p p–

Part Marks

1 7 B1 for y = x [+ c] or y = mx + 3 3 1 7 or x + 3 3

1

3 4p − 3q q or 4 4

1

uuur uuur 1 uuur M1 for PT = PS + QS soi 3 uuur or PT = PQ + QT soi

23(b)(i)

uuur 1 PT = P 3

2

23(b)(ii)

O, P and T are collinear oe

1 e.g. T is on OP produced

24(a)

23

2 M1 for 6x –18 or 5x + 5

24(b)(i)

−8

1

24(b)(ii)

−1 or 7 with correct working

3 M1 (m − 3)² correctly expanded to m² – 6 m +9 or (m − 3)² + 1 = 17 and M1 for m² – 6 m − 7 = 0 or ( m − 3 ) = ± 4 or SC1 for m = −1 or 7 with no working

© UCLES 2017

Page 6 of 6

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/12

Paper 1

May/June 2017

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 5 printed pages. © UCLES 2017

[Turn over

4024/12

Question

Answer

Marks

1(a)

7 15

1

1(b)

0.0012 oe

1

2(a)

1

2(b)

1

3

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Partial Marks

3 100 with 60, 4 and 20 seen

2 B1 for two from 60, 4 and 20 seen related to unrounded values

4

700

2 C1 for answer 900 200 × (360 − 80) oe or M1 for 80

5(a)

137

1

5(b)

085

1

6(a)

–7.5

1

6(b)

17

1 FT 9.5 – their (a), where –9 ⩽ their (a) ⩽ –7

7(a)

A ∩ B′ oe

1

7(b)

⊂

1

8(a)

2 hours 45 minutes

1

8(b)

17 [May]

2 C1 for answer 16 [May] 10 × 1000 or M1 for oe 30 × 20

9(a)

–1, 0, 1

1

9(b)

Correct fraction

1

9(c)

Irrational number between 2 and 3

1

© UCLES 2017

0.03 or

Page 2 of 5

E.g.

2 3 5 7 6 , , , , etc. 3 5 8 10 10

E.g. √5,

2π etc. 3

4024/12

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

Partial Marks

10(a)

187

1

10(b)

90

2 M1 for 65 × 6 and 60 × 5 soi

11

12(a)

12(b)

Correct method to eliminate one variable reaching ax = b or cy = d

M1

x=3 y = –0.5 oe

A2 A1 for either x = 3 or y = –0.5 oe Or after A0, C1 for a pair of values that satisfy either equation or for correct answers with no working

y=

[±]

2

12 oe x2

M1 for 3 =

3 k k soi or = 2 soi 2 4 4 2

1

1 oe 2

13(a)

150

1

13(b)

2

2

14(a)

5

2

14(b)

4x + k 4x + 5 or oe final answer 3 3

2 FT their k M1 for correct first step 3y − k e.g. x = or 4y = 3x – k or better 4

15(a)

Reflection y = –x oe

2 C1 for reflection or for y = –x oe

15(b)

Triangle vertices (–1, 2), (–1, 5), (–2, 4)

2 C1 for correct size and orientation, incorrect position or for 90° clockwise rotation about origin

16(a)

y = 2x + 3 oe

2 C1 for y = 2x + c o.e. or y = mx + 3 oe m ≠ 0 or 2x + 3 or M1 for gradient = 2 or intercept = 3 soi

16(b)

9

2

x × 4 oe 100 After 0 scored, C1 for answer 27 M1 for (162 – 150) = 150 ×

M1 for 7 =

M1 for

3 × 11 − k soi 4

5 − −1 3 = − oe 1− p 4

3 3 or for 5 = − × 1 + c and −1 = − × p + c 4 4 seen

© UCLES 2017

Page 3 of 5

4024/12

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

Partial Marks

17(a)

Angles in same segment are equal

1

17(b)

∠PQT = 55°

1

17(c)

∠SPQ = 70°

1

17(d)

∠SRQ = 110°

1 FT 180 – their (c)

18(a)

18

2

18(b)

345

2 B1FT for a correct partial area: 120 or 225 or 300 or 45 or 180

M1 for

v − 12 12 − v or oe 15 15

or M1FT for 12 × 25 + 0.5 × 15 × (their18 – 12) oe 19(a)

60

2 B1 for [angle sum of pentagon = ] 540 or (5 – 2) × 180 oe

19(b)

24 nfww

2 B1 for exterior angle = 15° or interior angle = 165° soi 360 − 30 180( n − 2) = oe or M1 for 2 n

20(a)(i)

2 × 33 or 2 × 3 × 3 × 3

1

20(a)(ii)

4

1

20(b)(i)

3 oe 2

1

20(b)(ii)

6

1

21(a)(i)

1 1 1 a+b a + b or (a + b) or 3 3 3 3 final answer

1

21(a)(ii)

1 2 1 a − 2b a – b or (a – 2b) or 3 3 3 3 final answer

1

Any two pairs of vectors from uuur uuur OA = BC oe uuur uuur OQ = PC oe uuur uuur QA = BP oe

2 B1 for any one pair of vectors stated

21(b)

B1 for two of these pairs of sides stated or one of these pairs of sides and this pair of angles stated

Alternative method: OA = BC OQ = PC ∠AOQ = ∠ BCP

© UCLES 2017

Page 4 of 5

4024/12

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

Partial Marks

22(a)

6

2 M1 for 720 = 15 × 8 × h soi

22(b)

396

2 FT their h C1FT for answer 276 or for answer 516 or M1FT for 8 × 15 + 2 × their 6 × 8 + 2 × 15 × their 6

22(c)

3.6 oe

1 FT 0.6 × their 6

23(a)

3 oe 4

2 M1 for 7x = 3(4 – 3x) or better

23(b)

2x + 3 final answer x−5

3 B1 for (2x + 3)(2x – 3) seen B1 for (2x – 3)(x – 5) seen

24(a)

Correctly completed tree diagram n−3 oe n −1 n−3 oe n n−4 oe n −1

2 C1 for one correct probability correctly positioned

24(b)

3 2 1 × = n n − 1 15

M1

Correct rearrangement with at least one further step to reach n2 – n – 90 = 0

A1

24(c)

10

2 B1 for solutions 10, –9 seen or M1 for (n – 10)(n + 9) [ = 0] or for

© UCLES 2017

Page 5 of 5

1±

( −1)2 − 4 × 1 × −90 2 ×1

or better

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/21

Paper 2

May/June 2017

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 6 printed pages. © UCLES 2017

[Turn over

4024/21

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Mark

Partial marks

1(a)

4 : 2 : 3 final answer

2 B1 for 24 : 12 : 54–(24+12) or 12 : 6 : 9

1(b)

c = 14, v = 2 and t = 13

2 B1 for 2 correct or 10 cars, 10 vans and 5 trucks soi

2(a)

36 000

2 M1 for seeing 36720 as 102[%]

2(b)

12.3

4 B1 for 14 688 or 40% B1 for 5508 or 32.6[%] to 32.7[%] or 0.326 to 0.327 M1 for 36720 − their14688 − their 5508 − 12000 or 36720 100 – (15 + their32.7 + their40)

3(a)

GCB, HPC, HPB, HCB, RPC,RPB, RCB

2 B1 for 5 correct and none incorrect or for 6 correct

3(b)(i)

3 1 or or 0.333(..) or 33.3(..)% 9 3

1 FT dep on B1 scored in (a)

3(b)(ii)

6 2 or or 0.666 – 0.667 or 66.6% – 66.7% 9 3

1 FT dep on B1 scored in (a)

3(b)(iii)

2 or 0.222(...) or 22.2(...)% 9

1 FT dep on B1 scored in (a)

4(a)(i)

 0 1    8 1

2

4(a)(ii)

1  −1 1    oe isw 4  −6 2 

2 B1 for for determinant = 4 soi or  −1 1  k   −6 2 

4(b)

1 4  2 14

− 3  or −2 

After 0 scored in (i) (ii) and (iii), 3 6 2 SC1 for , , k k k 0 1 or 2 elements correct in a 8 1 2 × 2 matrix with brackets

B1 for

2 B1 for 2C = 3B – A or –2C = A – 3B soi or  4 −3     14 −2 

 2 −1.5    oe  7 −1 

2 0  2 −1 or M1 for   + 2C = 3    4 −1  6 −1 5(a)

17

1

5(b)

Smooth curve through 7 correct points

3 Mark the curve first B2 for at least 5 ft plots correct B1 for at least 4 ft plots correct

© UCLES 2017

Page 2 of 6

4024/21

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Mark

Partial marks

5(c)

–1.7 to –1.4, –0.5 to –0.2, 1.7 to 2.0

2 FT B1 for 2 correct

5(d)

3 to 5 with tangent drawn

2 B1 for ruled solid tangent drawn

5(e)(i)

Correct ruled line drawn

1

5(e)(ii)

a = 7, b = 4

2 B1 for one correct or a = 6.8 to 7.2 and b = 3.8 to 4.2

5(e)(iii)

–2.4 to –2.1 or –0.7 to –0.5

1 FT

6(a)(i)

14.4[2…]

2 M1 for 122 + 82

6(a)(ii)

128.6o to 129o

3

12 15 or tan θ = 15 12 A1 for 38.6 to 38.7 or 51.3 to 51.4

M1 for tan θ =

After A0, SC1 for 90 + tan-1( 12 ) evaluated 15 15 ) evaluated or 180 – tan-1( 12

6(b)(i)

472 to 488

2 B1 for 6.3 to 6.5 seen

6(b)(ii)

F correctly placed

2 M1 for either TF = 6 cm plotted or correct angle

6(b)(iii)

242o to 248o

1

7(a)

3ab(4a – 5b2)

1

7(b)(i)

(2x + 3)2 isw

1

7(b)(ii)

2, –5

2 M1 for 2x + 3 = (±)√49 soi

7(c)

p+5 final answer 4

3

M2 for

4p + 4− 2p + 6 2p + 2− p +3 or 8 4

soi

4( p + 1) − 2( p − 3) or 2× 4 2( p + 1) − ( p − 3) 4 p −1 After 0, SC1 for answer or 2p + 10 or 4 p+5 M1 for

7(d)

© UCLES 2017

5 m < − , m < –0.833[…] final answer 6

Page 3 of 6

2

M1 for 6m + 8 < 3 or 3m + 4 <

3 2

4024/21

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Mark

Partial marks

SECTION B 8(a)

Correct diagram

1

8(b)

22 26 88 130

2 B1 for 2 or 3 correct

8(c)

4n + 6 oe isw

2 B1 for 4n ± k

8(d)

26

1

8(e)

(2n + 3)(2n + 2) leading to 4n2 + 10n + 6 with no errors

2 B1 for either (2n + 3) or (2n + 2) used

8(f)

4n2 + 6n oe

1

8(g)

7 cao

3 M1 for 4p2 + 10p + 6 = 8× their (4p + 6) A1 for 4p2 – 22p – 42[ = 0] oe or B2 for [p = 7] total 272 grey 272 or B1 for [p = 6] total 240 grey 240

9(a)

140o

2 M1 for 180 – (360 ÷ 9) or 180(9 – 2) ÷ 9

9(b)(i)

21.89.... with at least 72 + 182 – 2 × 7 × 18 × cos 115 seen

3 M1 for 72 + 182 – 2 × 7 × 18 × cos 115 A1 for 479.5 or 373 + 106.49.. or 373 + 106.5

9(b)(ii)

18.8o to 19o

3

9(b)(iii)

95.47o to 95.5o

4 B3 for 84.5 to 84.6

After 0, SC1 for 4n2 + 10n + 6 shown using alternative method

11sin28 16 sin B sin28 = or M1 for oe 11 16

M2 for sin B =

or M2 for sin E =

109 × 2 their DE × 21.9

1 or M1 for 109 = × 21.9 × their DE × sin E 2 10(a)(i)

60o angle at centre is twice angle at circumference

2 B1 for either correct

10(a)(ii)

70o

3 B2 for y = 20 ˆ = 30 or OBA ˆ = 30 or 240 or B1 for OAB

10(a)(iii)

110o

1 FT 180 – (a)(ii) provided not negative answer

© UCLES 2017

Page 4 of 6

4024/21

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Mark

10(b)(i)

120 π (r + 4)2 = π r 2 360 r2 +8r + 16 = 3r2 leading to r2 – 4r – 8 = 0 without error

3

10(b)(ii)

r = 5.46 to 5.47

3

Partial marks

120 π (r + 4)2 360 M1 for forming equation and expanding (r + 4)2

B1 for

−(−4) ± ( −4) 2 − 4 × 1 × −8 oe 2 −(−4) ± p or B1 for oe or 2 ×1

B2 for

q ± (−4) 2 − 4 × 1 × −8 oe r 11(a)

75 nfww

3

M2 for

∑ frequency × midvalue

or M1 for

80

oe

∑ fc

11(b)

25, 46, 64, 73, 78

1

11(c)

8 points correctly plotted and joined

2 FT increasing curve B1 for at least 6 points correctly plotted

11(d)(i)

74 to 76

1

11(d)(ii)

36 to 44

2 B1 for 52 to 56 and 92 to 96 seen

11(e)

54 to 62

3 B1 for 27 to 29 M1 for attempt to read at (80 – 2× their 28)

12(a)(i)

D correctly placed to the left of AC

2 B1 for DA = 9 or CD = 7

12(a)(ii)

44o to 48o

1 FT

12(a)(iii)(a)

2.9 to 3.1

1

12(a)(iii)(b)

19.1 to 20.8

2 B1 for 13.2 to 13.4 seen

Opposite angles are both obtuse or both acute so their total is not 180 Or opposite angles are not supplementary

1

12(b)(i)

© UCLES 2017

Page 5 of 6

4024/21

Question 12(b)(ii)(a)

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED Answers

Mark

Correct region shaded

Partial marks B1 for arc 6 cm from R B1 for angle bisector of Q B1 for perpendicular bisector of PR After B2, SC1 for ‘correct’ region shaded provided only slight inaccuracy with the other line/curve

12(b)(ii)(b)

© UCLES 2017

7.9 to 8.3

1 FT

Page 6 of 6

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/22

Paper 2

May/June 2017

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 8 printed pages. © UCLES 2017

[Turn over

4024/22

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Marks

Part marks

1(a)

9370

3 M1 for (1199×5) or B1 for 5995 or 2398 and 3597 and M1 for 14(55×2 +40×3)oe or B1 for 3220 or 1540 and 1680

1(b)

Bonus [cars] and 67

3 B2 for 67 or answer Bonus with 588 and 655 seen as total charged or M1 for 42×14 or 20×14+750×0.5[0]

2(a)

138 404 000 or 1.38404×108 isw

1

2(b)

Thailand

1

2(c)

4.95[12] × 107 final answer

1

2(d)

1.639 to 1.64

2

2(e)

15 400 000 oe final answer nfww

3

188169[000] − 185133[000] [×100] oe 185133[000] 188169[000] or × 100 185133[000]

M1 for

M2 for 15677 000 ÷

100 + 1.68 oe 100

or M1 for seeing 15 677 000 as 101.68[%] 3(a)

3 4

3(b)

5 or 0.3125 or 31.25% 16

© UCLES 2017

2 B1 for at least 6 correct

- - 6 8 6 9 12 8 12 16

1 FT their complete table (decimals or percentages correct to at least 3sf)

Page 2 of 8

4024/22

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Marks

Part marks

3(c)

3 cao 4

2

3(d)

No with square 6 and factors 7 seen or 6 7 square and factors seen or 16 16 1 4 4 4 9 16 and 1 2 2 3 3 6 6 seen or 12 22 22 22 32 42 and 1 2 2 3 3 6 6 seen

2

4(a)

1 0   8 8

2 B1 for 2 or 3 elements correct

4(b)

− 7    5

2

4(c)

1  2 1 4     − 2 − 1  or 2  − 4  2 

3

2  oe isw − 1 

B1 for

their 12 12 6 or or oe 8 16 16

6 7 or factors or 16 16 1 4 4 4 9 16 seen or 12 22 22 22 32 42 seen or 1 2 2 3 3 6 6 seen or square 6 and factors 7

B1 for square

−7  −7 − 7 k   or  or   or (–7 [,] 5) B1 for  or  5  k 5  5

B2 for

1  − 2 − 2   oe 3  2  4

 − 2 − 2  3 

or B1 for determinant = 2 soi or k   4

5(a)

9 final answer 10 x

1

5(b)

7x – 5y + 3 final answer

2 B1 for 7x – 5y + 3 seen or two of 7x, –5y, 3 in final answer

5(c)

–1.14, 1.47 final answers

3 B2 for

− (−1) ± (−1) 2 − 4 × 3 × −5 oe 2×3

or B1 for

© UCLES 2017

Page 3 of 8

q ± (−1) 2 − 4 × 3 × −5 − (−1) ± p oe or oe 2×3 r

4024/22

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Marks

Part marks

5(d)(i)

Ruled line through (0,2.5) and (5, 0)

2 B1 for ‘correct’ freehand line or line with a gradient of –0.5 or line through (0, 2.5) with negative gradient or line through (5, 0) with negative gradient

5(d)(ii)

Correct region unambiguously identified

1 FT provided their straight line with negative gradient and the 3 given lines form a quadrilateral below y = 4

7.387 to 7.392

2

6(a)

M1 for sin 38 =

PQ soi or 12

PQ 12 = soi sin 38 sin 90 6(b)

71(.0) to 71.02, 108.98 to 109(.0) nfww

4 B3 for one correct or M2 for sinS =

12sin52 12 cos 38 or 10 10

sinS sin 52 = oe or 12 10 [PR=]12cos38 or [PR=]12sin52 or or M1 for

[PR=] 12 2 − (their ( a ) )2 and SC1 for two answers that add to 180 7(a)

Correct pattern drawn

1

7(b)

15 10

2 B1 for 2 or 3 correct

7(c)

n2 oe final answer

1 e.g.

7(d)

465

1

© UCLES 2017

21 15

Page 4 of 8

(

1 2

) (

n 2 + 12 n +

1 2

n 2 − 12 n

)

4024/22

Question 7(e)

Answers

(

n2 –

1 2

n 2 + 12 n

Marks

)

Part marks

1

or

(

1 2

(n − 1) 2 + 12 (n − 1)

or

(

1 2

n 2 + 12 n – n

leading to 7(f)

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

)

)

(

1 2

)

n 2 − 12 n without error AG

m = 9 cao

3 M1 for 1 m 2 + 1 m = 5m 2 2 2 A1 for m – 9 m = 0 or m2 = 9 m or m – 9 = 0 or m + 1 = 10 or B2 for [m = 9] 5 m = 45 and crosses = 45 or B1 for values for 5 m and the number of crosses seen for at least m = 7 and 8 After 0, SC1 for answer 11

14.96 to 15[.0] nfww

3 M2 for 15.12 – 22 (= 224.01)

SECTION B 8(a)

or M1 for DC2 + 22 = 15.12 or 15.12 – their 22 with horizontal line seen or B1 for horizontal line and 2 soi 8(b)

© UCLES 2017

97.46 to 97.55

3

Page 5 of 8

9 2 + 112 − 15.12 oe 2 × 9 × 11 or B1 for 15.12 = 92+112–2×9×11×cos[A] oe

M2 for cos [A] =

4024/22

Question 8(c)

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED Answers

Marks

123.8 to 124.1 nfww

Part marks

4 M3 for soi

1 2

×9×11×sin(b)+ 12 × ( 4 + 6) × ( a ) oe with (a) ≠15.1

or M1 for

1 2

and M1 for

× 9 × 11 × sin (b) oe soi 1 2

× (4 + 6) × (a) oe with

(a) ≠ 15.1 soi 8(d)

2 FT (c) × 4

495.5 to 497

B1 for (figs 5)2 soi 9(a)

(x + 2)(10 – x) =10x + 20 – x2 – 2x y = 20 + 8x – x2 AG

2 B1 for (x + 2) and (10 – x) seen

9(b)

Smooth curve through 11 correct integer points

4 B3 for 6 or 7 correct integer points plotted or B2 for 4 or 5 correct integer points plotted or B1 for 2 or 3 correct integer points plotted

9(c)

9.1 to 9.4 with y = x drawn

2 B1 for y = x drawn or 9.1 to 9.4 with no line drawn/wrong line drawn

9(d)

–3, 6

4 B1 for 5x +2 soi M1 for their(5x + 2) = 20 + 8x – x2 leading to x2 – 3x – k [=0] or x2 – kx – 18[= 0] or equivalent 3 term quadratic A1 for (x + 3)(x – 6) [= 0] or

3 ± 32 − 4 ×1× −18 3 81 oe or ± oe 2 ×1 2 4

After A0, SC1 for answer 6 or –3

© UCLES 2017

Page 6 of 8

4024/22

Question 10(a)(i)

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED Answers

Marks

B and C correctly placed

Part marks

3 B2 for B or C correctly placed or B1 for a point on a bearing of 062° or a point on a bearing of 194°

10(a)(ii)

D on BC with ADB = 90°

1 FT

10(a)(iii)

2.7 to 3.1

1 dep on (a)(ii) and B or C correct

10(a)(iv)

1.2 to 1.4 oe

2 dep on (a)(ii) and B or C correct B1 for [CD] 5.5 to 6 and [DB] 7.3 to 7.7 or SC1 for answer 0.5 ⩽ n <1 if their CD > their DB or answer 1< n ⩽ 2 if their CD < their DB

10(a)(v)

0.714w to 0.834w oe or k – w where k is 18 to 20.5

1 FT

w their ( a )(iv )

if their (a)(iv) ≠ 1 and

dep on (a)(ii) 10(b)

Correct region shaded

4 B1 for arc 6 cm from E B1 for angle bisector of EAF B1 for perpendicular bisector of AF After B2, SC1 for ‘correct’ region shaded provided only slight inaccuracy with the other line/curve

11(a)(i)

55 ⩽ t < 60

1

11(a)(ii)

60.8 nfww

3 M2 for

∑ frequency× midvalue oe

or M1 for © UCLES 2017

Page 7 of 8

50

∑ ft

4024/22

May/June 2017

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answers

Marks

Part marks

11(a)(iii)

23 or 0.46 or 46% 50

2 B1 for 23 seen or 16 + 7 seen

11(b)(i)

34

1

11(b)(ii)

4.5

2 B1 for 31.5 to 32.5 and 36 to 37 seen

11(b)(iii)

(28, 0) (32, 15) (36, 45) (40, 60) plotted and points joined

3 B2 for at least 3 correct points plotted or B1 for 2 correct points plotted or (28, 0) (32, 15) (36, 45) and (40, 60) seen

32.56 to 32.58 or 32.6

3

12(a)

M2 for

72 × π × 20 + 20 oe 360

72 × π × 20 360 A1 for 12.56 to 12.58 or 12.6

or M1 for

After 0 or 1, SC1 for their ‘arc length’ + 10 + 10 soi 12(b)(i)

62.83 to 62.84 or 62.8

2

12(b)(ii)

4(.00) to 4.08 nfww

3 FT from their (b)(i) – (58.76 to 58.8) provided answer not negative M2 for their (b)(i) – 2 × 12 ×10 ×10 × sin ( 72 2 ) oe

M1 for

72 × π × 10 2 360

or M1 for [2×] 12(c)

© UCLES 2017

Add totals from (a) and (b) then divide by 2 Any half values are to be rounded down

4

Page 8 of 8

( ) oe soi

72 1 2 ×10 ×10 × sin 2

Cambridge International Examinations Cambridge Ordinary Level

* 1 3 2 2 1 2 6 1 5 9 *

MATHEMATICS (SYLLABUS D)

4024/11 May/June 2017

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 19 printed pages and 1 blank page. DC (ST/FC) 136385/1 © UCLES 2017

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2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Evaluate 0.2 # 0.08 .

Answer ........................................... [1] (b) Add one pair of brackets to make the statement below true. 2 # 3 + 4 # 5 = 70

2

[1]

(a) Find the perimeter of the shape below. All the angles are right angles. All the lengths are in centimetres. 6 1

4

Answer ..................................... cm [1] (b) On the grid below draw a trapezium with height 4 cm and area 18 cm2. One side of the trapezium has been drawn for you.

[1]

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3

3

A 25º

B

E D xº C

In the diagram AB is parallel to DC. AC and BD intersect at E. Triangle ADE is right-angled and isosceles with AD = DE. ABt D = 25º. Find x.

Answer x = ..................................... [2] 4

(a) Express 36 as the product of its prime factors.

Answer ........................................... [1] (b) Write down two prime numbers whose sum is 15.

Answer ........................................... [1]

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5

Carl spent t minutes on his English homework. He spent three times as long on his Mathematics homework as on his English homework. He spent a total of 2 hours 20 minutes on his English and Mathematics homework. Write down an equation to represent this information and hence find the value of t.

Answer t = ..................................... [2] 6

Complete the sentences below which describe two different types of quadrilateral. (a) A .................................................. has two pairs of equal sides and just one line of symmetry. [1]

(b) A ..................................................has two pairs of equal sides, no line of symmetry and rotational symmetry of order 2.

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5

7

D A

114º

E

143º

B

C

In the diagram AB is parallel to DE. t = 114º and CDE t = 143º. ABC t . Find BCD

t = .............................. [2] Answer BCD

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8

(a) A car travels at 84 km/h. Calculate the number of metres that the car travels in one minute.

Answer ....................................... m [1] (b) A runner completes a race in 12.3 seconds, correct to the nearest tenth of a second. What is the lower bound for the runner’s time?

Answer .........................................s [1] 9

A bag contains red and blue pegs. There are 40 pegs in the bag. The probability of choosing a red peg from the bag is 0.4 . (a) Work out the number of red pegs in the bag.

Answer ........................................... [1] (b) More red pegs are added to the bag. Work out the number of red pegs that must be added to the bag so that the probability of choosing a blue peg is 0.2 .

Answer ........................................... [2]

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10 (a) Write 248.367 (i) correct to 2 decimal places,

Answer ........................................... [1] (ii) correct to 2 significant figures.

Answer ........................................... [1] (b) Estimate, correct to the nearest whole number, the value of

3

3

8.36 + 63.58 .

Answer ........................................... [1] 11

Solve the simultaneous equations. 2x + 3y = 5 3x - y =- 9

Answer x = .................................... y = ..................................... [3]

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12 The ages of guests at a family party were recorded. The results are summarised in the table. Age (b years)

5 1 b G 10

10 1 b G 20

20 1 b G 30

30 1 b G 50

p

18

14

q

Frequency

The histogram below shows some of these results. 2.0

1.5 Frequency density 1.0

0.5

0

0

10

20 30 Age (b years)

40

50

(a) Use the histogram to find the value of (i) p,

Answer p = ..................................... [1] (ii) q.

Answer q = ..................................... [1] (b) Complete the histogram.

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13 (a) Evaluate

3 1 - . 5 8

Answer ........................................... [1] (b) Find A where A #

3 2 = . 7 5

Answer A = .................................... [1] (c) Find the fraction which is exactly halfway between

5 2 and . 8 3

Answer ........................................... [1] 14 (a) Write 0.000 186 in standard form.

Answer ........................................... [1] s = 1.3 # 10 7

(b)

t = 8 # 10 8

Giving each answer in standard form, find (i) t 2,

Answer ........................................... [1] (ii)

t - s.

Answer ........................................... [2]

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15 [ Volume of a pyramid =

1 × base area × perpendicular height ] 3 M

L N

12 9

The diagrams show a solid pyramid L cut into two parts, M and N, by a plane parallel to its base. The base of pyramid L is a rectangle 9 cm by 12 cm. The perpendicular height of pyramid L is 30 cm. (a) Work out the volume of pyramid L.

Answer ....................................cm3 [1] (b) The perpendicular height of pyramid M is

1 of the perpendicular height of pyramid L. 3

(i) Express the volume of M as a fraction of the volume of L.

Answer ........................................... [1] (ii) Calculate the volume of the solid N.

Answer ....................................cm3 [2]

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16 (a) Given that a = 3 and b =- 7 , evaluate (i)

2a - b ,

Answer ........................................... [1] (ii)

a2 + b2 .

Answer ........................................... [1] A = 2r 2 + 5

(b)

Rearrange the formula to make r the subject.

Answer r = ..................................... [2]

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12

17 The diagram shows triangle A. y 6 5 4 3 2 A

1 –6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

x

–1 –2 –3 –4 –5 –6

(a) Triangle B is the image of triangle A after reflection in the line y =- 1. Draw and label triangle B on the diagram.

[1]

(b) Triangle C is the image of triangle A after a stretch, stretch factor 2 with the y-axis invariant. (i) Draw and label triangle C on the diagram.

[2]

(ii) Find the matrix representing the transformation that maps triangle A onto triangle C.

Answer

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J K KK L

N O OO P

[1]

13

18 (a) Evaluate (i) 3–2,

Answer ........................................... [1] 2

(ii) 125 3 .

Answer ........................................... [1] 1

2a 2 b 5 2 m . (b) Simplify c 18a 4 b

Answer

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.......................................... [2]

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19 (a) 6 square metres of carpet cost $258. Work out the cost of 10 square metres.

Answer $ ......................................... [1] (b)

1 dirham = $0.30 Amin changes $90 into dirhams. Calculate the number of dirhams that Amin receives.

Answer ........................................... [1] (c) Sabah is filling a tank with water. It takes 20 minutes to fill the empty tank when the water flows at a rate of 2.4 litres/minute. Calculate the time it will take to fill the empty tank if the water flows at a rate of 4 litres/minute.

Answer ..............................minutes [2]

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15

20 Town

25

20

15 Distance from village (km)

10

5

Village

0 11 00

11 10

11 20

11 30 Time

11 40

11 50

12 00

The distance-time graph shows the journey of a red bus travelling from a village to a town. (a) Find the total length of time for which the bus is stopped during the journey. Answer ..............................minutes [1] (b) Find the average speed of the bus over the whole journey from the village to the town.

Answer .................................. km/h [1] (c) A yellow bus leaves the town at 11 25 and travels non-stop along the same road to the village at a constant speed of 50 km/h. (i) On the graph draw the distance-time graph for the yellow bus.

[1]

(ii) At what time does the yellow bus meet the red bus? Answer ........................................... [1]

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16

21 (a) In a sports club

24 members play basketball (B), 28 play cricket (C), 16 play football (F), 9 play basketball and cricket, 11 play cricket and football and 6 play basketball and football. Five members play all three games and eight members play none of these games. (i) Complete the Venn diagram to show this information. 

F

C

B

[2] (ii) Hence work out the total number of members in the club.

Answer ........................................... [1] (b) In another sports club, the number of members playing basketball (B), cricket (C) and football (F) are shown in the Venn diagram below. 

F 16 3 20

12

4 2

11

C

5 B

(i) Find n(F '). Answer ........................................... [1] (ii) Find n( ( F , C ) + B ').

Answer ........................................... [1] © UCLES 2017

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17

22

y 6 5 B

4 A

3 2 1 –5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

x

–1 –2

The diagram shows a line segment AB joining A (2, 3) and B (5, 4) . (a) Find the coordinates of the midpoint of AB. Answer (..................... , .....................) [1] (b) AB is mapped onto CD by the translation d

-3 n. 1

Find the coordinates of C. Answer (..................... , .....................) [1] (c) AB is mapped on to FG by a rotation of 90º clockwise with centre (1, 4). Find the coordinates of G. Answer (..................... , .....................) [1] (d) Find the equation of AB.

Answer ........................................... [2] © UCLES 2017

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18

23

R

Q

q

S P

O

p

OPRQ is a parallelogram and S is a point on PR such that PS : SR = 1 : 3. OP = p and OQ = q. (a) (i) Express PQ in terms of p and/or q.

Answer ........................................... [1] (ii) Express QS , as simply as possible, in terms of p and/or q.

Answer ........................................... [1] (b) T is a point on QS extended such that QT =

4 QS . 3

(i) Express PT , as simply as possible, in terms of p and/or q.

Answer ........................................... [2] (ii) What can you conclude about the points O, P and T ? ............................................................................................................................................... [1]

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19

24 (a) Solve

6 5 = . x+1 x-3

Answer x = ..................................... [2] (b)

f (x) = x - 3

g (x) = x 2 + 1

(i) Find f(− 5) .

Answer ........................................... [1] (ii) Find m given that g (m - 3) = 17 .

Answer m = ............... or ............... [3]

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20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/11/M/J/17

Cambridge International Examinations Cambridge Ordinary Level

* 8 2 9 4 7 0 3 2 1 5 *

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2017

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 19 printed pages and 1 blank page. DC (ST/FC) 136388/2 © UCLES 2017

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2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate

4 1 - . 5 3

Answer ........................................... [1] (b) Evaluate 0.2 # 0.006 .

Answer ........................................... [1] 2

(a) Shade one more small triangle in the shape below to make a pattern with one line of symmetry.

[1] (b) Shade two more small triangles in the shape below to make a pattern with rotational symmetry of order 2.

[1]

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3

3

By writing each number correct to one significant figure, estimate the value of 58.7 # 4.08 . 19.7 3

Answer ........................................... [2]

4

No 80º Yes

A group of students were asked if they wanted a later start to the school day. The pie chart summarises the results. 200 students said no. Work out the number of students who said yes.

Answer

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.......................................... [2]

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4

5

The diagram shows the position of two villages A and B. North

A

B

(a) Measure the bearing of B from A. Answer ........................................... [1] (b) The bearing of village C from A is 265°. Work out the bearing of A from C.

Answer ........................................... [1] 6

A thermometer measures temperature correct to the nearest degree. The outside temperature is measured as –8 °C. (a) Write down the upper bound of the outside temperature. Answer ...................................... °C [1] (b) The inside temperature is measured as 10 °C. Calculate the lower bound of the difference between the outside temperature and the inside temperature.

Answer ...................................... °C [1]

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7

(a) Use set notation to describe the shaded set in the Venn diagram.  A

B

Answer ........................................... [1] (b) Use set notation to complete the statement about sets C and D.  D C

Answer C ................................... D [1] 8

(a) A film starts at 22 35 and finishes at 01 20. How long, in hours and minutes, does the film last?

Answer .................. hours .................. minutes [1] (b) On 1 May, Leila starts to go swimming every day. She swims 30 lengths of the swimming pool every day. The swimming pool is 20 m long. Work out the date when Leila has swum a total of 10 km.

Answer ........................................... [2] © UCLES 2017

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6

9

3 (a) Write down all the integers that satisfy the inequality - G x 1 2 . 2

Answer ........................................... [1] (b) Complete the following inequality with a fraction.

3 1 2 ...................... 2 4 2

[1]

(c) Write down an irrational value of n that satisfies this inequality. 21n13

Answer ........................................... [1]

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7

10 (a) Here are the masses, in grams, of 8 apples. 189

175

185

192

202

161

174

196

Find the median mass.

Answer ........................................ g [1] (b) A bag contains 5 carrots. The mean mass of the carrots is 60 g. Another carrot is added to the bag. The mean mass of the 6 carrots is 65 g. Work out the mass of the carrot added to the bag.

Answer ........................................ g [2] 11

Solve the simultaneous equations. 5x - 2y = 16 3x + 4y = 7

Answer x = ..................................... y = ..................................... [3]

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8

12 y is inversely proportional to the square of x. The table shows some values for x and y. x

2

4

p

y

3

3 4

48

(a) Find the equation connecting x and y.

Answer ........................................... [2] (b) Find the value of p.

Answer p = ..................................... [1]

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9

13 (a) Rani has $240. She spends

5 of this on a new phone. 8

Work out the cost of the phone.

Answer $ ......................................... [1] (b) Anna invests $150 in an account that pays simple interest. She leaves the money in the account for 4 years. At the end of 4 years she has $162. Work out the rate of simple interest paid per year.

Answer ....................................... % [2] 14

f (x) =

3x - k 4

(a) Given that f(11) = 7, find the value of k.

Answer k = ..................................... [2] (b) Find f –1(x).

Answer f –1(x) = ............................. [2]

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10

15 The diagram shows triangles A and B. y 6 5 4 3 2 A

1 –6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

x

–1 –2 –3 B

–4 –5 –6

(a) Describe fully the single transformation that maps triangle A onto triangle B. Answer ............................................................................................................................................... ....................................................................................................................................................... [2] (b) Triangle A is mapped onto triangle C by a rotation, 90° anti-clockwise about the origin. On the diagram, draw triangle C.

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11

16 A is the point (0, 3), B is the point (1, 5) and C is the point (p, –1). (a) Find the equation of the line AB.

Answer ........................................... [2] (b) The gradient of the line BC is -

3 . 4

Find the value of p.

Answer p = ..................................... [2]

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12

17 P

T

125º X

S

O Q

35º

R

In the diagram, P, Q, R, S and T lie on the circle. QT is a diameter of the circle, centre O. X is the point of intersection of PS and QT. t = 125° and PStQ = 35°. PXT (a) Complete the following statement with a geometrical reason. t = 35° because ..................................................................................................................... [1] PTQ t . (b) Find PQT

t = .............................. [1] Answer PQT t . (c) Find SPQ

t = ............................... [1] Answer SPQ t . (d) Find SRQ

t = ............................... [1] Answer SRQ

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13

18 The diagram is the speed-time graph for 25 seconds of a car’s journey.

v Speed 12 (m/s)

0

0

15 Time (t seconds)

25

The car slows down uniformly from a speed of v m/s to a speed of 12 m/s in 15 seconds. It then travels at constant speed for a further 10 seconds. (a) The retardation of the car is 0.4 m/s2. Calculate the value of v.

Answer v = ..................................... [2] (b) Calculate the distance travelled by the car from t = 0 to t = 25.

Answer ....................................... m [2]

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14

19 (a) A pentagon has four angles of 2x° and one angle of x°. Calculate the value of x.

Answer x = ..................................... [2] (b) ABCD and EBCF are parts of two identical regular n-sided polygons. A

D B

C

E

30º F

The two polygons are joined together along edge BC. Angle DCF = 30°. Calculate the value of n.

Answer n = ..................................... [2]

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15

20 (a) (i) Write 54 as the product of its prime factors.

Answer ........................................... [1] (ii) Find the smallest possible integer m such that 54m is a cube number.

Answer m = .................................... [1] (b) Find the value of k in each of the following. (i)

27 = 3 k

Answer k = ..................................... [1] (ii)

1 -3 b l = 2k 4

Answer k = ..................................... [1]

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16

21

A

C Q

a

P

O

b

B

OACB is a parallelogram. OA = a and OB = b . P and Q are points on OC such that OP = PQ = QC. (a) Express, as simply as possible, in terms of a and b, (i)

OP ,

Answer ........................................... [1] (ii)

BP .

Answer ........................................... [1] (b) Show that triangles OAQ and CBP are congruent.

[2]

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17

22 h

8 15

A container is made out of thin material in the shape of a cuboid with an open top. The container has length 15 cm and width 8 cm. The volume of the container is 720 cm3. (a) Calculate the height, h cm, of the container.

Answer ..................................... cm [2] (b) Calculate the surface area of the outside of the container.

Answer ....................................cm2 [2] (c) Liquid is poured into the container. The liquid fills 60% of the container. Calculate the height of the liquid in the container.

Answer ..................................... cm [1]

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18

23 (a) Solve

7x =3. 4 - 3x

Answer x = ..................................... [2] (b) Simplify fully

2

4x - 9 . 2x 2 - 13x + 15

Answer ........................................... [3]

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19

24 A bag contains n balls. 3 of the balls are white. Two balls are taken from the bag, at random, without replacement. (a) Complete the tree diagram. First ball

Second ball 2 n –1

3 n

White .......... 3 n –1

..........

White

Not white White

Not white ..........

Not white

[2] (b) The probability that both balls are white is

1 . 15

Show that n 2 - n - 90 = 0 .

[2] (c) Find the value of n.

Answer ........................................... [2]

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20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/12/M/J/17

Cambridge International Examinations Cambridge Ordinary Level

* 5 4 5 6 0 7 1 4 6 7 *

4024/21

MATHEMATICS (SYLLABUS D)

May/June 2017

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 21 printed pages and 3 blank pages. DC (NH/FC) 136392/1 © UCLES 2017

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2

Section A [52 marks] Answer all questions in this section. 1

Trevor has a collection of 54 toy vehicles. Of these, 24 are cars, 12 are vans and the rest are trucks. (a) Write the ratio of cars to vans to trucks in its simplest form.

Answer

............ : ............ : ............ [2]

(b) Trevor decides that it is time to reduce his collection of vehicles. He sells c cars, v vans and t trucks. He finds that the ratio of cars to vans to trucks is now 2 : 2 : 1. Find c, v and t, given that he has sold • at least one of each type of vehicle • the smallest possible number of vehicles.

Answer c = ..................................... v = ..................................... t = ...................................... [2]

© UCLES 2017

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3

2

In 2016 Amira’s income was $36 720. (a) This was 2% more than her income in 2015. What was her income in 2015?

Answer $ ......................................... [2] (b) In 2016, Amira used her income of $36 720 in the following way. $12 000 was used for rent. 2 of her income was used for food and to pay bills. 5 15% of her income was spent on leisure. The rest of her income was saved. What percentage of her income did she save?

Answer ....................................... % [4]

© UCLES 2017

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4

3 Humanities:

Geography (G) History (H) Religious studies (R)

Science:

Physics (P) Chemistry (C) Biology (B)

A student has to choose one humanities subject and two different science subjects. (a) Complete the table to show the possible outcomes. Answer

Humanities

Science

G

P and C

G

P and B

[2] (b) Khalif chooses his subjects at random. (i) Find the probability that he chooses Geography. Answer ........................................... [1] (ii) Find the probability that he chooses Physics. Answer ........................................... [1] (iii) Find the probability that he chooses both Religious studies and Chemistry. Answer ........................................... [1] © UCLES 2017

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5

J2 0 NO K A =K O L4 -1P

4

J2 -1N OO B = KK 6 1 L P

(a) Calculate (i) BA,

Answer

[2]

(ii) B–1.

Answer

J K KK L

N O OO P

[2]

Answer

J K KK L

N O OO P

[2]

(b) Given that A + 2C = 3B , find C.

© UCLES 2017

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6

5

The table below is for y = x 3 - 3x - 1 . x

–3

–2

–1

0

1

2

y

–19

–3

1

–1

–3

1

3

(a) Complete the table.

[1]

(b) On the grid, draw the graph of y = x 3 - 3x - 1 . y 18 16 14 12 10 8 6 4 2 –3

–2

–1

0

1

2

3

x

–2 –4 –6 –8 –10 –12 –14 –16 –18 –20

[3] © UCLES 2017

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7

(c) Use your graph to solve x 3 - 3x - 1 = 0 .

Answer x = ..................................... [2] (d) Use your graph to estimate the gradient of the curve when x = -1.5 .

Answer ........................................... [2] (e) (i) On the grid draw the graph of

y = 4x + 3 .

(ii) The line y = 4x + 3 and the curve x 3 = ax + b .

[1]

y = x 3 - 3x - 1 can be used to solve the equation

Find the values of a and b.

Answer a = ............... b = ............... [2] (iii) Use your graph to find one of the negative solutions of x 3 = ax + b .

Answer x = ..................................... [1]

© UCLES 2017

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8

6

(a) D

15

B

North

12

A

8

C

A, B, C and D are four towns. B is 12 km due north of A, C is 8 km due east of A and D is 15 km due west of B. (i) Calculate the distance of B from C.

Answer ..................................... km [2] (ii) Calculate the bearing of A from D.

Answer .......................................... [3]

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(b)

North North

T S

The diagram shows the position of a clock tower, T, and a statue, S, drawn to a scale of 1 cm to 75 m. (i) Using measurements taken from the diagram, find the actual distance between T and S.

Answer ....................................... m [2] (ii) A fountain, F, is situated 450 m from T on a bearing of 210°. Draw and label F.

[2]

(iii) Using measurements taken from the diagram, find the bearing of F from S. Answer ........................................... [1]

© UCLES 2017

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7

(a) Factorise completely 12a 2 b - 15ab 3 .

Answer ........................................... [1] (b) (i) Write 4x 2 + 12x + 9 in the form ^cx + d h2 .

Answer ........................................... [1] (ii) Hence solve 4x 2 + 12x + 9 = 49 .

Answer x = ............... or ................ [2]

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11

(c) Express as a single fraction in its simplest form

^ p + 1h

2

-

^ p - 3h

4

.

Answer ........................................... [3] (d) Solve 2 ^3m + 4h 1 3 .

Answer ........................................... [2]

© UCLES 2017

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12

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 8

Pattern 1

Pattern 2

Pattern 3

Pattern 4

(a) Complete the diagram for pattern 4.

[1]

The table below shows some of the information for the number of tiles in pattern n. Pattern n

1

2

3

Number of grey tiles

10

14

18

Number of white tiles

10

28

54

Total number of tiles

20

42

72

4

5

110

156

(b) Complete the table.

[2]

(c) Find an expression, in terms of n, for the number of grey tiles in pattern n.

Answer ........................................... [2] (d) Pattern x has 110 grey tiles. Find x.

Answer x = ..................................... [1]

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13

(e) By considering the number of tiles along the outer edges of each pattern, show that the total number of tiles in pattern n is 4n 2 + 10n + 6 .

[2] (f) Hence find an expression, in terms of n, for the number of white tiles in pattern n.

Answer ........................................... [1] (g) In pattern p, the total number of tiles is equal to 8 times the number of grey tiles. Find p.

Answer p = ..................................... [3]

© UCLES 2017

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14

9

(a) Calculate the interior angle of a regular nine-sided polygon.

Answer ........................................... [2] (b)

A 18

115º 7

B

E

16

28º D

11

C

ABCDE is a pentagon. AB = 18 cm, BC = 16 cm, CD = 11 cm and EA = 7 cm. t = 115° and BDC t = 28° . EAB (i) Show that BE = 21.9 cm, correct to 3 significant figures.

[3]

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15

(ii) Calculate angle DBC.

Answer ........................................... [3] (iii) The perimeter of the pentagon is 62 cm. Given that the area of triangle BDE is 109 cm2, calculate the obtuse angle DEB.

Answer ........................................... [4]

© UCLES 2017

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16

10 (a)

A 2yº

120º D

xº

O

yº

B

C

A, B, C and D lie on the circumference of a circle, centre O. t = 2y° . t = 120° , ADB t = x° , OBD t = y° and DAO AOB (i) Find x, giving a reason for your answer. Answer

x = ........................... because ....................................................................................

............................................................................................................................................... [2] t . (ii) Find DAB

Answer ........................................... [3] t . (iii) Find BCD

Answer ........................................... [1] © UCLES 2017

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17

(b)

O 120º A

r+4 B

Sector OAB has radius (r + 4) cm and its area is the same as the area of a circle of radius r cm. (i) Show that r2 – 4r – 8 = 0 .

[3] (ii) Calculate r.

Answer r = ...................................... [3]

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11

80 people were each asked how much they spent on clothes last month. The results are summarised in the table below. Amount spent ($ c)

Frequency

0 1 c G 20

3

20 1 c G 40

8

40 1 c G 60

14

60 1 c G 80

21

80 1 c G 100

18

100 1 c G 120

9

120 1 c G 140

5

140 1 c G 160

2

(a) Calculate an estimate of the mean amount spent on clothes last month.

Answer $ ......................................... [3] (b) Complete the cumulative frequency table below. Amount spent ($ c) Cumulative frequency

c G 20 3

c G 40

c G 60

c G 80

c G 100

c G 120

c G 140

11

c G 160 80 [1]

(c) On the grid opposite, draw a cumulative frequency curve to represent this data.

[2]

(d) (i) Use your graph to estimate the median. Answer $ ......................................... [1] (ii) Use your graph to estimate the interquartile range.

Answer $ ......................................... [2] © UCLES 2017

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19 80

70

60

Cumulative frequency

50

40

30

20

10

0

20

0

40

60

80

100

120

140

160

Amount spent ($ c)

(e) The number of people who spent more than $85 last month is the same as the number of people who spent between $k and $85. Given that k is less than 85, use your graph to estimate the value of k.

Answer k = ..................................... [3] © UCLES 2017

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20

12 (a)

A

B

C

ABC is a triangle. B and D are points on opposite sides of the line AC. DA = 9 cm and CD = 7 cm. (i) Accurately draw and label the point D.

[2]

t . (ii) Measure DAB t = .............................. [1] Answer DAB (iii) (a) Measure the shortest distance from B to AC. Answer ..................................... cm [1] (b) Work out the area of triangle ABC.

Answer ....................................cm2 [2] © UCLES 2017

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21

(b)

P

S

Q

R

This is an accurate diagram of quadrilateral PQRS. (i) Give a reason why it is not possible for P, Q, R and S to be points on the circumference of a circle. Answer

....................................................................................................................................

............................................................................................................................................... [1] (ii) T is a point inside PQRS such that it is I more than 6 cm from R II nearer to R than P III nearer to PQ than QR. (a) Construct and shade the region within which T lies.

[4]

(b) Find the maximum possible length of RT. Answer ..................................... cm [1]

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© UCLES 2017

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23

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© UCLES 2017

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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/21/M/J/17

Cambridge International Examinations Cambridge Ordinary Level

* 3 8 7 5 9 0 5 3 9 5 *

4024/22

MATHEMATICS (SYLLABUS D)

May/June 2017

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 19 printed pages and 1 blank page. DC (LK/FC) 157824/2 © UCLES 2017

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2

Section A [52 marks] Answer all questions in this section. 1

(a) FLIGHTS TO SYDNEY Cost per person: $1199

INSURANCE COVER FOR UP TO 20 DAYS Cost per adult: $40

and

Cost per child: $30

ACCOMMODATION

OR

Cost per adult per night: $55

Cost for family (2 adults and up to 4 children): $155

Cost per child per night: $40

A family of 2 adults and 3 children travel to Sydney for a holiday lasting 14 nights. Calculate the lowest total cost of the flight, accommodation and insurance for their holiday.

Answer $ ............................................. [3] (b) BONUS CARS $42 per day for any mileage

VALUE CARS $20 per day and

$0.50 per mile

The family hires a car for 14 days and estimates their total mileage will be 750 miles. Which company charges less for this hire and by how much?

Answer ...................................... by $ .............................. [3] © UCLES 2017

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3

2

The table below shows the population, given to the nearest thousand, of some countries. Country

Population in 2014

Population in 2015

185 133 000

188 169 000

1 393 784 000

1 402 007 000

South Korea

49 512 000

49 765 000

Thailand

67 223 000

67 438 000

Pakistan China

(a) In 2015, how much larger was the population of Pakistan than the population of South Korea?

Answer ............................................. [1] (b) Which country had the smallest increase in population between 2014 and 2015?

Answer ............................................. [1] (c) Write the population of South Korea in 2014 in standard form.

Answer ............................................. [1] (d) Find the percentage increase in population of Pakistan from 2014 to 2015.

Answer ........................................ % [2] (e) The population of Cambodia in 2015 was 15 677 000. Given that the increase in population from 2014 to 2015 was 1.68%, calculate the population of Cambodia in 2014. Give your answer correct to 3 significant figures.

Answer ............................................. [3]

© UCLES 2017

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4

3

Rowena spins two fair spinners, each numbered 1 to 4. Her score is the value when the numbers on the two spinners are multiplied together. The table shows some of Rowena’s possible scores. ×

1

2

3

4

1

1

2

3

4

2

2

4

3 4 (a) Complete the table of possible scores.

[2]

(b) Find the probability that Rowena’s score is less than 4.

Answer ............................................. [1] (c) Find the probability that Rowena’s score is an even number. Give your answer as a fraction in its lowest terms.

Answer ............................................. [2] (d) Phoebe says that Rowena’s score is more likely to be a square number than a factor of 6. Is she correct? Show your working. Answer

[2]

© UCLES 2017

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5

J 3 2NO K A =K O L- 4 - 2P

4

J 5 3N OO B = KK 2 1 L P

J- 2N C = KK OO L 1P

(a) Calculate 2B – 3A.

Answer (b) Calculate BC.

J K KK L

N O OO P

Answer

[2]

[2]

(c) Calculate A–1 + A.

Answer

© UCLES 2017

4024/22/M/J/17

J K KK L

N O OO P

[3]

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6

5

(a) Express as a single fraction, as simply as possible,

1 2 + . 2x 5x

Answer ............................................. [1] (b) Simplify 4 ^3x - 2y + 1h - ^5x - 3y + 1h .

Answer ............................................. [2] (c) Solve 3x 2 - x - 5 = 0 , giving your answers correct to 2 decimal places.

Answer

x = .................. or .................. [3]

(d) y 6 5 4 3 2 1 0

1

2

3

4

5

6

x

(i) Draw the graph of x + 2y = 5 .

[2]

(ii) Shade the region defined by these inequalities and label it R. xG3

© UCLES 2017

yG4

y G 2x

4024/22/M/J/17

x + 2y H 5

[1]

7

6 P

Q

12 38º R

Triangle PQR has a right angle at P, angle PRQ = 38° and RQ = 12 cm . (a) Calculate PQ.

Answer

.................................... cm [2]

(b) S is a point such that angle PRS is a right angle and QS = 10 cm. Calculate the two possible values of angle QSR.

Answer

© UCLES 2017

4024/22/M/J/17

................... or ................... [4]

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8

7

Pattern 1

Pattern 2

Pattern 3

Pattern 4

Pattern 5

The diagrams show patterns made from crosses ( ) and circles ( ). (a) Draw pattern 5 above.

[1]

The table shows the number of crosses and circles in each pattern. Pattern number (n)

1

2

3

4

Number of crosses

1

3

6

10

Number of circles

0

1

3

6

Total number of crosses and circles

1

4

9

16

5

6

25

36

(b) Complete the table.

[2]

(c) Find an expression, in terms of n, for the total number of crosses and circles in pattern n.

Answer ............................................. [1] (d) An expression, in terms of n, for the number of crosses in pattern n is

1 2 1 n + n. 2 2

How many crosses are there in pattern 30?

Answer ............................................. [1]

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9

(e) Show that the number of circles in pattern n is

1 2 1 n - n. 2 2

[1] (f) The number of crosses in pattern m is equal to 5m. Find m.

Answer

© UCLES 2017

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m = ............................................. [3]

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10

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 8 A

9 11 E

15.1 B

6

4

D

C

ABCDE is the cross-section of a building. All the lengths are given in metres. (a) Calculate DC.

Answer ........................................ m [3] (b) Calculate angle EAB.

Answer ............................................. [3] © UCLES 2017

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11

(c) Calculate the area of the cross-section.

Answer ....................................... m2 [4] (d) A model of the building is made using the scale 1 : 50. What is the area of the cross-section of the model? Give your answer in square centimetres.

Answer ..................................... cm2 [2]

© UCLES 2017

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12

9

A random number, x, is generated, where x is any real number. (a) Manuel adds 2 to x. He subtracts x from 10. Manuel then multiplies these two results to give his number, y. Show that y = 20 + 8x - x 2 .

[2] (b) On the grid opposite, draw the graph of y = 20 + 8x - x 2 for 0 G x G 10 . Four points have been plotted for you.

[4]

(c) On the same grid, draw a suitable line to find the value of Manuel’s number, y, when it is the same as the random number, x.

Answer ............................................. [2]

© UCLES 2017

4024/22/M/J/17

13 y 40

35

30

25

20

15

10

5

0

0

1

2

3

4

5

6

7

8

9

10

x

(d) Jolene multiplies the random number, x, by 5 and then adds 2 to give her number, z. Calculate the possible values of x when Manuel’s number, y, and Jolene’s number, z, are the same.

Answer

© UCLES 2017

4024/22/M/J/17

x = .................. or .................. [4] [Turn over

14

10

North

A

The diagram shows the position of point A. Point B is 8 cm from A on a bearing of 062 °. Point C is 6.5 cm from A on a bearing of 194 °. (a) (i) Find and label B and C.

[3]

Point D is the point on BC that is the shortest distance from A. (ii) Find and label D.

[1]

(iii) Measure AD. Answer ....................................... cm [1] (iv) By taking measurements, find the ratio CD : DB. Give your answer in the form 1 : n.

Answer

1 : ............................................ [2]

(v) The area of triangle ADB is w cm2. Giving your answer in terms of w, find the area of triangle ADC.

Answer ..................................... cm2 [1] © UCLES 2017

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15

(b) F

E

A

The diagram shows the positions of A, E and F. Construct and shade the region inside triangle AEF that is

• • •

© UCLES 2017

less than 6 cm from E nearer to AF than to AE nearer to A than to F.

4024/22/M/J/17

[4]

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16

11

(a) The table below summarises the times taken by 50 athletes to run 400 m.

Time (t seconds) Frequency

50 G t 1 55

55 G t 1 60

60 G t 1 65

65 G t 1 70

70 G t 1 75

7

16

15

11

1

(i) State the modal class. Answer ............................................. [1] (ii) Calculate an estimate of the mean time taken by these athletes.

Answer .......................................... s [3] (iii) Calculate the probability that an athlete chosen at random took less than 60 seconds to run the 400 m.

Answer ............................................. [2]

© UCLES 2017

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17

(b) The cumulative frequency curve summarises the times taken by 80 boys to run 200 m. 80 70 60 Cumulative 50 frequency 40 30 20 10 0 25

30

35 Time (seconds)

40

45

(i) Find the median time. Answer .......................................... s [1] (ii) Find the interquartile range.

Answer .......................................... s [2] (iii) 60 girls also ran 200 m. The girl who took the longest time ran 200 m in 40 seconds. The girl who took the shortest time ran 200 m in 28 seconds. The lower quartile for the boys and the girls is the same. The interquartile range for the girls is 4 seconds. Draw the cumulative frequency curve on the grid above.

© UCLES 2017

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[3]

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18

12 O 72º

10

B

A C

OAB is a sector of a circle, centre O, and radius 10 cm. AÔB = 72° and C is the point on the arc AB such that OC bisects AÔB. (a) Calculate the perimeter of sector OAB.

Answer ....................................... cm [3] (b) (i) Calculate the area of sector OAB.

Answer ..................................... cm2 [2] (ii) Calculate the total shaded area.

Answer ..................................... cm2 [3] © UCLES 2017

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19

(c) O 72º

10

B

A D

D is the point on the arc AB such that AÔD : DÔB = 1 : 2 . Gavin says that the shaded area on this diagram is the same as the shaded area calculated in part (b)(ii). Is he correct? Show your working. Answer

[4]

© UCLES 2017

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20 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/22/M/J/17

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/11

Paper 1

May/June 2018

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

IGCSE™ is a registered trademark.

This document consists of 6 printed pages. © UCLES 2018

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4024/11

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • • •

the specific content of the mark scheme or the generic level descriptors for the question the specific skills defined in the mark scheme or in the generic level descriptors for the question the standard of response required by a candidate as exemplified by the standardisation scripts.

GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • • • • •

marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate marks are awarded when candidates clearly demonstrate what they know and can do marks are not deducted for errors marks are not deducted for omissions answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous.

GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

© UCLES 2018

Page 2 of 6

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question

Answer

Marks

Partial Marks

1(a)

2

1

1(b)

7

1

2(a)

12

1

2(b)

11 cao 35

1

9 1 15 0.3 0.32 31 3 40

2 B1 for one number incorrect but rest correct or for correct order but reversed

4(a)

Diagram completed correctly

1

4(b)

Diagram completed correctly

1

5(a)

(0)730 oe

2 B1 for 1030, 1420 or 9(h)50 seen or M1 for subtraction of 3(h) and 6(h) 50 seen

5(b)

60

1

5(c)

9000

1 FT from (b) × 150

6(a)

7 oe 16

1

6(b)

40

1

6(c)

20

1

7(a)

5 (items)

1

7(b)

4 (items)

1

3

© UCLES 2018

Page 3 of 6

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

Question 7(c)

Answer 3.85 or 3

Marks 2

17 20

May/June 2018

Partial Marks M1 for

∑ fx 20

or

77 20

7(d)

90

1

8(a)

52

1

8(b)

76

ˆ or TBA ˆ = 52 on 2 B1 for 104 seen or TAB diagram or in working

9

–1, 0, 1, 2

2 M1 for –4/3 < x or x ⩽2 or B1 for 3 correct and none incorrect

10

Correct region shaded

3 B1 for line parallel to AB 3 cm away for length of barn B1 for 2 correct semicircles radius 3 cm centre A and B B1 for region outside barn shaded between line parallel to AB and attempt at two arcs centred A and B

11

a = 5 and b = 0

2 B1 for a = 5 or b = 0

12(a)

9 oe 100

1

12(b)

60

1

12(c)

75

1

12(d)

(c) because based on a larger sample oe

1

13(a)

4 points correctly plotted

1

13(b)

positive

1

13(c)

Ruled line of best fit drawn

1

13(d)

4.35 – 4.55

1 Dependent on a line of best fit or FT their straight line of best fit with +ve gradient

14(a)

(2x – y)(a + 3b) oe

Final answer

2 B1 for a correct partial factorisation

14(b)

3( 3x + y)(3x – y)

Final answer

2 M1 for 3(9x² − y²) or (9x + 3y)(3x − y) or (9x − 3y)(3x + y)

15(a)

−7

1

15(b)

−33

1

15(c)

5 – 8x³

© UCLES 2018

Final answer

1

Page 4 of 6

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

May/June 2018

Partial Marks

16(a)

26

16(b)

3b 4a

17

106

3 M1 for [BC² =] 6² + 7² or better and 6× 7 M1 for [area triangle BCE =] or 21 2

18(a)

BC: constant speed 18 m/s for 50 s CD: deceleration 1.2 m/s² for 15 s

3 B1 for BC correct and B2 for CD completely correct or B1 for CD with one error or omission If 0 marks scored then SC1 for BC is constant speed and CD is deceleration

18(b)

1215

2 M1 for ½ x 18 x(50 + 85) oe or one correct area : 180 or 900 or 135 or SC1 for answer 1080

19(a)

28 800 000 oe

1

19(b)(i)

1.3 × 108 put into the table

1

19(b)(ii)

4.22 × 106 oe

2 B1 for 33 × 105 or [0].92 × 106 or figs 422

19(c)

Greenland

1

20(a)

3

1

20(b)

2.4

1

20(c)

8100

2

21(a)

 13    9

1

21(b)

n = −2

2

22(a)

5

1

22(b)

t = s³ − 4

2 B1 for s³ soi in final answer

23(a)

F

1

23(b)

A

1

23(c)

E

1

© UCLES 2018

1 2

Final answer

Page 5 of 6

B1 for

3 b[1] or [1] seen or in final answer 4 a

27 8 or soi 8 27 or M1 for 30 × 60 × 4.5

B1 for

 3  −4   11  M1 for   + n   =    4  3   −2  or 3 + (− 4n) = 1 or 4 + 3n = −2

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

Question 24(a)

24(b)

© UCLES 2018

Answer

Marks

12( x − 1) + 10( x + 2) 7 = ( x − 1)( x + 2) 2 or better

M1

24x − 24 + 20x + 40= 7x² + 7x − 14

M1

Completion to 7x² − 37x − 30 = 0 with no errors or omissions

A1

6, −

May/June 2018

Partial Marks

3 M2 for [0 = ] (7x + 5)(x − 6) or M1 for factors that when expanded give two terms correct or for (7x – 5)(x − 6) After 0 marks SC1 for both answers correct using formula

5 from factorisation 7

Page 6 of 6

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/12

Paper 1

May/June 2018

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

IGCSE™ is a registered trademark.

This document consists of 7 printed pages. © UCLES 2018

[Turn over

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • • •

the specific content of the mark scheme or the generic level descriptors for the question the specific skills defined in the mark scheme or in the generic level descriptors for the question the standard of response required by a candidate as exemplified by the standardisation scripts.

GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • • • • •

marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate marks are awarded when candidates clearly demonstrate what they know and can do marks are not deducted for errors marks are not deducted for omissions answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous.

GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

© UCLES 2018

Page 2 of 7

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question

Answer

Marks

1(a)

6 77

1

1(b)

[0].0099

1

2(a)

25 cao

1

2(b)

40 cao

1

2(c)

5 : 6 : 16 oe

1

3(a)

–1.2

–0.3 0.05

0.2

1.3

1

3(b)(i)

0.01 oe

1

3(b)(ii)

2.5 oe

1

360

2

4

Partial Marks

B1 for k = 90 if y =

k used x2 2

1 or M1 for 10 × 32 = y ×   oe 2 their k or FTM1 for y = 2

( 12 )

5(a)

(5t – 2)(5t + 2) final answer

1

5(b)

(x – 6)(x – 3y) final answer

2 B1 for a correct partial factorisation e.g. [–]6(x – 3y) or x(x – 3y) or x(x – 6 ) or [–]3(xy – 6y), etc.

6(a)

63.5

1

6(b)

200[.0]

1

© UCLES 2018

Page 3 of 7

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

7(a)

7(b)

Marks

May/June 2018

Partial Marks

1

A correct chord

1 or

–1

2 M1 for 4 × 3x = x – 11 or better or for 4 × 3x – (x – 11) = 0 or better

9(a)

19 final answer 6a

1

9(b)

2b final answer 3

2

600 and 16 and 0.30 seen and final answer 8000

2 B1 for two of 600, 16, 0.30 seen

8

10 11(a)

11(b)

−

20b3 oe seen 30b 2 10b 15 5 4b3 ÷ or M1 for × or for 2 15 4b3 4b3 2b

B1 for

1

1 oe 4

1− 2 x oe final answer 3x

2 M1 for correct first step:

y ( 3 x + 2 ) = 1 or x =

1 1 or 3x + 2 = y 3y + 2

or better 12(a)

80 oe 400

1

12(b)

200

1 FT (their(a)) × 1000 where 0 < their (a) < 1

13(a)

1.1

13(b)

70 cao

© UCLES 2018

0.5

0.2

0.1 oe

2 B1 for 2 or 3 correct 1

Page 4 of 7

4024/12 4

Cambridge C O Level – Mark M Schem me P PUBLISHED D

Question

Answer

Marks

Ma ay/June 201 18

Partiial Marks

14(a)

3600

2

14(b)

163

2 M1 for 2 × 170 + 20 x = their 3600

360   M1 for 180 × ( 22 – 2 ) oe or  180 0−  × 22 22   oe

or for ( theeir 3600 − 2 × 170 ) ÷ 20 oe o 15(a)

(6) nfww

2 B1 for 76 seen or for 770 seen or M1 for ( 30 × 1.2 + 20 × 2 ) − ( 400 × −0.5 + 300 × 3) oe

15(b)

Difference in profit betw ween Week 1 and Weekk 2 oe

1

16(a)

Correct com mpletion of th he curve

1

16(b)(i)

1.7

1

16(b)(ii)

1.3

1

16(b)(iii)

75

5 seen 2 B1 for 125 or SC1 forr answer 74 oor 76

17(a)

Correct net

2 B1 for onee correct trianngle in correect position

17(b)

36 nfww

2 M1 for areea of trianglee 1 1 = × 3 × 4 or × 3 × 5 soi 2 2

Correct reggion shaded bounded b by x = 2, x = 8, y = 5, y = 10 1 and x + y = 10

3 B1 for linee x + y = 10 B1 for at least three coorrect lines frrom x = 2, x = 8, y = 5, 5 y = 10

18

© UCLES 2018

Page 5 of 7

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

Question 19(a)

Answer

Marks

May/June 2018

Partial Marks

Acceptable perpendicular bisector of AB

1

19(b)(i)

Arc, centre C, radius 7 cm

1

19(b)(ii)

Bisector of angle BAC

1

P1 and P2 marked at intersections of their(a) with (b)(i) and (b)(ii)

1 dependent on correct types of loci in (b).

20(a)(i)

1.4 × 10 11 cao

1

20(a)(ii)

5 × 10 – 9 cao

2

20(b)

5

1

21(a)

71

1

21(b)

[p =] 2 [q =] 1

1 Both correct

21(c)

A=2 B=4 C=1

2 B1 for two correct or for (n + 1) 2 = n 2 + 2n + 1 or for (n + their q)2 = n 2 + 2n(their q) + (their q)2

19(c)

1 × 10−8 seen or 0.5 × 10 −8 seen 2 or 0.000 000 005 seen

B1 for

A+ B +C =7

or M1 for 4 A + 2 B + C = 17 9 A + 3B + C = 31 22(a)

106

1

22(b)

127

1

22(c)

59

1

22(d)

31

1 FT 90 – their(c)

© UCLES 2018

Page 6 of 7

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

Question 23(a)

Answer  − 2 −1     −4 −2 

Marks

May/June 2018

Partial Marks

2 B1 for two or three correct elements  6 −3   4 −1  or M1 for   – 2  oe  0 −2   2 0 2 1 or SC1 for answer    4 2

23(b)

 0 12  1  0 1  oe   or  2  −2 4   −1 2 

3

1  0 1 B2 for k   oe with k ≠ 2  −2 4  1  . . or for   oe 2  . .  0 12  or for 3 or 4 correct elements in   seen  −1 2  1 0 or M1 for Y = A – 1; or for Y = A – 1   0 1 or for determinant of A = 2  4 −1  a b   4a − c 4b − d  or B1 for    =   2b   2 0  c d   2a

24(a)

2

1

24(b)

Triangle with vertices (5, –1), (8, –1), (8, 1)

2 B1 for two correct vertices, soi or M1 for a line joining (10, –4 ) to a vertex of triangle B.

24(c)

 5    −1 

1

25(a)

u 10

1

25(b)

u 2

1

25(c)

55u

2 M1 for attempt to find a relevant area under the graph, soi by 50u or 5u or 60u

© UCLES 2018

Page 7 of 7

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/21

Paper 2

May/June 2018

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

IGCSE™ is a registered trademark.

This document consists of 6 printed pages. © UCLES 2018

[Turn over

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • • •

the specific content of the mark scheme or the generic level descriptors for the question the specific skills defined in the mark scheme or in the generic level descriptors for the question the standard of response required by a candidate as exemplified by the standardisation scripts.

GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • • • • •

marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate marks are awarded when candidates clearly demonstrate what they know and can do marks are not deducted for errors marks are not deducted for omissions answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous.

GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

© UCLES 2018

Page 2 of 6

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question 1(a) 1(b)(i)

Answer

Marks

( P ∪ Q)′ or P′ ∩ Q′ A

2

3

6 12 8 10 1

C

Partial Marks

1 2 B1 for 8 or more correct

B

4 9

5 7 11

1(b)(ii)

4

1 FT their Venn diagram provided no repeated elements

1(b)(iii)

1

1 FT their Venn diagram provided no repeated elements

1(b)(iv)

A′ ∩ B ∩ C

1

1(c)(i)

22 × 33 × 5

2 M1 for at least two correct stages in factor tree or ladder method

1(c)(ii)

2 × 32 × 5

2 B1 for 90 seen or 22 × 34 × 52

109.95 or 109.96

3 B2 for 2109.9(..) or 2110

2(a)

3

 1.8  or M2 for 2000 1 +  – 2000 oe  100  3

 1.8  or M1 for 2000 1 +  oe  100  2(b)

600

3 M1 for 54 × 12 (=648) 54 or (=50) oe 1.08  100 + 8  M1 for   x = their 648 oe soi  100  or their50 × 12

3(a)

9.5 oe

2 M1 for 4p – 2p = 7 + 12 or better

© UCLES 2018

Page 3 of 6

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question 3(b)

Answer

May/June 2018

Marks

Partial Marks

Correct method to eliminate one variable

M1

x = 1, y = –3

A2 A1 for x = 1 or y = –3 After A0, SC1 for two correct values with no working or two values that satisfy one of the original equations

3(c)

m final answer nfww 2m − 1

3 B1 for m(m + 3) B1 for (2m – 1)(m + 3)

3(d)

62.5 oe

3

4(a)

1 cao 6

1

4(b)

1 oe 660

2

4(c)(i)

8 8 4 7 , , , oe correctly placed 12 11 11 11

2 B1 for two correct

4(c)(ii)

1 oe 11

1

4(c)(iii)

16 oe 33

2

5(a)(i)

6n – 5 oe

2 M1 for 6n + k oe with k ≠ 0

5(a)(ii)

256 is not exactly divisible by 6 or 247 in sequence and next one is 253 oe

1

5(b)(i)

p2 – 3 oe

1

5(b)(ii)

p2 + 2p + 4 oe

1

5(c)(i)

Correct drawing

1

5(c)(ii)

28, 40

2 B1 for one correct

5(c)(iii)

t2 + 3t oe

2 B1 for t2 + .....

6(a)(i)

Correct construction with arcs

2 B1 for correct triangle with arcs missing or arc 6 cm from A or arc 9 cm from B

© UCLES 2018

Page 4 of 6

4 × (5)3 oe soi 8 3 4 5 or B1 for oe or   oe soi or b = ka3 8 2

M2 for b =

1 1 2 × × oe 12 11 10 1 1 2 1 × × or SC1 for or answer 12 12 12 864 1 1 2 , , or 12 11 10

M1 for

M1 for

4 8 8 4 × × or oe 12 11 12 11

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

May/June 2018

Marks

Partial Marks

6(a)(ii)

77° to 81°

1 FT their angle BAC

6(b)

79875 cao

2 B1 for 225 and 355 seen

6(c)(i)

66° alternate [angles]

2 B1 for 66

6(c)(ii)

79°

1 FT 145 – their 66

6(c)(iii)

RQT RTQ

B1

QT is common oe

B1

AAS oe

B1 Dep on previous B1

 15  15 + [2 ×] 3x + [2 ×]  × 3   x 

M1

90   Leading to 15 + 6 x +  without error x  

A1

7(a)

7(b)

4 B1 for 6x2 – 50x + 90 [= 0] oe

5.70 or 2.63 and 6x2 – 50x + 90 [= 0] seen

AND

B2FT for

−(−50) ± (−50) 2 − 4 × 6 × 90 2×6

or B1FT for or

(−50) 2 − 4 × 6 × 90

−(−50) ± r 2×6

After 0, SC2 for 5.70 or 2.63 7(c)(i)

74.25

1

7(c)(ii)

Correct smooth curve

2 B1FT for at least 5 points correctly plotted

7(c)(iii)

6.5 to 6.6 2.3 to 2.4

2 FT their graph B1FT for either correct

8(a)

 0 −1   1 0 

2 B1 for a correct row or column

8(b)

Triangle with vertices at (2, –3) (4, –3) (2,–4)

1

8(c)

Reflection in y = x

2 B1 for reflection or y = x

8(d)

Rectangle with vertices at (–1, 5) (–1, 6) (2, 6) (2, 5)

2

© UCLES 2018

Page 5 of 6

 −2  k  B1 for R translated by   or   k   3

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question 9(a)

Answer

May/June 2018

Marks

9.025 to 9.03

4

Partial Marks M3 for

70 1 × π × 82 − × 82 × sin 70 360 2

or

70 × π × 82 360 1 M1 for × 82 × sin 70 2 M1 for

9(b)(i)

9(b)(ii)

8 – 8cos 35 oe

M2 M1 for 8cos 35 (= 6.55..)

1.45 or 1.446 to 1.447 so yes

A1

192

2 B1 for two of 4, 16 and 3 soi 48 × 4 x × 24 or M1 for oe 16 × x × 1.5

10(a)

11 13

2

10(b)

13.7 or 13.70…

4 B1 for 146° AND

M1 for

12 [×60] oe 15

M2 for 122 + 22 − 2 × 12 × 2 × cos146 or M1 for 122 + 22 – 2 × 12 × 2 × cos 146 Alternative B1 for 9.95 or 9.948 to 9.949 or 6.71[0...] AND M2 for their 6.712 + (their 9.94 + 2) 2 or M1 for their 6.712 + (their9.94 + 2)2 10(c)

3.0 or 3.00 to 3.01

2

11(a)

Correct region indicated

3 B1 for ruled line x = 1 B1 for ruled line x + y = 5

11(b)(i)

6.32...

2 M1 for

11(b)(ii)

y = –3x + 10 oe

4 B3 for (2, 4) and y = –3x + c

M1 for tan .. =

figs105 oe figs2

(5 − −1) 2 + (5 − 3) 2

OR B2 for y = –3x + c OR

B1 for (2, 4) or and M1 for −

© UCLES 2018

Page 6 of 6

5−3 oe 5 − (−1)

1 their 1

3

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/22

Paper 2

May/June 2018

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

IGCSE™ is a registered trademark.

This document consists of 8 printed pages. © UCLES 2018

[Turn over

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • • •

the specific content of the mark scheme or the generic level descriptors for the question the specific skills defined in the mark scheme or in the generic level descriptors for the question the standard of response required by a candidate as exemplified by the standardisation scripts.

GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • • • • •

marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate marks are awarded when candidates clearly demonstrate what they know and can do marks are not deducted for errors marks are not deducted for omissions answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous.

GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

© UCLES 2018

Page 2 of 8

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

May/June 2018

Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question

Answer

Marks

Partial Marks

1(a)

17.6[0]

2 B1 for 7 (hours) 45 (minutes) or 7.75 (hours) or M1 for 682 ÷ (5 × their 7.75) oe

1(b)

275

2

1(c)

259[.00] cao

3

1(d)

Account B, $3118.53 and 3112.37 or 1.037[…] seen

4 M1 for [3000 ×] 1.011 × 1.012 × 1.014 oe M1 for [3000 ×] 1.0133 oe A1 for 3112.37 or 3118.53 or 1.037[…] or 1.0395[…]

2(a)

Correct frequency polygon (ruled lines)

2 B1 for 4 or 5 heights correct soi

2(b)

q=9

B2 M1 for [0×p] + 1×14 + 2×15 + 3×7 + 4×q + 5×5 + 6×2 oe

p = 17 – their q

B1 Strict FT provided q integer with 0 ⩽ q ⩽ 17

(100 − 16 ) x

= 231 oe 100 or SC1 for answer 44

M1 for

850 × 0.44 − 260 oe 0.44 or M1 for 850 × 0.44 or 260 ÷ 0.44 or (their 374 – 260) ÷ 0.44

M2 for

2(c)(i)

Correct labelled pie chart: C[omedy] , D[rama] , H[orror]

3 B2 for correct sectors without labels or incorrect labels or B1 for one correct sector or 90, 54 and 72 seen

2(c)(ii)

21 7 126 , , , 0.35 or 35% 60 20 360

1

2(c)(iii)

210 oe 3540

2

x = –1.8 oe

2 M1 for 3x + 7x = 12 – 30 or –7x – 3x = 30 –12 or better

3(a)

© UCLES 2018

Page 3 of 8

15 14 × [×2] 60 59 2 1  15  or SC1 for   or answer oe 16  60 

M1 for

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 3(b)

Answer

Marks

May/June 2018

Partial Marks

Correct method to eliminate one variable

M1

x = 2.5 oe y = –6

A2 A1 for either x = 2.5 or y = –6 After A0, SC1 for a pair of values that satisfy either equation or for correct answers with no working

v final answer nfww 2v + 3

3 B1 for v(v – 8) seen B1 for (2v + 3)(v – 8) seen

4(a)(i)

Correctly completed Venn diagram

1

4(a)(ii)

36

1

4(a)(iii)

13

1 FT n(A ∪ B) from their Venn diagram provided no repeated elements in sets A and B

4(a)(iv)

1, 4, 6, 9, 12, 18

1 FT provided no repeated elements in sets A and B

4(b)

1540

2 B1 for answer 1540k, where k is an integer or for 2 × 2 × 5 × 7 and 2 × 5 × 7 × 11 seen or 2, 2, 5, 7, 11

4(c)

18

2 B1 for answer 2, 3, 6 or 9 or for 2 × 3 × 3 × 5 × 5 and 2 × 3 × 3 × 17 seen or 2, 3, 3 with 25 and 17

5(a)(i)

25.7 or 25.72 to 25.73

2

5(a)(ii)

4.3[0] or 4.298…

2

5(b)(i)

1 2 π r × 9.5 = 115 3

3(c)

or r 2 =

5(b)(ii)

108 or 107.7 to 107.8

134 × 2 × π × 11 oe 360

 134  d  180 − 134  d or sin  oe M1 for cos  = = 2  2  11   11

M1 Correct substitution into volume equation

3V or better πh

r = 3.39[9…] or 3.40[00]

M1 for

or correct rearrangement

A1 3 M2 for π × 3.4 × 9.52 + 3.4 2 or M1 for l 2 = 9.52 + 3.42 soi

© UCLES 2018

Page 4 of 8

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

May/June 2018

Partial Marks

6(a)

5.5, 5.5 oe

1 Both correct

6(b)

Correct smooth curve

3 B2FT for 8 or 9 points correctly plotted or B1FT for 6 or 7 points correctly plotted

6(c)

tangent drawn at x = 1.5

B1 Dependent on a curve drawn between x = 1 and x =2

–1.7 to –1.3

B1

x ⩽ 0.6 to 0.9 x ⩾ 5.1 to 5.4

2 B1 for one correct or SC1 for answers reversed

6(e)(i)

Ruled line passing through (0, 3) and (4, 0) crossing curve twice

2 B1 for short or unruled line or for two correct points plotted

6(e)(ii)

A = –9, B = –4

2 B1 for either correct or 2x2 –9x – 4 [=0]  x2  12 − 3x oe or M1 for  − 3x + 2  = 4  2 

6(d)

After 0, SC1 for A = –9.2 to –8.8 and B = –4.2 to – 3.8 7(a)

sin CAB =

3.7sin 42 2.8

M2

M1 for

3.7 2.8 = oe sin CAB sin 42

OR  3.7 sin 42  Cl AB = sin −1    2.8 

OR sin CAB sin 42 and = 3.7 2.8 sin=0.88[42...]

C lAB = 62.15[4…] 7(b)

[0]17.2°

A1 2 M1 for 135 + 62.2 – 180 oe

© UCLES 2018

Page 5 of 8

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 7(c)

Answer 10.5 to 10.6

Marks

May/June 2018

Partial Marks

4 B3 for 4.05 to 4.06 OR M2 for 2.82 + 3.7 2 − 2 × 2.8 × 3.7 × cos(180 − 42 − 62.2) oe or M1 for 2.82 + 3.7 2 − 2 × 2.8 × 3.7 × cos(180 − 42 − 62.2) oe OR

2.8sin(180 − 42 − 62.2) oe sin 42 sin(180 − 42 − 62.2) sin 42 = oe or M1 for AB 2.8

M2 for

OR

3.7sin(180 − 42 − 62.2) oe sin 62.2 sin(180 − 42 − 62.2) sin 62.2 or M1 for oe = AB 3.7 M2 for

OR

l = 75.8 B1 for ACB ∠BAX = ∠OCX, alternate [angles] ∠ABX = ∠COX, alternate [angles] ∠AXB = ∠CXO, [vertically] opposite

3 B1 for two correct pairs of angles B1 for correct reason for one pair of angles

8(b)(i)

4c

1

8(b)(ii)

9a – 6c or 3(3a – 2c)

2 B1 for answer 9a + kc or ka – 6c (k ≠ 0)

8(c)(i)

3:2

2 B1 for 3k : 2k, where k is an integer

8(c)(ii)

9:4

1 FT their 32 : their 22

8(c)(iii)

4:5

1

9(a)(i)

12 × 60 oe x

1

9(a)(ii)

8 × 60 oe x − 1.5

1

8(a)

After 0 in (i) and (ii), SC1 for

12 x

© UCLES 2018

Page 6 of 8

8 and (a)(i) x − 1.5

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 9(a)(iii)

Answer

Marks

M1 FT their (a)(i) and (a)(ii) if functions of x

720 ( x − 1.5 ) + 480 x

M1

= 110 or

720(x – 1.5) + 480x = 110x(x – 1.5)

A1 Correct elimination of correct brackets

With a minimum of one intermediate step establishes 22x2 – 273x + 216 = 0

A1

−(−273) ±

( −273)2 − 4 × 22 × 216

B2

or

10(b)

© UCLES 2018

1 hour 59 minutes cao

(–1,

1 ) or (–1, 0.5) cao 2

1 oe 2

( −273)

2

− 4 × 22 × 216

−( −273) ± their 55521 2 × 22 2 273   or for  x −  44  

273  273   216  ±   −  44  44   22 

11.56 and 0.85 cao

B1 for or for

2

10(a)

c d + = e where p, px qx + r q, r, c, d and e are numeric and non zero, AND either correctly uses a common denominator for their fractions or correctly removes their fractions

Dep on equation of form

720x – 1080 + 480x = 110x2 – 165x

2 × 22

9(b)

Partial Marks

720 480 + = 110 oe x x − 1.5

x ( x − 1.5 )

9(a)(iv)

May/June 2018

B1 3

1

1

Page 7 of 8

20 [×60] oe their11.56 − 1.5 or M1 for their11.56 – 1.5 20 or for their x

M2 for

4024/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 10(c)

Answer [Gradient of BC =]

−8 4

1 −8 × = −1 hence perpendicular 2 4

Marks

May/June 2018

Partial Marks

M1 Alternative 1: M1 for 1 1 × mBC = −1 or mBC = − oe leading to A1 2 0.5 mBC = –2 −8 = –2 hence A1 for gradient of BC = 4 perpendicular Alternative 2: JJJG  10  JJJG  6  M1 for AB =   oe and AC =   oe  3  −5  2 2 2 2 2 A1 for (4 +8 ) + (6 +3 ) = (10 +52) hence perpendicular

10(d)

10(e)

(0, –9)

31.3 or 31.30…

2 B1 for one value correct  −4   4  or M1 for   +   oe or  −1   −8 

 6   −6    +   oe  −6   − 3 

(

) oe

4

M3 for [2×]

32 + 62 + 42 + (−8) 2

or M2 for 42 + ( −8) 2 oe or 32 + 6 2 oe or M1 for 42 + (–8)2 oe or 32 + 62 oe

© UCLES 2018

Page 8 of 8

Cambridge International Examinations Cambridge Ordinary Level

* 9 3 3 7 4 7 0 1 8 2 *

MATHEMATICS (SYLLABUS D)

4024/11 May/June 2018

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 18 printed pages and 2 blank pages. DC (SC/SW) 152343/3 © UCLES 2018

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Evaluate

3.5 - 1.9 . 0.8

Answer .......................................... [1] (b) Evaluate 9 + 6 ' 3 - 4 .

Answer .......................................... [1] 2

(a) Work out 15% of 80.

Answer .......................................... [1] (b) Work out

3 2 - . 5 7

Give your answer as a fraction in its simplest form.

Answer .......................................... [1] 3

Write these numbers in order of size, starting with the smallest. 1 3

0.32

15 40

0.3

9 31

Answer .............. , .............. , .............. , .............. , .............. [2] smallest

© UCLES 2018

4024/11/M/J/18

3

4

(a) The diagram shows part of a shape which is symmetrical about the line L. Complete the shape. L

[1] (b) The diagram shows part of a shape which has rotational symmetry of order 2 about the point O. Complete the shape.

O

[1]

© UCLES 2018

4024/11/M/J/18

[Turn over

4

5

A plane leaves London on a flight to Dubai. (a) The plane lands in Dubai where the local time is 17 20. The flight time is 6 hours 50 minutes. The local time in Dubai is 3 hours ahead of the local time in London. Calculate the local time in London when the flight left.

Answer .......................................... [2] (b) At one time during the flight the temperature inside the plane is 17 °C. The temperature outside the plane is − 43 °C. Work out the difference between the inside and outside temperatures.

Answer ..................................... °C [1] (c) The plane leaves London where the temperature outside is 17 °C. The plane rises to a height where the temperature outside is − 43 °C. The temperature decreases by 2 °C with every increase of 300 m in height. Calculate the increase in height of the plane.

Answer ...................................... m [1]

© UCLES 2018

4024/11/M/J/18

5

6

(a) What fraction of this 4 × 4 square is shaded?

Answer .......................................... [1] (b) A youth club has 150 members. 60 of the members are girls. What percentage of the club members are girls?

Answer ...................................... % [1] (c) Ben is given some money. He spends some of it and saves the remainder. The ratio of the money he spends to the money he saves is 3 : 1. He spends $15. Calculate the amount of money Ben was given.

Answer $ ........................................ [1]

© UCLES 2018

4024/11/M/J/18

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6

7

Usama recorded the number of items bought by each of 20 customers at a shop. The results are shown in the table. Number of items bought

1

2

3

4

5

6

Number of customers

3

0

5

3

7

2

(a) Write down the mode. Answer .......................................... [1] (b) Find the median number of items bought.

Answer .......................................... [1] (c) Calculate the mean number of items bought.

Answer .......................................... [2] (d) Usama draws a pie chart to show the data. Calculate the angle of the sector on the pie chart which represents the number of people who bought 3 items.

Answer .......................................... [1]

© UCLES 2018

4024/11/M/J/18

7

8 C A

O

38°

B

T

A, B and C are points on the circumference of a circle centre O. t = 38°. O is the midpoint of BC and ABC Tangents are drawn from T to touch the circle at A and B. t . (a) Calculate BCA

t = ............................. [1] Answer BCA t . (b) Calculate ATB

t = .............................. [2] Answer ATB 9

Find the integers that satisfy 1 1 3x + 5 G 11.

Answer .......................................... [2]

© UCLES 2018

4024/11/M/J/18

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8

10 The scale diagram below shows a barn ABCD. AB = 7 m and BC = 4 m. On the diagram 1 cm represents 1 m. A horizontal rail is attached to the outside wall of the barn from A to B. Jasper is a dog attached to a rope 3 m long. The other end of the rope is attached to the rail and can slide along it. On the diagram, shade the region where Jasper can go.

D

A

C

Barn

4

7

B

Scale: 1 cm to 1 m.

© UCLES 2018

[3]

4024/11/M/J/18

9

J 2 aNJ- 4 bN J 7 KK OOKK OO = KK 3 1 3 2 L PL P L15

11 Find a and b.

10NO O 2P

Answer a = .......................................... b = .................................... [2] 12 Basia records the colour of 100 cars passing the school gate. Her results are recorded in the table. Colour of car Frequency

Black

Grey

Red

Blue

Other

43

18

12

9

18

(a) Use Basia’s results to estimate the probability that the next car seen is a blue car. Answer .......................................... [1] (b) In the next hour, 500 cars pass the school gate. Use Basia’s results to estimate the number of these cars that are red.

Answer .......................................... [1] (c) Colin records the colour of the next 100 cars passing the school gate. His results are shown in the table below. Colour of car Frequency

Black

Grey

Red

Blue

Other

34

10

18

28

10

Use Basia’s and Colin’s combined results to estimate the number of red cars that would be seen when 500 cars pass the school gate. Answer .......................................... [1] (d) Which of the estimates in part (b) or in part (c) is likely to be the best? Give a reason for your decision. The best estimate is ............... because ................................................................................................... ............................................................................................................................................................. [1]

© UCLES 2018

4024/11/M/J/18

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10

13 The table below shows the masses of 10 mothers and their babies at birth. Mass of mother (kg)

64

90

54

102

57

105

70

89

57

75

Mass of baby (kg)

4.1

4.5

3.6

4.5

3.9

5.5

3.9

4.3

3.2

4.4

6

5

Mass of baby (kg)

4

3

2

1

0

50

60

70 80 Mass of mother (kg)

90

(a) On the grid, complete the scatter diagram. The first six points have been plotted for you.

100

110

[1]

(b) What type of correlation is shown on the scatter diagram? Answer ........................................... [1] (c) On the scatter diagram, draw a line of best fit.

[1]

(d) Anna has a mass of 82 kg and gives birth to a baby. Use your line of best fit to estimate the mass of her baby. Answer ...................................... kg [1]

© UCLES 2018

4024/11/M/J/18

11

14 Factorise completely (a) 2ax - 3by + 6bx - ay ,

Answer .......................................... [2] (b) 27x 2 - 3y 2 .

Answer .......................................... [2] 15 (a) Find f ^5h.

f ^xh = 3 - 2x

g ^xh = 4x 3 - 1

Answer .......................................... [1] (b) Find g ^- 2h.

Answer .......................................... [1] (c) Find and simplify f ^4x 3 - 1h.

Answer .......................................... [1]

© UCLES 2018

4024/11/M/J/18

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12

16 (a) Evaluate 3 3 - 3 0 .

Answer .......................................... [1] 1

(b) Simplify completely

J 9a 3 b 3 N2 KK O 5O . 16 ba L P

Answer .......................................... [2] 17 B

6 E

A 7

C

D

The diagram shows a square ABCD joined to a right-angled triangle BEC. BE = 6 cm and EC = 7 cm. Calculate the area of the pentagon, ABECD.

Answer ................................... cm2 [3]

© UCLES 2018

4024/11/M/J/18

13

18 25

20 B

C

15 Speed (m/s) 10

5

0

A 0

D 20

40 60 Time (seconds)

80

100

The speed-time graph shows the motion of a car. (a) Describe fully the motion of the car represented by each of the lines AB, BC and CD on the graph. AB has been done for you. AB

Accelerates for the first 20 s at 0.9 m/s2.

BC ............................................................................................................................................................. CD ...................................................................................................................................................... [3]

(b) Find the total distance travelled by the car during this motion.

Answer ...................................... m [2]

© UCLES 2018

4024/11/M/J/18

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14

19 (a) One day in 2016 the population of Nepal was 28 795 701. Write this number correct to three significant figures.

Answer .......................................... [1] (b) The table below shows the approximate population of some countries in 2016 and their land areas. Country

Population

Land area in km2

Brazil

2.1 # 10 8

8.5 # 10 6

Greenland

5.6 # 10 4

2.2 # 10 6

Hong Kong

7.4 # 10 6

1.1 # 10 3

India Nigeria

3.3 # 10 6 9.2 # 10 5

1.9 # 10 8

(i) The population of India was approximately 130 000 000. In the table above complete the row for India. Write the number in standard form.

[1]

(ii) Calculate the total land area of India and Nigeria. Give your answer in standard form.

Answer ................................... km2 [2] (iii) Which country in the table has the smallest population per km2 ?

Answer .......................................... [1]

© UCLES 2018

4024/11/M/J/18

15

20 40

20 h

A paving slab is a cuboid with length 40 cm, width 20 cm and depth h cm. Its volume is 2400 cm3. (a) Find the value of h.

Answer h = .................................... [1] (b) Calculate the volume of concrete needed to make 1000 of these slabs. Give your answer in m3.

Answer ..................................... m3 [1] (c) A mathematically similar slab has length 60 cm. Calculate the volume of concrete, in cm3, needed to make one of these larger slabs.

Answer ................................... cm3 [2]

© UCLES 2018

4024/11/M/J/18

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16

21

J3N p = KK OO L4 P

J- 4N q = KK OO L 3P

(a) Write 3p - q as a column vector. Answer

f

p

[1]

(b) R is the point (11, −2) and O is the point (0, 0). The vector OR can be written in the form p + nq , where n is an integer. Find the value of n.

Answer n = .................................... [2] 22

s=

3

t+4

(a) Find s when t = 121. Answer s = .................................... [1] (b) Rearrange the formula to make t the subject.

Answer t = .................................... [2]

© UCLES 2018

4024/11/M/J/18

17

23 y

O

y

x

Figure A

Figure D

x

Figure B

y

O

O

y

O

Figure E

x

Figure C

y

x

O

y

x

O

x

Figure F

State which of the figures above could be the graph of (a) y = x 3 + 2 ,

Answer .......................................... [1]

2 (b) y = , x (c)

Answer .......................................... [1]

y = 2 - x2 .

© UCLES 2018

Answer .......................................... [1]

4024/11/M/J/18

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18

24 (a) Show that

12 10 7 + = can be simplified to give the equation 7x 2 - 37x - 30 = 0 . x+2 x-1 2

[3]

(b) Solve, by factorisation, 7x 2 - 37x - 30 = 0 .

Answer

© UCLES 2018

4024/11/M/J/18

x = .................... or x = .................... [3]

19

BLANK PAGE

© UCLES 2018

4024/11/M/J/18

20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2018

4024/11/M/J/18

Cambridge International Examinations Cambridge Ordinary Level

* 5 9 7 0 8 2 5 9 2 4 *

MATHEMATICS (SYLLABUS D)

4024/12 May/June 2018

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NH/CGW) 172437/5 R © UCLES 2018

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Evaluate

4 2 - . 11 7

Answer ........................................... [1] (b) Evaluate 0.9 # 0.011 .

Answer ........................................... [1] 2

(a) Cecil bought a camera for $120. After two years he sold it for $90. Calculate the percentage loss.

Answer ....................................... % [1] (b) Some money is shared between Miriam and Nina in the ratio 2 : 3. What percentage of the total money shared does Miriam receive?

Answer ....................................... % [1] (c) Given that a : b = 5 : 6 and b : c = 3 : 8 find a : b : c.

Answer ............. : ............. : ............. [1]

© UCLES 2018

4024/12/M/J/18

3

3

0.05

–0.3

1.3

–1.2

0.2

(a) Arrange the five numbers in order, starting with the smallest. Answer ............... , ............... , ............... , ............... , ............... [1] smallest (b) For the five numbers, find (i) the mean,

Answer ........................................... [1] (ii) the range. Answer ........................................... [1] 4

y is inversely proportional to the square of x. Given that y = 10 when x = 3, find y when x =

1 . 2

Answer y = ..................................... [2]

© UCLES 2018

4024/12/M/J/18

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4

5

(a) Factorise 25t2 - 4.

Answer ........................................... [1] (b) Factorise x2 - 6x - 3xy + 18y.

Answer ........................................... [2] 6

A rectangle has length 64 mm and width 37 mm each correct to the nearest millimetre. (a) Write down the lower bound for the length. Answer .................................... mm [1] (b) Calculate the lower bound for the perimeter of the rectangle.

Answer .................................... mm [1]

© UCLES 2018

4024/12/M/J/18

5

7

(a) Triangle OPQ is part of a figure that has rotational symmetry of order 2 about the point O. Complete the figure. Q

P O

[1] (b) The diagram shows a circle, its centre, and two chords. Add one chord, to give a diagram that has one line of symmetry.

[1]

© UCLES 2018

4024/12/M/J/18

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6

8

Solve

4 1 = . x - 11 3x

Answer x = ..................................... [2]

© UCLES 2018

4024/12/M/J/18

7

9

Express each of the following as a single fraction in its simplest form. (a)

2 5 + 3a 2a

Answer ........................................... [1] (b)

5 15 2' 2b 4b 3

Answer ........................................... [2] 10 By writing each number correct to 2 significant figures, calculate an estimate of 596 # 16.12 . 0.2984

Answer ........................................... [2]

© UCLES 2018

4024/12/M/J/18

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8

11

f(x) =

1 3x + 2

(a) Find f(–2).

Answer ........................................... [1] (b) Find f –1(x).

Answer f –1(x) = ............................. [2] 12 A dice is thrown 400 times. The results are shown in the table. Number thrown

1

2

3

4

5

6

Frequency

65

80

70

75

50

60

(a) Find the relative frequency of throwing the number 2.

Answer ........................................... [1] (b) Imran throws the dice 1000 times. How many times would you expect the number 2 to be thrown?

Answer

© UCLES 2018

4024/12/M/J/18

.......................................... [1]

9

13 In a school of 270 children, the distance each child can swim was recorded. The distances are summarised in the table. Distance (d metres)

0 G d 1 100

100 G d 1 200

200 G d 1 500

500 G d 1 1000

Number of children

110

50

60

50

Frequency density (a) Complete the table to show the frequency densities.

[2]

(b) Calculate an estimate for the number of children who could swim more than 400 metres.

Answer ........................................... [1] 14 An irregular polygon has 22 sides. (a) Calculate the sum of all its interior angles.

Answer ........................................... [2] (b) Two of the angles in the polygon are each 170°. The remaining 20 angles are equal to each other. Calculate the size of one of the 20 equal angles.

Answer ........................................... [2]

© UCLES 2018

4024/12/M/J/18

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10

15 During two weeks, a shopkeeper records the number of packets of two different types of tea he sells and the profit he makes from them. Week 1 • Type A tea, 30 packets sold, profit of $1.20 on each packet • Type B tea, 20 packets sold, profit of $2 on each packet Week 2 • Type A tea, 40 packets sold, loss of $0.50 on each packet • Type B tea, 30 packets sold, profit of $3 on each packet This information can be represented by these matrices. ^30 20h

^40 30h

1.2 e o 2

- 0.5 e o 3

- 0.5 1.2 o. (a) Work out ^30 20h e o - ^40 30h e 2 3

Answer

[2]

(b) Explain the meaning of your answer to part (a). ................................................................................................................................................................... .............................................................................................................................................................. [1]

© UCLES 2018

4024/12/M/J/18

11

16 The masses of 200 beetles were measured. The results are summarised in the cumulative frequency table and part of the cumulative frequency curve is drawn. Mass (m grams)

m G 0.5

mG1

m G 1.5

mG2

m G 2.25

m G 2.5

mG 3

Cumulative frequency

0

25

75

150

170

185

200

200

150

Cumulative frequency

100

50

0

0

0.5

1

1.5

2

2.5

3

Mass (m grams)

(a) Complete the cumulative frequency curve.

[1]

(b) Use the curve to find an estimate for (i) the median, Answer ........................................ g [1] (ii) the lower quartile, Answer ........................................ g [1] (iii) the number of beetles that have a mass greater than 1.85 grams.

Answer ........................................... [2] © UCLES 2018

4024/12/M/J/18

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12

17 The diagram shows a pyramid. The square base, ABCD, has an edge of 3 cm. The base is horizontal, and vertex E is vertically above D, where ED = 4 cm.

E 4 D

C 3

A

3

B

(a) On the grid below, complete the accurate drawing of a net of the pyramid. Do not draw outside the grid.

[2] (b) Calculate the total surface area of the pyramid.

Answer ....................................cm2 [2] © UCLES 2018

4024/12/M/J/18

13

18 y 12 10 8 6 4 2 0

2

4

6

8

10

12 x

The region R is defined by the inequalities 2 G x G 8 5 G y G 10 x + y H 10. On the diagram, shade and label the region R.

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[3]

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19

C

A

B

(a) On the diagram, construct the perpendicular bisector of AB.

[1]

(b) On the diagram, construct the locus of points inside triangle ABC, that are (i) 7 cm from C,

[1]

(ii) equidistant from AB and AC.

[1]

(c) P is any point which is equidistant from A and B and more than 7 cm from C and nearer to AC than AB. Find the extremes of the possible positions of P and label them P1 and P2 .

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[1]

15

N = 2 # 108

20

(a) Giving your answers in standard form, find the value of (i) N # 700,

Answer ........................................... [1] (ii)

1 . N

Answer ........................................... [2] (b) Find the smallest positive integer M, given that MN is a cube number.

Answer M = ................................... [1]

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21 The first four terms, u1, u2, u3 and u4, in a sequence of numbers are given below. u1

=

1 # 3 + 22

=

7

u2

=

2 # 4 + 32

=

17

u3

=

3 # 5 + 42

=

31

u4

=

4 # 6 + 52

=

49

(a) Evaluate u5 .

Answer ........................................... [1] (b) The nth term of the sequence, un , is of the form n(n + p) + (n + q)2 . Write down the value of p and the value of q.

Answer p = ..................................... q = ..................................... [1] (c) un can also be written in the form An2 + Bn + C . Find the values of A, B and C.

Answer A = .................................... B = .................................... C = .................................... [2]

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22

A 53° 62°

O x° t°

D y° C

T

z° B

The diagram shows a circle, centre O, that passes through A, B, C and D. The tangents at A and B meet at T. t = 53° . t = 62° and DAB ATB (a) Find x.

Answer x = ..................................... [1] (b) Find y.

Answer y = ..................................... [1] (c) Find z.

Answer z = ..................................... [1] (d) Find t.

Answer t = .................................... [1]

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18

A =e

23

4 -1 o 2 0

B=e

6 -3 o 0 -2

(a) Find the matrix X, such that 2A + X = B .

Answer

f

p

[2]

1 0 o. (b) Find the matrix Y, such that AY = e 0 1

Answer

© UCLES 2018

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[3]

19

24 y 6 5 4

B

3 2 1 0

A 1

2

3

4

5

6

7

8

9

10

11

x

–1 –2 –3 –4 –5

Triangle A is mapped onto triangle B by a translation, followed by an enlargement with centre (10, – 4). The translation maps triangle A onto triangle C. The enlargement maps triangle C onto triangle B. (a) Write down the scale factor of the enlargement. Answer .......................................... [1] (b) Draw triangle C on the grid.

[2]

(c) Find the column vector that represents the translation that maps triangle A onto triangle C. Answer

f

p

[1]

Question 25 is printed on the next page

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20

25 The diagram is the speed–time graph for 60 seconds of a train’s journey. At the beginning of this part of the journey the train is travelling at u m/s.

Speed (m/s)

u

0

0

50

60

Time (t seconds)

Giving each answer in its simplest form, find expressions in terms of u, for (a) the deceleration for the last 10 seconds,

Answer ................................... m/s2 [1] (b) the speed when t = 55,

Answer .................................... m/s [1] (c) the distance travelled during these 60 seconds.

Answer ....................................... m [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2018

4024/12/M/J/18

Cambridge International Examinations Cambridge Ordinary Level

* 9 7 8 4 1 2 2 5 8 2 *

4024/21

MATHEMATICS (SYLLABUS D)

May/June 2018

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Essential working must be shown for full marks to be awarded. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100.

This document consists of 20 printed pages. DC (SC/SW) 152341/6 © UCLES 2018

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2

1

(a) Use set notation to describe the shaded region in the Venn diagram.

P

Q

Answer .......................................... [1] (b)

 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {x : x is a factor of 12} B = {x : x is a multiple of 2} C = {x : x is a square number} (i) Show this information on the Venn diagram below.

A

B

C

[2] (ii) Find n ^A + Bh. Answer .......................................... [1] (iii) Find n ^A + ^B , Chlh. Answer .......................................... [1] (iv) One subset in the Venn diagram in part (b)(i) has no elements. Use set notation to describe this subset. Answer .......................................... [1]

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(c) (i) Write 540 as the product of its prime factors.

Answer .......................................... [2] (ii) p is the smallest possible integer such that 540p is a square number. Find

540p , giving your answer as the product of its prime factors.

Answer .......................................... [2] 2

(a) Sami invests $2000 in an account paying compound interest at a rate of 1.8% per year. Calculate the total interest paid to Sami after 3 years.

Answer $ ....................................... [3] (b) Theresa takes out a loan. She repays the loan over one year at a rate of $54 per month. The total she repays is 8% greater than the value of the original loan. Work out the value of the original loan.

Answer $ ....................................... [3]

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4

3

(a) Solve 4 ^ p - 3h = 2p + 7 .

Answer p = .................................... [2] (b) Solve these simultaneous equations. 2x - y = 5 7x + 2y = 1 Show your working.

Answer x = .......................................... y = .................................... [3]

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(c) Simplify

m 2 + 3m . 2m 2 + 5m - 3

Answer .......................................... [3] (d) b is directly proportional to the cube of a. Given that b = 4 when a = 2 , find b when a = 5.

Answer b = .................................... [3]

© UCLES 2018

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4 T

R

I

G

O

N

O

M

E

T

R

Y

Twelve lettered tiles spelling the word TRIGONOMETRY are placed inside a bag. (a) A tile is taken at random from the bag. Find the probability that the tile shows a letter R. Give your answer as a fraction in its simplest form.

Answer .......................................... [1] (b) All the tiles are placed back in the bag, a tile is then taken at random and placed on the table. A second tile is taken at random and placed to the right of the first tile. A third tile is taken at random and placed to the right of the second tile. 1st

2nd

3rd

Find the probability that, in the order the tiles were placed on the table, they spell GET.

Answer .......................................... [2]

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7

(c) Vowels are the letters A, E, I, O and U. All other letters are consonants. All the twelve tiles are placed back in the bag and two tiles are taken at random, without replacement. (i) Complete the tree diagram. First tile

Second tile 3 11

4 12

vowel

......... ......... .........

vowel

consonant vowel

consonant

.........

consonant

[2] (ii) Find the probability that the tiles both show vowels.

Answer .......................................... [1] (iii) Find the probability that one tile shows a vowel and one tile shows a consonant.

Answer .......................................... [2]

© UCLES 2018

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5

(a)

1, 7, 13, 19, 25, … (i) Find an expression, in terms of n, for the nth term of this sequence.

Answer .......................................... [2] (ii) Explain why 251 is not a term in this sequence.

Answer ....................................................................................................................................... .............................................................................................................................................. [1] (b) Here is another sequence. 5, 8, 13, 20, 29, … The pth term of this sequence is p 2 + 4 . Write down an expression, in terms of p, for the pth term of these sequences. (i) –2, 1, 6, 13, 22, …

Answer .......................................... [1] (ii) 7, 12, 19, 28, 39, …

Answer .......................................... [1]

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9

(c) The diagrams below show the first three patterns in a sequence. The patterns are made from short diagonal lines.

Pattern 1

Pattern 2

Pattern 3

(i) Draw Pattern 4 on the dotty grid below.

[1] (ii) Complete the table below for the number of short lines in Patterns 4 and 5. Pattern

1

2

3

4

Number of short lines

4

10

18

5

[2] (iii) Find an expression, in terms of t, for the number of short lines in Pattern t.

Answer .......................................... [2]

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10

6

(a) ABC is a triangle with AC = 6 cm and BC = 9 cm. AB has been drawn below. A

B

(i) Using a ruler and a pair of compasses only, construct triangle ABC.

[2]

t . (ii) Measure BAC Answer .......................................... [1] (b) A rectangular field has dimensions 220 m by 350 m, each correct to the nearest 10 metres. Calculate the upper bound for the area of the field.

Answer ..................................... m2 [2]

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(c)

P

Q

66°

79°

35°

S

R

T

The points P, Q, R and S lie on the circumference of a circle. PQRS is a trapezium with PQ parallel to SR. t = 79°. t = 66°, QTR t = 35° and TQR T is the point on SR such that QPT t , giving a reason for your answer. (i) Find PTS t = ............ because ............................................................................................ Answer PTS .............................................................................................................................................. [2] t . (ii) Find PTQ Answer .......................................... [1] (iii) Complete the statements below to show that triangle PQT is congruent to triangle RTQ. 1.

Angle PTQ = Angle ..............................

2.

Angle PQT = Angle ..............................

3.

................................................................

Triangle PQT is congruent to triangle RTQ. Congruency condition ...................................

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[3]

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7 3

x

The diagram shows the net of an open box of height 3 cm. The area of the base of the box is 15 cm2. The length of the rectangular base is x cm. The total area of the net is A cm2. (a) Show that A = 15 + 6x +

90 . x

[2] (b) Graham has one of these open boxes. The total area of the net of his box is 65 cm2. Write down an equation in x and solve it to find the length of the base of Graham’s box. Give your answer correct to 2 decimal places.

© UCLES 2018

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Answer .................................... cm [4]

13

(c) (i) Complete the table below for A = 15 + 6x +

90 . x

x

2

3

4

5

6

7

A

72

63

61.5

63

66

69.9

8

[1] (ii) Draw the graph of A = 15 + 6x +

90 for 2 G x G 8 . x

A 80 78 76 74 72 70 68 66 64 62 60

2

3

4

5

6

7

8 x

[2] (iii) Delilah has one of these open boxes. The area of the net of her box is 68 cm2. Use your graph to find the length and width of Delilah’s box.

Answer length ......................... cm width ......................... cm [2]

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8

The grid shows triangles A and B and rectangle R. y 6 5 4 3

A

R

2 1 –6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6 x

–1 –2 B

–3 –4 –5 –6

(a) Triangle A is mapped onto triangle B by the single transformation K. Find the matrix representing transformation K.

Answer

f

p

[2]

(b) Triangle B is mapped onto triangle C by a reflection in the y-axis. On the diagram, draw triangle C.

© UCLES 2018

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15

(c) Triangle A is mapped onto triangle C by the single transformation L. Describe fully the single transformation L. Answer ......................................................................................................................................... [2] J- 2N (d) Rectangle R is mapped onto rectangle S by a translation by the vector KK OO . L 3P On the diagram, draw rectangle S. [2]

© UCLES 2018

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9

8 70°

The diagram shows a sector of a circle of radius 8 cm and angle 70°. (a) Calculate the shaded area.

Answer ................................... cm2 [4]

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17

(b)

16 x

A piece of chocolate is in the shape of a prism with the shaded area from part (a) being its cross section. The rectangular base of the chocolate is 16 cm by x cm. The piece of chocolate is to be placed in a box which is a cuboid of size 16 cm by x cm by 1.5 cm. (i) Show that the chocolate will fit inside the box.

[3] (ii) These boxes are to be packed in cartons in the shape of a cuboid. The size of each carton is 48 cm by 4x cm by 24 cm. Find the maximum number of boxes that can be packed inside one carton.

Answer .......................................... [2]

© UCLES 2018

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18

10 A boat leaves A and travels 12 km to B. (a) The boat leaves A at 10 25 and travels at an average speed of 15 km/h. At what time does the boat arrive at B?

Answer .......................................... [2] (b) B

North

2

C

12

56° A

The bearing of B from A is 056°. B is 2 km due west of C. Calculate AC.

Answer .................................... km [4]

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(c) D cliff B

2 km

C

C is the base of a cliff. The top of the cliff, D, is vertically above C. DC is perpendicular to BC and DC = 105 m. Calculate the angle of elevation of D from B.

Answer .......................................... [2]

© UCLES 2018

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20

11

(a) y 6 5 4 3 2 1 0

1

2

3

4

5

6

x

The grid shows the line 4y = x + 2 . By drawing appropriate lines, indicate the region R defined by all these inequalities. xH1

x+y G 5

4y H x + 2

[3]

(b) A is the point (–1, 3) and B is the point (5, 5). (i) Calculate the length AB.

Answer .......................................... [2] (ii) Find the equation of the line perpendicular to AB that passes through the midpoint of AB.

Answer .......................................... [4] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2018

4024/21/M/J/18

Cambridge International Examinations Cambridge Ordinary Level

* 5 7 9 8 8 0 2 1 3 2 *

4024/22

MATHEMATICS (SYLLABUS D)

May/June 2018

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Essential working must be shown for full marks to be awarded. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100.

This document consists of 19 printed pages and 1 blank page. DC (NH/CGW) 172436/4 R © UCLES 2018

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2

1

(a) Each week Leah works 5 days and is paid a total of $682. Each day she works from 08 45 until 12 15 and then from 13 15 until 17 30. Calculate Leah’s hourly rate of pay.

Answer $ ......................................... [2] (b) Carlos buys a new bicycle. After one year he sells it for $231. He makes a loss of 16% on the price he paid. Calculate the price Carlos paid for the bicycle.

Answer $ ......................................... [2] (c) The exchange rate between dollars ($) and euros (€) is $1 = €0.44 . Henry changes $850 to euros for his holiday. He spends €260 when he is on holiday. He changes the rest of the money back to dollars at the same exchange rate. Calculate how much money in dollars he receives. Give your answer correct to the nearest dollar.

Answer $ ......................................... [3]

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(d) Anya has $3000 to invest in a savings account for 3 years. She can choose from these two accounts. Account A

Year 1 Year 2 Year 3

1.1% interest 1.2% interest added to end of Year 1 total 1.4% interest added to end of Year 2 total

Account B

Fixed rate of compound interest 1.3% per year

She chooses the account that will give her more money at the end of the 3 years. Decide which account she chooses and find the amount she will have in her account at the end of 3 years.

Answer Account ............................. $ ......................................... [4]

© UCLES 2018

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4 2

(a) Jenny recorded the time, in minutes, of 40 movies. The table summarises her results.

Time (t minutes)

60 1 t G 80

80 1 t G 100

100 1 t G 120

120 1 t G 140

140 1 t G 160

2

7

15

11

5

Frequency

On the grid, draw a frequency polygon to represent this information. 16 14 12 10 Frequency

8 6 4 2 0 60

70

80

90

100

110

120

130

140

150

160

Time (t minutes)

[2] (b) Jenny asked 60 people how many movies they had each watched in the last month. The table summarises her results. Number of movies

0

1

2

3

4

5

6

Frequency

p

14

15

7

q

5

2

The mean number of movies watched is 2.3 . Find the value of p and the value of q.

Answer p = ..................................... q = ..................................... [3]

© UCLES 2018

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(c) Jenny also asked which type of movie each of the 60 people preferred. The table summarises her results. Type of movie Frequency

Action

Comedy

Drama

Horror

24

15

9

12

(i) Complete the pie chart to represent the results.

Action

[3] (ii) One of the 60 people is chosen at random. Find the probability that this person preferred drama or horror movies.

Answer ........................................... [1] (iii) Two of the 60 people are chosen at random. Calculate the probability that they both preferred comedy movies.

Answer ........................................... [2]

© UCLES 2018

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6

3

(a) Solve 3(x + 10) = 12 - 7x .

Answer x = ..................................... [2] (b) Solve the simultaneous equations. Show your working. 4x - 3y = 28 6x + y = 9

Answer x = ..................................... y = ..................................... [3] (c) Simplify

2

v - 8v . 2v 2 - 13v - 24

Answer ........................................... [3] © UCLES 2018

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4

(a)  ={x : x is an integer 1 G x G 18} A = {x : x is a prime number} B = {1, 2, 3, 4, 6, 9, 12, 18}  A

2

1 3

6

4 18

12

9

B

(i) Complete the Venn diagram to illustrate this information.

[1]

(ii) Complete the description of the set B. Answer B = { x : x is a factor of ............ } [1] (iii) Find n(A , B) . Answer ........................................... [1] (iv) List the elements of Al + B . Answer

............................................................................... [1]

(b) Find the lowest common multiple (LCM) of 140 and 770.

Answer ........................................... [2] (c) A rectangular field measures 450 m by 306 m. The whole field is divided into identical square plots with no land remaining. Find the largest possible side length for the squares.

Answer ....................................... m [2] © UCLES 2018

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8

5

(a) O 134°

11

A

B

OAB is a sector of a circle, centre O, radius 11 cm. t = 134° . AOB (i) Calculate the length of the arc AB.

Answer ..................................... cm [2] (ii) Calculate the shortest distance from O to the line AB.

Answer ..................................... cm [2]

© UCLES 2018

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9

(b) [Volume of a cone =

1 2 rr h] 3

[Curved surface area of a cone = rrl]

9.5

A cone has height 9.5 cm and volume 115 cm3. (i) Show that the radius of the base of the cone is 3.4 cm, correct to 1 decimal place.

[2] (ii) Calculate the curved surface area of the cone.

Answer ....................................cm2 [3]

© UCLES 2018

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10

6

(a) Complete the table for y = x

-1

y

x2 - 3x + 2 . 2

0

1

2

3

4

5

6

2

–0.5

–2

–2.5

–2

–0.5

2

7

[1]

(b) Draw the graph of y =

x2 - 3x + 2 for -1 G x G 7 . 2

y 6

4

2

0

–1

1

2

3

4

5

6

7

x

–2

–4 [3]

(c) By drawing a tangent, estimate the gradient of the curve at x = 1.5 .

Answer ........................................... [2]

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(d) Complete these inequalities to describe the range of values of x where y H 0.

Answer x G ..................................... x H ..................................... [2] (e) (i) On the same grid, draw the line 4y + 3x = 12 .

[2]

(ii) The x-coordinates of the points of intersection of this line and the curve are the solutions of the equation 2x2 + Ax + B = 0 . Find the value of A and the value of B.

Answer A = .................................... B = .................................... [2]

© UCLES 2018

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7

North

A 135°

2.8

C 3.7

42° B

A yacht sails the triangular route shown. The bearing of B from A is 135°. t = 42°. BC = 3.7 km, AC = 2.8 km and ABC t = 62.2°, correct to 1 decimal place. (a) Show that CAB

[3] (b) Find the bearing of A from C.

Answer ........................................... [2]

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13

(c) The yacht sails from A to B to C to A. Calculate the total length of the route.

Answer ..................................... km [4]

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14

8

Y

A

B X

O

C

OYC is a triangle. A is a point on OY and B is a point on CY. AB is parallel to OC. AC and OB intersect at X. (a) Prove that triangle ABX is similar to triangle COX. Give a reason for each statement you make.

.................................................................................................................................................................... .................................................................................................................................................................... .................................................................................................................................................................... ............................................................................................................................................................... [3]

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(b) OA = 3a and OC = 6c and CB : BY = 1 : 2 . Find, as simply as possible, in terms of a and/or c (i)

AB,

Answer AB = ................................. [1] (ii)

CY .

Answer CY = ................................ [2] (c) Find, in its simplest form, the ratio (i) OX : XB,

Answer .................... : .................... [2] (ii) area of triangle COX : area of triangle ABX,

Answer .................... : .................... [1] (iii) area of triangle AYB : area of trapezium OABC.

Answer .................... : .................... [1]

© UCLES 2018

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16

9

(a) On Monday, Ravi goes on a 20 km run. (i) His average speed for the first 12 km is x km/h. Write down an expression, in terms of x, for the time taken for the first 12 km. Give your answer in minutes.

Answer ............................. minutes [1] (ii) His average speed for the final 8 km of the run is 1.5 km/h slower than for the first 12 km. Write an expression, in terms of x, for the time taken for the final 8 km of the run. Give your answer in minutes.

Answer ............................. minutes [1] (iii) Ravi takes 110 minutes to complete the full 20 km. Form an equation in x and show that it simplifies to 22x2 - 273x + 216 = 0 .

[4]

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17

(iv) Solve the equation 22x2 - 273x + 216 = 0 . Show your working and give each answer correct to 2 decimal places.

Answer x = ................or x = .............. [3] (b) On Friday, Ravi ran the whole 20 km at the same average speed that he ran the final 8 km on Monday. Calculate the time Ravi took to run 20 km on Friday. Give your answer in hours and minutes, correct to the nearest minute.

Answer ............ hours .......... minutes [3]

© UCLES 2018

4024/22/M/J/18

[Turn over

18

4 10 A is the point (–4, –1) , B is the point (2, 2) and BC = e o . -8 (a) Find the coordinates of the midpoint of AB.

Answer ( ................... , ..................) [1] (b) Find the gradient of AB.

Answer ........................................... [1] (c) Show that BC is perpendicular to AB.

[2] (d) ABCD is a rectangle. Find the coordinates of point D.

Answer ( ................... , ..................) [2]

© UCLES 2018

4024/22/M/J/18

19

(e) Calculate the perimeter of rectangle ABCD.

Answer ...................................units [4]

© UCLES 2018

4024/22/M/J/18

20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2018

4024/22/M/J/18

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the October/November 2013 series

4024 MATHEMATICS (SYLLABUS D) 4021/11

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the October/November 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – October/November 2013

Question 1

2

3

6

Mark

(a)

15 oe 16

1

(b)

9 cao

1

(a)

0.024

1

(b)

0.2 22%

(a)

2:9

1

(b)

4.8 (0) oe in dollars and/or cents

1

1 3

2

4

5

Answers

2 9

Paper 11

Part marks

1

Two numbers between 2 and 2

(a)

4d + 20 oe

1

(b)

(d – 5)2 oe

1

(a)

135

1

(b)

1.2 × 106

1

20

2

7

Syllabus 4024

C1 for one correct number. or B1 for 3x < 7, 7 1 or for x < , or for x < 2 3 3 3x 7 < or 3 3

Dep. on three correct approximations seen. B1 for 8.8536 ≈ 3 or ((38.982 ≈ 39 or 40) and 6.0122 ≈ 6 or 6.0)

8

9

(a)

4 cao 9

1

(b)

4 cao 81

1

(a)

20

1

(b)

10

2

M1 for 60 ×

© Cambridge International Examinations 2013

20 oe 120

Page 3

10

Mark Scheme GCE O LEVEL – October/November 2013

210˚

1

(b)

330˚

1

(c)

43

1

(a)

3.75, or 3

(b)

320

2

C1 for figs 32 or M1 for 5 × 40 × 40 × 40 or 5 × 403

(a)

All of 4, 5, 6, 6, 4

2

C1 for 3 or 4 correct values

(b)

18 cao 43

1

(a)

5 − , or –0.625, only 8

1

(b)

7 oe 2x + 3

2

(a)

( A ∪ B) ∩ C

1

(b)

(i)

6

1

(ii)

d, e, f

1

13

14

15

16

17

Paper 11

(a)

11

12

Syllabus 4024

3 , only 4

1

(a)

0, or none

1

(b)

40

1

(c)

147

1

(a)

(i)

5

1

(ii)

3

1

(b)

13

1

(a)

y > 4 oe y < 4x oe

1 1

(b)

3

1

B1 for 2x “y” + 3x = 7 oe (condone swaps of x and “y”) – both variables on the same side.

If 0 scored, then B1 for y ... 4x, oe, and y ... 4, oe, with incorrect inequalities for ... .

© Cambridge International Examinations 2013

Page 4

Mark Scheme GCE O LEVEL – October/November 2013

Syllabus 4024

Paper 11

18

76 WWW

3

M2 for a completely correct method to find an equation for x. or M1 for 66 + 70 + 120 + 90 + 90 + y = 180k where k > 2, k ≠ 4 and x = 360 – y. or B2 for 284 WWW for the missing interior angle. or B1 for (6 – 2) × 180 or 720 (if as angle sum of the hexagon) used.

19

8πx3

3

C2 for a correct, unsimplified answer. or 1 2 B1 for π × (2 x ) × 7 x , 3 28 3 πx seen or for 3 1 and B1 for, π × x 2 × 4 x , 3 4 3 or for πx seen 3

(a)

6 35

1

(b)

0

1

(c)

17 35

2

(a)

(i)

4q – 2p, or –2p + 4q, only

(ii)

5q ft their (i) + 2p + q, simplified

20

21

22

8 13 , or for 35 35 17 or B1 for their (5 × 7)

C1 for

1 1

(b)

kp + their (ii)

(c)

10

1

(a)

54˚

1

(b)

36˚

1

(c)

61˚

1

(d)

25˚

1

In (a), award C1 if both answers are correct, but not in their simplest form.

1

© Cambridge International Examinations 2013

Page 5

23

Mark Scheme GCE O LEVEL – October/November 2013

1 , or (–) 0.2, only 5

(a)

(–)

(b)

4

1

(c)

11

2

Syllabus 4024

1

C1 for 5. or M1 for trap. = or M1 for

24

25

Paper 11

1 2

1 2

× 10 × (6 + u ) = 85 oe

× 10 × (u − 6) = 85 − 6 × 10 oe

A + B = 5 correctly obtained from 15 = 10 + A + B

1

4A + B = 2 correctly obtained from B 11 = 10 + 2 A + 2

1

(b)

both A = –1 and B = 6

2

(c)

9 cao

1

(a)

Reflection x = –1 oe indep

1 1

(b)

Triangle with vertices (0, 6), (–1, 5), (–2, 5)

2

(c)

4

1

(a)

1 3     0 −2 

2

C1 for 2 or 3 correct elements

(b)

 1 −18     6 13 

2

C1 for 2 or 3 correct elements

(c)

 3 0   oe  0 3

1

(a)

26

C1 if one correct

indep. – but lost if more than one transf. named. C1 for 2 correct vertices, or for a triangle with vertices (0, 2), (1, 3), (2, 3).

© Cambridge International Examinations 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the October/November 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/12

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the October/November 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – October/November 2013

Syllabus 4024

Paper 12

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Question 1

2

3

5

2.38 oe

1

(b)

80 (.0)(0)

1

(a)

1

9 20

1

(b)

0.0602

1

(a)

–7

1

8

x+6 oe 2 (0)3 hours 48 minutes

1

(b)

2 5

1

44%

Part marks

1

(a)

4 9

(a)

1

(b)

1

8

2

(a)

3.5 × 10 7

1

(b)

1.4 × 10 –6

1

3 7

2

6

7

Mark

(a)

(b) 4

Answers

B1 for “k” = 40 or M1 either for 20 × 2 = 5y oe; or for (their k)/5, when y = “k”/x used

7x = C , or for c cx = 3C; where c and C are integers (not 0).

B1 for 7x = c , or for

© Cambridge International Examinations 2013

Page 3

Mark Scheme GCE O LEVEL – October/November 2013

Syllabus 4024

Paper 12

9

200

2

Dep. on three correct approximations seen. B1 for either √35.78 ≈ 6, or 3 1005 ≈ 10

10

Any number between 4 and 5

2

B1 for x < 5 , or for 5 > x seen. This may appear as, e.g., 4 < x < 5.

11 (a)

45.5°

1

(b)

151°

2

9 25

1

(b)

3 or 3t –3 t3

1

(c)

1 x2 or x 2 y −1 3 3y

1

12 (a)

1 and y = – 4 2

13

Both x =

14 (a)

1.35

1

(b)

1.1

1

(c)

104

1

B C D

1

(b)

E

1

(c)

y<

15 (a)

1 x oe 2

3

C1 for 151 < x ≤ 151.2 or M1 for 360 – 46.5 – 162.5 or M1 for 360 – 46 – 162 – 1

C2 for either x or y correct WWW or C1 for a pair of values that satisfy either equation

1

© Cambridge International Examinations 2013

Page 4

Mark Scheme GCE O LEVEL – October/November 2013 76

16

3

Syllabus 4024

Paper 12

Dep. on volume expressions in terms of a3. C2 for 76a, or 76a2, or 76(π)a3 , 76 76 76 , or 2 , or 3 or a a a B1 for a 3-spheres volume of 4 3 π × (2a ) × 3 or 32πa3 3 and B1 for a cylinder volume of π × (3a)2 × 12a or 108πa3 ; or B1 for both 108π… and 32π…without a3 .

(5t – 2)(5t + 2)

1

(b)

2r 2 (3H − h)

1

(c)

(4x – 3)(2y + 1)

2

16

1

(b)

Rectangle, base 2 to 3, height 6 units Rectangle, base 7 to 9, height 2 units

1 1

(c)

ft

17 (a)

18 (a)

19 (a)

15 31 + their ( p )

1

(2, 1)

1

2 or any equiv. value 3

(b)

−

(c)

13

B1 for partial factorisation 4x(2y + 1) or –3(2y + 1) or 2y(4x – 3) seen

1

2

C1 for (√) 52 or M1 for 62 + (–4)2, or for 62 + (4)2 , etc.

© Cambridge International Examinations 2013

Page 5

20 (a)

Mark Scheme GCE O LEVEL – October/November 2013 Reflection y = x oe

1 1

(b) (i) Triangle with vertices (–1, 0), (–3, 0), (–3, 1)  0 − 1  (ii)  1 0 

but lost if more than one transf. named indep. – but lost if more than one transf. named

1 1

(b)

1 15

1

(c)

4 15

2

3 2 2 1 × × × oe 6 5 6 5 or for any complete possibility diagram such as the one below, correctly used.

M1 for

2 3 3 4 4 4

22 (a)

48°

1

(b)

66°

1

(c)

24°

1

(d)

35°

1

152 – 12 = 8 × (1 + 2 + 3 + 4 + 5 + 6 + 7)

1

(b)

(2n + 1)2 – 12 oe

1

(c)

(2n + 1)2 = 4n2 + 4n + 1 or (2n + 1)2 – 12 = 4n2 + 4n , or (2n)(2n + 2)

B1

Division of both sides by 8 and result obtained correctly

M1

23 (a)

24 (a)

96° to 98°

(ii) acceptable bisector of angle ABC 10 to 10.3

2 – 32 32 42 42 42

3 23 – 33 43 43 43

3 23 33 – 43 43 43

1

(b) (i) acceptable perpendicular bisector of AB

(c)

Paper 12

1

1

21 (a)

Syllabus 4024

1 1 1

dep.on both (b) marks

© Cambridge International Examinations 2013

4 24 34 34 – 44 44

4 24 34 34 44 – 44

4 24 34 34 44 44 –

Page 6

Mark Scheme GCE O LEVEL – October/November 2013

Syllabus 4024

Paper 12

16

1

(b)

150

1

(c)

45 WWW or ft

(d)

10

1

Establishing, with reasons, that two pairs of angles are equal; and a conclusion (or an introductory statement), that the triangles are similar. e.g. ABˆ D = BDˆ C (alternate angles) ADˆ B = BCˆ D (given) Since two angles are equal, triangles ABD and BDC are similar.

2

B1 for ABˆ D = BDˆ C , with mention of alternate angles

2

B1 for

25 (a)

26 (a)

(b) (i) 6.3

(ii)

4 9

750 − their (b ) + 15 20

2

750 − their (b ) 20 or M1 for ½ × (k + k – 15) × 20 = 750 or M1 for 20( k – 15) + their(b) = 750 oe C1 for

1

© Cambridge International Examinations 2013

BC 6 = oe 4.2 4

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the October/November 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/21

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the October/November 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – October/November 2013

Qu 1

2

Answers

Paper 21

Part Marks

(a) (i) 468

1

(ii) 700

1

(iii) 550

2

B1 for factor

(b) 19 926

3

M2 for

(a) Correct triangle

2

B1 for 40° or 8 cm.

(b) Complete locus

2

B1 for at least one parallel line or at least one circular arc.

(c) P correctly placed ft 3

Mark

Syllabus 4024

2ft

(a) (2,3)

1

4 oe 8

1

(b)

(c) 2 ft

2ft

8 (d)    4

1

(e) (–3,–2) and (13,6) ft

3ft

1.10 soi 1.56

x x − = ±3 or 81 82 x x or seen B1 for 81 82

B1 for perpendicular bisector of BC or Arc centre A radius 6.5

M1 for y = (b)x + c

B2 for one correct point or 8  h − 5  or M2 for   = ( ±)  4  k − 2 M1 for AB = (±)CD

4

(a) 3.5 < x Y=4

1

(b) Correct frequency polygon

2

(c) (i) Completed table

1

(ii) Correct cumulative frequency curve.

2 ft

(d) (i) ft at y = 50 (3.4)

1ft

(ii) ft at y = 10 (2.3)

1ft

B1 for 5 correct plots or all heights consistently mis-plotted.

P1 for 5 points plotted ft (and joined) or All points consistently mis-plotted.

© Cambridge International Examinations 2013

Page 3

5

Mark Scheme GCE O LEVEL – October/November 2013

(a) 1

1

(b) (i) 5(x + y)

1

(ii) (3x + 4 )(3x – 4) (c) (i) (2x – 3)(x + 4) (ii)

6

3 –4 2

1

1ft

(d) 4

2

B1 for k = 36 or k M1 for L = 2 soi d

(a) (i) 19.93 from correct rounding

2

M1 for

3

M1 for

(b) (i) 25

CD = cos50 oe 31

31 = cos50 oe and AC M1 for AC – 19.93 SC If 2nd M not earned, A1 for 48.2

1

(ii) 37.2 or 37.3

3

PR QR = tan65 oe or = tan55 oe and 52 52 M1 for PR – QR SC If 2nd M not scored, A1 for 111.5 or 74.26 M1 for

3

B1 for angle EAD = angle DAC and B1 for either AE = AC or AD common

2

B1 for angle AED = z or z = x + y

(b) 228

2

B1 for 132 seen or (angle SQR =) 21 and (angle SRQ =) 27 soi

(a) 7.14

3

M2 for reaching 72 + r² = 10² soi or M1 for correct right angled triangle soi

(b) (i) Equiangular triangles established

3

B2 for two pairs with no reason. Or for one pair of equal angles with reason. Or B1 for any pair of equal angles.

2

M1 for

(a) (i) The three facts for Congruency stated (ii) (x =) z – y oe isw

8

Paper 21

1

(ii) 28.3

7

Syllabus 4024

(ii) x² – 18x + 55 (=0) correctly found

x 11 = oe 5 18 − x

© Cambridge International Examinations 2013

Page 4

Mark Scheme GCE O LEVEL – October/November 2013

(iii) 3.9 14.1

3

B1 for

Syllabus 4024

Paper 21

(−18) 2 − 4 × 1 × 55 soi and

− (−18) + (or −) their104 soi 2 ×1 If B1 or B0 at this stage, allow p± q M1 for both values of r

B1 for

(iv) 10.2 ft 9

1ft

(a) 4050

1

(b) Correct plots ft and curve

3

(c) (1700) ft

1

(d) (i) (870) ft

2

(ii) Rate of increase (of number of bacteria per hour) (e) (k =) 50 (a =) 3 (f)

10

1

(i) Correct straight line

2

(ii) 3.45 ft

1

(a) (i) 11.9

(iii) 9.1% ft

B1 for k×2πr×h

4

M1 for ½ × 0.8 × 0.8(× sin90) oe and 90 )π × 0.8² and M1 for ( 360 M1 for(their 0.5026 – their 0.32) × 9.5 M1 for

(a)(ii) × 100 19.1

1

(ii) 22 ft

3ft

(a) (i) Shear, scale factor  1 1.5    0 1 

L1 for correct intercept or Correct gradient

2

2ft

(b) (i) 19 100

(ii)

M1 for a tangent at t = 2.5

1

(ii) 1.73 or 1.74

11

P2 for 5 correct plots ft or P1 for 4 correct plots ft

3 2

25(000) = N and their (b)(i) × 6(0) B1 for N × 10³

M1 for figs

2

B1 for Shear only or SF 1.5

2

B1 for one element incorrect or  a b  1 3 3   4 6 12    =   M1 for   c d  2 2 6   2 2 6 

© Cambridge International Examinations 2013

Page 5

Mark Scheme GCE O LEVEL – October/November 2013

(b) (i) Triangle C

2

(ii) Stretch(ing) (iii)

1 1 0   oe isw 2  0 2 

5 sin 65 correctly obtained. sin 65 − sin 45

(ii) 22.7 or 22.8 (b) (i) –

2

1 0  soi or B1 for det = 2 soi or   0 2  2 0  p q   1 0    =   M1 for   0 1  r s   0 1 

2

B1 for one element incorrect or  2 0  1 1.5    M1 for   0 1  0 1 

3

M1 for

BC AC = oe soi and sin 65 sin 45 B1 for AC = BC – 5 oe

1

11 isw 40

3

11 ft 40

1ft

(c) Correct triangle DEG

1

(d) 6

3

(ii)

B1 for two vertices correct or  2 0  4 6 12    M1 for   0 1  2 2 6 

1

 2 3  (c)   0 1

(a) (i)

Paper 21

1

(iv) 2 : 1 oe

12

Syllabus 4024

M2 for 13² = 6² + 10² – 2×6×10×cosPRQ or M1 for 13² = 6² + 10² + 2×6×10×cosPRQ 33 or A1 for 120 M1 for 13² = 6² + 10² – ×6×10×cosPRQ 33 A1 for – 60

B1 for Triangle LMN with angle M = 30 soi and 1 M1 for × LM × MN × sin 30 soi 2

© Cambridge International Examinations 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level

MARK SCHEME for the October/November 2013 series

4024 MATHEMATICS (SYLLABUS D) 4024/22

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the October/November 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2

Mark Scheme GCE O LEVEL – October/November 2013

Qu 1

Answers (a) 3760

Mark 3

(c) 2

54.1

(a) (i) 1.24 isw (ii) x = 3 y = 5

1 12

(b) (i)

B1 for a correct ∆ such as

(a)

−

1 8

(b) 6x³ – 3 or 3 (2x³ –1) (i) (9x – 4) (x + 1) (ii)

4

1 (40 + 58)×38 oe soi 2

2

M1 for (BC² = ) 38² + (58 – 40)²

2

M1 for tan CDE =

2

M1 for (0 × 4) + 35 × 1 + 2 × 6 + 3 × 5

2

B1 for either x = 3 or y = 5 or M1 for 37 × 1 + 2y + 3 × 5 = 62 oe soi or for x + 37 + y + 5 = 50 soi

58 oe 42

3

B2 if no or incorrect labels or One correct angle with an additional label. B1 for one angle in tolerance or Two angles calculated.

2

B1 for 1 or – 8 M1 for

(c)

1 × 34 × 40 2

1

(ii) Correct pie chart labelled.

3

Paper 22

Part Marks

B1 for (b) 42(.0)

Syllabus 4024

4 –1 9

2

or

(− 4)2 + (− 3)2 (− 4)2 − 2 (− 4)(− 3)

−4+

M1 for 6x³ – 2x + 9x² – 3 – 9x² + 2x

1 1

(d) 27, 28, 29

2

B1 for such as n, n + 1, n + 2 seen

(a) 72 justified

2

B1 for 72 or either D or E = 90

(b) (i) Congruency established

3

B1 + B1 for two pairs of equal sides SC1 After 0, accept all sides the same oe.

(ii) (a) Kite (b) 90

1 1

© Cambridge International Examinations 2013

Page 3

5

Mark Scheme GCE O LEVEL – October/November 2013

(a) (i) 3

Paper 22

1

(ii) {4, 8, 10}

1

(b) 66

2

(c)

1

(i)

/

(ii) C ∩ ( A ∪ B ) oe 6

Syllabus 4024

M1 for y + 13 + 11 = 90 oe or B1 for 52 soi

1

(a) (i) 899

1

(ii) 33.5

2

B1 for figs

(iii) 900

2

M1 for x +

3

M2 for 600 +

(a)

6   7 15   

2

B1 for 2 correct entries or for  10   4       − 5  or  − 12  soi  15   0     

(b)

13    10 

2

B1 for one entry correct or for both 13 and 10 seen but not in this form.

(c)

(i)

(b) 4.5

7

1  4 0   oe isw 4  2 1 

 − 2 0  (ii)   − 2 1

2400 − 1596 oe 2400

20 x = 1080 or 100 B1 for 120 seen

3R × 600 = 681 or 100 R = (681 – 600) and M1 for 600 × 100 A1 for 13.5 or 600 × (3)R B1 for soi 100

2

 1 0  = 4 soi or B1 for det   − 2 4

2

1 0  soi B1 for three entries correct or  0 1

© Cambridge International Examinations 2013

 4 0    2 1

Page 4

8

Mark Scheme GCE O LEVEL – October/November 2013

(a) 44.5

3

Syllabus 4024

M1 for numerical

Paper 22

θ × 2π × 6 oe 360

and M1 for their arc + 12 If second M not scored, A1 for 32.46 or 5.24 soi. SC1 after 0 for 2π6 seen (= 37.7) (b) 97.4

(c)

9

2

x = cos 25 (= 5.44) oe and 6 M1 for their 5.44 + 6. If the second M not scored, A1 for 5.44 SC1 after 0 for identifying a right-angled triangle that would lead to x = 5.44.

(i) 11.4

3

(ii) 19.0

4

M1 for

2

P1 for at least 5 correct plots

(a) Correct plots and curve (b) (– 0.8) (c)

θ × π × 62 360 SC1 after 0 for π6² (= 113) seen

M1 for numerical

2ft

(i) – b

1

(ii) Completed table

1

(iii) Correct curve

1

(iv) – (0.8 ± 0.2) cao

1

(d) (i) Correct straight line

M1 for

1 × 6 × 6 × sin 50 oe and 2 A1 for 13.79 (correct triangle only) M1 for 12 × (c) (i) soi and 12 × (c) (i) − A × 100 M1 for 12 × (c) (i)

M1 for the tangent drawn at x = 0.75

1

(ii) (0.3) (1.7)

1ft

(iii) 2x² - 4x + 1( = 0) or equivalent three term expression.

2ft

M1 for x +

© Cambridge International Examinations 2013

1 = 4 – x oe 4

Page 5

10

Mark Scheme GCE O LEVEL – October/November 2013

(a) (i) 11.9

(ii) 265° cao

(b) (i)

(ii)

M3 for 8 2 + 6 2 − 2 × 8 × 6 × cos 115 M2 for 8² + 6² – 2 × 8 × 6 × cos 115 M1 for 8² + 6² + 2 × 8 × 6 × cos 115 and A1 for 7.71 or M1 for 8² + 6² – 8 × 6 × cos 115 and A1 for 10.96 or M1 for 8² + 6² – 2 × 8 × 6 × sin 115 and A1 for 3.60 or M1 for 8² – 6² – 2 × 8 × 6 × cos 115 and A1 for 8.28

2

B1 for 85, 95 seen or M1 for 200 – 115.

2

200 sin 65 sin 36 correctly obtained sin 35 sin 44

2

(iv) 2.34 ft or

PR 200 oe = sin 65 sin RPQ B1 for 180 – (44 + 36 + 65)

M1 for

M1 for

SR PR oe = sin 36 sin 44

1 200 + (b) (iii) 200

Paper 22

4

200 sin 65 correctly obtained sin 35

(iii) 267

Syllabus 4024

1ft

© Cambridge International Examinations 2013

Page 6

11

(a)

Mark Scheme GCE O LEVEL – October/November 2013 10 p − 29 ( p + 2)(2 p − 3)

(b) (i)

Final Answer

320 isw x

3

Syllabus 4024

7 (2 p − 3) − 4 ( p + 2 ) ( p + 2)(2 p − 3) B1 for 14p – 21 – 4p – 8

Paper 22

M1

seen

1

(ii) 2x² + 5x – 20 (= 0) correctly found

3

M2 for their

320 320 – their = 80 oe 1 x x+2 2

320 320 – their = – 80 oe 1 x x+2 2 320 SC1 after 0 for seen. 1 x+2 2 M2 for their

(iii) 2.15

– 4.65

3

B1 for B1 for

5 2 − 4 × 2 × (− 20 ) soi and

− 5 ± their 185

soi 2× 2 If B1 or B0 at this stage, allow M1 for both p± q values of r

(iv) 69

2

M1 for

320 their + ve x + 2.5

© Cambridge International Examinations 2013

oe

Page 7

12

Mark Scheme GCE O LEVEL – October/November 2013

(a) (i) 6.08

Syllabus 4024

Paper 22

1

 2   (ii)   − 1 .5 

2

 −1 1 6 B1 for   or   oe or 2 1  − 2

(

)

M1 for EH = EA + AH  2   (iii)   − 1 .5 

1

(iv) Equal and parallel

1

(v) Shows G is midpoint of CD

2

Dependent on (ii) and (iii) correct.  − 3  − 2   6  M1 for   +   +   oe seen or  0   − 4 1  1  B1 for CD = 2CG =    − 3

(

)

(b) (i) Correct triangle (B)

2

B1 for two vertices correct or positive enlargement centre (1, 2) or an enlargement scale factor 1.5.

(ii) Correct triangle (C)

2

B1 for two vertices correct or negative enlargement centre (1, 2) or An enlargement scale factor – 0.5.

(iii) 1 : 9 oe

1

© Cambridge International Examinations 2013

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 6 7 4 9 0 1 1 4 9 5 *

4024/11

MATHEMATICS (SYLLABUS D)

October/November 2013

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NH/KN) 67169/1 © UCLES 2013

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate

2 34 – 1 13 . 16



Answer

................................................ [1]

Answer

................................................ [1]

Answer

................................................ [1]

(b) Evaluate 5 + 3 # 2 + 2 (2 - 3) .

2

(a) Evaluate 0.02 # 1.2 .



(b) Arrange these values in order of size, starting with the smallest. 22%

2 9

0.2

Answer ........................ , ......................... , ........................ [1] smallest

© UCLES 2013

4024/11/O/N/13

For Examiner’s Use

3 3

(a) Express the ratio 30 minutes to 2 41 hours in its lowest terms. Give your answer in the form m : n, where m and n are integers.

For Examiner’s Use

Answer ................ : ................. [1] (b) Find the simple interest on $200 for 4 years at 0.6% per year.

4

Answer $ .............................................. [1] Find two solutions of the inequality 3x + 4 < 11 that lie between 2 and 3.

Answer x = ............. and ............ [2]

© UCLES 2013

4024/11/O/N/13

[Turn over

4 5

The length of a side of a square is given as d cm, correct to the nearest 10 cm. Find an expression in terms of d for (a) the upper bound of the perimeter of the square,



Answer

.......................................... cm [1]

Answer

......................................... cm2 [1]

Answer

................................................ [1]

Answer

................................................ [1]

(b) the lower bound of the area of the square.

6

(a) Evaluate 5 # 10 0 + 3 # 10 1 + 1 # 10 2 .

(b) Find (5 # 10 8) # (2.4 # 10 - 3) . Give your answer in standard form.



7

By making suitable approximations, estimate the value of Show clearly the approximate values you use.



© UCLES 2013

Answer

4024/11/O/N/13

38.982 # 8.8536 . 6.0122

................................................ [2]

For Examiner’s Use

5 8

Giving each answer as a fraction in its lowest terms, evaluate (a)

3 # ^2h3 , 6#9

2 -2

3 (b) c m 2

Answer

................................................ [1]

Answer

................................................ [1]

Answer

............................................% [1]

.

9

For Examiner’s Use

(a) A television priced at $500 is sold for $400. Find the percentage discount.



(b) Tax on the original price of a radio is charged at 20% of the original price. After tax was included, a customer paid $60 for the radio. Calculate the tax charged.



© UCLES 2013

Answer $ ............................................. [2]

4024/11/O/N/13

[Turn over

6 10 In the diagram, the triangle ABC is equilateral.

For Examiner’s Use

North A

B



C

C is due East of B. (a) Find the bearing of B from A.



Answer

................................................ [1]

Answer

................................................ [1]

(b) Find the bearing of A from C.



(c) A boat sails around a course represented by triangle ABC. It started at 13 38 and finished at 14 21. How many minutes did it take?



© UCLES 2013

Answer

4024/11/O/N/13

................................................ [1]

7 11

A model of a car is made to a scale of

1 40

.

For Examiner’s Use

(a) The height of the actual car is 1.5 m. Find the height, in centimetres, of the model.



Answer

.......................................... cm [1]

(b) The luggage capacity of the model is 5 millilitres. Find the luggage capacity, in litres, of the actual car.



Answer

....................................... litres [2]

12 The lengths of the leaves of a plant were measured. The results are shown in the table. Length (x centimetres)

1<xG3

3<xG4

4<xG5

5<xG7

7 < x G 10

Frequency

8

5

6

12

12

Frequency density (a) Complete the table to show the frequency densities.

[2]

(b) One leaf is chosen at random. Find an estimate of the probability that this leaf is more than 6 cm long.

© UCLES 2013

Answer 4024/11/O/N/13

................................................ [1] [Turn over

8 13

f(x) =

7 - 3x 2x

For Examiner’s Use

(a) Find f(4) .



Answer

................................................ [1]

(b) Find f –1(x) .



© UCLES 2013

Answer f –1(x) = ................................... [2]

4024/11/O/N/13

9 14 (a) Express, in set notation, the subset shaded in the diagram.

For Examiner’s Use

 A

B

C



Answer ................................................ [1] (b)  = {a, b, c, d, e, f, g, h} P = {a, b, c} Q = {b, c, d, e, f} (i) Find n ^P , Qh.



Answer

................................................ [1]

Answer

................................................ [1]

(ii) List the members of the subset P l + Q .



© UCLES 2013

4024/11/O/N/13

[Turn over

10 15 This figure has rotational symmetry of order 3.

For Examiner’s Use

y°

53° 40°

x°

(a) How many lines of symmetry does the figure have?

Answer

................................................ [1]

(b) Find x.



Answer x = .......................................... [1] (c) Find y.



© UCLES 2013

Answer y = ........................................... [1]

4024/11/O/N/13

11 16 (a) An ordinary die is thrown 15 times. These are the numbers thrown. 4

5

3

2

2

5

For Examiner’s Use

6

1

6

3

5

2

5

1

3

(i) Find the mode.



Answer

................................................ [1]

Answer

................................................ [1]

(ii) Find the median.

(b)

–20

–8

x

The mean of these three numbers is –5. Find x.



© UCLES 2013

Answer x = .......................................... [1]

4024/11/O/N/13

[Turn over

12 17 The diagram shows the points A (1, 4), B (3, 12) and C (15, 4). The equation of the line through B and C is 2x + 3y = 42.

For Examiner’s Use

y B (3, 12)

C (15, 4)

A (1, 4) O

x

The region inside triangle ABC is defined by three inequalities. One of these is 2x + 3y < 42. (a) Write down the other two inequalities.



Answer



................................................ ................................................ [2]

(b) How many points, with coordinates (10, k), where k is an integer, lie inside the triangle ABC ?



© UCLES 2013

Answer

4024/11/O/N/13

................................................ [1]

13 18 The diagram shows a hexagon.

120°

70°

For Examiner’s Use

Find x. x° 66°



Answer x = ........................................... [3]

19 [Volume of a cone =

1 2 πr  h] 3

Cone 1 has radius 2x cm and height 7x cm. Cone 2 has radius x cm and height 4x cm. Find an expression, in terms of π and x, for the difference in the volume of the two cones. Give your answer in its simplest form.



© UCLES 2013

Answer

4024/11/O/N/13

.........................................cm3 [3]

[Turn over

14 20 Two bags contain beads. The first bag contains 2 white, 2 red and 3 black beads. The second bag contains 3 white and 2 black beads. One bead is taken, at random, from each bag. The tree diagram is shown below. First bead

For Examiner’s Use

Second bead

3 5 2 5

white

2 7 2 7

white

black

3 5

white

2 5

red

3 7

black

3 5

white

2 5

black

black

Find the probability that (a) both beads are white,



Answer

................................................ [1]

Answer

................................................ [1]

Answer

................................................ [2]

(b) both beads are red, (c) exactly one bead is black.



© UCLES 2013

4024/11/O/N/13

15 21 A

For Examiner’s Use

B 2p + q C 2q – p D

E

In the diagram, BC = 2p + q, CD = 2q – p and D is the midpoint of CE. (a) Express, in its simplest form, in terms of p and/or q (i)

CE ,

(ii)

Answer

................................................ [1]

Answer

................................................ [1]

BE .



(b) Given that AB = kp, express AE in terms of k, p and q.



Answer

................................................ [1]

(c) Given that AE is parallel to BC, find k.



© UCLES 2013

Answer k = ........................................... [1]

4024/11/O/N/13

[Turn over

16 22 C B A

122° Q P

36° E

D

In the diagram, the circles, centres P and Q, intersect at B and E. ABC and APE are straight lines. BD is parallel to AE. t = 122°. t = 36° and BQC BEA t . (a) Find BAE



Answer

t =..................................... [1] BAE

Answer

t = .................................... [1] EBD

Answer

t = .................................... [1] BDC

Answer

t = .................................... [1] DBQ

t . (b) Find EBD

t . (c) Find BDC

t . (d) Find DBQ



© UCLES 2013

4024/11/O/N/13

For Examiner’s Use

17 23 The diagram is the speed-time graph of part of a train’s journey. The train slows down uniformly from a speed of u m/s to a speed of 6 m/s in 10 seconds. During the next 20 seconds it travels at a constant speed of 6 m/s. It then slows down uniformly to a stop after a further 30 seconds.

Speed (m/s)

For Examiner’s Use

u

6

0

0

10

30 Time (t seconds)

60

(a) Calculate the retardation from t = 30 to t = 60.



Answer

........................................m/s2 [1]

Answer

......................................... m/s [1]

(b) Calculate the speed of the train when t = 40.



(c) The distance travelled by the train from t = 0 to t = 10 is 85 m. Find u.



© UCLES 2013

Answer u = .......................................... [2]

4024/11/O/N/13

[Turn over

18 24 The first and second terms of a sequence are 15 and 11 respectively. The nth term of the sequence is 10 + An +

For Examiner’s Use

B . n

(a) Show that A + B = 5 and 4A + B = 2.

[2] (b) Solve the simultaneous equations. A+B=5 4A + B = 2



Answer A = ..........................................



B = ......................................... [2] (c) Hence find the third term of the sequence.



© UCLES 2013

Answer

4024/11/O/N/13

................................................ [1]

19 25 The diagram shows triangles A and B and the point P (0, 4).

For Examiner’s Use

y 7 6 5 4

P

3 2

B

A

1 –6

–5

–4

–3

–2

–1

0

1

2

3

4

5

x

(a) Describe fully the single transformation that maps triangle A onto triangle B. Answer ....................................................................................................................................... .............................................................................................................................................. [2] (b) Triangle A is mapped onto triangle C by an enlargement, centre P, scale factor - 21 . On the diagram, draw triangle C. (c) Find the value of



[2]

area of triangle A . area of triangle C

Answer

................................................ [1]

Question 26 is printed on the following page.

© UCLES 2013

4024/11/O/N/13

[Turn over

20 26

A=c (a) Find c

2 -3 m 1 4

For Examiner’s Use

5 -3 m – 2A. 2 6



Answer

f

p

[2]

Answer

f

p

[2]

f

p

[1]

(b) Find A # A .



(c) Write down, as a 2 # 2 matrix, the answer to 3 # A # A - 1 .



Answer

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

4024/11/O/N/13

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 8 1 4 4 8 3 1 2 5 6 *

4024/12

MATHEMATICS (SYLLABUS D)

October/November 2013

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NF/SW) 67168/2 © UCLES 2013

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Amy buys 3 drinks at $1.86 each and 1 drink for $2.04. She pays for the 4 drinks with a $10 note. How much change should she receive?



Answer $ ............................................ [1] (b) $180 is shared between Ali and Ben so that Ali’s share : Ben’s share = 4 : 5. Find Ali’s share.



2

Answer $ ............................................ [1]

(a) Evaluate

3 14 - 1 45 .



Answer

............................................... [1]

Answer

............................................... [1]

(b) Evaluate 3.01 × 0.02 .



© UCLES 2013

4024/12/O/N/13

For Examiner’s Use

3 3

f(x) = 2x – 6

For Examiner’s Use

(a) Evaluate f `- 21 j .



Answer

............................................... [1]

(b) Find f −1(x).

Answer f −1(x) = .................................. [1]



4

(a) A journey started at 07 44 and finished at 11 32. How long, in hours and minutes, did the journey take?

Answer

............... hours ............... minutes [1]

(b) Arrange these values in order, starting with the smallest. 4 9

2 5

44%

Answer .................... , .................... , .................... [1] smallest

© UCLES 2013

4024/12/O/N/13

[Turn over

4 5

(a) In the diagram, two small triangles are shaded.

For Examiner’s Use

Shade one more small triangle, so that the diagram will then have one line of symmetry.

[1] (b) In the diagram, two small squares are shaded. Shade two more small squares, so that the diagram will then have rotational symmetry of order 2.

[1]

6

y is inversely proportional to x. Given that y = 20 when x = 2, find y when x = 5.



© UCLES 2013

Answer y = ......................................... [2]

4024/12/O/N/13

5 7

(a) Write the number 35 000 000 in standard form.



Answer (b) Giving your answer in standard form, evaluate



8

For Examiner’s Use

4.2 # 10 - 2 . 3 # 10 4

Answer

Solve the equation



© UCLES 2013

............................................... [1]

............................................... [1]

3x + 1 x - = 1. 2 3

Answer x = ......................................... [2]

4024/12/O/N/13

[Turn over

6 9

By making suitable approximations, estimate the value of Show clearly the approximate values you use.



Answer

3

35.78 # 1005 . 0.3012

For Examiner’s Use

............................................... [2]

10 Find one value of x that satisfies both x > 4 and 17 – 4x > 2 – x.



11

Answer

............................................... [2]

B

In the diagram, t = 46°, correct to the nearest degree, AOB t = 162°, correct to the nearest degree. AOC 46° O 162°

A

C

t . (a) Write down the lower bound for AOB

Answer

............................................... [1]

Answer

............................................... [2]

t . (b) Find the lower bound for BOC



© UCLES 2013

4024/12/O/N/13

7 12 (a) Evaluate

5 -2 c m . 3

For Examiner’s Use



Answer

............................................... [1]

Answer

............................................... [1]

Answer

............................................... [1]

1

9 2 (b) Simplify c 6 m . t

2x 3 y (c) Simplify . 6xy 2



13 Solve the simultaneous equations.



4x − 3y = 140 2x + y = −3

Answer x = .........................................



© UCLES 2013

y = ......................................... [3]

4024/12/O/N/13

[Turn over

8 14 The times taken by each of 120 runners to react to the starting gun were recorded. The cumulative frequency curve summarises the results. 120

100

80 Cumulative frequency 60

40

20

0

0

1 Time (seconds)

2

(a) Find the upper quartile.

Answer

............................................ s [1]

Answer

............................................ s [1]

(b) Find the 40th percentile.



(c) Find the number of students who took less than 1.5 seconds.



© UCLES 2013

Answer

4024/12/O/N/13

............................................... [1]

For Examiner’s Use

9 15

For Examiner’s Use

y D

E

O

The diagram shows the three lines O, A, B, C, D, E and F.

C

F

B

A

x

x = 1, y = 1 and x + y = 4 and the seven points

(a) Which of these seven points lie in the region defined by x + y > 4?

Answer

............................................... [1]

(b) Which one of these seven points lies in the region defined by x < 1, y > 1 and x + y < 4?



Answer

............................................... [1]

(c) Given that O is (0, 0) and C is (4, 2), find the inequality that defines the region below the line that passes through O and C.



© UCLES 2013

Answer

4024/12/O/N/13

............................................... [1]

[Turn over

10 16 [Volume of a sphere = 43 rr 3 ]

For Examiner’s Use

Three spheres, each of radius 2a cm are placed inside a cylinder of radius 3a cm and height 12a cm. Water is poured into the cylinder to fill it completely.

12a

The volume of water is kπa3 cm3. Find the value of k.

3a



© UCLES 2013

Answer k = ......................................... [3]

4024/12/O/N/13

11 17 (a) Factorise 25t 2 – 4.

For Examiner’s Use



Answer

............................................... [1]

Answer

............................................... [1]

Answer

............................................... [2]

(b) Factorise completely 6r 2H − 2r 2h .

(c) Factorise completely 8xy + 4x – 6y – 3.



© UCLES 2013

4024/12/O/N/13

[Turn over

12 18 In an experiment with a group of snails, the distance moved in one minute by each snail was recorded. Some of the results are shown in the table and illustrated in the histogram. Distance (x centimetres)

2<x3

3<x4

4<x5

5<x7

7<x9

Frequency

6

9

12

p

4

For Examiner’s Use

12 10 8 Frequency density 6 4 2 0

0

1

2

3

4

5 6 Distance (cm)

7

8

9

10

x

(a) Use the histogram to find the value of p.



Answer p = ......................................... [1] (b) Complete the histogram.

[2]

(c) One snail is chosen at random. Find the probability that this snail did not move more than 4 cm.



© UCLES 2013

Answer

4024/12/O/N/13

............................................... [1]

13 19 P is (−1, 3) and Q is (5, −1).

For Examiner’s Use

(a) Find the coordinates of the midpoint of PQ.



Answer (............... , ..............) [1] (b) Find the gradient of the line PQ.



Answer

............................................... [1]

(c) Given that the length of PQ = 2 n units, where n is an integer, find the value of n.



© UCLES 2013

Answer n = ........................................ [2]

4024/12/O/N/13

[Turn over

14 20

For Examiner’s Use

y 4 3 2

A

1 B –4

–3

–2

0

–1

1

2

3

4 x

–1 –2 –3 –4

The diagram shows triangles A and B. (a) Describe fully the single transformation that maps triangle A onto triangle B. Answer ...................................................................................................................................... ............................................................................................................................................. [2] (b) Triangle A is mapped onto triangle C by the transformation T. T is a rotation, centre the origin, through 270° clockwise. (i) On the diagram, draw triangle C.

[1]

(ii) Find the matrix that represents T.



© UCLES 2013

Answer

4024/12/O/N/13

f

p

[1]

15 21 2

3

3

4

4

For Examiner’s Use

4

The numbers 2, 3, 3, 4, 4, 4 are written on six cards. Two cards are chosen, at random, without replacement, to form a 2-digit number. The first card chosen shows the number of Tens. The second card chosen shows the number of Units. First card

Second card

Tens

Units

Expressing each answer in its simplest form, find the probability that the two cards show (a) a number greater than 20,

Answer

............................................... [1]

Answer

............................................... [1]

Answer

............................................... [2]

(b) the number 33,

(c) the number 43 or the number 32.



© UCLES 2013

4024/12/O/N/13

[Turn over

16 22

For Examiner’s Use

A D 132°

O 59° C

T

B

In the diagram, the points A, B, C and D lie on the circle centre O. TA and TB are tangents touching the circle at A and B respectively. t = 132°, ACD t = 59° and AOC is a straight line. AOB t . (a) Find ATB



Answer

t  = ................................... [1] ATB

Answer

t = .................................. [1] BDA

Answer

t = ................................. [1] BDC

Answer

t = .................................. [1] OBD

t . (b) Find BDA

t . (c) Find BDC

t . (d) Find OBD



© UCLES 2013

4024/12/O/N/13

17 23 The first four lines of a pattern of numbers are shown below. 1st line

32

−

12

=

8×1

2nd line

52

−

12

=

8 × (1 + 2)

3rd line

72

−

12

=

8 × (1 + 2 + 3)

4th line

92

−

12

=

8 × (1 + 2 + 3 + 4)

For Examiner’s Use

(a) Write down the 7th line of the pattern. Answer ................................................................................................................................ [1] (b) Write down an expression, in terms of n, to complete the nth line of the pattern. Answer ............................................................................... = 8 × (1 + 2 + 3 + 4 + … + n) [1] (c) Using the nth line of the pattern, show that 1 + 2 + 3 + 4 + … + n =

n (n + 1) . 2

[2]

© UCLES 2013

4024/12/O/N/13

[Turn over

18 24 The diagram at the bottom of the page shows triangle ABC.

For Examiner’s Use

t . (a) Measure BAC

Answer

............................................... [1]

(b) On the diagram, construct the locus of points, inside the triangle ABC, that are (i) equidistant from A and B,

[1]

(ii) equidistant from AB and BC.

[1]

(c) These two loci meet at the point P. Label the point P on the diagram and measure CP.

Answer CP = ................................ cm [1]

A

B

C

© UCLES 2013

4024/12/O/N/13

19 25 The diagram is the speed-time graph of a car’s journey.

For Examiner’s Use

20 Speed (m/s)

0

0

15 k Time (t seconds)

(a) Find the speed when t = 12.



Answer

....................................... m / s [1]

(b) Find the distance travelled by the car from t = 0 to t = 15.



Answer

.......................................... m [1]

(c) The distance travelled by the car from t = 0 to t = k is 750 m. Find k.

Answer k = ........................................ [2]

(d) The retardation of the car is 2 m / s2.

Find the number of seconds it takes to slow down and stop.



Answer

............................................ s [1]

Question 26 is printed on the following page. © UCLES 2013

4024/12/O/N/13

[Turn over

20 t . t = BCD 26 In the diagram, AB is parallel to DC and ADB A 4.2

4

For Examiner’s Use

B

6 C

D

(a) Explain why triangles ABD and BDC are similar.

[2] (b) AB = 4 cm, BD = 6 cm and AD = 4.2 cm. (i) Calculate BC.



Answer (ii) Write down the value of



......................................... cm [2]

area of triangle ABD . area of triangle BDC

Answer

............................................... [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

4024/12/O/N/13

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 6 3 1 7 7 7 6 4 0 6 *

4024/21

MATHEMATICS (SYLLABUS D)

October/November 2013

Paper 2 

2 hours 30 minutes

Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 24 printed pages. DC (LEG/CGW) 84304/2 R © UCLES 2013

[Turn over

2









Section A [52marks]











Answerallquestionsinthissection.

1

(a) Therateofexchangebetweendollars($)andpounds(£)is$1.56=£1. Therateofexchangebetweeneuros(€)andpoundsis€1.10=£1.





(i) Amychanges£300intodollars.







CalculatehowmanydollarsAmyreceives.



Answer $............................................. [1]









(ii) Benchanges€770intopounds. CalculatehowmanypoundsBenreceives.



Answer £............................................. [1]









(iii) Chrischanges$780intoeuros.

©UCLES2013

CalculatehowmanyeurosChrisreceives.

Answer € ............................................ [2] 4024/21/O/N/13

For Examiner’s Use

3

(b) DebbiechangedsomedollarsintoJapaneseyen. Therateofexchangewas81dollars=1yen.





Emmachangedthesamenumberofdollarsintoyen. TherateofexchangeforEmmawas82dollars=1yen.





Emmareceived3feweryenthanDebbie.





Giventhatthenumberofdollarschangedeachtimeisx,findx.



©UCLES2013

For Examiner’s Use

Answer ............................................... [3]

4024/21/O/N/13

[Turn over

4 2

t =40˚andAC=8cm. (a) ConstructthetriangleABCinwhich BAC





For Examiner’s Use

CisabovethelineAB,whichisdrawnforyou.

A

B



[2]



(b) Constructthelocusofallthepointsoutsidethetrianglethatare2cmfromtheperimeterof thetriangle. [2]



(c) FindandlabelthepointP, insidethetriangle,thatis6.5cmfromAand equidistantfromBandC.

©UCLES2013

4024/21/O/N/13

[2]

5 3

ThelineAB joinsthepointA(–2,1)tothepointB(6,5).



(a) FindthecoordinatesofthemidpointofAB.



Answer (..............,..............)

[1]

(b) FindthegradientofAB.



Answer ............................................... [1]



(c) AB intersectsthey-axisatthepoint(0,c).





Findc.



For Examiner’s Use

Answer ............................................... [2] (d) Express ABasacolumnvector.



Answer



(e) Cisthepoint(5,2)andDisthepoint(h,k). ThelinesAB andCD areequalinlengthandparallel.





[1]

FindthecoordinatesofeachofthepossiblepointsD.



©UCLES2013

Answer (..............,..............)and(..............,..............)[3]

4024/21/O/N/13

[Turn over

6 4

Thetableshowsthedistributionofthemassesof100babiesatbirth.

Mass (xkg)

1.5<xG2 2<xG2.5 2.5<xG3 3<xG3.5 3.5<xG4 4<xG4.5 4.5<xG5

Number ofbabies

For Examiner’s Use

3

12

20

24

25

14

2

(a) Writedownthemodalclass.



Answer ............................................... [1]

 

(b) Forthispartofthequestionusethegridbelow.  Usingascaleof4cmtorepresent1kg,drawahorizontalx-axisfor1 G x G 5.  Usingascaleof2cmtorepresent5babies,drawaverticalaxisforfrequencyfrom0to30.





Usingyouraxes,drawafrequencypolygontorepresenttheseresults.



©UCLES2013

[2]

4024/21/O/N/13

7

(c) (i) Completethecumulativefrequencytablebelow.





Mass(xkg)

xG2

x G 2.5

Cumulativefrequency

3

15

xG3

x G 3.5

xG4

x G 4.5

For Examiner’s Use

xG5 100

[1]

(ii) Onthegridbelowdrawasmoothcumulativefrequencycurvetorepresenttheseresults. 100

90

80

70

60 Cumulative 50 frequency 40

30

20

10

0

1

1.5



(d) Useyourcurvetoestimate





(i) themedianmass,





(ii) the10thpercentile.



©UCLES2013

2

2.5

3 Mass (kg)

3.5

4

4.5

5 x

[2]

Answer .......................................... kg[1]

Answer .......................................... kg[1]

4024/21/O/N/13

[Turn over

8 5

(a) Solve

2 = 1. 3- x



Answer  ............................................... [1]



(b) Factorise





(i) 5x + 5y ,



Answer  ............................................... [1]

(ii) 9x 2 - 16 .



Answer  ............................................... [1] (c) (i) Factorise 2x 2 + 5x - 12 .



For Examiner’s Use

Answer  ............................................... [1]

(ii) Useyouranswertopart (c)(i)tosolvetheequation 2x 2 + 5x - 12 = 0 .



©UCLES2013

Answer x=.................or.................[1]

4024/21/O/N/13

9

(d) Asourceoflightisobservedfromadistanceofdmetres. Theamountoflightreceived, Lunits,isinverselyproportionaltothesquareofthedistance.





For Examiner’s Use

GiventhatL=9whend=2,findthevalueofLwhend=3.



©UCLES2013

Answer ............................................... [2]

4024/21/O/N/13

[Turn over

10 6

(a)

For Examiner’s Use

A

D

C

50°

B

31





t = 50candBC = 31m. t = 90c, ACB InthetriangleABC, ABC t = 90c. DisthepointonAC suchthat BDA





(i) ShowthatCD=19.93m,correctto2decimalplaces.



[2]

(ii) CalculateAD.



©UCLES2013

Answer ...........................................m[3]

4024/21/O/N/13

11

(b)

For Examiner’s Use

S 10°

55° 52

P

R

Q

  

  

TwoboatsareatthepointsPandQ. RSisaverticalcliffofheight52m. t = 10cand QStR = 55c. PSQ





(i) StatetheangleofdepressionofP fromS.



Answer ............................................... [1]

(ii) Calculatethedistance,PQ,betweentheboats.



©UCLES2013

Answer  ...........................................m[3]

4024/21/O/N/13

[Turn over

12 7

(a)

For Examiner’s Use

A E C D B





t and IntriangleABC,Disthepoint onBC suchthatAD bisects BAC E isthepointonABsuchthatAE = AC.





(i) ShowthattrianglesAEDandACD arecongruent.



[3]

t = zc, t = xc, EDB t = ycand ACB (ii) Giventhat ABD findxintermsofyandz.



©UCLES2013

Answer x=......................................... [2]

4024/21/O/N/13

13

(b)

For Examiner’s Use

P S R Q





t andRSbisects PRQ t . IntrianglePQR,QSbisects PQR t t PQR = 42cand PRQ = 54c.





FindreflexangleQSR.



©UCLES2013

Answer ............................................... [2]

4024/21/O/N/13

[Turn over

14









Section B [48marks]











Answerfourquestionsinthissection.











Eachquestioninthissectioncarries12marks.

8

(a)

For Examiner’s Use

B 14 10

A O





Inthediagram,thecircleseachhavecentreO. ABisachordofthelargercircleandalsoatangenttothesmallercircle. AB =14cmandtheradiusofthelargercircleis10cm.





Findtheradiusofthesmallercircle.



Answer  ......................................... cm[3] (b) S

Q T R

P





Inthediagram,PQ andRSarechordsofacirclethatintersectatT.





(i) ShowthattrianglesPST andRQTaresimilar.

 ©UCLES2013

[3] 4024/21/O/N/13

15



(ii) S x

5

For Examiner’s Use

Q

T 11 R P





ST =5 cm,TR=11cmandTQ=xcm.





GiventhatPQ = 18 cm,showthatxsatisfiestheequation x 2 - 18x + 55 = 0 .



[2]

(iii) Solvetheequation x 2 - 18x + 55 = 0 . Giveeachsolutioncorrectto1decimalplace.



Answer x=.................or.................[3]

(iv) FindthedifferencebetweenthelengthsofPTandTQ.



©UCLES2013

Answer  ......................................... cm[1]

4024/21/O/N/13

[Turn over

16 9  

Thenumberofbacteriainacolonytrebles everyhour. Thecolonystartswith50bacteria. Thetablebelowshowsthenumberofbacteria(y)inthecolonyaftert hours. Time (t hours)

0

1

2

2.5

3

3.5

Numberof bacteria(y)

50

150

450

780

1350

2340

For Examiner’s Use

4



(a) Completethetable.

[1]



(b) Onthegridontheoppositepageplotthepointsinthetable,andjointhemwitha smoothcurve.

[3]



(c) Useyourgraphtofindthenumberofbacteriainthecolonywhent=3.2.



Answer ............................................... [1] (d) (i) Bydrawingatangent,estimatethegradientofthecurvewhent=2.5.



Answer  ............................................... [2]

(ii) Whatdoesthisgradientrepresent? Answer........................................................................................................................ ..................................................................................................................................... [1]



(e) Giventhattheequationofthegraphis y = ka t , findkanda.



Answer k=..................a=.................[1]



(f) Thenumberofbacteriainanothercolonyisgivenbytheequation y = 500 + 500t .





(i) Onthesameaxes,drawagraphtorepresentthenumberofbacteriainthiscolony.



[2]

(ii) Statethevalueoftwhenthenumberofbacteriaineachcolonyisthesame.

©UCLES2013

Answer ............................................... [1] 4024/21/O/N/13

17 y

For Examiner’s Use

5000

4500

4000

3500

3000 Number of bacteria 2500

2000

1500

1000

500

0

1

2

3

4

t

Time (t hours)

©UCLES2013

4024/21/O/N/13

[Turn over

18 10 Afueltankerdeliversfuelinacylindricalcontaineroflength9.5mandradius0.8m.

(a) Afterseveraldeliveries,thefuelremaininginthecontainerisshowninthediagram. 9.5 O 0.8

A

B





t = 90c. AB ishorizontal,Oisthecentreofthecircularcross-sectionand AOB





(i) Calculatethecurvedsurfaceareaofthecontainerthatisincontactwiththefuel.

Answer ......................................... m2[2]





(ii) Calculatethevolumeoffuelremaininginthecontainer.

Answer ......................................... m3[4]





(iii) Calculatethisvolumeremainingasapercentageofthevolumeofthewholecontainer.

©UCLES2013

Answer  ...........................................%[2] 4024/21/O/N/13

For Examiner’s Use

19

(b) Thefuelispumpedthroughacylindricalpipeofradius4.5cmatarateof300cm/s.





(i) Calculatethevolumepumpedin1second.

Answer  ....................................... cm3[1]



For Examiner’s Use



(ii) Calculatethetimetaken,inminutes,topump25000litresoffuel. Giveyouranswercorrecttothenearestminute.



©UCLES2013

Answer  ................................. minutes[3]

4024/21/O/N/13

[Turn over

20 11 ThediagramshowstrianglesAandB.

For Examiner’s Use

y 10 8 6 4 A

2 0



2

B

4

6

8

10

12

14

16

18

20

22

24

26

x

(a) (i) DescribefullythesingletransformationthatmapstriangleA ontotriangleB. Answer ......................................................................................................................... ...................................................................................................................................... [2]





(ii) Findthematrixthatrepresentsthistransformation.

Answer  f



p



(b) TriangleB ismappedontotriangleCbythetransformationrepresentedbythe 2 0 m.  matrix c 0 1





(i) Onthegridabove,drawandlabeltriangleC.





(ii) Givethenameofthistransformation.





©UCLES2013

[2]

[2]

Answer  ............................................... [1]

4024/21/O/N/13

21



(iii) Find the matrix that represents the inverse transformation that maps triangle C onto triangleB.

Answer  f





[2]

(iv) FindtheratioareaoftriangleC :areaoftriangleB.



p

For Examiner’s Use

Answer .....................:.....................[1] (c) FindthematrixthatrepresentsthesingletransformationthatmapstriangleA ontotriangleC.



Answer f

p

[2]

_________________________________________________________________________________ ©UCLES2013

4024/21/O/N/13

[Turn over

22 12 (a)

For Examiner’s Use

A 65°

C 45° B





t = 65c. t = 45cand BAC IntriangleABC, ABC AC is5cmshorterthanBC.





(i) Showthat BC =

5 sin 65 . sin 65 - sin 45



[3]

(ii) FindthelengthofBC.



©UCLES2013

Answer  ......................................... cm[1]

4024/21/O/N/13

23

(b)

For Examiner’s Use

P

13

Q

6

10

R

S





IntrianglePQR,PQ=13cm,QR=6cmandRP=10cm. QRisproducedtoS.





t ,givingyouranswerasafractioninitslowestterms. (i) Findthevalueofcos PRQ



Answer ............................................... [3]

t . (ii) Hencewritedownthevalueofcos PRS



Answer ............................................... [1]

Turn over for The reST of ThiS queSTion

©UCLES2013

4024/21/O/N/13

[Turn over

24

(c)

For Examiner’s Use

F

D

E





TriangleDEGhasthesameareaastriangleDEF,butisnotcongruenttotriangleDEF. ThepointG islowerthanDEandGE=EF.





DrawthetriangleDEGinthediagramabove.



t = 30candML=2MN. (d) IntriangleLMN, LMN





[1]

WhentheareaoftriangleLMNis18cm2,calculateMN.



Answer  ......................................... cm[3]

Permissiontoreproduceitemswherethird-partyownedmaterialprotectedbycopyrightisincludedhasbeensoughtandclearedwherepossible.Everyreasonableefforthasbeen madebythepublisher(UCLES)totracecopyrightholders,butifanyitemsrequiringclearancehaveunwittinglybeenincluded,thepublisherwillbepleasedtomakeamendsat theearliestpossibleopportunity. UniversityofCambridgeInternationalExaminationsispartoftheCambridgeAssessmentGroup.CambridgeAssessmentisthebrandnameofUniversityofCambridgeLocal ExaminationsSyndicate(UCLES),whichisitselfadepartmentoftheUniversityofCambridge.

©UCLES2013

4024/21/O/N/13

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 8 0 9 4 8 7 4 2 7 1 *

4024/22

MATHEMATICS (SYLLABUS D)

October/November 2013

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 24 printed pages. DC (LEG/SW) 67172/1 © UCLES 2013

[Turn over

2











Section A [52 marks] Answer all questions in this section.

1 C B 58

40 A

34

F

38

E

42

D



ABCD is a level field. F and E are points on AD such that BF and CE are perpendicular to AD. BF = 40 m and CE = 58 m. AF = 34 m, FE = 38 m and ED = 42 m.



(a) Calculate the area of the field.

Answer .......................................... m2 [3]

© UCLES 2013

4024/22/O/N/13

For Examiner’s Use

3 (b) Calculate the length of BC.

For Examiner’s Use

Answer ........................................... m [2]

t . (c) Calculate CDE

Answer ................................................ [2]

© UCLES 2013

4024/22/O/N/13

[Turn over

4 2



(a) The results of a survey of the number of cars owned by 50 families are given in the table below.



Number of cars

0

1

2

3

Number of families

4

35

6

5

(i) Calculate the mean number of cars per family.

Answer ................................................ [2]



(ii) When the same 50 families were surveyed at a later date, the results were as follows.

Number of cars

0

1

2

3

Number of families

x

37

y

5





The mean number of cars per family stayed the same as before.





Find x and y.

Answer

x = ......................................... y = .......................................... [2]

© UCLES 2013

4024/22/O/N/13

For Examiner’s Use

5

(b) A service station sells diesel, unleaded and super unleaded fuel. During one week, 13 500 litres of diesel and 36 000 litres of unleaded were sold. The total number of litres of fuel sold that week was 54 000.





For Examiner’s Use

(i) What fraction of the total number of litres sold was super unleaded? Give your answer in its lowest terms.

Answer ................................................ [1]







(ii) Complete the pie chart to represent the amounts of fuel sold. Answer

Diesel

[3]

© UCLES 2013

4024/22/O/N/13

[Turn over

6

a + a2 + b2 when a = - 4 and b = - 3. a 2 - 2ab Give your answer as a fraction.

3

(a) Find the value of





Answer ................................................ [2]

(b) Expand the brackets and simplify

^3x 2 - 1h^2x + 3h - x ^9x - 2h.

Answer ................................................ [2]

(c) (i) Factorise

9x 2 + 5x - 4 .

Answer ................................................ [1]

© UCLES 2013

4024/22/O/N/13

For Examiner’s Use

7



(ii) Use your answer to part (c)(i) to solve the equation



(d) The sum of three consecutive integers is 84.





9x 2 + 5x - 4 = 0 .

For Examiner’s Use

Answer

x = .................. or ................. [1]

Answer

............. , ............. , ............. [2]

Find these three integers.



© UCLES 2013

4024/22/O/N/13

[Turn over

8 4

(a) AB and BC are chords of a circle centre O. D is the midpoint of AB and E is the midpoint of BC. t = 108c. ABC

B

108°

C

E

For Examiner’s Use

t giving your reasons. Find DOE D

O

A

t = .......................... because .......................................................................... Answer DOE .............................................................................................................................................. [2]

(b)

R P

Q S





A circle centre P and a circle centre Q intersect at R and S.





(i) Show that triangle PRQ is congruent to triangle PSQ.

[3] © UCLES 2013

4024/22/O/N/13

9



(ii)

For Examiner’s Use

R T

P

Q

S





RS and PQ intersect at T.





(a) State the name of the special quadrilateral PRQS.

Answer ................................................ [1] t . (b) Find PTR

Answer ................................................ [1]

© UCLES 2013

4024/22/O/N/13

[Turn over

10 5

(a)  = {x : x is an integer and 2 G x G 12 } M = {x : x is a multiple of 3} P = {x : x is a prime number}





(i) a ! M

For Examiner’s Use

P

Find a.

Answer ................................................ [1]



(ii) Find (M

P)l .

Answer ................................................ [1] (b) In a survey, 90 people were asked “Do you own a car?” and “Do you own a bicycle?”. A total of 27 people said they owned a bicycle. Of these, 13 owned only a bicycle. 11 people owned neither a car nor a bicycle. By drawing a Venn diagram, or otherwise, find how many people said that they owned a car.

Answer ................................................ [2]

© UCLES 2013

4024/22/O/N/13

11

(c) The Venn diagrams show a Universal set, , and subsets A, B and C.





(i) Shade the set (A

C)l

For Examiner’s Use

B.

 B

A

C

[1]





(ii) Express in set notation the subset shaded in this diagram.

 B

A

C

Answer ................................................ [1]

© UCLES 2013

4024/22/O/N/13

[Turn over

12 6

(a) (i) The cost price of bicycle A is $620. The shopkeeper sells it and makes a profit of 45%.





Calculate the selling price.

Answer $ .............................................. [1]







(ii) In a sale, the price of bicycle B is reduced from $2400 to $1596. Calculate the percentage reduction given.

Answer ............................................% [2]







(iii) Tax on the original price of bicycle C is charged at 20% of the original price. After tax has been included, Matthew pays $1080 for this bicycle. Calculate the original price.

Answer $ .............................................. [2]

(b) Ada invests $600 in an account that earns simple interest. At the end of 3 years, the investment is worth $681.





Calculate the rate of simple interest per year.

Answer ............................................% [3]

© UCLES 2013

4024/22/O/N/13

For Examiner’s Use

13

7



(a) Express as a single matrix

(b) Express as a single matrix



(c) A = c













2 1 5 f - 1 p - 4 f - 3 p. 3 0

c

7 -1 2 0

For Examiner’s Use

Answer

[2]

Answer

[2]

1 3 m f 0 p. 4 2

1 0 m -2 4

(i) Find A - 1 .

Answer

f

p

[2]

Answer

f

p

[2]

(ii) B + 3I = A where I is the 2 # 2 identity matrix.

© UCLES 2013

Find B.

4024/22/O/N/13

[Turn over

14 Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks.

8 A

6 O

310°

B



The diagram shows a sector AOB of a circle with centre O and radius 6 cm. The angle of the sector is 310c.



(a) Calculate the total perimeter of the sector.

Answer .......................................... cm [3] (b) Calculate the area of the sector.

Answer .........................................cm2 [2]

© UCLES 2013

4024/22/O/N/13

For Examiner’s Use

15

(c) This sector is cut from a rectangular piece of card of height 12 cm and width w cm.

A

6 O

310°

For Examiner’s Use

12

B

w



One edge of the rectangular piece of card passes through A and B. The other edges are tangents to the circle.





(i) Calculate the value of w.

Answer ................................................ [3]







(ii) When the sector is cut out, the triangle AOB is retained. The rest of the rectangular piece of card, shown shaded, is discarded as waste. Calculate the percentage of the rectangular piece of card that is discarded as waste.

Answer ...........................................% [4]

© UCLES 2013

4024/22/O/N/13

[Turn over

16 9



1 y = x+ . x The table below shows some values of x and the corresponding values of y. The values of y are correct to 2 decimal places where appropriate. The variables x and y are connected by the equation

For Examiner’s Use

x

0.25

0.5

0.75

1

1.25

1.5

1.75

2

y

4.25

2.5

2.08

2

2.05

2.17

2.32

2.5

(a) On the grid, plot the points given in the table and join them with a smooth curve. y 5

4

3

2

1

–2

–1

0

1

2 x

–1

–2

–3

–4

–5 © UCLES 2013

[2] 4024/22/O/N/13

17

(b) By drawing a tangent, estimate the gradient of the curve when x = 0.75.

For Examiner’s Use

Answer ................................................ [2]

1 (c) Let f (x) = x + . x





(i) Given that f (a) = b , find f (- a) in terms of b.

Answer ................................................ [1]



1 (ii) Hence, or otherwise, complete the table below for y = x + . x x y

–2

–1.75

–1.5

–1.25

–1

–0.75

–0.5

–0.25

–2 [1] 1 for - 2 G x G - 0.25. x





(iii) On the grid opposite, draw the graph of y = x +





(iv) Write down an estimate for the gradient of the curve when x =- 0.75.

[1]

Answer ................................................ [1]

(d) (i) On the grid opposite, draw the graph of the straight line y = 4 - x .









[1]

(ii) Write down the x-coordinate of each of the points where the graphs of y = 4 - x and 1 y = x+ intersect. x

Answer x = ........... and ........... [1]



(iii) Find the equation for which these x values are the solutions. Give your equation in the form Ax 2 + Bx + C = 0 .

Answer ................................................ [2]

© UCLES 2013

4024/22/O/N/13

[Turn over

18 10 (a)

For Examiner’s Use

North

A

6

C

115°

8

B



Two boats sail from A. One boat sails to B, and the other boat sails to C. t = 115c. AB = 8 km, AC = 6 km and BAC





(i) Calculate the distance, BC, between the boats.

Answer ..........................................km [4]



(ii) The bearing of B from A is 200c.





Find the bearing of A from C.

Answer ................................................ [2] © UCLES 2013

4024/22/O/N/13

19

(b)

For Examiner’s Use

P 36°

S

44° R

200

65°





t = 65c and QSP t = 44c. In triangle PQS, SQP t = 36c. R is the point on QS such that QR = 200 m and RPS





(i) In triangle PQR, by using the sine rule, show that PR =

Q

200 sin 65 . sin 35

[2]



(ii) Hence show that SR =

200 sin 65 sin 36 . sin 35 sin 44

[2]



(iii) Hence find the length of SR.





(iv) Hence evaluate

Answer ............................................m [1]

area of triangle SPQ . area of triangle PQR

Answer ................................................ [1]

© UCLES 2013

4024/22/O/N/13

[Turn over

20

7 4 . p + 2 2p - 3

11 (a) Express as a single fraction, in its simplest form,

For Examiner’s Use

Answer ................................................ [3]

(b) The distance between London and York is 320 km . A train takes x hours to travel between London and York.





(i) Write down an expression, in terms of x, for the average speed of the train.

Answer .......................................km/h [1]



(ii) A car takes 2 21 hours longer than a train to travel between London and York. The average speed of the train is 80 km/h greater than the average speed of the car. Form an equation in x and show that it simplifies to 2x 2 + 5x - 20 = 0 .

[3]

© UCLES 2013

4024/22/O/N/13

21



(iii) Solve the equation

2x 2 + 5x - 20 = 0 , giving your answers correct to 2 decimal places.

Answer



For Examiner’s Use

x = ................. or ................. [3]

(iv) Hence find the average speed of the car correct to the nearest km/h.

Answer .......................................km/h [2]

© UCLES 2013

4024/22/O/N/13

[Turn over

22 12 (a) B

F

For Examiner’s Use

C

G E

D H A







6 (i) AD = c m 1 Calculate AD .

Answer ................................................ [1] 1 (ii) AE = c m 2









H is the midpoint of AD.





Find EH .

Answer

© UCLES 2013

4024/22/O/N/13

f

p

[2]

23



(iii) BF = c

1.5 m 0

CG = c

0.5 m -1.5

For Examiner’s Use

F is the midpoint of BC.

Find FG .



Answer











f

p

[1]

(iv) Use your answers to parts (ii) and (iii) to complete the following statement.

The lines EH and FG are ............................................. and ............................................. [1] (v) Given that E is the midpoint of AB, show that G is the midpoint of CD.

[2] Turn over for The reST of ThIS queSTIon © UCLES 2013

4024/22/O/N/13

[Turn over

24

(b)

y

For Examiner’s Use

7

6

5 A

4

3

2

1

O

1

2

3

4

5 x





Triangle A has vertices (1, 2), (1, 5) and (3, 5).





(i) An enlargement, centre (1, 2), scale factor 1.5, maps triangle A onto triangle B.

















Draw triangle B.

[2]

(ii) An enlargement, centre (1, 2), scale factor - 0.5, maps triangle A onto triangle C. Draw triangle C. (iii) Find the ratio

[2]

area of triangle C : area of triangle B.

Answer .................... : .................... [1] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

4024/22/O/N/13

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/11

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

Paper 11

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied

Question 1

2

3

4

Mark

(a)

41 006

1

(b)

240 000

1

(a)

12

1

(b)

(0).08

1

(a)

3 cao 100

1

(b)

82

1

(a)

64

1

(b)

67

1

(2a – 3b)(c + 2d)

2

(a)

8 9

1

(b)

28

1

(c)

90

1

5

6

Answers

Part marks

B1 for one of the partial factorisations c(2a – 3b); 2d(2a – 3b); 2a(c + 2d); –3b(c + 2d) or their negatives, seen.

7 A correct method to eliminate one variable

M1

Either x = 4 or y = –1 WWW.

A1

Both x = 4 and y = –1 WWW.

A1 If [0] earned, then award C1 for a pair of values that satisfy either equation.

© Cambridge International Examinations 2014

Page 3

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

Paper 11

(a)

9

1

(b)

8

1

(c)

25

1

9

8 WWW

3

10 (a)

P ∩ Q ∩ R' oe

1

47

2

M1 for Cricket set inside the Football set, e.g. in a Venn diagram; Ans. = 30+8+9; “30 play both cricket and football”.

 330     417 

2

B1 for 330 or 417 in a (2 by 1) matrix, or for (330 417).

1 dep

Must refer to (i) the amount earned (money, earings, $, etc) and (ii) the two weeks.

8

(b)

11 (a) (b)

12 (a) (b)

P shows the amount earned in Week 1 and Week 2, oe 930

1

2 s − an oe n

2

d=

13

14 (a) (b)

15 (a) (b)

5v 2 64

M1 for a recognisable attempt at Pythagoras’ Theorem with sides 10 and 6. M1 for (AT2 =) 102 – 62 oe

M1 for correct first step, e.g. 2s = an + bn; s = na/2 + nb/2 or B1 for a correct expression for b seen in working, but followed by an error. M1 for d=kv2, or for 5 = k × 64; B1 for k = 5/64, or for

d 40 2 = 2 5 8

125

3

3.65

1

60 WWW

3

B1 for 192; or for cost price = $120, soi by (profit =) $72.  their192 − their120  M1 for   × 100 oe their120  

Triangle ABC drawn with an acceptable C.

2

21 to 22 inclusive, WWW; Or FT their triangle, provided the perp. height is not one of the sides, WWW.

2

B1 for AC = 7 cm or B1 for ∠ CAB = 130° M1 for 1 2 base × height with matching base and height.

© Cambridge International Examinations 2014

Page 4

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

Paper 11

x + y = 6 drawn correctly

1

(b)

2y + x = 4 drawn correctly

1

(c)

Correct region shaded, (FT for sloping lines with one correct line).

2

B1 for R correctly bordered by the lines y = 2 and x = –1; or FT appropriate shading between their sloping lines, provided one is correct

1

AG

20 WWW

3

B1 for 22 500 or 0.18 figs 225 soi and M1 for 3 figs18

14 41

1

(b)

149

1

(c)

(i)

16 (a)

17 (a)

(b)

18 (a)

Valid method, with leading to 180

1

2

(11 + 7) × 4 × 5

2 5 10 17

oe,

1

(ii) n2 – 1 oe

1

1.36 × 109

1

(i) 5.6 × 109

1

(ii) 7.93 × 105

2

20 (a)

F

1

(b)

C

1

(c)

B

1

(d)

E

1

(i) … alternate (angles) …

1

(ii) 119o

2

120 WWW

2

19 (a) (b)

21 (a)

(b)

B1 for figs 793, or for N × 105 with 1 < N < 10.

180 − 58 , 2 or B1 for a base angle = 61o

M1 for

C1 for 240. M1 for 2x + 80 + 95 + 125 = 540, oe

© Cambridge International Examinations 2014

Page 5

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

Paper 11

42

1

(b)

Correct plots at 20, 40, 60, 90, 120 and CF curve drawn

2

B1 for three or four correct plots

(c)

(i) 62 to 64 inclusive

1

FT from their CF graph

(ii) 41 to 46 inclusive WWW, FT (F80–F50) from their graph.

2

M1 for attempt to calculate (F80–F50) from their graph.

(i) the point B marked correctly

1

(ii) the point C marked correctly

1

(iii) the point D marked correctly

1

(i) q – p

1

22 (a)

23 (a)

(b)

(ii)

2

(iii)

1

3

p+

1

3

q–

(4 3 ) p, or FT their(ii) – 2p

3

If [0] scored in (a), in (aiii) award B1 for  − 6 the vector   soi.  1 

1

q

2

M1 for OT = OR + RT Or for OT = OP + PR + RT Or for OT = OQ + QR + RT Or equivalents in terms of p and q.

© Cambridge International Examinations 2014

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/12

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Question 1

2

3

4

5

6

Mark

(a)

5.11 oe

1

(b)

2 hours and 35 minutes

1

(a)

59

1

(b)

T=

(a)

–0.5

1

(b)

0.1

1

(a)

–5

1

(b)

x+6 2

oe

1

(a)

1200 cao

1

(b)

3

1

(a)

Correct region shaded

1

(b)

3

1

25

2

(a)

1 : 2 oe

1

(b)

1 : 8 oe, or ft their(a) cubed

1

7

8

Answers

13M + 20 oe seen 500

Part marks

1

B

A

C

C1 for figs. 25 figs 9 or M1 for oe 60 × 60

© Cambridge International Examinations 2014

Paper 12

Page 3

Mark Scheme Cambridge O Level – October/November 2014

(a)

54.25

1

(b)

d + 0.5 d + 0.5 , or ft , seen 54.25 their (a )

1

10

12

2

11 (a)

1

1

9

(b)

41

(c)

(2n + 1 )2 oe

1

12 (a)

5.67 × 10–4

1

(b)

6 × 10 –12

2

13 (a)

140

1

(b)

1.2

2

14 (a)

10

1

216

2

(b)

40

81

(all three)

Syllabus 4024

Paper 12

B1 for “k” = 72 or M1 for 9 × 8 = 6y oe or M1 for y = (their k)/6 when y = “k”/x used

1

C1 for figs 6, or for the index –12

7  M1 for 3 ×  − 1 ; or 5   their (a )  3×  − 1 ; oe   100 or a complete algebraic method.

M1 for π × 6 ×10 =

x × πr2 360

x × 2πr 360 where r = 10 or their(a). Where radians are used, method must 180 . include multiplication by π

or 2 × π × 6 =

15 (a) (b)

720

1

20

2

M1 for ( π × 62 × d ) (oe) = kπ where k = 720 or their(a)

© Cambridge International Examinations 2014

Page 4

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

16 (a)

 −4     −3 

1

(b)

 −3     −4 

1

(c)

5 cao

1

p5 – 3

2

B1 for p5 , or for – 3.

3x2

2

C1 for 3; C1 for x2

4a(1 – 4a)

1

(b)

(3b – c)(3b + c)

1

(c)

(x + 5)(x – y)

2

4

1

90°

1

two 150° } correctly obtained

1

two 135° } correctly obtained

1

17 (a) (b) 18 (a)

19 (a) (b)

Paper 12

B1 for one of the partial factorisations x(x – y); 5(x – y); x(x + 5); y(x + 5), or their negatives.

If [0] earned for the two 150s, award M1 for using 360° correctly in a quadrilateral, or for using 540° correctly in a pentagon, or for using 720° correctly in a hexagon, to find the 135. If [0] earned in (b), then B1 for (angle sum of a hexagon equals) 720° seen.

© Cambridge International Examinations 2014

Page 5

Mark Scheme Cambridge O Level – October/November 2014

20 (a)

68

1

(b)

44

1

(c)

112 or ft 180 – their(a)

1

(d)

44 or ft their(b)

1

Correct completion of tree diagram

1

21 (a) (b)

1 10 17 (ii) or ft from their tree diagram 50 (i)

Syllabus 4024

Paper 12

1 2

22 (a)

1.2

1

(b)

3.6

1

(c)

480

2

M1 for 3 2 2 1  × or their (bi )} + × their   5 5 5 4

M1 for

1 × (20 + 60) × 12 oe 2

or B1 for 180, or 240, or 60, or 420, or 300, as a correct evaluation of an identifiable appropriate area. (8, 10)

1

(b)

x > 8 oe 2y > 12 + x oe

1 1

(c)

(9, 11)

1

137° to 140° inclusive

1

(i) perp. bisector of AB

1

(ii) circle, centre C, radius 4 cm

1

(iii) correct region (bottom part) shaded

1

23 (a)

24 (a) (b)

If 0 scored, then C1 for x > 8 oe and 2y > 12 + x oe.

© Cambridge International Examinations 2014

Page 6

25 (a)

Mark Scheme Cambridge O Level – October/November 2014  1   − , 1  2 

Paper 12

1

6 7

(b)

−

(c)

(i) (10, –8)

2

1 3

1

(ii)

Syllabus 4024

1

C1 for one correct coordinate

1 7

1

(b)

 −1 −4     2 0

2

C1 for 2 or 3 correct elements.

(c)

(2 0), or (14 × their (a) 0) ft

2

M1 for ( Y =) ( 6 2 ) A–1 seen. If (x y) A = (6 2) is used, then award M1 at the stage where an attempt to solve the simultaneous eqns. is made.

26 (a)

© Cambridge International Examinations 2014

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/21

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2014

Syllabus 4024

Paper 21

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Question

Answers

1

6

1

(ii)

1 500

1

(iii)

2.7

1

(b)

9

1

(c) (i)

3.5

2

B1 for 1.2 seen or division by 120 20 x = 4.2 or M1 for x + oe 100

Special promotion tin + working

2

M1 attempt at one rate

15 05 or 3 05 pm

2

B1 for (0)9 05 or (0)3 50 seen

(a) (i)

(ii) 2

(a)

Mark

Part Marks

or M1 for 21 50 + 11 15 or 21 50 + 6 (b)

11 hours 55 minutes

2

(c) (i)

290 (280 to 300)

1

45 or ft from their (c)(i)

1

(d)

827

2

M1 for 683 + k × 24

(a) (i)

Correct quadratic graph through 11 points

3

B2 for curve through at least 8 ft points or for 11 ft points or B1 for 16 in the table twice or for 6 ft points

(ii)

3

(ii)

– 2.35 to – 2.25 and 4.25 to 4.4

(iii)

3.25 to 4.75

2ft 2

B1 for (0)1 45 or 5 hours and 55 minutes seen or M1 for 13 40 – (0)7 45 + 6 oe

B1 for one correct solution or M1 for y = 2 drawn B1 for tangent drawn at x = 3 or for a gradient in range

© Cambridge International Examinations 2014

Page 3

Mark Scheme Cambridge O Level – October/November 2014 2.54, – 3.54

(b)

3

Syllabus 4024

Paper 21

Working seen and www B1 for 12 − 4 × 1 × (−9)

soi

− 1 ± their 37 2 ×1 After B1 or B0 so far,

and B1 for

M1 for both real values of their

4

5

6

p± q r

(c)

( y =) − 3 x + 1

2

B1 for ( y =) − 3 x + c or ( y =)mx + 1 or M1 for (i) theoretical or (ii) practical

(a)

p = 12, q = 16

2

B1 for one correct Or M1 for k × 5 or l × 2.5 where k and l are attempts to read from the histogram

(b) (i)

29.5

3

M1 for sum of the midvalues × frequency and M1 for division by 60

(ii)

2070

2

M1 for attempt to use upper bounds of individual intervals

(a)

19.46 seen

4

Working seen. No wrong working. M2 for 14 2 + 8 2 − 2 × 14 × 8 × cos 122 and A1 for 378.7 soi or M1 for an incorrect formula with one error and A1 for 141.3 or 319.35 or 250.7 soi

(b)

37.5 to 37.6

3

(c)

247 to 248

4

(a)

−1

1

(b)

x+7 2

2

M1 for x = 2 y − 7

3

B1 for 2(3g) – 7 = g + 4 soi and B1 for mg = 11 or 5g = n or SC1 after B0 for solving their linear f(3g) = g + 4

(c)

g = 2.2 or 2

11 1 or 5 5

14 sin 122 19.5 sin B sin 122 = or M1 for oe 14 19.5 SC1 for correct method for wrong angle M2 for

M1 for 0.5 × 8 × 8 × sinC = 26 and A1 for 54.34 and M1 for 180 – their 54.34 or 238 – their 54.34 SC1 after 0 for CE = 8

oe

soi y+7 or SC1 for the answer 2

© Cambridge International Examinations 2014

soi

Page 4

7

Mark Scheme Cambridge O Level – October/November 2014

1

( y =) − 4

2

M1 for 4y – 6y – 3 = 5 or correctly rearranges their linear equation

(b)

3w final answer w+2

3

B1 for 15w(w – 2) and B1 for 5(w + 2)(w – 2)

(c) (i)

p( p + 20) or p 2 + 20 p

1

Correct equation and the given form correctly derived.

2

(ii)

(iii) (a)

p = 50 and p = – 70

2

70

(a) (i)

112 to 116

1

(ii)

Perpendicular bisector of AB

1

(iii) (a)

Correct region shaded.

2

(iv) (b) (i) (ii)

1ft

Accept their positive p + 20

M1 for clearly identifiable arc centre B radius 8 cm

Yes as path of D passes through the shaded region

2

M1 for line from their D on a bearing 075

9.43

2

M1 for (PR2 =) 52 + 82

6.38 to 6.39

3

M2 for sin53 =

1

correct triangle

2

(c)

x = − 2 .5

1

(d)

4

1

(e)

Correct octagon

2

(b)

M1 for (p ± h)(p ± k) where hk = 3500

1

−1

(a)

M1 for 35( p 2 + 20 p ) and A1 for 35( p 2 + 20 p ) = 122500 And the given form established.

(b)

(b) 2.9 to 3.1

9

Paper 21

3 or 0.75 4

(a) (i) (ii)

8

Syllabus 4024

x oe 8 or B1 for correct triangle

soi

B1 for two vertices correct or for an incorrect reflection

M1 for 6 correct vertices or octagon scale factor 2 incorrectly placed

© Cambridge International Examinations 2014

Page 5

(f)

Mark Scheme Cambridge O Level – October/November 2014

(i)

1575

2

(ii)

30

1

(iii)

10350

2ft

2x

1

(b) 4x

1

10 (a) (i) (a)

(c)

90 − 2 x oe

Syllabus 4024

B1 for any correct relevant area such as 2025 or 1125 or 112.5 soi or M1 for a complete, consistent, method

ft their 900 + 6 × their 1575 B1 for 450 seen or M1 for complete, consistent, method

1ft

19

3

M2 for 180 − 3 x = 123 oe ˆ or B1 for BE 0 = (180 − 123)

22.3

2

M1 for

476 to 477

4

23 to 25

1

(ii)

12 45 (pm)

1

(iii)

1.9

1

(iv) (a)

Straight lines to (14 45, 5.4) and from (14 45, 5.4) to (15 39, 0)

2

(ii)

(b) (i)

(ii)

11 (a) (i)

Paper 21

(b) 6 cao

40 × π × 82 360

40 ×π × 16 360 and M1 for 2 × their 22.3 and B1 for 8 × 20 M1 for

M1 for straight line d = 5.4 or straight line from their (14 45, 5.4) to (15 39, 0)

1

(b) (i)

Correct sectors and labels

2

(ii)

5 or 0.417 or 0.4166.... 12

1

(iii)

41 oe, 0.621 66

3

M1 for sector of 30 or 150

5 4 6 5 × − × oe 12 11 12 11 5 4 6 5 × × or M1 for such as or 12 11 12 11 After 0, SC1 for 5 6 5 1 6 1 (2) × × + (2) × × + (2) × × 12 12 12 12 12 12

M2 for 1 −

© Cambridge International Examinations 2014

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2014 series

4024 MATHEMATICS (SYLLABUS D) 4024/22

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2014

Question 1

2

3

Answers

(a) (i) 30%

Mark 2

(ii) 305

3

(iii) 15 000

2

(b) (i) 65400

1

(ii) 294

1

(iii) 877

2

(a) (i) 23

1

(iii) Parallel lines established

1

(b)

Convincing argument

3

(a)

1 or 0.0625 16

1

(b)

42 or 0.164 oe 256

3

(ii)

(d)

Paper 22

Part Marks M1 for figs(5625 ÷ 18 750) or SC1 for 70(%) as final answer

22 oe and 100 18750 − their 2887.5 M1 for 52

M1 for (13125) ×

25 x = 18750 oe 100 or B1 for ÷ 125 M1 for x +

B1 for use of the quotient of the rates

1

(ii) 90 with reason

(c) (i) 26

Syllabus 4024

This must have e.g. XQ = XY justified. If there is no justification, then MAX B2 from B1 for XQ = XY oe And B1 for relating this to the perimeter of PXZ Or B1 for equal (alternate or bisected) angles

7 3 × 16 16 7 3 or B1 for both and 16 16 7 or SC1 after 0 for 40

B2 for (2 ) ×

1

m = 5 n = −3

2

p = 17

2

B1 for one correct or M1 for correct substitution and evaluation of the other variable or for an equation in one variable M1 for p × their m − 4 × their n(= 97 ) oe

© Cambridge International Examinations 2014

Page 3

4

(a) (i) 105

6

7

2

197.2 (m2)

Syllabus 4024

Paper 22

1 B1 for   × 7 × 3 × 10 2 or M1 for Area of cross section × 10 soi

4

M1 for 32 + 72 and M1 for area of one triangular face and M1 for area of one rectangular face

(b) (i) 0.845

2

M1 for

(ii) 0.280

2

(ii)

5

Mark Scheme Cambridge O Level – October/November 2014

(a)

63.7 or 63.6 (m)

(b)

9540 to 9560

2

h = sin 25 oe 2

y = tan[...] oe 0.6 or SC1 for 25 M1 for

M1 for π ×

d = 100 2

3ft

M1 for πr 2 soi and M1 for their circular area + 100 × their (a)

(c) (i) 18.7 to 19.0 (m)

3ft

M1 for 2πR And M1 for their 2πR − 200 or πR − 100

(ii) 30.8 to 31.1

2ft

M1 for

(a)

Correct shape ABCD

(b)

115 – 125 m

2ft

(a) (i) Convincing argument

3

4

θ × 2πr oe 360

) B1 for ABC = 56 ) B1 for BAD = 104 M1 line CD // AB A1 for perpendicular length 4.5

M1 for their CD www e.g. need to see b – a and

5 (b – a) 3

B1 for DE = b – a oe 2 2 B1 for DB = a or EC = b oe soi 3 3 (ii) 9 : 25 oe (b) (i) Triangle with vertices (6, 1), (10, 1), (10, 4)

2

B1 for at least 3 : 5 oe seen

2

B1 for two vertices correct

(ii) Stretch(ing)

1

 2 0    2 1

2

(iii)

B1 for one error or M1 for multiplication in the correct order

© Cambridge International Examinations 2014

Page 4

(iv)

8

Mark Scheme Cambridge O Level – October/November 2014

1  0  2    −1 1

2ft

(a) (i) 2.24 (ii)

B1 for

Syllabus 4024

Paper 22

 1 0 1  or their ft values or  2  − 2 2

1

(h = ) T

2

g

4π 2

oe

3

4π 2 h oe g and M1 for any correct transposition at any stage

M1 for T 2 =

(b)

14

2

B1 for 42 or 16 or M1 for 45 − p − 3 = 2 p

(c)

–5.5 oe

3

M1 for 3(2 x − 3) + 4(5 − x ) oe soi and M1 for 6 x − 4 x = 9 − 20 soi oe

(d)

–0.41 –3.26

3

B1 for 112 − 4 × 3 × 4 soi and B1 for

− 11 ± their73 2×3

After B1 or B0 so far p± q r

M1 for both real values of 9

(a) (i) 11.05 confirmed

1

1 × 5 × 7 × sin PQR 2

(ii) 39.1° or 39.2°

2

M1 for

(iii) 136.3°

3

M1 for 8 × 2 × sin ZWX =

1 × 4 × 6 × sin 67 2

oe and A1 for 43.7o soi or M1 for 180 − their 43.7 soi (b) (i) 6.16

3

M2 for 9 2 + 12 2 − 2 × 9 × 12 × cos 30 soi or M1 for cosine formula with 1 error and A1 for 412 (soi by 20.3), 131.5 (soi by 11.5) or 117 (soi by 10.8)

(ii) 41.4

3

M2 for cos CAM =

9 2 + 122 − 12.52 oe 2 × 9 × 12 or M1 for 12.5 2 = 9 2 + 12 2 − 2 × 9 × 12 cos θ oe After 0, SC1 for theirA – 30, or one of M or C

© Cambridge International Examinations 2014

Page 5

Mark Scheme Cambridge O Level – October/November 2014 11 11

1

(b)

correct scales, plots (ft) and curve

3

(c)

2 (±0.5)

10 (a)

2ft

(d) (i) –5 cao

1

(ii) (a) –1 (b) 5

2

(0.6) (3.4)

(e)

3ft

Syllabus 4024

Paper 22

P2 correct scales and at least 7 plots (ft) or All plots correct ft or P1 for aleast 7 plots (ft) or Correct scales drawn Dependent on tangent drawn at x = 3 M1 for tangent at x = 3

B1 for either B1 for x 2 − 4 x − 1 = −3 soi and B1 for the line y = −3 or M1 for x 2 − 4 x − 1 = k and A1 for the line y = k SC3 for 0 for new curve drawn

histogram correct

3

H2 for four columns correct or H1 for one correct frequency density

(b) (i) correct plots and give curve

2

P1 for at least 4 correct plots

11 (a)

(ii) (a) (195) (g)

1ft

(b) 72 to 88 (g) (iii)

2ft

50 78 72 32 4

(iv) (a) 36 cao

B1 for 152 to 158 and 230 to 240 Or M1 for UQ – LQ

1 1

(b) 85 or 86 or ft (th Percentile)

2ft

B1 for 15 or 14.4 or ft Or M1 for subtraction from 240 or 250

© Cambridge International Examinations 2014

Cambridge International Examinations Cambridge Ordinary Level

* 2 6 7 1 3 3 0 5 3 7 *

4024/11

MATHEMATICS (SYLLABUS D)

October/November 2014

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (CW/SG) 97865/3 © UCLES 2014

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Write the number forty one thousand and six in figures.



Answer

......................................... [1]

Answer

......................................... [1]

Answer

......................................... [1]

Answer

......................................... [1]

Answer

......................................... [1]

Answer

......................................... [1]

(b) Write 237 400 correct to two significant figures. 2

(a) Evaluate 10 + 2n 2 when n =-1 .

(b) Evaluate 0.4 # 0.2 .

3

(a) Write 3% as a fraction.

(b) Work out 90 - 16 ' 2 .



© UCLES 2014

4024/11/O/N/14

3

4

x is an integer between 50 and 70 . Write down the value of x when (a) x is a cube number,



Answer

......................................... [1]

Answer

......................................... [1]

(b) x is a prime factor of 268 .

5

Factorise



© UCLES 2014

2ac - 3bc - 6bd + 4ad .

Answer

4024/11/O/N/14

........................................................ [2]

[Turn over

4

6

(a) Express as a single fraction

2 3 ' . 3 4



Answer

......................................... [1]

Answer

......................................... [1]

(b) A bag of sweets contains mints and toffees only. There are 21 mints in the bag. One quarter of the sweets are toffees. Calculate the total number of sweets in the bag.

(c) $360 is shared in the ratio 3 : 5 .

Calculate the difference between the larger share and the smaller share.



© UCLES 2014

Answer $ ...................................... [1]

4024/11/O/N/14

5

7

Solve the simultaneous equations. 2x - 3y = 11 5x - 4y = 24



Answer x = ........................................



y = ................................... [3]

8

(a) Find n when

33 # 3 # 35 = 3n .



Answer n = ................................... [1] 3

(b) Find the value of 32 5 .



Answer

......................................... [1]

Answer

......................................... [1]

N-2

J1 (c) Find the value of K O . L5P



© UCLES 2014

4024/11/O/N/14

[Turn over

6

9 A

O

X

4

T

B

The diagram shows a circle, centre O, with radius 6 cm. Tangents are drawn from T to touch the circle at A and B. OXT is a straight line intersecting the circle at X with XT = 4 cm. Calculate AT.



© UCLES 2014

Answer

4024/11/O/N/14

................................... cm [3]

7

10 (a) Use set notation to describe the shaded subset in the Venn diagram.  P

R

Q



Answer (b) In a group of students

......................................... [1]

30 play cricket, 38 play football and 9 play neither cricket nor football.

Find the lowest possible number of students in the group.



© UCLES 2014

Answer

4024/11/O/N/14

......................................... [2]

[Turn over

8

11

John works in a shop. The matrix below shows the number of hours he worked on Monday to Friday, Saturday, and Sunday during two different weeks. Monday to Friday Week 1 Week 2

J K L

30 35

Saturday

Sunday

5 6

0 2

N O P

The matrix below shows the pay that he received per hour on Monday to Friday, Saturday, and Sunday. $/hr J 9N K O KK12OO L15P

(a) P =

Monday to Friday Saturday Sunday J30 K L35

5 6

0N O 2P

J 9N K O KK12OO L15P

Find P.

Answer P =



[2]

(b) Explain the meaning of the information given by matrix P. ............................................................................................................................................................ ....................................................................................................................................................... [1]

© UCLES 2014

4024/11/O/N/14

9

12

s=

n ( a + b) 2

(a) Evaluate s when n = 200, a = 3.6 and b = 5.7 .



Answer s = ................................... [1] (b) Rearrange the formula to make b the subject.



Answer b = ................................... [2]

13 When the speed of a car is v m/s, its braking distance is d m. d is directly proportional to the square of v. When the speed of the car is 8 m/s the braking distance is 5 m. Find the formula for d in terms of v and hence find the braking distance when the speed of the car is 40 m/s.



Answer Formula d = ............................................



Braking distance = .......................... m [3]

© UCLES 2014

4024/11/O/N/14

[Turn over

10

14 A shopkeeper sells fruit at the prices shown in the table below.

Oranges

35 cents each

Apples

$2.40 per kg

Melons

$1.85 each

(a) Sabah buys 750 g of apples and one melon. Calculate how much she pays.



Answer $ ..................................... [1] (b) The shopkeeper buys

100 oranges for $25, 50 kg of apples for $80 and 20 melons for $15.

He sells all of these oranges, apples and melons at the prices shown in the table. Calculate his percentage profit.



© UCLES 2014

Answer

4024/11/O/N/14

..................................... % [3]

11

t = 130º. 15 (a) Draw triangle ABC with AB = 8 cm, AC = 7 cm and CAB AB has been drawn for you.

A

B

[2] (b) By making suitable measurements, find the area of triangle ABC.



© UCLES 2014

Answer

4024/11/O/N/14

................................. cm2 [2]

[Turn over

12

16 y 8

6

4

2

–2

0

2

4

6

8

10 x

–2

–4

(a) On the grid above, draw the graph of

x+y = 6.

[1]

(b) On the grid above, draw the graph of

2y + x = 4 .

[1]

(c) On the grid above, shade and label the region R, defined by the following inequalities. x+y G 6

© UCLES 2014

2y + x H 4

yH2

x H-1

4024/11/O/N/14

[2]

13

17 5 11 4

7

The diagram shows a scoop used for measuring washing powder. The scoop is a prism. Its cross-section is a trapezium. The trapezium has height 4 cm and parallel sides of length 7 cm and 11 cm. The width of the scoop is 5 cm. (a) Show that the volume of the scoop is 180 cm3.

[1] (b) A scoop used in industry is geometrically similar to the scoop above. It has a volume of 22.5 litres. Calculate the height of the industrial scoop.



© UCLES 2014

Answer

4024/11/O/N/14

....................................cm [3]

[Turn over

14

18 (a) The term-to-term rule for a sequence is

multiply the previous term by 3 and subtract 1 . The first three terms in this sequence are 1, 2 and 5 . Write down the next two terms in this sequence.



Answer ................... , ................... [1] (b) The nth term of a second sequence is given by the expression 4n - 3 . Find the number in this sequence that is closest to 150 .



Answer (c) The nth term of a different sequence is given by the expression

......................................... [1]

n2 + 1 .

(i) Write down the first four terms of this sequence.



Answer ........... , ........... , ........... , ........... [1] (ii) Hence write down an expression, in terms of n, for the nth term of the following sequence. 0

3

8



© UCLES 2014

15

.....

Answer

4024/11/O/N/14

......................................... [1]

15

19 (a) In 2013 the population of China was approximately 1 360 000 000 . Write this number in standard form.

(b)

p = 8 # 10 5

Answer

......................................... [1]

Answer

......................................... [1]

Answer

......................................... [2]

q = 7 # 10 3

Giving your answers in standard form, find (i) pq,

(ii)

p - q.



© UCLES 2014

4024/11/O/N/14

[Turn over

16

20 y

O

y

x

Figure A

x

Figure B

y

O

O

y

Figure D

O

Figure E

x

Figure C

y

x

O

y

x

O

x

Figure F

State which figure could be the graph of







(a) y = x 3 + 1,

Answer Figure ............................. [1]

(b) y = x 2 - 3,

(c)

Answer Figure ............................. [1]

y = 3x ,

Answer Figure ............................. [1]

(d) y = (x - 3) 2 .

© UCLES 2014

Answer Figure ............................. [1]

4024/11/O/N/14

17

21 (a) B

C

A

58° D

F E

In the diagram the lines ABC and DEF are parallel. t = 58º. AB = AE and AED (i) Complete the statement below. t = 58º because ................................................................................................................... EAB ............................................................................................................................................... [1] t . (ii) Calculate EBC



Answer

t = ............................ [2] EBC

(b) A pentagon has interior angles of 80º, 95º and 125º. Each of the remaining angles is equal to xº. Calculate the value of x.



© UCLES 2014

Answer x = ................................... [2]

4024/11/O/N/14

[Turn over

18

22 Each member of a group of 100 people was asked how long they spent at a gym one afternoon. The results are summarised in the cumulative frequency table below. Time (t mins)

t G 20

t G 40

t G 60

t G 90

t G 120

Cumulative frequency

6

20

46

88

100

(a) How many people spent between 60 and 90 minutes at the gym?

Answer

......................................... [1]

(b) On the grid below, draw the cumulative frequency curve to represent the information in the table. 100

80

60 Cumulative frequency 40

20

0

0

20

40

60 Time (t minutes)

80

100

120

[2]

(c) Use your cumulative frequency curve to estimate (i) the median time spent at the gym,

Answer

........................... minutes [1]

(ii) the number of people who spent between 50 and 80 minutes at the gym.

© UCLES 2014

Answer 4024/11/O/N/14

......................................... [2]

19

23 (a) f

A

J3N J4N J-1N f =K O g =K O h =K O L2P L1P L 2P The vector f and the point A are shown on the grid. On the grid, mark and label (i) the point B when AB = f + g ,

[1]

(ii) the point C when AC =- 2h ,

[1]

(iii) the point D when AD = 2f - 3g .

[1]

The rest of this question is on the next page.

© UCLES 2014

4024/11/O/N/14

[Turn over

20

(b) p

P

O

R q

Q

In the diagram, OP = p and OQ = q . R is the point on PQ such that PR : RQ = 1 : 2 . (i) Express PQ, as simply as possible, in terms of p and q.



Answer

......................................... [1]

(ii) Express OR, as simply as possible, in terms of p and q.



Answer

......................................... [1]

(iii) T is a point such that TR = 2 OP . Express OT , as simply as possible, in terms of p and q.



Answer

......................................... [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/11/O/N/14

Cambridge International Examinations Cambridge Ordinary Level

* 7 0 1 1 7 0 6 6 3 5 *

4024/12

MATHEMATICS (SYLLABUS D)

October/November 2014

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NF/SLM) 83226/3 © UCLES 2014

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

Mavis went to a café to meet some friends. (a) She bought 3 drinks at $1.42 each and 1 cake for 85 cents. How much did she spend altogether?



Answer $ .......................................... [1] (b) She left home at 10.45 a.m. and returned at 1.20 p.m. How long, in hours and minutes, was she away from home?

Answer ..................... hours and ..................... minutes [1]

2

A cookery book states that the time it takes to cook some meat is 13 minutes for every 500 grams of meat + 20 minutes. (a) Calculate the number of minutes it takes to cook 1.5 kg of meat.



Answer

............................................. [1]

Answer

............................................. [1]

(b) It takes T minutes to cook M grams of meat. Find a formula for T.

© UCLES 2014

4024/12/O/N/14

3 3

In an experiment, a red die and a blue die were thrown 10 times. Each time, the score on the red die was subtracted from the score on the blue die. The results are given below. 5

−4

−3

4

0

2

−1

−3

3

−2

For these results, find (a) the median,



Answer

............................................. [1]

Answer

............................................ [1]

Answer

............................................. [1]

Answer

f -1 (x) = ............................. [1]

(b) the mean.



4

f ^xh = 2 ^x - 3h (a) Evaluate f ` 12 j .

(b) Find f -1 ^xh.



© UCLES 2014

4024/12/O/N/14

[Turn over

4 5

(a) Write the value of 1234.567, correct to 2 significant figures.

(b) Write down an estimate for the value of

28 r



6

Answer

............................................. [1]

Answer

............................................. [1]

.

(a) On the Venn diagram, shade the set C l + ^A , Bh. 

A

B

C [1] (b) % = { −1, 0, 1, 2, 3, 4, 5, 6 } P = { −1, 0, 1, 2 } Q = " x2 : x ! P , Find n ^ Q h.



© UCLES 2014

Answer

4024/12/O/N/14

............................................. [1]

5 7

A car travels at 90 km / h. How many metres does it travel in 1 second?



8

Answer

............................................. [2]

Answer

................. : ....................... [1]

Answer

................. : ....................... [1]

Two bottles are geometrically similar. The ratio of the areas of their bases is 1 : 4. Write down the ratios of their (a) heights,

(b) volumes.



© UCLES 2014

4024/12/O/N/14

[Turn over

6 9

The time taken to run a race is given as 54.3 seconds, correct to the nearest 0.1 of a second. (a) Find the lower bound for the time taken.



Answer

.......................................... s [1]

(b) The distance run is given as d metres, correct to the nearest metre. Write down an expression, in terms of d, for the maximum possible average speed, in metres per second.



Answer

..................................... m / s [1]

10 y is inversely proportional to x. Given that y = 9 when x = 8 , find y when x = 6 .



© UCLES 2014

Answer y = ....................................... [2]

4024/12/O/N/14

7 11

The sequence of diagrams below shows small black and small white squares in an arrangement to form large squares.

Diagram 1

Diagram 2

Diagram 3

The table below shows the numbers of black and white squares in each diagram. Diagram (n)

1

2

3

Black squares

5

13

25

White squares

4

12

24

Total number of black and white squares

9

25

49

4

(a) For each diagram, how many more black squares are there than white squares?

Answer ............................................. [1] (b) On the table, complete the column for Diagram 4.

[1]

(c) Write down an expression, in terms of n, for the total number of black and white squares in Diagram n.

Answer ............................................. [1]

12 (a) Write the number 0.000 567 in standard form.

Answer (b) Giving your answer in standard form, evaluate

3 # 10 . 5 # 10 6



© UCLES 2014

............................................. [1]

-5

Answer

4024/12/O/N/14

............................................. [2]

[Turn over

8 13

A

3 5

B

C

7

E

D

In the diagram, BE = 5 cm, CD = 7 cm and AE = 3 cm.

BE is parallel to CD. (a) Express CD as a percentage of BE.



Answer

........................................ % [1]

Answer

....................................... cm [2]

(b) Find ED.



© UCLES 2014

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9 14

10 x° 6

r

A hollow cone has a base radius 6 cm and slant height 10 cm. The curved surface of the cone is cut, and opened out into the shape of a sector of a circle, with angle x° and radius r cm. (a) Write down the value of r.

Answer r = ....................................... [1] (b) Calculate x.



© UCLES 2014

Answer x = ....................................... [2]

4024/12/O/N/14

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10 15 [The volume of a sphere is 43 rr 3 ] 20 spheres, each of radius 3 cm, have a total volume of kr cm 3 . (a) Find the value of k.



Answer k = ....................................... [1] (b) The spheres are inside an open cylinder, with radius 6 cm. The cylinder stands on a horizontal surface and contains enough water to cover the spheres. Calculate the change in depth of the water when the spheres are taken out of the cylinder.



© UCLES 2014

Answer

4024/12/O/N/14

....................................... cm [2]

11 16

y

A

x

O

A is the point (5, 5)

AB = c

4 m -3

(a) AB is mapped onto CD by a reflection in the y-axis. Find CD.



Answer

............................................. [1]

(b) AB is mapped onto AE by a rotation, centre A, through an angle of 90° clockwise. Find AE .



Answer

............................................. [1]

Answer

............................................. [1]

(c) Find AB .



© UCLES 2014

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12 17 (a) Simplify p 2 ^ p 3 - 3p -2h.



Answer

............................................. [2]

Answer

............................................. [2]

Answer

............................................. [1]

Answer

............................................. [1]

Answer

............................................. [2]

1 3

(b) Simplify ^27x 6h .



18 (a) Factorise completely 4a - 16a 2 .

(b) Factorise 9b 2 - c 2 .

(c) Factorise

x 2 - 5y - xy + 5x .



© UCLES 2014

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13 19

The diagram shows a figure made from four identical hexagons. It has both line and rotational symmetry. (a) What is the order of the rotational symmetry?

Answer

............................................. [1]

(b) Each marked angle is 60°. Find the other angles in one of the hexagons.

Answer

© UCLES 2014

................ , ................ , ................ , ................ , ................ [3]

4024/12/O/N/14

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14 20 A y°

x°

B

136° O

T

t°

D

z° C

In the diagram, A, B, C and D lie on the circle, centre O. CO is parallel to DA. The tangents to the circle at A and C meet at T. t = 136° . AOC (a) Find x.



Answer x = ....................................... [1] (b) Find y.



Answer

y = ...................................... [1]

Answer

z = ...................................... [1]

(c) Find z.

(d) Find t.



© UCLES 2014

Answer t = ....................................... [1]

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15 21 A bag contains 5 balls, 2 of which are blue and 3 are red. One ball is taken, at random, from the bag. If it is red it is put back into the bag. If it is blue it is not put back into the bag. A second ball is taken, at random, from the bag. Part of the tree diagram that represents these outcomes is drawn below. First ball

Second ball

1 4 2 5

blue

blue

3 4 red

3 5 red

(a) Complete the tree diagram.

[1]

(b) Expressing each answer as a fraction in its simplest form, find the probability that (i) both balls taken are blue,



Answer

............................................. [1]

Answer

............................................. [2]

(ii) the second ball taken is blue.



© UCLES 2014

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[Turn over

16 22 The diagram shows the speed-time graph of a cyclist’s journey.

12 Speed (m/s)

0

0

30

50

60

Time (t seconds) (a) Find the retardation.



Answer

.................................... m / s2 [1]

Answer

..................................... m / s [1]

(b) Find the speed when t = 9.



(c) Find the distance travelled by the cyclist from t = 0 to t = 60.



© UCLES 2014

Answer

4024/12/O/N/14

......................................... m [2]

17 23 y

A

C B

x

O x = 8, The diagram shows the three lines which intersect at the points A, B and C.

x + y = 21 and 2y = 12 + x

(a) Find the coordinates of B.



Answer ( ................... , ...................) [1] (b) The region inside triangle ABC is defined by three inequalities. One of these is x + y 1 21.



Write down the other two inequalities.



Answer

............................................. ............................................. [2]

(c) Find the coordinates of the point, with integer coordinates, that is inside triangle ABC.



© UCLES 2014

Answer ( ................... , ...................) [1]

4024/12/O/N/14

[Turn over

18 24 The diagram shows the positions, on a map, of three boats A, B and C. The map has a scale of 1 cm to 1 km. (a) Find the bearing of B from A.

Answer

............................................. [1]

(b) A fourth boat, D, is •

closer to B than to A,

•

less than 4 km from C.

By drawing appropriate loci find, and shade, the region in which D is situated.

North

A

C

B

© UCLES 2014

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[3]

19 25 P is ^- 4, 4h and Q is ^3, - 2h. M is the midpoint of PQ. (a) Find the coordinates of M.



Answer ( ................... , ...................) [1] (b) Find the gradient of the line PQ.



Answer

............................................. [1]

(c) Q is the midpoint of the line PQR. (i) Find the coordinates of R.



Answer ( .................... , ..................) [2] (ii) Write down the value of

PM . MR



Answer

............................................. [1]

Question 26 is printed on the following page. © UCLES 2014

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[Turn over

20 26 A =c

3 -1

1 m 2

A -1 = k c

2 1

-1 m 3

(a) Find the value of k.



Answer k = ....................................... [1] (b) Find the matrix X, where 2A + X = c

5 0

-2 m. 4



Answer

[2]

Answer

[2]

(c) Find the matrix Y, where YA = ^6 2h.



Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/12/O/N/14

Cambridge International Examinations Cambridge Ordinary Level

* 8 1 7 5 4 1 1 5 7 3 *

4024/21

MATHEMATICS (SYLLABUS D)

October/November 2014

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (KN/FD) 97063/3 © UCLES 2014

[Turn over

2 Section A [52 marks] Answer all questions in this section. 1

(a) The table shows some of the nutritional information for a 300 g tin of soup. Carbohydrate Fat Fibre Sodium

18 g 20.1 g 0.6 g 1.38 g

(i) What percentage of the 300 g tin of soup is carbohydrate?



Answer ....................................... % [1] (ii) What fraction of the 300 g tin of soup is fibre? Give your answer as a fraction in its lowest terms.



Answer .......................................... [1] (iii) Of the carbohydrates, 15% are sugars. How many grams of sugars are in one tin of soup?



Answer ........................................ g [1] (b) I need 2500 g of soup. How many 300 g tins of soup do I need to buy?

Answer .......................................... [1]



© UCLES 2014

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3 (c) During March there is a special promotion and the soup is on sale in tins containing 20% extra. (i) These tins of soup each contain 4.2 g of protein. How much protein was contained in each original 300 g tin of soup?

Answer ........................................ g [2]



(ii) The special promotion tins cost $0.80 . The soup can also be bought in larger tins containing 500 g for $1.12 . Is it better value to buy the 500 g tin or the special promotion tin? Show your working.

[2]

© UCLES 2014

4024/21/O/N/14

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4 2

Hendrik travels by plane from London to Bangkok. When it is 04 00 local time in London it is 10 00 local time in Bangkok. (a) The flight takes 11 hours and 15 minutes. If he leaves London at 21 50 local time, what is the local time in Bangkok when he arrives?

Answer .......................................... [2]



(b) On his return journey, Hendrik leaves Bangkok at 07 45 local time and arrives back in London on the same day at 13 40 local time. How long was his return flight?

Answer



................... hours ................... minutes [2]

(c) The graph opposite shows the exchange rate between British Pounds (£) and Thai Baht (THB) on the day Hendrik arrives in Bangkok. (i) Use the graph to estimate the cost in British Pounds of an item costing 13 000 THB.



Answer £ ....................................... [1] (ii) The exchange rate can be written as £1 = k THB. Find k.

Answer .......................................... [1]

© UCLES 2014

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5 60 000

50 000

40 000 Thai Baht (THB) 30 000

20 000

10 000

0

0

200

400

800

600

1000

1200

British Pounds (£)

(d) The cost of flights from London to Bangkok is shown in the table below. For this cost, passengers are allowed to take luggage up to the weight shown. Passengers taking more than this weight of luggage pay an excess charge at the rate shown. Cost of flight

Weight of luggage included

Charge per extra 1 kg

Business Class

£1932

30 kg

£24

Economy Class

£683

23 kg

£24

Calculate the total cost of Hendrik flying Economy Class from London to Bangkok with luggage weighing 29 kg.

Answer £ ....................................... [2]

© UCLES 2014

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6 3

(a) (i) Complete the table and hence draw the graph of y = x 2 - 2x - 8 . x

–4

y

–3

–2

–1

0

1

2

3

4

5

7

0

–5

–8

–9

–8

–5

0

7

6

y 20

15

10

5

–4

–3

–2

–1

0

1

2

3

4

5

6 x

–5

–10

[3] (ii) Use your graph to solve x 2 - 2x - 8 = 2 .

Answer x = ............... or ................ [2]



(iii) By drawing a tangent, estimate the gradient of the curve at (3, –5) .

Answer .......................................... [2]



© UCLES 2014

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7 (b) Solve algebraically x 2 + x - 9 = 0 , giving your answers correct to 2 decimal places.

Answer x = ............... or ................ [3]



(c) The x-coordinates of the intersection of the line L and the curve y = x 2 - 2x - 8 are the solutions of the equation x 2 + x - 9 = 0 . Find the equation of the line L.



© UCLES 2014

Answer .......................................... [2]

4024/21/O/N/14

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8 4

(a) The histogram represents the distribution of the masses, in grams, of individual apples in a box. 9 8 7 6

5 Frequency density 4 3 2 1 0

80

90

85

95

100

105

110

115

120

Mass (g)

This information is summarised in the table below. Mass (m g)

Frequency

80

< m G

90

5

90

< m G

95

8

95

< m G 100

p

100

< m G 102.5

q

102.5 < m G 105

20

105

< m G 110

23

110

< m G 120

10

Calculate p and q.



© UCLES 2014

Answer p = .............. q = .............. [2]

4024/21/O/N/14

9 (b) The mass of each plum in a box is recorded correct to the nearest 5 grams. Mass (to the nearest 5 g)

Frequency

10 – 15

6

20 – 25

18

30 – 35

25

40 – 45

10

50 – 55

1

(i) Calculate an estimate of the mean mass of a plum.



Answer ........................................ g [3] (ii) Calculate the upper bound for the total mass of plums in the box.

Answer ........................................ g [2]

© UCLES 2014

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[Turn over

10 5 B

8

122° A

C

14

t = 122° . In triangle ABC, AC = 14 cm, BC = 8 cm and ACB (a) Show that AB = 19.5 cm, correct to 3 significant figures.

[4] t . (b) Calculate ABC

© UCLES 2014

Answer .......................................... [3] 4024/21/O/N/14

11 (c) A rhombus, BDEC, of area 52 cm2 and sides 8 cm is placed next to triangle ABC as shown in the diagram. B

8

A

122° 14

C

D

E

t is an obtuse angle, calculate the reflex angle ACE t . Given that BCE



© UCLES 2014

Answer .......................................... [4]

4024/21/O/N/14

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12 6

f(x) = 2x – 7 (a) Calculate f(3) .

Answer f(3) = ................................ [1]



(b) Find f - 1 (x) .

Answer f - 1 (x) = ........................... [2]



(c) Find the value of g given that f(3g) = g + 4 .

Answer g = .................................... [3]



© UCLES 2014

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13 BLANK PAGE

SECTION B STARTS ON THE NEXT PAGE

© UCLES 2014

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[Turn over

14 Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a) Solve (i)

4x =1, 3



Answer x = ..................................... [1] (ii)

4y - 3 (2y + 1) = 5 .



Answer y = .................................... [2] (b) Simplify

15w - 30w . 5w 2 - 20 2

Answer .......................................... [3]

© UCLES 2014

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15 (c)

The diagram shows the plan of a patio made from rectangular paving slabs. The width of each paving slab is p cm. The length of each paving slab is 20 cm longer than its width. (i) Find an expression, in terms of p, for the area, in cm2, of one paving slab. Answer ....................................cm2 [1]



(ii) Given that the area of the patio is 12.25 m2, show that p satisfies the equation p 2 + 20p - 3500 = 0 .

[2] (iii) (a) Solve by factorisation p 2 + 20p - 3500 = 0 .

Answer p = ............... or ................ [2]



(b) Hence state the length of each paving slab. Answer ..................................... cm [1]

© UCLES 2014

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16 8

(a)

North

A

B

The scale drawing shows two coastal towns, A and B. The scale of the drawing is 2 cm to 1 km. (i) Measure the bearing of B from A. Answer .......................................... [1]



(ii) Draw the locus of points equidistant from A and B.

[1]

(iii) A rock, C, is known to be less than 4 km from B and nearer to A than B. (a) Construct and shade the region in which C must lie.

[2]

(b) Find the shortest possible distance between A and C. Answer ..................................... km [1] (iv) A boat, D, starts at the point 3.5 km due south of A and sails on a bearing of 075°. Draw the path of D and state, with a reason, whether it is possible that D collides with C. Answer ................................................................................................................................. [2]

© UCLES 2014

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17 (b) P

8

Q

37° S

5

R

t = 37° . The diagram shows a triangle PQR with PQR t = 90° , PS = 8 cm and SR = 5 cm. S is the point on QR such that PSR Calculate (i) PR,

Answer ..................................... cm [2]



(ii) the shortest distance from S to PQ.

Answer ..................................... cm [3]

© UCLES 2014

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18 9

y 6 5 4 3 2 A

1 –6

–5

–4

–3

–2

0

–1

1

2

3

4

5

6 x

–1 –2 B

–3 –4 –5 –6

The diagram shows triangle A and octagon B. (a) Find the gradient of the line of symmetry of triangle A. Answer .......................................... [1]



(b) Triangle A is mapped onto triangle C by a reflection in the line y = x . Draw and label triangle C.

[2]

(c) Write down the equation of the line of symmetry of octagon B that is parallel to the y-axis. Answer .......................................... [1]



(d) State the order of rotational symmetry of octagon B. Answer .......................................... [1]



(e) Octagon B is mapped onto octagon D by an enlargement, scale factor 2 and centre (–3, –3). Draw and label octagon D.

© UCLES 2014

[2]

4024/21/O/N/14

19 (f) A mat is made from six identical octagons, each similar to octagon B, and two squares, as shown in the sketch below.

The lengths of the short sides of the octagons are each 15 cm. (i) Calculate the area of one of these octagons.

Answer ....................................cm2 [2]



(ii) Find the length of a diagonal of one of the squares. Answer ..................................... cm [1]



(iii) Calculate the total area of the mat.

Answer ....................................cm2 [2]



© UCLES 2014

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[Turn over

20 10 (a) D 2x° A O

E

C

B

A, B, C and D are points on the circumference of a circle, centre O. The diameter AC intersects BD at E. t = 2x° . BDC (i) Find an expression, in terms of x, for t , (a) BAC Answer .......................................... [1]



t , (b) BOC Answer .......................................... [1]



t . (c) OCB Answer .......................................... [1]



t = x° and DEC t = 123° . (ii) Calculate x when OBE

Answer x = .................................... [3]



© UCLES 2014

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21 (b)

8

20

40°

The cross-section of a prism is a sector of a circle, radius 8 cm and angle 40°. The prism is 20 cm long. Calculate (i) the area of the cross-section,

Answer ....................................cm2 [2]



(ii) the total surface area of the prism.

Answer .................................... cm2 [4]



© UCLES 2014

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[Turn over

22 11

(a) One day, two brothers, Zac and Tom, leave their home at different times. They meet at the library before going to the swimming pool. The travel graph represents Zac’s journey to the swimming pool.

6 Swimming pool 5

4 Library 3 Distance from home (km) 2

1

0 12 00

13 00

14 00 Time of day

15 00

16 00

(i) How much time does Zac spend at the library?

Answer ............................. minutes [1]



(ii) Tom leaves their home at 12 30 and cycles to the library at 14 km/h. Calculate the time Tom arrives at the library.

Answer .......................................... [1] © UCLES 2014

4024/21/O/N/14

23 (iii) How far is the swimming pool from the library?

Answer .................................... km [1] (iv) Zac stays at the swimming pool for an hour and a quarter. He then walks home at a constant speed, arriving at 15 39 . (a) Complete his travel graph.

[2]

(b) Calculate Zac’s speed, in kilometres per hour, as he walks home.



Answer .................................. km/h [1] The rest of this question is on the next page.

© UCLES 2014

4024/21/O/N/14

[Turn over

24 (b) A bag contains 5 red counters, 6 blue counters and 1 green counter. (i) Complete the pie chart to represent this data.

Red

[2] (ii) Ahmed takes a counter at random from the bag. Find the probability that the counter is red. Answer .......................................... [1]



(iii) Simeon takes two counters at random from the bag of twelve counters. He places them next to each other on a table. Find the probability that the two counters are different colours.



Answer .......................................... [3]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/21/O/N/14

Cambridge International Examinations Cambridge Ordinary Level

* 5 9 6 5 4 2 2 3 9 3 *

4024/22

MATHEMATICS (SYLLABUS D)

October/November 2014

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (CW/JG) 83229/2 © UCLES 2014

[Turn over

2

Section A [52 marks] Answer all questions in this section. 1

(a) In 2013, Mary worked for Company A. Her salary for the year was $18 750. (i) $5625 of her salary was not taxed. What percentage of her salary was not taxed?



Answer

....................................... % [2]

(ii) The remaining $13 125 of Mary’s salary was taxed. 22% of this amount was deducted for tax. Mary’s take-home pay was the amount remaining from $18 750 after tax had been deducted. She received this in 52 equal amounts as a weekly wage. Calculate Mary’s weekly wage.



Answer $ ......................................... [3] (iii) In 2012 Mary had worked for Company B. When she moved from Company B to Company A, her salary increased by 25% to $18 750. Calculate her salary when she worked for Company B.



© UCLES 2014

Answer $ .......................................... [2]

4024/22/O/N/14

3

(b) The rate of exchange between pounds (£) and Indian rupees (R) is £1 = R87.21. The rate of exchange between pounds (£) and Swiss francs (F) is £1 = F1.53. (i) Mavis changed £750 into Indian rupees. How many rupees did she receive?



Answer

................................. rupees [1]

(ii) David changed F450 into pounds. How many pounds did he receive?



Answer £ .......................................... [1] (iii) Brian changed R50 000 into Swiss francs. How many Swiss francs did he receive?



© UCLES 2014

Answer

4024/22/O/N/14

..................................francs [2]

[Turn over

4

2

(a) E

B F C

A

67° D

A, B, C and D are points on the circumference of the circle and AC is a diameter. AFBE and DCE are straight lines. t = 67°. DF is perpendicular to AE and CDF t . (i) Find AED



Answer

t = ................................ [1] AED

t , giving a reason for your answer. (ii) Find CBE

Answer

t = ...................... because .................................................................................. CBE

............................................................................................................................................... [1] (iii) Explain why DF is parallel to CB.

Answer ........................................................................................................................................ ............................................................................................................................................... [1]

© UCLES 2014

4024/22/O/N/14

5

(b) P

X

Y

Z

Q

R

t and PRQ t intersect at Y. In the triangle PQR, the bisectors of PQR The straight line XYZ is parallel to QR. Prove that the perimeter of triangle PXZ = PQ + PR.

[3]

© UCLES 2014

4024/22/O/N/14

[Turn over

6

3 p

4

11

5

–4

7

spinner X

3 –1

spinner Y

In a game, when it is Mary’s turn, she spins each of these fair spinners once. Mary’s score for the turn is worked out using the formula xm + yn, where x is the number on spinner X and y is the number on spinner Y. The possibility space diagram shows Mary’s possible scores.

y (number on spinner Y )

x (number on spinner X ) 5

7

11

p

–4

37

47

67

97

–1

28

38

58

88

3

16

26

46

76

4

13

23

43

73

(a) Find the probability that Mary’s score is less than 15.

Answer

............................................ [1]

(b) Calculate the probability that on two consecutive turns, Mary scores less than 40 on one and more than 75 on the other.



© UCLES 2014

Answer

4024/22/O/N/14

............................................ [3]

7

(c) The diagram shows 7 on spinner X and –1 on spinner Y. Using the formula, the score for this turn is 7m – n = 38. (i) Using the table, find 7m + 3n.



Answer

............................................ [1]

(ii) Hence find m and n.



Answer m = ..........................................



n = ..................................... [2] (d) Find p.



© UCLES 2014

Answer p = ...................................... [2]

4024/22/O/N/14

[Turn over

8

4

(a) 7 3 10

The diagram shows a solid triangular prism. The dimensions are in metres. (i) Calculate the volume of the prism.



Answer

.......................................m3 [2]

Answer

.......................................m2 [4]

(ii) Calculate the total surface area of the prism.



© UCLES 2014

4024/22/O/N/14

9

(b) 0.6 y B 0.6 y B

A

2 25°

25°

h

A

The diagrams show the cross-sections of a ramp A and a triangular prism B. The triangular prism B can move up and down the ramp A. The ramp is inclined at 25° to the horizontal. (i) When the prism has moved 2 m up the ramp, it has risen h metres vertically. Calculate h.



Answer h = ....................................... [2] (ii) As it moves, the uppermost face of the prism B remains horizontal. The length of the horizontal edge of the face is 0.6 m. The length of the vertical edge of the prism is y metres. Calculate y.



© UCLES 2014

Answer y = ....................................... [2]

4024/22/O/N/14

[Turn over

10

5 100

d

The diagram shows the perimeter of a 400 m running track. It consists of a rectangle measuring 100 m by d metres and two semicircles of diameter d metres. The length of each semicircular arc is 100 m. (a) Calculate d.



Answer d = ....................................... [2] (b) Calculate the total area of the region inside the running track.



© UCLES 2014

Answer

4024/22/O/N/14

.......................................m2 [3]

11

(c) A

T 3 S O

S is the starting point and finishing point for the 400 m race for a runner in the inside lane. A runner in an outer lane is always 3 m from the inner perimeter. The runner in the outer lane starts at A, runs 400 m and finishes at T. TS = 3 m. (i) Calculate the length of the arc TA.



Answer

........................................ m [3]

Answer

t = ................................ [2] AOT

(ii) O is the centre of a semi-circular part of the track. t . Calculate AOT



© UCLES 2014

4024/22/O/N/14

[Turn over

12

6

ABCD is a field in the shape of a trapezium. t = 104° and the distance between the parallel sides of the field is 90 m. t = 56°, BAD ABC (a) Using a scale of 1 cm to 20 m, draw a plan of the field. AB has been drawn for you.

A

B

[4] (b) Find the actual distance CD.



© UCLES 2014

Answer CD = ............................... m [2]

4024/22/O/N/14

13

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a) B D a

A

E

b

C

In the triangle ABC, D divides AB in the ratio 3 : 2, and E divides AC in the ratio 3 : 2 . AD = a and AE = b. (i) Show, using vectors, that DE is parallel to BC.

[3] (ii) Find the ratio

Area of triangle ADE : Area of triangle ABC.



© UCLES 2014

Answer .................... : ....................[2]

4024/22/O/N/14

[Turn over

14

(b) y 8

6

4

2

0

A

2

4

6

8

10

x

Triangle A has vertices (3, 1), (5, 1) and (5, 4). The transformation S1 is represented by the matrix c

2 0 m. 0 1

S1 maps triangle A onto triangle B. (i) Draw and label triangle B.

[2]

(ii) What type of transformation is S1?



© UCLES 2014

Answer

4024/22/O/N/14

............................................ [1]

15

(iii) The transformation S2 is represented by the matrix c

1 1

0 m. 1

Find the matrix that represents the combined transformation S2S1.



Answer

f

p

[2]

(iv) The combined transformation S2S1 maps triangle A onto triangle C. Find the matrix which represents the transformation that maps triangle C onto triangle A.



© UCLES 2014

Answer

4024/22/O/N/14

f

p

[2]

[Turn over

16

8

(a) T = 2π

h g

(i) Find T when h = 125 and g = 981.



Answer T = ....................................... [1] (ii) Make h the subject of the formula.



Answer h = ....................................... [3] (b) Solve the equation 45 – ( p + 3) = 2p.



© UCLES 2014

Answer p = ....................................... [2]

4024/22/O/N/14

17

(c) Solve the equation

2x - 3 5 - x + = 0. 4 3



Answer x = ....................................... [3] (d) Solve the equation 3y2 + 11y + 4 = 0 . Give your answers correct to 2 decimal places.



© UCLES 2014

Answer y = ................ or ................ [3]

4024/22/O/N/14

[Turn over

18

9

(a)

A 4 67° B

C

6

t = 67°. In triangle ABC, AB = 4 m, BC = 6 m and ABC (i) Show that the area of triangle ABC is 11.05 m2 correct to 2 decimal places.

[1] (ii)

P 5 Q

R

7

In triangle PQR, PQ = 5 m and QR = 7 m. Area of triangle PQR = Area of triangle ABC. Find the acute angle PQR.



Answer

............................................ [2]

(iii) 2

W

8

Z

X Y

In the parallelogram WXYZ, WX = 8 m and WZ = 2 m. Area of parallelogram WXYZ = Area of triangle ABC. Find the obtuse angle ZWX.

© UCLES 2014

Answer 4024/22/O/N/14

............................................ [3]

19

(b) AB, AC and CD are three rods. They can be fixed together in different positions. (i) AC = 9 cm and M is a fixed point on AB such that AM = 12 cm. D 12

A

M

B

30° 9 C

t = 30°, calculate CM. When CAM



Answer CM = ..............................cm [3]

(ii) M D

12

A

B

12.5

9 C

In another position, the end D of the rod CD is fixed at the point M. CD = 12.5 cm. t . Calculate the increase in CAM

© UCLES 2014

Answer 4024/22/O/N/14

............................................ [3] [Turn over

20

10 The table below is for y = x 2 - 4x - 1. x y

–2

–1

0

1

2

3

4

5

4

–1

–4

–5

–4

–1

4

(a) Complete the table.

6

[1]

(b) Using a scale of 2 cm to 1 unit, draw a horizontal x-axis for - 2 G x G 6 . Using a scale of 2 cm to 5 units, draw a vertical y-axis for - 10 G y G 15. Plot the points from the table and join them with a smooth curve.

[3] (c) By drawing a tangent, estimate the gradient of the curve at x = 3.



© UCLES 2014

Answer

4024/22/O/N/14

............................................ [2]

21

(d) (i) Find the least value of y.



Answer (ii)

............................................ [1]

y G 4 for a G x G b . Find the least possible value of a and the greatest possible value of b.



Answer a .............................................



b ........................................ [2] (e) Use your graph to solve the equation x 2 - 4x + 2 = 0 . Show your working to explain how you used your graph.



© UCLES 2014

Answer

4024/22/O/N/14

............................................ [3]

[Turn over

22

11

(a) 100 students were each asked how long they spent talking on their mobile phone during one day. The results are summarised in the table. Time (t minutes)

0 1 t G 10

10 1 t G 20

20 1 t G 40

40 1 t G 60

Frequency

10

30

12

16

60 1 t G 80 80 1 t G 100 20

12

On the axes below, draw a histogram to represent these results. 3

Frequency density

2

1

0

0

20

40

60

80

100

Time (t minutes)

[3] (b) The masses, in grams, of 240 potatoes were found. The cumulative frequency table for these results is shown below. Mass (m grams)

m G 50

m G 100

m G 150

m G 200

m G 250

m G 300

m G 350

Cumulative frequency

0

4

54

132

204

236

240

© UCLES 2014

4024/22/O/N/14

23

(i) Draw a smooth cumulative frequency curve to illustrate this information. 250

200 Cumulative frequency 150

100

50

0

0

50

100

150

200 Mass (m grams)

250

300

350

[2]

(ii) (a) Find the median.

Answer

............................................ [1]

Answer

............................................ [2]

(b) Find the inter-quartile range. (iii) Complete the frequency table below. Mass 50 1 m G 100 100 1 m G 150 150 1 m G 200 200 1 m G 250 250 1 m G 300 300 1 m G 350 (m grams) Frequency

4 [1] (iv) A potato with a mass greater than 250 grams is classed as extra large. (a) How many of these potatoes are extra large?



Answer

............................................ [1]

(b) Which percentile of the distribution can be used to find this number? © UCLES 2014

Answer 4024/22/O/N/14

............................................ [2]

24

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2014

4024/22/O/N/14

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/11

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2015

Question 1

2

3

4

19

1

(b)

8 oe 45

1

(a)

8

1

(b)

48; or FT 6 × their(a)

(a)

700

1

(b)

147; or 3 × 72

1

(a)

320

1

(b)

150

1

4

9

2*

30 700

1

(b)

(0).538

1

(0).28 oe

2*

(a)

123

(b)

7 WWW

(a)

11

1

(b)

x2

1

(c)

8

1

–8 and 2

1

(b)

–3

1

(c)

–2, 0, 2 all three

1

(0).75

1

10 (a)

11 (a) (b) 12 (a) (b)

Part marks

1

(a)

7 8

Mark

(a)

5 6

Answers

Syllabus 4024

M1 for

( 50 ) − ( 34 ) 2

2

B1 for (0).4 oe seen

1 2*

M1 for 5a – 2 = 33 oe

4.65

2*

M1 for 5.5 – (0).85

4 WWW

2*

M1 for (3.8 × 5) soi by 19

3

1

© Cambridge International Examinations 2015

Paper 11

Page 3

13 (a) (b) 14 (a)

Mark Scheme Cambridge O Level – October/November 2015 3 2.08; or 2

8 ,or better and isw 100

(± ) 1

2*

M1 for numerical

∑ fx 50

1*

3

999

1

(c)

4

1

15

17 16d − c

16 (a)

7.53 × 10 −5

1

6.045 × 10 24

2

17

Paper 11

1

(b)

(b)

Syllabus 4024

3*

1 or 5 WWW

3*

M1 for squaring both sides M1 (indep.) for collecting both their x terms onto one side and the numerical terms onto the other side

C1 for figs. 6.0(4)5 or for A × 1024 where 1< A < 10 Either M1 for 5 + (3 − t ) 2 = 9 and M1 for t 2 − 6t + 5 = 0 ; or M1 for (3 − t ) 2 = 4 and M1 for 3 − t = ±2

18 (a) (b) 19 (a) (b)

21

1

5p + 1 oe

2

295°

1

Perpendicular bisectors of AB and BC with region around B shaded

2*

20 (a) (i) 20

1

(ii) 40

1

(b) 21 (a)

(b)

300 WWW; or FT 5 × {their(i) + their (ii)}

2*

C1 for 5p + c; or for kp + 1 (k ≠ 0)

B1 for either perpendicular bisector correct

M1 for

1 × (their 20 + their 40) × 10 oe 2

Pie chart completed accurately, and labelled with Bananas and Oranges

2*

M1 for 4 × 18 (= 72) oe or for 4 × 32 (= 128) oe

20

2*

M1 for

72 − 60 × 100 oe 60

© Cambridge International Examinations 2015

Page 4

22 (a) (b) 23 (a) (b)

(c)

Mark Scheme Cambridge O Level – October/November 2015 16 – 9x

1

x+5 3x − 1

3*

15a + 12c = 324 seen

1

Correctly equating one set of coefficients

M1

Correct method to eliminate one variable

M1

Either a = 16 or c = 7 WWW

A1

Both a = 16 and c = 7 WWW

A1

99; or FT (4 × their a + 5 × their c) provided both a and c are positive

1

112°

2*

(b) (i) 37.5° WWW

2*

24 (a)

(ii) 12.56 25 (a)

Two corresponding pairs of angles equated, with reasons, from ˆ = FCB ˆ opp. angles of a parm. BAE ˆ = CFB ˆ alternate angles ABE

Syllabus 4024

Paper 11

B1 for ( 3x + 1 )( x + 5 ) oe B1 for ( 3x + 1 )( 3x – 1 ) oe

If A0, then C1 for a pair of values that satisfy either original equation.

ˆ = 31° ; or for PRS ˆ = 68°; B1 for PRQ ˆ = 180° – their PRS ˆ or for PTS ˆ , or other angle at the centre, M1 for EOD 360 − 60 (= 75°) = 4

60 × 2 × 3.14 × 12 or better 360

2*

M1 for

2*

B1 for any one pair, with correct reason

ˆ = CBF ˆ alternate angles AEB

BC 6 = oe 5 4

(b)

7.5 oe

2*

M1 for

(c)

12x

2*

B1 for seeing 4x or 9x as ∆ABE or ∆BCF respectively

© Cambridge International Examinations 2015

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/12

Paper 1, maximum raw mark 80

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2015

Question 1

2

5

0.009(0...)

1

(b)

1.8

1

(a)

59.3(0)

1

(b)

90

1

(±) 12 WWW

2*

3 , or –0.6 5

(a)

−

(b)

x −1 oe 4

Part marks

B1 for “k” = (±) 6, from y = “k”√x or M1 for 18 × √4 = y × √9 oe or M1 for (their k) × √4 oe provided y = “k”√x used

1 (*)

0.0505

1

(b)

0.06(0)(0) oe from 9, 0.2 and 30

1*

 − 2 − 1    −1 5 

2

C1 for 2 or 3 correct elements

1

(a) X

X

(b)

1

X

d, a, b, e, c

2

(a)

55

1

(b)

6.5, or FT 61.5 – their(a)

1

4.5 × 10 –6

1

2.4 × 10 16

1

5.6 × 10 8

1

11 (a)

1

1

(b)

2 3

1

(c)

81x6

1

8 9

Paper 12

1

(a)

6 7

Mark

(a)

3

4

Answers

Syllabus 4024

10 (a) (b) (i) (ii)

C1 for four correct when one is covered up

© Cambridge International Examinations 2015

Page 3

Mark Scheme Cambridge O Level – October/November 2015

Question 12 (a) (b) (i) (ii) 13

14 (a) (b)

Answers

Mark

2 × 32 × 11 oe

1

12, or 22 × 3

1

90, or 2 × 32 × 5

1

x = 45

1

y = 20

1

z = 115

1

20

1

1 WWW

2*

15 (a)

Paper 12

Part marks

(80 + 45) 45 + 80 or for 25 = oe 25 4+t or B1 for total time = 5 hours

M1 for

1

B

A

Syllabus 4024

C

6

1

10, 14, 16

1

( 2p – 3q )( 2p + 3q )

1 (*)

( 2n – 1 )( n + 3 )

1 (*)

9 y + 8x 12 xy

1

17 (a)

28

1

(b)

62

1

(c)

48 or FT 110 – their (b)

1

(b) (i) (ii) 16 (a) (i) (ii) (b)

18 (a)

(b)

x > 3; y < 6; y > x +

5

1 2

; oe all three

2

1

C1 for 2 correct; or for x ⩾ 3; y ⩽ 6; y ⩾ x +

1 2

; oe all three

or for one correct strict inequality, and the other two correct, but with equality as well.

© Cambridge International Examinations 2015

Page 4

Mark Scheme Cambridge O Level – October/November 2015

Question

Answers 12 WWW

19

Mark 3*

Syllabus 4024

Paper 12

Part marks M1 for starting to solve the problem correctly, using exterior angles sum = 360 or interior angles sum = 180 × 3x –360 oe and A1 for correct equation(s) in their variable(s), e.g. 2x(180 – 155) + x(180 – 140) = 360 oe or 155 × 2x + 140 × x = 180 × 3x –360 oe  2 × 155 + 140  (n – 2)×180 = n ×   oe 3    2 × 155 + 140  n × [180 –   ] = 360 oe 3   450x = 180(n – 2) and n = 3x or M2 for a complete method, clearly explained, that does not use algebra

65.4

1

(ii)

64

1

(iii)

160

1

Parallel CF curve from ( 62, 0 ) to ( 72, 400 )

1

(0)96 to (0)98

1

Perpendicular bisector of BC.

1

Bisector of angle ABC.

1

DA = 80 to 84 km

1

1 (4, − ) 2

1

(b)

5 6

1

(c) (i)

4

1

–2.5, or any equiv.

1

1 1 1 1 4 4 4 4

1

5

1

20 (a) (i)

(b) 21 (a) (b) (i) (ii) (c)

22 (a)

(ii) 23 (a) (b) (i) (ii)

6

7 8

 15  10 3 0    16  16 16 or FT from their (bi) table

Dependent on two acceptable intersecting loci

1

© Cambridge International Examinations 2015

Page 5

Mark Scheme Cambridge O Level – October/November 2015

Question (c)

24 (a)

Answers

Mark

7 oe WWW 16

2*

43

1

47 cao

(b)

997

1

(c)

(–)10

1

(d)

407

1

(e)

39

1

25 (a)

1.5

1

(b)

15k – 75; or 15( k – 5 )

2*

(c) (i)

Horizontal line from ( 0, 12 ), going to, or beyond, t = k.

1

25 WWW or FT for correctly solving 12k = their (b), provided k > 10

1*

(ii)

26 (a)

(b) (i)

(ii)

Syllabus 4024

 2 2 8    0 1 3

2

1 1 0   or any equiv seen 2  0 2 

1*

1 2 1  2 4   , or   2  0 2  0 1

2*

Paper 12

Part marks

1 × ( sum of (bii) table) oe, 4 or for ∑x y, attempt, where x and y are corresponding values in the two tables

M1 for

M1 for

1 2

× 10 × 15 + (k – 10) × 15 oe seen

C1 for 4 or 5 correct elements in a 2 × 3 matrix

2 M1 for M  0  a b  2  or   c d  0

© Cambridge International Examinations 2015

0  = 1  0  1  1  0

2  0 0 1

2  oe 1  1  = their (a) oe 3 

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/21

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2015

Question 1

2

Answers

Syllabus 4024

Mark

Paper 21

Part marks

(a)

2730

2

B1 for 230 or 2557.5[0] seen or M1 for 2500 + 2500 × 0.023 × 4 oe

(b)

262.5[0] final answer

2

B1 for 1012.5[0] seen or M1 for 0.15 × 750 + 36 × 25 oe

(c)

w = 4.65 x = [0].75 y = 40.5[0] z = 31.35

5

B1 for [w = ] 4.65 B1 for [x = ] [0].75 B2 for [y = ] 40.5[0] or M1 for 32.4[0] ÷ 0.8 oe B1ft for 31.35

(a) (i)

19.2[…] or 3 41

2

M1 for [AB2 = ] 122 + 152 or better

128.6 to 128.7 or 129

3

(ii)

their12 oe 15 A1 for 38.6 to 38.7 M1 for tan θ =

B1ft for [ ABˆ C = ] their θ + 90 Alternative method M2 for complete method using cosine rule for cos ABC using their 19.2 44.8[2…]

(b)

3

M2 for

7 sin 65 9

Or M1 for

3

(a) (i)

(ii)

(b)

 3 4    −1 2

1  1  2 − 2   or  2 4  3 −1 3  4

 4 − 2   oe 0 − 6

1 −  2  oe isw 1 −  4

9 7 oe = sin 65 sin x

2

B1 for one row or one column correct

2

B1 for det = 4 soi

 2 − 2  or for   3 −1 2

B1 for one row or one column correct  − 2 1  oe Or M1 for 2C = – 4   0 3 or for –

© Cambridge International Examinations 2015

1 C= 2

 − 2 1    0 3

Pag P ge 3

Mar M k Sch S hem me e Cam mbrridge e O Le eve el – Oct O tob berr/N Nov vem mb ber 20 015 5

Quesstio on

Ma ark k

3 0  311   2 5  271  275   2 0

2

( ) (ii)

Am mou untt [inn centts] forr eaach weeek k

1

(iii))

85.75 5 caao

1

(cc) (i))

4

A werrs Answ

(a a)

B

(cc) (i)) P

2

5

(a a)

Pa artt m marks B1 1 for fo 2 elem men nts corrrecct in i a 3 by y1m maatrix x orr all 3 vaaluees corr c rectt inn do ollaars orr 160 0 11950 + 11   M for M1 f  9975 5 + 174 40  11300 + 14 450 0  

C

′ E ∩ (D ∪ F ) oor (D ∪ F )′ ∩ E

1

Orr E ∩ D ' ∩ F '

2

B1 1 for fo 8 oor 9 nu umb berrs ccorrrecttly plaaceed or o for f 10 0 nu um mberrs cor c rrecctly y pllaceed wit w th one o e ad ddittion nal nu umb berr orr fo or 1, 3, 4,, 5, 7, 9 see s en corr c rectly po osittion nedd an nd no n num mbberss po osittion nedd in ncorrrecctlyy

Q 3

Pape P er 2 21

1

A

(b b)

Sylllab S bus 4 24 402

7

6

5

1 9

4

8

1 10

( ) (ii)

7

1ft

(iii))

3 o oe 10 0

2 2ft

3xx 2 y(2 y 2 − 5x 5 )

2

B1 1 for fo the t eir 3 seeen n ass nuum meraatorr off a fraactio on so oi B1 1 for fo 3x 2 (2 y 3 − 5xyy) orr 3yy(2 x 2 y 2 − 5x 3 )

5x) orr x 2 y(6 y 2 − 15 orr 3xxy(2 xy 2 − 5x 2 )

A − 5x) orr 3xx 2 y(A orr 3xx 2 y(2 y 2 − B)

© Ca amb brid dge e In nterrnattion nal Ex xam mina atio ons s 20 015 5

Page 4

Mark Scheme Cambridge O Level – October/November 2015

Question

8 3

(b)

x = ± 1.63[...] or

(c) (i)

Correct region shaded with 4 correct lines

(ii) 6

Answers

(a) (i) (ii) (b) (i)

–

±

1 oe 2

a = 1, b = –3 5.38 to 5.39 or b–

29

1 1 a or (2b − a ) final answer 2 2 1 1 a or (a + 4b ) final answer 2 2

(ii)

2b +

(iii)

λ:3λ

Syllabus 4024

Mark

Paper 21

Part marks

4( x + 2) + 2 x = 3 soi x( x + 2) M1dep for 4x + 8 + 2x = 3x2 + 6x or better

3

M1 for

3

B2 for 3 or 4 correct lines or B1 for 2 correct lines

2

B1 for (3, 3) or (1, 4) soi

2

B1 for one correct

2

M1 for

52 + 22

1

1

2dep

1 a seen 4 1 or n(b + a ) seen 4 1 1 or OF = OE oe or k = 2 2

B1dep for b +

© Cambridge International Examinations 2015

Page 5

Mark Scheme Cambridge O Level – October/November 2015

Question

Syllabus 4024

Paper 21

Answers

Mark

Part marks

(a)

A correct shape with one of diagonal lines as line of symmetry

1

(b)

Correct shape

2

B1 for three additional triangles drawn round M, at least two correct Or SC1 for

(c) (i)

C at (3, 1) (3, 3) (4, 3)

2

B1 for either vertical or horizontal correct Or for two vertices correct and correct orientation

(ii)

y = x oe

1

(iii)

 − 1 Translation    3

2

(iv) (a)

(2, 0)

1

SECTION B 7

(4, –1)

Rotation, 90o clockwise, (0,0) oe

2

(c)

 0 1    −1 0

1

(a)

πr2 + πr (r + 4) with correct working leading to 6r(r + 2)

2

(b)

48, 90

1

(c)

Correct shape curve through 7 correct points

2

B1ft for at least 5 correct points plotted

(d)

[h = ]

8r + 16 or 2 2r + 4

2

M1 for (r + 4)2 = r2 + h2 or better

[h = ]

( r + 4) 2 − r 2 or better

2

M1 for 8r + 16 = 144 oe

(b)

8

(4, 0)

 − 1 B1 for translation or    3 Or M1 for D seen at (1, 3), (3, 3), (3, 4)

(e)

16

B1 for two correct from: Rotation, 90° clockwise oe, (0, 0) oe

M1 for πr2 + πr (r + 4) or πr (r + r + 4)

© Cambridge International Examinations 2015

Page 6

Mark Scheme Cambridge O Level – October/November 2015

Question (f)

Answers

Syllabus 4024

Mark

(i)

4.8 to 4.95

1

(ii)

8 cao

2

Paper 21

Part marks

B1 for 7.[…] or M1 for substituting their f(i) into ( r + 4) 2 − r 2

9

4 [minutes] 18 [seconds]

1

1 [minute] 0 [seconds]

2

B1 for attempt to read at 12.5 and 37.5

(b)

10, 12, 13, 5, 2

2

B1 for 3 correct

(c)

17 [minutes] 30 [seconds]

2

B1 for three times only seen including 6, 5:30 and time in range 5:30 < t ⩽ 6

(d) (i)

23

1

7 or 0.14 50

2

4 oe 175

2

(a) (i) (ii)

(ii)

(e)

10 (a) (i)

(ii)

1 (x + 15)(x – 3) = 75 2

M1

Correct expansion leading to x2 + 12x – 195 = 0 www

A1

9.2 cao

3

B1ft for their 2 + their 5 seen or time = 5 [mins] seen 2 oe Or SC1 for answer 50

a a −1 × where a < 50 50 49 8 7 and seen Or B1 for 50 49 16 8 Or SC1 for answer oe or answer oe 175 625 M1 for

Or equivalent equation for area

B2 for 9.19[8…] or 9.2[0] seen OR B1 for 12 2 − 4 × 1 × −195 soi And B1 for

(iii)

7.3

2

− 12 ± their 924 oe 2

M1 for 2AD – 0.8 + 15 + their 9.2 = 38.0 oe Or 2BC + 0.8 + 15 + their 9.2 = 38.0 oe Or SC1 for answer [BC = ] 6.5

© Cambridge International Examinations 2015

Page 7

Mark Scheme Cambridge O Level – October/November 2015

Question (b) (i)

(ii)

11 (a) (i)

Answers

Syllabus 4024

Mark

Paper 21

Part marks B1 for LMˆ N = 108° seen

72°

2

4 7

3

M2 for 126 : their 72 soi or B1 for 126 seen 7 Or SC2 for answer 4

9.19[…]

2

M1 for

1 × 4 × 6 × sin 50 2

(ii)

183 to 184

1ft

ft 20 × their 9.19

(iii)

310 to 310.5

5ft

ft 292 + 2 × their 9.19 B3 for 4.60 or 4.59[8…] or M2 for 42 + 62 – 2× 4 × 6 × cos 50 or M1 for cosine formula with one error AND M1 for 20×(4 + 6 + their4.60) + 2×their9.19 oe

(b)

21.3[2…]

4

B1 for correct change of units soi M1 for use of π × r2 × 0.7 = 0.1 M1 for r 2 =

© Cambridge International Examinations 2015

0.1 soi 0.7 × π

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level

MARK SCHEME for the October/November 2015 series

4024 MATHEMATICS (SYLLABUS D) 4024/22

Paper 2, maximum raw mark 100

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

Page 2

Mark Scheme Cambridge O Level – October/November 2015

Question 1

Answers

(a) (i) (a)

(b) (ii)

(b)

396

Mark 2

110 isw

Syllabus 4024

Paper 22

Part Marks M1 for

60 × 360 + 15×12 or 100

B1 for

60 × 360 seen 100

1ft 26 x = 569.80 oe or 100 B1 for ÷ by figs 74

770

2

M1 for x –

1.21

3

M2 for

850 x = 550 oe or 1.87

B1 for

850 or 1.87 or 850 or 550 or 1.87 850 550 850

x or 550 1.87 x

2

14

(a)

2

M1 for

1 × CA × (11 − 7) oe or 2

SC 1 for 28

3

(8 − (−2)) 2 + (7 − 11) 2

(b)

10.8

2

(c)

22.8

2ft

B1 for [BC =] 5 soi or M1 for (b) + theirBC + CA

(d)

21.8

2ft

M1 for tanA =

(a) (i)

Convincing explanation

1

(ii)

28

2

(iii)

76

1ft

(b) (i) (ii)

M1 for

(11 − 7) oe (8 − (−2))

) B1 for OCD = 124 or triangle COD isosceles soi

Convincing explanation

2

B1 for a correct pair of equal angles stated

2.5

3

B1 for 8.5 – SR or 8.5 – QS seen and M1 for

© Cambridge International Examinations 2015

12 QS 12 8.5 − SR = or = 5 8.5 − QS 5 SR

Page 3

Mark Scheme Cambridge O Level – October/November 2015

Question 4

Answers

Syllabus 4024

Mark

Paper 22

Part Marks 1 4 × × π × r3 = 20 soi or 2 3 SC1 for 1.68

(a) (i)

2.12

2

M1 for

(ii)

6.79

2

B1 for

3

50 or 20

3

20 oe or 50

3

M1 for  5  = 20 oe x

187

(b)

3

50

M1 for π(figs 15)2 oe and M1 for  1 × 4 × π × (figs 55)2 – 50 × 2 

their πr 5

2

(a)

51.2

2

M1 for AC2 + 402 = 652 oe

(b)

12.7

2

M1 for

AF = sin25 oe 30

(c)

40.4

3

M1 for

35 = cos30 oe and a further AG

M1 for (AG = ) 6

35 oe cos 30

–4.62 –2.38 final answer

2

B1 for one value SC1 for both –4.6 and –2.4

(B = ) 7 (C = ) 11

3

M1 for ( x +

(b)

x < –2

2

M1 for isolating 3x and – 6 soi

(c)

(x + 3y)(6 – t) oe

2

M1 for the correct extraction of a common factor at any stage

(d)

(a = ) 17 (b =) – 16

4

M1 for equalising one set of coefficients or substitution and a further M1 for eliminating one variable or simplifying an equation in one variable and A1 for 17 and A1 for – 16 After A0, SC1 for correct substitution into one of the original equations to find the other variable

(a) (i)

(ii)

7 2 5 ) = and 2 4 B1 for one correct value

© Cambridge International Examinations 2015

Page 4

Mark Scheme Cambridge O Level – October/November 2015

Question 7

Answers

Syllabus 4024

Mark

Part Marks

(a)

Fully shown

2

M1 for the area sine formula

(b)

2x2 – 19x + 6 (= 0) correctly obtained

3

B1 for both x + 12 and 4 + 2x – 5 and

x(2 x − 5) 1 = their ( x + 12)their (4 + 2 x − 5) 3

M1 for (c) (i)

9.17 0.33

3

B1 for

(−19) 2 − 4 × 2 × 6 soi and

B1 for

− (−19) ± their 313 soi and 2× 2

M1 for both real values of (ii)

8

Paper 22

0.33 with reason

p± q r

1 M2 for (BC2=) c(i)2 + (2c(i)–5)2 – 2×c(i)×(2c(i)–5)×cos25 or M1 for correct formula with one error and A1 ft for correct evaluation from their M1 SC1 for x2 + (2x–5)2 – 2x(2x–5)cos25 oe

(d)

6.35

3ft

(a) (i)

2.62

2

M1 for

25 × 2π × 6 360

(ii)

7.85

2

M1 for

25 × π × 62 360

(b) (i)

39.3

1ft

(ii)

88.8

3ft

B1 for 30 or 60 or M1 for 5× (a)(i) and indep M1 for 2×(a)(ii)

(iii)

471 to 472

2ft

B1 for height = 15 and radius = 12 soi

(c) (i) (ii)

(h =)

800 πr 2

1

h is divided by 4 oe

1

© Cambridge International Examinations 2015

Page 5

Mark Scheme Cambridge O Level – October/November 2015

Question 9

Answers

Syllabus 4024

Mark

Part Marks

(a)

36

1

(b)

Correct plots ft and curve

2

P1 for 6 correct plots ft

(c) (i)

4 < gradient < 6

2ft

B1 for tangent at t = 4

Speed oe

1

(d)

Their 2.5

2ft

B1 for their 1.8 and their 4.3

(e) (i)

Their 1.65 towards Their 4.7 away from

2ft

B1 for one correct ft

(ii)

48 – 20 = 12 oe isw t

(ii)

t2 +

(iii)

–32 cao

1

Correct histogram

3

10 (a)

Paper 22

1

If 3 not scored, up to 2 marks from: B1 for correct fd’s (allow one error) B1 for correct column widths B1 for correct heights from their fd’s

(b)

95 < t ⩽ 100

1

(c)

98.2

3

M1 for

∑ fx

B1 for division by 80 seen (d)

28 oe 80

1

(e) (i)

992 oe 6320

2

M1 for 2 ×

(ii)

64 oe 6320

2

M1 for

© Cambridge International Examinations 2015

32 31 or 32 × 31 × 80 79 80 80

4 8 4 8 or 2 × × × 80 79 80 80

Page 6

Mark Scheme Cambridge O Level – October/November 2015

Question

Answers

Mark

11 (a) (i)

6.08

1

(ii)

1    4

2

(iii) (a) (b) (iv)

 4    − 7

1

GD = 2 FH stated or appropriate numerical vector statement

1

M1 for AF = AH + HF oe or 1 6   2  1 

dep

1ft

Correct image

1

(ii)

Centre (4, 0) oe Scale factor ×2 oe

2

(iii)

(5, 2)

1

(iv)

Correct image

2

(b) (i)

Paper 22

Part Marks

B1 for

(9.5, 3)

Syllabus 4024

B1 for either

B1 for either Stem of flag R on or parallel to y = – x or Hypotenuse of flag parallel to y-axis. SC1 for correct clockwise rotation

© Cambridge International Examinations 2015

Cambridge International Examinations Cambridge Ordinary Level

* 3 4 2 7 9 9 6 4 8 9 *

4024/11

MATHEMATICS (SYLLABUS D)

October/November 2015

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NF/SW) 110300/3 © UCLES 2015

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1



(a) Work out 12 + 6 ÷ 3 + 1 × 5.

7 3 - . (b) Work out 9 5

2 B

A



12

5

Answer

........................................ [1]

Answer

........................................ [1]

C

D

ABCD is a quadrilateral with BC parallel to AD. CD is perpendicular to BC. BC = 5 cm and AD = 12 cm. The area of triangle BCD is 20 cm2. (a) Find CD.



Answer

.................................. cm [1]

Answer

................................. cm2 [1]

(b) Find the area of triangle ABD .



© UCLES 2015

4024/11/O/N/15

3

3

A number written as the product of its prime factors is 22 × 52 × 7. (a) Evaluate this number.



Answer

........................................ [1]

(b) The lowest common multiple of 22 × 52 × 7 and another number, N, is 22 × 3 × 52 × 72. Find the lowest possible value of N.

4

Answer N = ................................. [1] The exchange rate between pounds (£) and dollars ($) is £1 = $1.60 . (a) Amit changes £200 to dollars. Calculate the number of dollars he receives.



Answer $ ...................................... [1] (b) Ayesha changes $240 to pounds. Calculate the number of pounds she receives.



© UCLES 2015

Answer £ ...................................... [1]

4024/11/O/N/15

[Turn over

4

5

T

P

34 Q S

R

The diagram shows a square PQRS and a right-angled triangle PST. The area of the square is 50 cm2. ST = 34 cm. Calculate PT.

6

Answer

.................................. cm [2]

Answer

........................................ [1]

Answer

........................................ [1]

(a) Write 30 682 correct to three significant figures.

(b) Given that 538 × 210 = 112 980, evaluate 112.98 ÷ 210.



© UCLES 2015

4024/11/O/N/15

5

7

Paul takes examinations in Maths and Physics. The probability that he passes Maths is 0.7 . The probability that he passes Physics is 0.6 . The results in each subject are independent of each other. Calculate the probability that he passes Maths and does not pass Physics.

8

Answer (a)

........................................ [2]

cos yc =- 0.54 where 90 1 y 1 180 One solution of the equation cos xc = 0.54 is x = 57 , correct to the nearest whole number.





Find y correct to the nearest whole number.



Answer y = .................................. [1] (b) Solve

5a - 2 = 11 . 3



© UCLES 2015

Answer a = .................................. [2]

4024/11/O/N/15

[Turn over

6

9

(a) p

27

33

q

9

r

Given that p is directly proportional to q, find the value of r.



Answer r = .................................. [1] (b) x

2

10

y

25

1

Complete the sentence below describing the relationship between x and y.



y is inversely proportional to

........................................ [1]

(c) M is directly proportional to L3. How many times larger is M when L is multiplied by 2?



© UCLES 2015

Answer

4024/11/O/N/15

........................................ [1]

7

10 Here is a list of numbers.

−8

−5

−3

−2

0

2

4

9

(a) Write down two numbers from the list that have a difference of 10.



Answer

................ and ................. [1]

Answer

........................................ [1]

(b) Find the sum of the numbers in the list.

(c) It is given that - 4 G 2x G 7 .

Write down all the numbers from the list which satisfy this inequality.

11

Answer

........................................ [1]

An empty box has a mass of 0.8 kg correct to the nearest 0.1 kg. (a) Write down the lower bound for the mass of the empty box.



Answer

................................... kg [1]

(b) The box is filled with books. The total mass of the box and the books is 6 kg correct to the nearest kilogram. Work out the lower bound for the mass of the books.



© UCLES 2015

Answer

4024/11/O/N/15

................................... kg [2]

[Turn over

8

12 A group of five numbers has a mean of 3.8 and a median of 3. The numbers 3 and 6 are added to the group. (a) Find the mean of the seven numbers.



Answer

........................................ [2]

Answer

........................................ [1]

(b) Find the median of the seven numbers.



© UCLES 2015

4024/11/O/N/15

9

13 Each member of a group of 50 people was asked how many films they watched in a month. The results are shown in the table below. Numbers of films watched

Frequency

0

5

1

12

2

13

3

15

4

4

5

1

(a) Find the mode.

Answer

........................................ [1]

Answer

........................................ [2]

(b) Calculate the mean number of films watched in a month.



© UCLES 2015

4024/11/O/N/15

[Turn over

10

14 (a) Evaluate 9

- 12

.



Answer

........................................ [1]

Answer

........................................ [1]

103 – 100.

(b) Evaluate

3 2

(c) Solve x = 8 .



Answer x = .................................. [1]

15 4=

cx + 1 dx - 1

Find x in terms of c and d.



© UCLES 2015

Answer x = .................................. [3]

4024/11/O/N/15

11

16 (a) The mass of a dust particle is approximately 0.000 075 3 g. Write this mass in standard form.



Answer

..................................... g [1]

Answer

................................... kg [2]

(b) The mass of the Earth is 5.972 × 1024 kg. The mass of the Moon is 7.3 × 1022 kg. Find the total mass, in kg, of the Earth and the Moon. Give your answer in standard form.

17

f ^xh = 5 + x 2 Find t given that f ^3 - th = 9 .

© UCLES 2015

Answer t = .............. or ............... [3] 4024/11/O/N/15

[Turn over

12

18 A sequence of patterns is made using dots and lines.

Pattern 1

Pattern 2

Pattern 3

Pattern number ( p)

1

2

3

Number of dots (d )

6

11

16

(a) Complete the table for Pattern 4.

4

[1]

(b) Find a formula for the number of dots, d, in Pattern p.



© UCLES 2015

Answer d = .................................. [2]

4024/11/O/N/15

13

19 North

A

C

B

The land region shown has wheat storage depots at A, B and C. (a) Given that the bearing of C from A is 115°, find the bearing of A from C.



Answer

........................................ [1]

(b) Local farmers take their wheat to the nearest depot. By drawing suitable accurate constructions, find and shade the region which is served by the depot at B.

© UCLES 2015

4024/11/O/N/15

[2]

[Turn over

14

20

Speed (m/s)

0



5

15

Time (t seconds)

The diagram shows the first 15 seconds of a car’s journey. The car starts from rest. The acceleration of the car from t = 0 to t = 5 is 4 m/s2. The acceleration of the car from t = 5 to t = 15 is 2 m/s2. (a) Find the speed of the car when (i) t = 5,



Answer

................................. m/s [1]

Answer

................................. m/s [1]

(ii) t = 15.

(b) Find the distance travelled by the car between t = 5 and t = 15.



© UCLES 2015

Answer

4024/11/O/N/15

.................................... m [2]

15

21 The table shows the masses of different fruits sold at a market stall on one day.

Fruit

Apples

Pears

Oranges

Bananas

Total

Mass (kg)

30

10

18

32

90

(a) Complete the pie chart to illustrate the data.

Apples

Pears

[2] (b) The stallholder buys apples for 60 cents per kilogram. She sells them all for 72 cents per kilogram. Calculate her percentage profit.



© UCLES 2015

Answer .................................... % [2]

4024/11/O/N/15

[Turn over

16

22 (a) Expand and simplify 10 − 3(3x − 2).

(b) Simplify fully

........................................ [1]

Answer

........................................ [3]

3x 2 + 16x + 5 . 9x 2 - 1



© UCLES 2015

Answer

4024/11/O/N/15

17

23 A group of 15 adults and 12 children are going on a coach to a concert. The tickets for the coach cost $a for each adult and $c for each child. The total cost for the coach tickets is $324. (a) Show that 5a + 4c = 108.

[1] (b) For a different group of 2 adults and 3 children the cost is $53. Solve the simultaneous equations. 5a + 4c = 108 2a + 3c = 53



Answer a = ........................................



c = .................................. [4] (c) Find the cost for a group of 4 adults and 5 children to travel on the coach.



© UCLES 2015

Answer $ ...................................... [1]

4024/11/O/N/15

[Turn over

18

24 (a) P

T

118° Q

S 99° R





P, Q, R, S and T are points on the circumference of a circle. PQ = QR. t = 99°. t = 118° and QRS PQR t . Find PTS Show all your working.



Answer

t = ............................ [2] PTS

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/11/O/N/15

19

(b) B

A

60° O E

C

D





A, B, C, D and E are points on the circumference of a circle, centre O. t = 60c. AE = ED = DC = CB and AOB t . (i) Find ECD Show all your working.



Answer

t = ........................... [2] ECD

Answer

.................................. cm [2]

(ii) The radius of the circle is 12 cm. Calculate the length of the minor arc AB. Use r = 3.14 .



Question 25 is printed on the next page © UCLES 2015

4024/11/O/N/15

[Turn over

20

25

B

C

4

A

5

D

E 2 F



ABCD is a parallelogram. BEF and CDF are straight lines. AB = 4 cm, DF = 2 cm and AE = 5 cm. (a) Show that triangles ABE and CFB are similar. Give reasons for each of your statements.

[2] (b) Calculate BC.



Answer

.................................. cm [2]

(c) Triangle DFE is also similar to triangle ABE. Given that the area of triangle DFE is x cm2, find the area of ABCD in terms of x.

© UCLES 2015

Answer 4024/11/O/N/15

................................. cm2 [2]

Cambridge International Examinations Cambridge Ordinary Level

* 1 5 2 4 7 1 9 7 3 3 *

4024/12

MATHEMATICS (SYLLABUS D)

October/November 2015

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (LK/SG) 100474/4 © UCLES 2015

[Turn over

2 ElEctronic calculators must not bE usEd in this papEr 1

(a) Evaluate 0.03 × 0.3 .



Answer ................................................. [1] (b) Evaluate 5 – 2(3 – 1.4) .



2

Answer ................................................. [1]

(a) A trader buys 7 items for $4.10 each and 5 items for $6.40 each. He sells all of them for $10 each. Calculate his profit.



Answer $ ................................................. [1] (b) Find the simple interest on $450 for 5 years at 4% per annum.



© UCLES 2015

Answer $ ................................................. [1]

4024/12/O/N/15

3 3

y varies directly as the square root of x. Given that y = 18 when x = 9, find y when x = 4.



Answer y = ................................................. [2]

4

f(x) = 1 + 4x 2 (a) Find f `- j . 5



Answer ................................................. [1] (b) Find f –1(x).



© UCLES 2015

Answer f –1(x) = ................................................. [1]

4024/12/O/N/15

[turn over

4 5

(a) Write the number 0.050 462 correct to 3 significant figures.



Answer ................................................. [1] (b) By writing each number correct to 1 significant figure, estimate the value of 8.94 # 0.201 . 28.8



6

Answer ................................................. [1]

Evaluate 3 c

0 3 1 5 m- 2 c m. -3 1 -4 -1



© UCLES 2015

Answer

4024/12/O/N/15

[2]

5 7

(a) In the diagram, seven small triangles are shaded. Shade two more small triangles, so that the diagram will then have rotational symmetry of order 3.

[1] (b) In the diagram, ten small hexagons are shaded. Shade one more small hexagon, so that the diagram will then have exactly one line of symmetry.

[1]

8

a, b, c, d and e are five numbers, such that d < a < c a < e < c a < b < e Arrange these numbers in order, starting with the smallest.

Answer ............... , ................ , ................ , .............. , ................ [2] smallest

© UCLES 2015

4024/12/O/N/15

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6 9

At an athletics event, Dave and Ed each threw a javelin. Dave threw 60 m, correct to the nearest 10 metres. Ed threw 61 m, correct to the nearest metre. (a) Write down the lower bound for the distance thrown by Dave.



Answer ............................................. m [1] (b) Calculate the greatest possible difference between the distance thrown by Dave and the distance thrown by Ed.



Answer ............................................. m [1]

10 (a) Express the number 0.000 004 5 in standard form.

Answer ................................................. [1] (b)

p = 6 × 108

q = 4 × 107

Expressing each answer in standard form, find (i) p × q,



Answer ................................................. [1] (ii) p – q.



© UCLES 2015

Answer .................................................. [1]

4024/12/O/N/15

7 11

3 0 (a) Evaluate c m . 2 Answer ................................................. [1]

3 -1 (b) Evaluate c m . 2



Answer ................................................. [1] (c) Simplify (9x3)2 .



Answer ................................................. [1]

12 (a) Express 198 as the product of its prime factors.



Answer ................................................. [1] M = 22 × 3 × 52

(b)

N = 23 × 32 × 7

(i) Find the largest number that divides exactly into M and N.



Answer ................................................. [1] (ii) Find the smallest value of k, such that M × k is a cube number.



© UCLES 2015

Answer k = ................................................. [1]

4024/12/O/N/15

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8 13 z° 40.9

y

77° 38.1

20 x

45

78°

These two quadrilaterals are congruent. The lengths are in millimetres. Find the values of x, y and z.



Answer x = .................................................



y = .................................................



z = ................................................. [3]

14 Meeraa went on a journey from P to Q to R. The first part of the journey, from P to Q, took 4 hours to travel 80 km. (a) Find the average speed for the journey from P to Q.



Answer ....................................... km/h [1] (b) In the second part of the journey, from Q to R, she travelled 45 km. Her average speed for both parts of the whole journey from P to Q to R was 25 km/h. Find the time taken for the second part of the journey, from Q to R.



© UCLES 2015

Answer .................................... hour(s) [2]

4024/12/O/N/15

9 15 (a) On the Venn diagram, shade the set B + (A , C )l . 

B

A

C

[1] (b) % = { 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 } W = { x : x is a multiple of 2 } H = { x : x is a multiple of 3 } (i) Find n (W ∪ H ).



Answer ................................................. [1] (ii) List the members of W + H l .



© UCLES 2015

Answer ................................................. [1]

4024/12/O/N/15

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10 16 (a) Factorise (i) 4p2 – 9q2,



Answer ................................................. [1] (ii) 2n2 + 5n – 3.



Answer ................................................. [1] (b) Express

3 2 + as a single fraction. 4x 3y



© UCLES 2015

Answer ................................................. [1]

4024/12/O/N/15

11 17 B

T

A O

y° E

z°

x° 62° 70° C

D

In the diagram, A, B, C, D and E lie on the circle, centre O. AC is a diameter. The tangent to the circle at C meets the line AB produced at T. t = 62° and ACD t = 70° . ACB (a) Find x.



Answer x = ................................................. [1] (b) Find y.



Answer y = ................................................. [1] (c) Find z.



© UCLES 2015

Answer z = ................................................. [1]

4024/12/O/N/15

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12 18 y C

B

A

O

x

The sides of the triangle ABC are formed by the straight lines with equations x = 3,

y = 6,

1 y = x + . 2

(a) The region inside the triangle is defined by three inequalities. Write down these three inequalities.

Answer ................................................. ................................................. ................................................. [2] (b) The point (4, k), where k is an integer, lies inside the triangle. Find the value of k.



© UCLES 2015

Answer k = ................................................. [1]

4024/12/O/N/15

13 19 All the angles of a polygon are either 155° or 140°. There are twice as many angles of 155° as 140°. Find the number of sides of the polygon.



© UCLES 2015

Answer ................................................. [3]

4024/12/O/N/15

[turn over

14 20 The masses of 400 goats were measured. The results are shown in the cumulative frequency graph.

Cumulative frequency

400

300

200

100

0

58

60

62

64

66

68

70

72

Mass (kilograms)

(a) Use the graph to find (i) the median,

Answer ........................................... kg [1] (ii) the 30th percentile,



Answer ........................................... kg [1] (iii) the number of goats whose mass is more than 66 kg.



Answer ................................................. [1] (b) It was noticed later that the scales used were faulty and that the true readings should all be 2 kg more. On the grid above, draw the true cumulative frequency graph.

© UCLES 2015

4024/12/O/N/15

[1]

15 21 The diagram shows the positions of three ships A, B and C. It is drawn to a scale of 1 cm to 20 km. (a) Find, by measurement, the bearing of C from A.

Answer ................................................. [1] (b) On the diagram construct the locus of points, inside triangle ABC, that are (i) equidistant from B and C,

[1]

(ii) equidistant from AB and BC.

[1]

(c) A ship D is • equidistant from B and C, and • equidistant from AB and BC. Label the position of D on the diagram and find the actual distance of D from A. Scale:1 cm to 20 km B

North

A C



© UCLES 2015

Answer DA = .......................................... km [1]

4024/12/O/N/15

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16 22 P is the point (1, –3) and Q is the point (7, 2). (a) Find the coordinates of the midpoint of PQ.



Answer ( .................... , .................... ) [1] (b) Find the gradient of the line PQ.



Answer ................................................. [1] (c) The line, L, with equation 2x – 5y = k, passes through the point Q. (i) Find the value of k.



Answer k = ................................................. [1] (ii) The line x + Ay = 3 is parallel to L. Find the value of A.



© UCLES 2015

Answer A = ................................................. [1]

4024/12/O/N/15

17 23 A fair 4-sided spinner is numbered 1, 2, 3 and 4. (a) Anil spins it once. He gets his score by doubling the number obtained. Complete the table to show the probabilities of his scores. Score

2

4

6

8

Probability [1] (b) Billie spins it twice. She gets her score by adding the numbers obtained. (i) Complete the possibility diagram. First spin

Second spin

+

1

2

3

4

1

2

3

4

5

2

3

4

5

6

3

4

5

6

7

4

[1]

(ii) Complete the table showing the probabilities for some of Billie’s scores. Score Probability

>2 15 16

>4

>6

>8

[1] (c) Find the probability that Billie scores more than Anil.



© UCLES 2015

Answer ................................................. [2]

4024/12/O/N/15

[turn over

18 24 The first term of a sequence is 13. The following terms are found by alternately adding 4 and 6 to the previous term. The first six terms are 13

17

23

27

33

37

(a) Write down the next two terms of the sequence.

Answer ................................................. [1] (b) Write down the value of the term that is closest to 999.



Answer ................................................. [1] (c) Write down the difference between the values of the 91st and 93rd terms.



Answer ................................................. [1] (d) Find the 80th term.



Answer ................................................. [1] (e) The nth term is 203. Find n.



© UCLES 2015

Answer n = ................................................. [1]

4024/12/O/N/15

19 25 20 car A

15

Speed (m/s) 10 5 0

0

k

10 Time (t seconds)

The diagram shows the speed-time graph of car A. (a) Find the acceleration of car A when t = 7.

Answer ........................................ m/s2 [1]



(b) Find an expression, in terms of k, for the distance moved by car A between t = 0 and t = k, where k 2 10 . Give your answer in its simplest form.



Answer ............................................ m [2] (c) Car B travels at a constant speed of 12 m/s in the same direction as car A. (i) On the diagram, sketch the speed-time graph of car B.

[1]

(ii) When t = 0, car B passes car A. When t = k, car A overtakes car B. Find the value of k.



Answer k = ................................................. [1] Question 26 is printed on the next page

© UCLES 2015

4024/12/O/N/15

[turn over

20 26 A, B and C are three triangles. T1, T2 and T3 are three transformations such that T1(A) = B, T2(A) = C and T3(C) = B. The vertices of triangle A are (1, 0), (0, 1) and (1, 3). The matrix that represents T1 is c (a) Find c

2 2 1 0 mc 0 1 0 1

2 0

2 m. 1

1 m. 3

(b) The matrix that represents T2 is c (i) Find the inverse of c

2 0

Answer

[2]

Answer

[1]

Answer

[2]

2 0 m. 0 1

0 m. 1

(ii) The matrix that represents T3 is m. Find m.



Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/12/O/N/15

Cambridge International Examinations Cambridge Ordinary Level

* 8 3 4 8 8 5 5 3 5 6 *

4024/21

MATHEMATICS (SYLLABUS D)

October/November 2015

Paper 2 

2 hours 30 minutes

Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 19 printed pages and 1 blank page. DC (NH/FD) 110304/3 © UCLES 2015

[Turn over

2 Section A [52marks] Answerallquestionsinthissection.

1

(a) Timinvests$2500inabankpayingsimpleinterestat2.3%peryear. Whatisthetotalamountofmoneyinthebankattheendof4years?



Answer $.......................................... [2] (b)

TABLET

FINANCE OFFER

$750

Pay15%of$750asdepositand 36monthlypaymentsof$25.

Chrisbuysthetabletusingthefinanceoffer. Howmuchmoredoeshepaythanifhehadpaid$750forit?



Answer $.......................................... [2] (c) Lavinbuyssomesweets,pensandpaperatherlocalshop. Theshopisoffering20%discountonallitems. Thisisherreceipt. Itemsandprices

Cost($) w 4.50 z

0.3kgofsweetsat$15.50perkg 6pensat$xperpen Paper

y

Totalbeforediscount Totalafterdiscount

32.40

Findthemissingvaluesw,x,yandz.



Answer w=.....................................



 x=......................................



 y=......................................



 z=...................................... [5]

© UCLES 2015

4024/21/O/N/15

3 2

(a) ABCDEisapentagonwithonelineofsymmetry. t = CDE t = 90° . BC=DE=10cm,DC=30cmand BCD TheshortestdistancebetweenA andDCis22cm.

A

E

B

10

10

D

(i) CalculateAB.



C

30

Answer ...................................... cm[2] (ii) Calculate ABˆ C .



Answer ............................................ [3] t =65°. (b) IntrianglePQR,PQ=7cm,PR=9cmand PQR

P

t . Calculate PRQ 7

Q

© UCLES 2015

65°

9

R

Answer ............................................ [3] 4024/21/O/N/15

[Turn over

4 3

1 (a) A= e -2

3 -1 o   B= e 2 -3

2 o 2

Find (i) 2A –B,

(ii) B–1.



Answer f

p

[2]

Answer f

p

[2]

Answer f

p

[2]

(b) ThematrixCsatisfiesthefollowingequation. 





3C+4 e

-2 0

1 o=C 3

FindC.



© UCLES 2015

4024/21/O/N/15

5 (c) Theresasellsraspberriesandblackcurrants. Thefirstmatrixshowsthenumberofkilogramsofeachfruitshesellsduringthreedifferentweeks. Thesecondmatrixshowsthepriceperkilogram,incents,ofthefruitTheresasells. 





raspberries





Week1





Week2





Week3 3 (i) D= f 1.5 2

f

blackcurrants

3

2

1.5

3

2

2.5

p

price/kg

f

650

raspberries

580

blackcurrants

p

2 650 m 3 pc 580 2.5

FindD.



Answer 

[2]

(ii) ExplainthemeaningoftheinformationgivenbymatrixD. Answer.................................................................................................................................. [1] (iii) Findthetotalamount,indollars,thatTheresagetsforthefruitshesells.



© UCLES 2015

Answer $......................................... [1]

4024/21/O/N/15

[Turn over

6 4

(a) Shadethesubset (A+B),C. Answer



A

B

C

 

[1] (b) Usesetnotationtodescribethesubsetshadedinthediagram. 

D

E

F



Answer ............................................ [1] (c) ={1,2,3,4,5,6,7,8,9,10} P={x:xisanoddnumber} Q={x:xisasquarenumber} (i) Writethemembersof  inthecorrectregionsontheVenndiagram. Answer 

P

Q



[2] (ii) Staten(Ql ).



Answer ............................................ [1] (iii) Anumber,m,ischosenatrandomfrom. Findtheprobabilitythatmisamemberof P + Q l .

© UCLES 2015

Answer ............................................ [2] 4024/21/O/N/15

7 5

(a) Factorisecompletely 6x2y3–15x3y.



Answer ............................................ [2] 4 2 = 3. (b) Solve  + x x+2



Answer x=................ or................[3] (c) (i) ShadeandlabeltheregionRdefinedbythesefourinequalities.









xH1    yG4    x+yG6    yHx

Answer

y 7 6 5 4 3 2 1 0

1

2

3

4

5

6



7

x

[3] (ii) ThepointMistheintersectionof x=1 and y=4. ThepointNistheintersectionof x+y=6 and y=x. Findthegradientof MN.

© UCLES 2015

Answer ............................................ [2] 4024/21/O/N/15

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8 6

(a) Thediagramshowsthevectors PQandQR.





a 5 PQ = c m and QR = c m. 2 b

Q

P R





   (i) Findaandb.



Answer a=............... b=...............[2] (ii) Calculate

PQ . 



Answer ............................................ [2] (b) OACBisaparallelogram. OA = a, OB = b andDisthepointsuchthat2OB = BD . EisthemidpointofCD.

A

C

a F

O

b

B

E

D

(i) ExpressCE ,assimplyaspossible,intermsofaandb.



Answer ............................................ [1] (ii) Express OE ,assimplyaspossible,intermsofaandb.



Answer ............................................ [1] (iii) FisapointonBCsuchthatOF = kOE . Find BF:FC.

© UCLES 2015

Answer .....................:....................[2] 4024/21/O/N/15

9 Section B [48marks] Answerfour questionsinthissection. Eachquestioninthissectioncarries12marks. 7

(a)

Theshadedtriangle,drawnonthegrid,ispartofaquadrilateralwithonelineofsymmetry. Theareaofthequadrilateralistwicetheareaofthetriangle. Giventhatthelineofsymmetryisnotvertical,completethequadrilateral.

[1]

(b)

M

Theshadedtriangle,drawnonthegrid,ispartofashapewhoseareais4timestheshadedareaand hasrotationalsymmetryoforder4aboutM. Completetheshape. © UCLES 2015

[2] 4024/21/O/N/15

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10 (c)

y 8 7 6 5 4

A

3 2 1 B –4

–3

–2

–1

0

1

2

3

4

5

6

7

8

x

–1 –2

ThediagramshowstriangleAandtriangleB. 3 (i) TriangleAismappedontotriangleCbythetranslationPwithvector e o. -1 DrawandlabeltriangleC.

[2]

(ii) TriangleAismappedontotriangleBbyareflectionQ. Writedowntheequationofthelineofthisreflection.

Answer ............................................ [1] (iii) TriangleCismappedontotriangleDbyreflectionQ. DescribefullythesingletransformationthatmapstriangleBontotriangleD.

Answer .................................................................................................................................. [2]

© UCLES 2015

4024/21/O/N/15

11 (iv) TransformationRisareflectionintheline y=0. RQ(A)=E. 





(a) FindthecoordinatesoftheverticesoftriangleE.

Answer .......................................................................................................................... [1] 





(b) DescribefullythesingletransformationthatmapstriangleAontotriangleE. Answer ............................................................................................................................... ....................................................................................................................................... [2]







(c) FindthematrixwhichrepresentsthetransformationthatmapstriangleAontotriangleE.



© UCLES 2015

Answer

4024/21/O/N/15

[1]

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12 8

[Curved surface area of a cone = πrl]

l

h

r

Thediagramshowsasolidconewithradiusrcm,heighthcmandslantheightlcm. Sulemanmakessomesolidcones. Theslantheightofeachofhisconesis4cmmorethanitsradius. Use π = 3 throughout this question. (a) Showthatthetotalsurfacearea,A cm2,ofeachofSuleman’sconesisgivenby A=6r(r+2).



[2] (b) Completethetablefor A=6r(r+2). r

0

1

A

0

18

2

3

4

5

6

144

210

288



[1] (c) Onthegridopposite,drawthegraphof A=6r(r+2).

[2]

(d) Findanexpressionforhintermsofr.



© UCLES 2015

Answer h=...................................... [2]

4024/21/O/N/15

13 A 300

250

200

150

100

50

0

1

2

3

4

5

6

r

(e) TheheightofoneofSuleman’sconesis12cm. Calculateitsradius.



Answer ...................................... cm[2] (f) AnotherofSuleman’sconeshasasurfaceareaof200cm2. (i) Useyourgraphtofindtheradiusofthiscone.



Answer ...................................... cm[1] (ii) Thisconeisplacedinaboxofheightpcm,wherepisaninteger. Findthesmallestpossiblevalueofp. p

© UCLES 2015

Answer p=...................................... [2] 4024/21/O/N/15

[Turn over

14 9

Thecumulativefrequencygraphforthelengthsofthe50tracksonAbi’sMP3playerisshownbelow. 50

40 Cumulative frequency 30

20

10

0 2:30

3:00

3:30

4:00

4:30

5:00

5:30

6:00

Length of track (minutes : seconds)

(a) Usethegraphtofind (i) themedian,

Answer ............ minutes............seconds[1] (ii) theinterquartilerange.



Answer ............ minutes............seconds[2] (b) Usetheinformationonthegraphtocompletethefrequencytableforthelengthofthetracks. Length(minutes:seconds)

Frequency

2:301lengthG3:00

3

3:001lengthG3:30

5

3:301lengthG4:00 4:001lengthG4:30 4:301lengthG5:00 5:001lengthG5:30 5:301lengthG6:00  © UCLES 2015

[2] 4024/21/O/N/15

15 (c) AbiplaysthreetracksfromherMP3playerwithnobreakbetweenthem. Giventhatnotrackisrepeated,whatisthemaximumpossiblelengthoftimetakentoplaythese tracks?



Answer ............ minutes............seconds[2] (d) AbitravelsonatrainfromstationAtostationF. TheexacttimesthetrainarrivesatandleavesstationsAtoFareshownbelow. Station

A

B

C

D

E

F

Arrive

–

1003

1006

1011

1015

1021

Depart

0958

1004

1007

1012

1016

–

(i) Howmanyminutesdidherjourneytake?

Answer ............................................ [1] (ii) AbistartsplayingtracksatrandomfromherMP3playerassheleavesstationA. WhatistheprobabilitythatthefirsttrackisstillplayingwhenshearrivesatstationB?



Answer ............................................ [2] (e) AbiplaystwodifferenttracksatrandomfromherMP3player. Whatistheprobabilitythatneithertrackislongerthan3minutes30seconds?



© UCLES 2015

Answer ............................................ [2]

4024/21/O/N/15

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16 10 (a) A

D

x

B

C

15

ABCDisatrapeziumwithABparalleltoDC. DC=15cmandAB=xcm. TheperpendiculardistancebetweenABandDCis3cmlessthanthelengthofAB. TheareaofABCDis75cm2. (i) Showthat x2+12x–195=0.



[2] (ii) FindAB,givingyouranswercorrectto1decimalplace.



Answer ...................................... cm[3] (iii) ADis0.8cmlongerthanBC. Giventhattheperimeterofthetrapeziumis38.0cm,calculateAD.

© UCLES 2015

Answer ...................................... cm[2] 4024/21/O/N/15

17 (b) Anothertrapezium,LMNO,hasLMparalleltoON. ThereflexangleLMN=252°.

O

N

t . (i) CalculateMNO















L



M

Answer ............................................ [2] t : LMN t : MNO t = 1: k . t = 1: 2 and OLM (ii) Theratiosoftheanglesinsidethetrapeziumare LON Findk, givingyouranswerasafractioninitssimplestform.



© UCLES 2015

Answer ............................................ [3]

4024/21/O/N/15

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18 11

(a)

4

20

50° 6

Thediagramshowsasolidtriangularprism. Alllengthsaregivenincentimetres. (i) Calculatetheareaofthecross-sectionoftheprism.

Answer .....................................cm2[2]

(ii) Calculatethevolumeoftheprism.

Answer .....................................cm3[1]

(iii) Calculatethetotalsurfaceareaoftheprism.

Answer .....................................cm2[5]

© UCLES 2015

4024/21/O/N/15

19 (b) Acylinderhasaheightof70cmandavolumeof0.1m3. Calculatetheradiusofthecylinder,givingyouranswerincentimetres.















© UCLES 2015







Answer ...................................... cm[4]

4024/21/O/N/15

20 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/21/O/N/15

Cambridge International Examinations Cambridge Ordinary Level

* 8 8 7 3 8 0 1 1 0 5 *

4024/22

MATHEMATICS (SYLLABUS D)

October/November 2015

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 24 printed pages. DC (AC/FD) 100478/4 © UCLES 2015

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2

Section A [52 marks] Answer all questions in this section 1

(a) Fatima and Mohammed buy new bikes. (i) Fatima buys a city bike costing $360. She pays 60% of the cost then pays $15 per month for 12 months. (a)

How much does Fatima pay altogether?



Answer $ ........................................ [2] (b) Express this amount as a percentage of the original cost.



© UCLES 2015

Answer .................................... % [1]

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3

(ii) Mohammed pays $569.80 for a mountain bike in a sale. The original price had been reduced by 26%. Calculate the original price of the mountain bike.





Answer $ ........................................ [2] (b) The rate of exchange between pounds (£) and dollars is £1 = $1.87 . The rate of exchange between pounds (£) and euros (€) is £1 = € x . Rose changed $850 and received €550 . Calculate x.



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Answer x = .................................... [3]

4024/22/O/N/15

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4

2

A is the point (8, 7), B is the point (–2, 11) and C is the point (1, 7).

(a) Calculate the area of triangle ABC.

Answer ............................... units2 [2]



© UCLES 2015

4024/22/O/N/15

5

(b) Calculate the length of AB.



Answer ................................. units [2] (c) Calculate the perimeter of triangle ABC.



Answer ................................. units [2] t . (d) Calculate BAC



© UCLES 2015

Answer .......................................... [2]

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6

3

(a) B

A

34°

6 O

C 3 E D

AC is a diameter of the circle, centre O. BCD and OED are straight lines. AC = 6 cm and CD = 3 cm. t = 34°. BAC t = 56°. (i) Explain why BCA



[1] t . (ii) Find COD



Answer .......................................... [2] t . (iii) Find OCE



© UCLES 2015

Answer .......................................... [1]

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7

(b) T P

Q

S

R

t . In the diagram, PS is the bisector of QPR QPT and QSR are straight lines. RT is parallel to SP. (i) Explain why PT = PR.

[2] (ii) This diagram shows part of the above diagram. PQ = 12 cm, PR = 5 cm and QR = 8.5 cm. P 12 5 Q 8.5

It is given that

S

R

PQ QS = . PR SR

Find SR.



© UCLES 2015

Answer .................................... cm [3]

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8

4

[The volume of a sphere is

4 3 rr ] 3

(a)

A spoon used for measuring in cookery consists of a hemispherical bowl and a handle. The internal volume of the hemispherical bowl is 20 cm3. The handle is of length 5 cm. (i) Find the internal radius of the hemispherical bowl.



Answer .................................... cm [2] (ii) The hemispherical bowl of a geometrically similar spoon has an internal volume of 50 cm3. Find the length of its handle.



© UCLES 2015

Answer .................................... cm [2]

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9

(b) [The surface area of a sphere is 4πr2]

An open hemisphere of radius 5.5 cm is used to make a metal kitchen strainer. 50 holes are cut out of the curved surface. Assume that the piece of metal removed to make each hole is a circle of radius 1.5 mm. Calculate the external surface area that remains.

Answer .................................. cm2 [3]



© UCLES 2015

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10

5 B D H

F

E

A

G

C

The diagram shows a vertical radio mast, AB. Three of the wires that hold the mast in place are attached to it at F, H and D. The base A of the mast, and the ends E, G and C of the wires are in a straight line on horizontal ground. (a) The wire CD has length 65 m. It is attached to the mast at D where AD = 40 m. Calculate AC.



© UCLES 2015

Answer ...................................... m [2]

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11

(b) The wire EF makes an angle of 25° with the horizontal and is of length 30 m. Calculate AF .



Answer ...................................... m [2] (c) AH = 35 m. The wire HG makes an angle of 30º with the mast AB. Calculate HG.



© UCLES 2015

Answer ...................................... m [3]

4024/22/O/N/15

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12

6

7 5 (a) (i) Solve the equation ` x + j = ! . 2 2 Give both answers correct to 2 decimal places.



Answer x = ................ or ................ [2]

7 5 are also the solutions of x 2 + Bx + C = 0 , (ii) The solutions of ` x + j = ! 2 2 where B and C are integers. Find B and C.



Answer B = .............. C = ............... [3] (b) Solve the inequality 7 – 3x > 13.



© UCLES 2015

Answer x ....................................... [2]

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13

(c) Factorise 6x – 3yt + 18y – xt .



Answer .............................................. [2] (d) Solve these simultaneous equations. 3a + 4b = –13 5a + 6b = –11



© UCLES 2015

Answer a = ................................... b = ................................... [4]

4024/22/O/N/15

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14

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7 B

x A

D

12

θ° 2x – 5 C

4

E

ABD and ACE are straight lines. BD = 12 cm and CE = 4 cm. AB = x cm and AC = (2x – 5) cm. Angle BAC = θ°. (a) Show that

area of triangle ABC AB # AC = . AD # AE area of triangle ADE

[2] (b) It is given that

area of triangle ABC 1 = . 3 area of triangle ADE

Using the result from part (a), form an equation in x and show that it simplifies to 2x 2 - 19x + 6 = 0 .

[3] © UCLES 2015

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15

(c) (i) Solve the equation 2x 2 - 19x + 6 = 0 , giving your answers correct to 2 decimal places.



Answer x = .................. or .................. [3] (ii) State, with a reason, which of these solutions does not apply to triangle ABC. Answer ................................................................................................................................. [1] (d) Given that θ = 25, calculate BC.



© UCLES 2015

Answer .................................... cm [3]

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16

8

(a) OAB is a sector of a circle, centre O, radius 6 cm. t = 25°. AOB

O

(i) Calculate the length of the arc AB.



A

6 25° 6

B

Answer .................................... cm [2] (ii) Calculate the area of the sector OAB.

Answer .................................. cm2 [2]



(b) The sector OAB from part (a) is the cross-section of a slice of cheese. O

The slice has a height of 5 cm.

25° 6

(i) Calculate the volume of this slice of cheese.

A

6 B

5

Answer .................................. cm3 [1]



(ii) Calculate the total surface area of this slice of cheese.

Answer .................................. cm2 [3]

© UCLES 2015

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17

(iii) Another 25° slice of cheese has 3 times the height and twice the radius. Calculate its volume.

Answer .................................. cm3 [2]



(c) A dairy produces cylindrical cheeses, each with a volume of 800 cm3. The height h cm and the radius r cm can vary.

r h

(i) Express h in terms of r.



Answer .......................................... [1] (ii) What happens to the height if the radius is doubled?

Answer .................................................................................................................................. [1]

© UCLES 2015

4024/22/O/N/15

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18

9

The distance, d metres, of a moving object from an observer after t minutes is given by d = t2 +

48 - 20 . t

(a) Some values of t and d are given in the table. The values of d are given to the nearest whole number where appropriate. t

1

1.5

2

2.5

3

3.5

4

4.5

5

6

d

29

14

8

5

5

6

8

11

15

24

7

Complete the table.

[1]

(b) On the grid, plot the points given in the table and join them with a smooth curve.

40

30 Distance (d metres) 20

10

0

1

2

3

4 5 Time (t minutes)

6

7

[2] (c) (i) By drawing a tangent, calculate the gradient of the curve when t = 4.



Answer .......................................... [2] (ii) Explain what this gradient represents. Answer ................................................................................................................................. [1]

© UCLES 2015

4024/22/O/N/15

19

(d) For how long is the object less than 10 metres from the observer?



Answer ............................ minutes [2] (e) (i) Using your graph, write down the two values of t when the object is 12 metres from the observer. For each value of t, state whether the object is moving towards or away from the observer. Answer When t = .................., the object is moving .................................. the observer. When t = .................., the object is moving .................................. the observer.

[2]

(ii) Write down the equation that gives the values of t when the object is 12 metres from the observer.



Answer .......................................... [1] (iii) This equation is equivalent to t3 + At + 48 = 0. Find A.



© UCLES 2015

Answer A = .......................................... [1]

4024/22/O/N/15

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20

10 The length of time taken by 80 drivers to complete a particular journey is summarised in the table below. Time (t minutes)

60 1 t G 80

80 1 t G 90

Number of drivers

4

10

90 1 t G 95 95 1 t G 100 100 1 t G 110 110 1 t G 130 14

20

24

8

(a) Using a scale of 2 cm to represent 10 minutes, draw a horizontal axis for times from 60 minutes to 130 minutes. Choose a suitable scale for the vertical axis and draw a histogram to represent this information.

[3]

© UCLES 2015

4024/22/O/N/15

21

(b) In which of the intervals does the median time lie?



Answer .......................................... [1] (c) Calculate an estimate of the mean time taken to complete the journey.



Answer ............................ minutes [3] (d) One driver is chosen at random. Calculate the probability that this driver took 95 minutes or less for the journey.



Answer .......................................... [1] (e) Two of the 80 drivers are chosen at random. (i) Calculate the probability that both took more than 100 minutes for the journey.



Answer .......................................... [2] (ii) Calculate the probability that one took 80 minutes or less and the other took more than 110 minutes.



© UCLES 2015

Answer .......................................... [2]

4024/22/O/N/15

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22

11

(a) B

G

C

F

A

E

H

D

ABCDE is a pentagon. AFB, AHE and BGC are straight lines. (i)

J6N AE = K O . L1P Calculate AE .



Answer ................................... units [1] J 2 N O. (ii) H is the midpoint of AE, and FH = K L- 3.5P Find AF .

Answer

© UCLES 2015

4024/22/O/N/15

[2]

23

(iii) G divides BC in the ratio 1 : 2. J2.5N J- 1N BG = K O and CD = K O . L0P L- 7P (a) Find GD.



Answer .......................................... [1] (b)

Explain why GD is parallel to FH.

[1] (iv) B is the point (3, 10). Find the coordinates of D.



Answer (................... , ...................) [1]

Question 11(b) is printed on the next page

© UCLES 2015

4024/22/O/N/15

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24

(b)

y

8 B C 4 A

–8

–4

0

4

8

x

–4

J- 3N (i) Flag A is mapped onto flag T by the translation K O . L- 6P Draw, and label, flag T.

[1]

(ii) Describe fully the enlargement that will map flag A onto flag B. Answer ................................................................................................................................... [2] (iii) Find the centre of the rotation that will map flag A onto flag C. Answer (................... , ...................) [1] (iv) Rotate flag B through 45° anticlockwise about the origin. Label the image R.

[2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015

4024/22/O/N/15

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/11

Paper 1

October/November 2016

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 5 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

Mark

Syllabus 4024

Paper 11

Part marks

(a)

17 h 30

1

(b)

(0).0033

1

(a)

7

1

(b)

30

1

(a)

13 cao 40

1

(b)

7 9 0.38 0.4 20 25

1

(a)

4.8(0)

1

(b)

24

1

(a)

360 cao

1

(b)

4

1

6

15

2*

B1 for “k” = –150 provided y = “k”/x is used. or M1 for –50 × 3 = –10y oe or M1 for y = (their k)/(–10) when y = “k”/x is used.

7

40

2*

M1 for

(a)

7

1

(b)

4 yx −1 4y ; or 3 3x

1

(a)

0.155 cao

1

(b)

20 WWW

1*

4.5 × 10 8

1

1

2

3

4

5

8

9

10 (a) (b)

3 × 10 9

2*

© UCLES 2016

360 ; or 171n = 180(n – 2) oe 180 − 171

C1 for A × 109 with 1 ⩽ A < 10; or for 3 × 10 11 or B1 for 0.3 × 10 10

Page 3

2*

3 – 10x oe

(b) 12 (a) (i) (ii)

9

1

89

1

A

Syllabus 4024

Paper 11

1

0.35 oe

11 (a)

(b)

Mark Scheme Cambridge O Level – October/November 2016

B

C1 for 10x – 3 or B1 for 10 “y” = 3 – “x”

1

13 (a)

0.5 oe

1

(b)

2 oe 3

1*

(c)

(–) 8

1

14 (a)

2.7 oe

2*

(b)

4 oe 5

1*

M1 for

BC 1.8 oe = 6 4

Mark lost if a second transformation is named.

Rotation 90° clockwise oe, centre (3, 1)

1 1

vertices: (–2, 4), (–4, 0), (–4, 4)

2*

B1 for two correct vertices, or for vertices (2, 0), (4, 0), (4, 4)

16 (a)

5(1 – 2t)(1 + 2t)

2*

C1 for (1 – 2t)(1 + 2t) or B1 for one of 5(1 – 4t 2); (5 + 10t)(1 – 2t); (5 – 10t)(1 + 2t)

(b)

(3y – 2x)(y + 3)

2*

B1 for one of the partial factorisations y(3y – 2x); 2x(y + 3); 3(3y – 2x); 3y(y + 3); or their negatives, seen.

15 (a) (b)

© UCLES 2016

Page 4

Mark Scheme Cambridge O Level – October/November 2016

17 (a)

57°

1

(b)

33°

1

(c)

FT 180° – their (a); or 123°

(d)

220°

18

Syllabus 4024

Paper 11

1* 1

Correctly equating one pair of coefficients or expressing one variable in terms of the other.

* M1

A correct method to eliminate one variable.

M1

Either x = –4 or y = 2 WWW.

A1

Both x = –4 and y = 2 WWW.

A1

If [0] earned, then award C1 for a pair of values that satisfies either equation. If only M1 + M1 earned, then award B1 for a correct substitution of their first solution into one, or a correct linear combination of both, of the original equations.

19 (a)

the point P marked correctly

1

(b)

the point Q marked correctly

1

(c)

–a – 2b oe

2

20 (a)

125° to 129°

1

correct arc

1

(ii)

correct straight line

1

(iii)

PD =3.4 to 3.8 cm WWW

(b) (i)

21 (a)

(b)

(c)

 0 −5    7 9

 73 1  3 1 ; or  1   7  −1 2  − 7 equivalent seen 1 0   0 1

1 dep

2

1 7 2 7

  ; or any 

2*

1

© UCLES 2016

C1 for –a; or for – 2b

Dependent on correct types of loci, that intersect. C1 for 2 or 3 correct elements; or for 3 or 4  12 −1  elements of  .  −1 9  C1 for

1 7

 . .  3 1 1   ; or for k  ,k≠ 7  . .  −1 2 

Page 5

Mark Scheme Cambridge O Level – October/November 2016

Syllabus 4024

v−4 8 = oe 8 10 or B1 for 6.4 oe; or for 1.6 oe; seen M1 for

10.4 or any equivalent

2*

(b)

80

2*

C1 for 140 or M1 for 10 × (4 + 12)/2 oe

(c)

Curve, concave upwards, from (0, 0) to ( 10, their(b )

1

independent

22 (a)

Straight line from (10, their(b)) to (15, 60 + their(b))

1

7, 21

1

(b)

2n – 1 oe

1

(c)

FT 3 × their (b) provided this is a function of n; or 6n – 3 oe

(d) (i)

48

1

3n 2

2*

23 (a)

(ii)

24 (a) (b)

(c)

independent

1

(9, 2)

1

x < 9 oe

1

y > 2 oe

1

x – y > 3 oe

1

a=8

1

b=4

Paper 11

1

© UCLES 2016

M1 for a sensible method, e.g. writing terms as 3×1, 3×4, 3×9, ... or B1 for An2 + Bn + C, A ≠ 0 from a valid method.

In (b), if [0] scored for x < 9 and y > 2 then C1 for both {x ... 9 or x ... their(9)} and {y ... 2 or y ... their(2)}

In (c), if [0] scored then C1 for a = 4 and b = 8; or for a = 6 and b = 3.

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/12

Paper 1

October/November 2016

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 6 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – October/November 2016

Question 1

(a) (b)

2

3

Answers

Mark

2.457

Syllabus 4024

Paper 12

Part marks

1

2 oe fraction; or 0.031 to 0.032 63

1 (*)

(a)

123.456

1

(b)

(0).0643

1 1

(a) X

1

(b) X

4

5

(a)

2.05

(b)

− 34

(a)

41°

1

(b)

245°

1

6

1 –0.7

74%

0.7

1

3.98 ≈ √4 or 2, and 602.3 ≈ 600 (or 602),

and 2.987 ≈ 3 all three seen

M1* A1

C1 for 400 WAW.

(±)400 (or 401, 401.3 or better, from 602) Triangle with vertices (1, 1) (1, 5) (7, 5)

2*

(a)

5.13 × 10 5

1

(b)

2.4 × 10 – 8

2*

(a)

20 25

1 1

(b)

Rectangle with base 35 to 50 and height 2

1

7 8

9

B1 for two correct approximations. Could be implied by 2×200 or 1 200/3.

© UCLES 2016

B1 for two correct vertices

C1 for A × 10 – 8 with 1 ⩽ A < 10 or for 2.4 × 10 – 10 ; or B1 for 24 × 10 – 9 or for 0.000 000 024

Page 3

Mark Scheme Cambridge O Level – October/November 2016

Question 10

Answers

Mark

(a)

–3.5 or any equivalent

1

(b)

1 3

2*

Syllabus 4024

Paper 12

Part marks

M1 for 5 = 4 + 3x or B1 for ( f –1(x) = ) or B1 for x =

x−4 oe 3

1 , followed by further 3

work 11

(a)

(b) 12 (a) (b) 13

4 nfww

2*

p 4

B1 for “k” = 36 from y = k/x 2 or M1 for 9 × 22 = y × 32 oe or M1 for (their k) / 32 oe

1

0

1

0.8 oe

2*

M1 for (15×1 + 6×2 + 3×3 + 4×1)/50

Correct triangle

3*

Following an attempt at a rotation of 110° about O, award C2 for two correct vertices or C1 for one correct vertex. If [0] scored then either B1 for arc(s) of correct radii, centre O, (from A, B or C); or B1 for AOA’ or BOB’ or COC’ = 110°

14 (a)

B

A

1

C

(b)

8

2*

A correct method to eliminate one variable

* M1

15 Either x = 5 or y = –6 WWW

A1

Both

A1

x = 5 and y = –6 WWW

© UCLES 2016

M1 for 23 + 17 – (36 – 4) or M1 for 23 – x + x + 17 – x + 4 = 36 oe or B1 for S ∩ F’ = 15 or F ∩ S’ = 9

If [0] earned, then award C1 for a pair of values that satisfy either equation. If only M1 earned, then award B1 for a correct substitution of their first solution into one, or a correct linear combination of both, of the original equations.

Page 4

Mark Scheme Cambridge O Level – October/November 2016

Question 16 (a) (b)

Answers

Mark

13

Paper 12

Part marks

1

(±)

1

9 16

(c)

4y3

1

17 (a)

200

1

15 : 1

2*

(b)

Syllabus 4024

C/B1 for any correct unsimplified ratio, e.g. 210 : 14; 105 : 7;

30 7 14 : 1; : ; 3.5 : 2 60 2

14/60 or M1 for 3.5×60×60 : 14×60; 3.5×60 : 14 or B1 for 3½ hrs = 18 (a)

3

4

5

3

–

5

6

4

5

–

7

5

6

7

–

1

(b)

0

(c)

4 oe ; or FT their table 12

19 (a) (b)

20

–

1 1

1.65

1

15.15

2*

3(2x – 1) + 4(x – 2); or 6x – 3 + 4x – 8; or 10x – 11 their(10x – 11) = 24 or 3.5 oe WWW

7 × 60; or 210 seen. 2

M1*

their (10 x − 11) =2 12

M1* A1

© UCLES 2016

M1 for their(a) + 100 × 135/1000 or B1 for 13.5 seen.

Page 5

Mark Scheme Cambridge O Level – October/November 2016

Question 21

Answers

Syllabus 4024

Mark 3*

600 WWW

Paper 12

Part marks M2 for

π × 202 ×16 4× 3

π × 23

or B1 for (Volume of water =) π × 202 × 16 or for (Volume of one drop =) 43 × π × 23 soi 22

(a)

Perpendicular bisector of AB.

1

(b)

Bisector of angle ABC.

1

(c)

Correct (bottom right) region shaded.

1

FT for two intersecting lines – slightly inaccurate but correct types of loci.

14

2*

M1 for 25 – 1×1 – 2×2 – 12 × 4 × 3 oe disection.

18 nfww

2*

B1 for sloping side = 5

68

1

(b)

146

1

(c)

34; or FT their (a)/2; or FT 180 – their(b)

(d)

56

1

(0, 4 13 )

1

(b)

x ⩾ 1 oe, y ⩾ 2 oe, 3y + 2x ⩾ 13 oe – all three

2

(c)

(6, 2)

1

23 (a)

(b) 24 (a)

25 (a)

26 (a) (i) 2n – 1 oe (ii) 421 (b) (i) 8 (ii) 14

1

1 1 1 1

© UCLES 2016

C1 for one or two correct, or for x ... 1 oe, y ... 2 oe, 3y + 2x ... 13 oe, with incorrect “...” .

Page 6

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

Mark

Syllabus 4024 Part marks

(–)0.9 oe

1

(b)

420

2*

M1 for 12 × 20 × (12 + 30) oe

(c)

25

2*

M1 for (k – 20) × 12 = 60 oe or C1 for k = 5

27 (a)

© UCLES 2016

Paper 12

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/21

Paper 2

October/November 2016

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 7 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – October/November 2016

Question 1

2

Mark

133

1

(ii)

20

1

(iii)

1900

2

(b)

22 22 or 10 22 pm

1

(c)

6600 final answer

(d)

(a) (i)

1995 105

2

M1 for

1000000 oe 4 × 38

8.93

2

B1 for 100.5 or 11.25 used

(a)

2.71 or 2.711[…]

1

(b)

3p( 3p – 2q ) final answer

1

(c)

9a2 + 6ab + b2 final answer

1

6t + 1 6t + 1 or 2 final (2t + 1)(3t + 1) 6t + 5t + 1 answer

3

2

(f)

50

3

(a) (i)

[∠PBQ = ] 180 – 2a or 2(90 – a)

1

(ii)

[∠APD = ] 90 – a

1

(iii)

[∠DAP = ] 2a

1

(iv)

[∠ADP = ] 90 – a

1

3.3

1

30.4[19..]

2

(b) (i) (ii)

M1 for 4( 3t + 1 ) – 3( 2t + 1 ) soi B1 for 6t + 1 seen as numerator or (2t + 1)(3t + 1) oe seen as denominator

–3, –4, –5

(e)

Paper 21

Part marks

M1 for

(d)

3

Answers

Syllabus 4024

© UCLES 2016

9 oe 4 Or SC1 for answer –3, –4, –5, –6 or answer –2, –3, –4, –5 M1 for n < –

B1 for x + (x – 12) + (2x – 24) = 112 oe and B1 for x = 37 or M1 correct evaluation of amount for Chuku using their expression and their x

M1 for 4.7 × sin 54 oe

Page 3

Mark Scheme Cambridge O Level – October/November 2016

Question 4

5

Answers

Mark

Syllabus 4024

Paper 21

Part marks 1 × 4 × π × (9 − 0.8) 2 2 Or SC1 for answer 508.9 to 509.0…

M1 for

(a)

422 or 423 or 422.4 to 422.6

2

(b)

440 or 440.0 to 440.2

5

B1 for 8.2 used 2 B1 for π r 3 used 3 M1 for Bowl: 3 1 4 1 4 3  2  3 × π × 9 −  2  3 × π × ( 9 − 0.8 ) oe     M1 for Cylinder: π × 3.82 × 1.5

(a)

3.76 to 3.77…

2

M1 for

(b)

9.99 to 10.01

3ft

FT their (a) + 6.235[…] M2 for [OB = ] 1.8 tan 60 oe [...] or M1 for tan 60 = oe 1.8

(c) (i)

Full calculation, including calculation for 2 OC = 3.6 and radius = TC + OC AG

(ii)

2.28

1ft

© UCLES 2016

120 × 2 × π × 1.8 oe 360

1.8 oe OC or OC2 = 1.82 + their OB2 M1 for cos 60 =

FT 5.4 – their OB

Page 4

Mark Scheme Cambridge O Level – October/November 2016

Question 6

7

Answers

Mark

Syllabus 4024

Paper 21

Part marks

(a)

[DT = ]10.8 or 10.816 to 10.82

2

M1 for DT 2 = 62 + 92 oe

(b)

139 or 139.2 to 139.3

3

B1 for BT = 10 M1 for sum of areas of four triangles seen, with at least 3 of the following 1 1 correct: × 8 × 6 , × 9 × 6 , 2 2 1 1 × 8 × their DT , × 9 × their BT 2 2

(c)

504

2

M1 for 9 × 8 × 5 or

(d)

50.7° final answer

3

M1 for finding an acute angle in triangle THG. 11 9 or tan […] = e.g. tan […] = 9 11 A1 for 50.7[...]° or 39.28 to 39.3°

(a)

283°

1

(b)

055°

1

(c)

[AB = ] 15.4 or 15.36[…]

3

B1 for ABC = 74° AB 19 = M1 for sin 51 sin ABC

(d)

[DC = ] 20.08 to 20.1

3

M2 for [DC 2 =] 192 + 272 – 2 × 19 × 27 × cos 48 or M1 for cosine formula with one error

(e)

Correct working leading to 114 minutes or 1 hour 54 minutes

4

M1 for AX = 19 × cos 48 or for CX = 19 × sin 48

1 ×9×8× 6 3

M1 for DX = 27 – their AX Or for DX =

their DC 2 − their CX 2

M1 for Time = 216 ×

© UCLES 2016

their DX oe 27

Page 5

Mark Scheme Cambridge O Level – October/November 2016

Question 8

Mark

(a)

0.2 or 0.21[2…]

1

(b)

Correct axes

B1

Correct shape curve through 9 correct points

B2

Clear, correct, tangent drawn

M1

2.2 to 2.5

A1

Ruled line from (–0.4, 0) to (2, 3.6)

1

(c)

(d) (i)

9

Answers

(ii)

y = 1.5x + 0.6 or y =

(iii) (iv)

3 3 x+ 2 5

Syllabus 4024

Paper 21

Part marks

B1ft for at least 7 correct points plotted

2

B1 for m = 1.5 oe or for c = 0.6 oe or for correct equation in a different form

0 and 3.1 to 3.2

1ft

FT intersections of their ruled line with their curve

A = 2.4 to 2.6

1

B=1

1

(a)

42

1

(b)

17

3

B2 for 0.9 × 1.3 or for answer 117 or B1 for 27 × 182 or 0.27 × 182 and their 4914 − their 4200 M1 for × 100 oe their 4200

(c) (i)

(30 − y ) × (140 + 4 y ) oe isw 100

2

B1 for (30 – y) or (140 + 4y) soi

2

B1 FT for 4200 – 140y + 120y –4y2 = 4000 or better FT equating their product from (ii) with 40, eliminating fraction and expanding brackets

3

B2 for ( y + 10 )( y – 5 ) or B1 for ( y + a )( y + b ) where ab = –50 or a + b = 5 OR B1 for 225 soi

(ii)

(iii)

Forms equation (30 − y ) × (140 + 4 y ) = 40 100 then correct working leading to y 2 + 5y – 50 = 0 y = –10 , 5

AG

and B1 for

© UCLES 2016

−5 ± their 225 oe 2

Page 6

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

(iv) 10 (a) (i)

(ii)

Mark

160 cao

1

Correct histogram with linear scale on frequency density axis

3

B2 for all 5 heights correct with axis scaled OR B1 for at least 3 correct frequency densities soi and B1 for all 5 bars correct widths

39.4[4…]

3

B1 for use of correct midpoints

(b) (i)

33 oe 95

1

(ii)

48 oe 95

2

(iii)

12 cao

1

(iv)

91 oe 190

2

M1 for

13

2

M1 for

(ii) (a)

(b) (i)

Paper 21

Part marks

M1 for

11 (a) (i)

Syllabus 4024

JJJG JJJG JJJG  6   0   6  [ BD = ] BA + AD =  + =  1  −11  k   k − 11 AG

Σfx 135

3 8 2 12 × + × 5 19 5 19 24 Or SC1 for answer 95 M1 for

k k −1 where n > k > 1 × n n −1 (−5) 2 + 122

Or JJJG JJJG JJJG  0   −6   6  [ BD = ] AD − AB =   −   =    k   11   k − 11

(b)

8.5

2

 6   12  M1 for using 2 ×  =   k − 11  −5 

(c)

4.5

1

or FT their (i) – their k

Reflection

1

x = 0 or y-axis

1

© UCLES 2016

Page 7

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

(ii) (a) (b)

Mark

( 3½, 1 ) , ( 7, 2 ), ( 8, 2 )

2

 −1 3     0 1

2

© UCLES 2016

Syllabus 4024

Paper 21

Part marks B1 for 1 or 2 correct pairs of coordinates  −1 0  B1 for   used  0 1 or M1 for  a b   − 12 −1 −2   3 12 =  × 2 2  1 c d  1

7 8  2 2

Cambridge International Examinations Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/22

Paper 2

October/November 2016

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

This document consists of 7 printed pages. © UCLES 2016

[Turn over

Page 2

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

Part

1

(a) (i)

3.6

1

(ii)

109

2

730.25

3

Paper 22

Part Marks

B1 for 756 + 24×922.25 soi or SC1 for

(b)

Syllabus 4024

B1 for

24 × 922.25 × 100 oe 21 000

127 × 21 000 soi 100

M1 for 381 + 36 x = their total amount oe 1000

(c)

3

M1 for x +

5x = 21 000 oe and 100

M1 for 21 000 − their 2016 price oe 2

(a)

ab Final answer 6

2

M1 for correct transition to multiplication soi

(b)

1 oe 5

2

B1 for 5(h − k )

(c)

(3m − 2n)(3m + 2n) Final ans.

1

(d)

( p − 2)(q − 3) oe

2

B1 for −q(2 − p) or −3( p − 2) seen or M1 if brackets removed and rearranged and extraction of p or 2 or for a correct extraction of a common factor after a sign error.

(e) (i)

(ii)

2 −2

−

8 oe 5

2

B1 for one correct or

−16 cao

2

B1 for either or M1 for (5 x − 1)2 = 92 or 8 ( x − 2)( x + ) = 0 oe ft or 5 Uses e(i) to form simultaneous equations or x=

© UCLES 2016

1 ± 9 − B ± B 2 − 20C ≡ 5 10

Page 3

Mark Scheme Cambridge O Level – October/November 2016 Part

Syllabus 4024

Paper 22

Question

Answers

Part Marks

3

(a)

3.75

(b)

Correct curve ft

2ft

B1 for 4 correct plots ft

(c)

( 0.3 to 0.5) ft

2ft

M1 for a reasonable tangent at x = 2.5

(d)

0 cao (3.05 to 3.25) ft

2ft

B1 for either

(e) (i)

y =4− x

1

2

M1 for x3 + 10 x − 80 = 0 ≡

x 2 ( x − 10) = 20

ax + b oe

4

(ii)

L drawn on the grid ft

1ft

Dependent on at least 1 mark in (e)(i).

(iii)

(3.55) ft

1ft

Dependent on at least 1 mark in (e)(i).

AD = cos 27 oe 3

(a) (i)

2.67

2

M1

(ii)

4.57

3

M2 for CD =

(b)

53.1

126.9

3

3 oe or sin 41

M1 for

3 = sin 41 oe CD

M1 for

1 ˆ = 6 oe and × 3 × 5 × sin PQR 2

A1 for 53.1 or SC1 for supplementary angles from sin ˆ = k. PQR

5

(a)

TAB ATB Statement mentions tangent and radius ABT

2

B1 for 2 pairs of equal angles.

(b)

2.1

3

M1 for

AC CD = oe soi and AB BT

M1 for

7 CD oe OR = 10 3

B1 for (AB =) 10

© UCLES 2016

Page 4

Mark Scheme Cambridge O Level – October/November 2016

Syllabus 4024

Paper 22

Question

Answers

Part

6

(a)

 4 4   1 7

2

B1 for 3 entries correct.

(b)

 2 4   2 9

2

B1 for 3 entries correct.

(c)

4

2

 2x  B1 for one correct or   seen  3x + 2 

(d)

1  3 −2    oe isw 5 1 1 

2

 3 −2  B1 for det B = 5 soi or   soi 1 1 

(a) (i)

1.98

1

(±) x 2 − a 2 Final answer

2

7

(ii) (b) (i) (ii)

7

(PQ =)

17 x+5

Part Marks

M1 for x 2 = a 2 + b 2 oe

1

3 x 2 + 15 x − 85 (=0) oe shown

3

M1 for (AB =)their(PQ) + 3 and M1 for ( their(PQ + 3) × x = 17 or

(iii)

3.38

−8.38

3

B1 for 152 − 4 × 3 × (−85) soi and B1 for

−15 ± their1245 soi and 2×3

M1 for both real values of

(iv)

20.8

2ft

© UCLES 2016

p± q r

M1 for their(PQ) and x + 5 evaluated using x = the positive root from (b)(iii). or for their perimeter in algebraic form

Page 5

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

8

Dependent on 4 fig. term calculated using any version of π.

(a) (i)

Part 3

Syllabus 4024

Paper 22

Part Marks M1 for arc length

M1 for R = 20 ×

48 × 2π R soi and 360

360 1 × oe 48 2π

48 × π R2 360

(ii)

239

2

M1 for

(iii)

20.7

2

M1 for 2πr =

(b) (i)

200

3

M1 for l 2 = 42 + 7.52 oe soi and

312 × 2π R oe 360

A1 for (l =) 8.5

(ii) 9

2.5 326 ft

(a)

2 4ft

B1 for 8 : 5 soi M2 for  652 = 1102 + 702 − 2 × 110 × 70 × cos ACB soi or M1 for the cosine rule with one error. and A1 for 33.9 or 146.1 or 59.2 and

 B1 ft for 360 − their ACB oe SC 2 for 109.1 or 37.0 92.2

(b)

3

M2 for AD 110 oe = sin(70 + 58)or (180 − (70 + 58)) sin 70 soi or

M1 for 70 + 58 or 180 – (70 + 58)

(c) (i)

(ii)

17 70 or tan BYC= 70 17

13.6 or 13.7

2

M1 for tan YBC =

16.5

3

M1 for Figs

110 soi and 24

B1 for × by

60 × 60 oe soi 1000

© UCLES 2016

Page 6

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

Part

10 (a) (i)

6b − 3a oe isw

1

(ii)

2b − a oe isw

1ft

(iii)

2 : 3 cao NB www

4

Syllabus 4024

Paper 22

Part Marks

M1+ M1 for two of JJJG JJJG JJJG OC = OA + AC JJJG JJJG JJJG CD = CB + BD JJJG JJJG JJJG OD = OB + BD

JJJG A1 for OC = 2a + 2b ft or JJJG CD = 3a + 3b ft or JJJG OD = 5a + 5b (b) (i) (ii) (a)

Reflection y = − x oe

2

B1 for either

Triangle C with vertices (2, 3),(2, 2), (5, 5)

2

B1 for two vertices correct or M1 for a correct construction line involving H(2, 1) or H(2, 0)

(b)

1

(c)

1 0    1 1 

1 1ft

© UCLES 2016

Page 7

Mark Scheme Cambridge O Level – October/November 2016

Question

Answers

Part

11 (a) (i) (a)

40 to 41

1

(b)

23 to 27

2

(c)

225 to 245

1

(ii)

79 to 80

1

(iii)

Paper1 e.g. Paper 2 has median 54 oe Using (i)(a), (i)(c) or (ii) with numerical justification – accept reasonable attempts to read the graphs correctly.

1

Syllabus 4024

Paper 22

Part Marks

B1 for 52 ±1 or 27 ±1

2 oe 4

1

(ii)

2 oe 20

1

(iii)

12 oe 20

2

B1 for

(iv)

18 oe 60

2

B1 for any correct sequence of three coins, 3 2 1 2 3 1 2 1 3 × × or × × or × × 5 4 3 5 4 3 5 4 3

(b) (i)

© UCLES 2016

3 2 2 3 × or × seen 5 4 5 4

Cambridge International Examinations Cambridge Ordinary Level

* 2 6 4 0 4 8 0 1 7 9 *

4024/11

MATHEMATICS (SYLLABUS D)

October/November 2016

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (ST/SW) 123263/4 © UCLES 2016

[Turn over

2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

1 3 (a) Evaluate 3 - 2 . 5 6

Answer .......................................... [1] (b) Evaluate 0.03 # 0.11 .

Answer .......................................... [1] 2

The paper on a roll is 4.5 metres long. Mary cuts as many pieces as possible, each of length 60 cm, from the roll. (a) Calculate the number of pieces.

Answer .......................................... [1] (b) Calculate the length of paper that remains on the roll.

Answer .................................... cm [1]

© UCLES 2016

4024/11/O/N/16

3

3

(a) Express 32 12 % as a fraction in its simplest form.

Answer .......................................... [1] (b) Arrange these values in order of size, starting with the smallest. 9 25

0.38

Answer

4

7 20

0.4

.................... , ..................... , ..................... , ................... [1] smallest

(a) One kilogram of tea costs $16. Calculate the cost of 300 grams of tea.

Answer $ ....................................... [1] (b) Find the simple interest on $400 for 3 years at 2% per annum.

Answer $ ....................................... [1]

© UCLES 2016

4024/11/O/N/16

[Turn over

4

5

(a) Write the number 357.864

correct to 2 significant figures. Answer .......................................... [1]

(b) Estimate, correct to the nearest whole number, the value of

3

67 . 1.03

Answer .......................................... [1] 6

y is inversely proportional to x. Given that y = -50 when x = 3, find y when x = -10.

Answer y = .................................... [2]

© UCLES 2016

4024/11/O/N/16

5

7

Each interior angle of a regular polygon is 171°. Find the number of sides of the polygon.

Answer .......................................... [2] 8

(a) Evaluate 23 - 20 .

Answer .......................................... [1] (b) Simplify

12xy . 9x 2

Answer .......................................... [1]

© UCLES 2016

4024/11/O/N/16

[Turn over

6

9

The cumulative frequency graph shows information about the reaction times of 60 people. 60 50 40

Cumulative frequency 30 20 10 0

0

0.05

0.1

0.15 Time (seconds)

0.2

0.25

0.3

Use the graph to estimate (a) the lower quartile, Answer .......................................... [1] (b) the number of people who have a reaction time of more than 0.2 seconds.

Answer ........................................... [1]

© UCLES 2016

4024/11/O/N/16

7

10 (a) Write the number 450 000 000 in standard form.

Answer .......................................... [1] (b) Giving your answer in standard form, evaluate

1.5 # 10 5 . 5 # 10 -5

Answer .......................................... [2] 11

f (x) =

3-x 10

(a) Evaluate f (– 12 ) .

Answer .......................................... [1] (b) Find f –1(x).

Answer f –1(x) = .......................................... [2]

© UCLES 2016

4024/11/O/N/16

[Turn over

8

12 (a)  = { 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96 } P = { x : x is an even number } Q = { x : x is a multiple of 3 } (i) Find n(P , Q).

Answer .......................................... [1] (ii) Given that y   and that y is a prime number, write down the value of y.

Answer y = .................................... [1] (b) In the Venn diagram, shade the region represented by A' + B. 

A

B

[1]

© UCLES 2016

4024/11/O/N/16

9

13 During one day, the temperature, in °C, was recorded every 2 hours. The twelve results are given below. -3

-2

–1

1

2

4

5

4

2

0

-2

–2

For these results, find (a) the median,

Answer ..................................... °C [1] (b) the mean,

Answer ..................................... °C [1] (c) the difference between the highest and the lowest of these temperatures.

Answer ..................................... °C [1]

© UCLES 2016

4024/11/O/N/16

[Turn over

10

14 C Q 1.8 A

4

P

2

B

In the diagram, triangles APQ and ABC are similar. BC is parallel to PQ and AP = 4 cm, PB = 2 cm and PQ = 1.8 cm. (a) Find BC.

Answer .................................... cm [2] (b) Find

area of triangle APQ . area of quadrilateral PBCQ

Answer .......................................... [1]

© UCLES 2016

4024/11/O/N/16

11

15 y 5 4 3 B

2

A

1 –5

–4

–3

–2

–1

0

1

2

3

4

5

6

x

–1 –2 –3 –4 –5 –6 (a) Describe the single transformation that maps triangle A onto triangle B. Answer ............................................................................................................................................... ....................................................................................................................................................... [2] (b) Triangle A is mapped onto triangle C by an enlargement, centre (0, 2) and scale factor -2. Draw, and label, triangle C on the diagram.

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[2]

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16 Factorise completely (a) 5 - 20t 2 ,

Answer .......................................... [2] (b) 3y 2 - 2xy - 6x + 9y .

Answer ........................................... [2]

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17 B

C 70°

A

33°

D

O E

In the diagram, the points A, B, C, D and E lie on the circle centre O. AD is a diameter. ˆ = 33° and ACE ˆ = 70°. DAC (a) Find C DA   ˆ .

 

Answer  C DA   ˆ = ............................. [1]

ˆ . (b) Find DEC

ˆ = .............................. [1] Answer DEC

ˆ . (c) Find ABC

ˆ = ............................... [1] Answer ABC ˆ . (d) Find reflex EOA

ˆ = .............................. [1] Answer reflex EOA

© UCLES 2016

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18 Solve the simultaneous equations.

2x + 5y =

2

3x + 4y = -4

Answer x = .......................................... y = .................................... [4]

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19

R

O a

b

The diagram shows the points O and R and the vectors a and b. (a) Given that OP = 2a, mark and label the position of P on the grid.

[1]

(b) Given that OQ = 2b – a, mark and label the position of Q on the grid.

[1]

(c) Express OR in terms of a and b.

Answer OR = ............................... [2]

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20 The diagram shows the quadrilateral ABCD. ˆ (a) Measure DCB. ˆ = ............................. [1] Answer DCB (b) (i) Construct the locus of points, inside the quadrilateral, that are 8 cm from B. (ii) Construct the locus of points, inside the quadrilateral, that are 5 cm from AB.

[1] [1]

(iii) These two loci meet at P. Mark, and label, the point P on the diagram and measure PD. Answer .................................... cm [1]

A

D

C

B

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21

J2 - 1N O A=K 3P L1 (a) Evaluate

J 3 3A - 2 K L- 2

1N O. 0P

Answer

J K K K L

N O O O P

[2]

Answer

J K K K L

N O O O P

[2]

Answer

J K K K L

N O O O P

[1]

(b) Find A–1 .

(c) Write down the single matrix that is equivalent to A–1 A.

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22 The diagram is the speed-time graph of part of a car’s journey. 12 Speed (m /s) 4 0

0

5 10 Time (t seconds)

15

(a) Find the speed when t = 8.

Answer .................................... m/s [2] (b) Find the distance travelled by the car from t = 0 to t = 10.

Answer ...................................... m [2] (c) On the diagram below sketch the distance-time graph for t = 0 to t = 15. 160 120 Distance (metres)

80 40 0

0

5 10 Time (t seconds)

15

[2]

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23

Triangle 1

Triangle 2

Triangle 3

Triangle 4

The diagrams show a sequence of triangles made up of identical sticks. Each triangle has two more sticks on each edge than its previous triangle. The table shows information relating to this sequence. Triangle number

1

2

3

Number of sticks on each side

1

3

5

x

Number of sticks in the triangle

3

9

15

y

n

4

(a) Complete the column for triangle 4.

[1]

(b) Find an expression, in terms of n, for x. Answer x = .................................... [1] (c) Find an expression, in terms of n, for y. Answer y = .................................... [1] (d) The total number of sticks in the first triangle The total number of sticks in the first two triangles The total number of sticks in the first three triangles

= = =

3 12 27

(i) Write down the total number of sticks in the first four triangles. Answer

......................................... [1]

(ii) Find an expression, in terms of n, for the total number of sticks in the first n triangles.

Answer

......................................... [2]

Question 24 is printed on the next page © UCLES 2016

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20

24

y B

A

C

O

x

A is the point (5, 2) and B is the point (9, 6). AC is parallel to the x-axis. CB is parallel to the y-axis. The equation of the line AB is x - y = 3. (a) Find the coordinates of C.

Answer (.................... , ..................) [1] (b) The region inside triangle ABC is defined by three inequalities. Write down these inequalities. Answer ................................................ ................................................ ........................................... [3] (c) The point (a, b), where a and b are integers, lies inside triangle ABC. 1 It also lies on the line y = x . 2 Find the value of a and the value of b.

Answer a = .......................................... b = .................................... [2] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

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Cambridge International Examinations Cambridge Ordinary Level

* 6 5 1 9 9 4 5 4 6 6 *

4024/12

MATHEMATICS (SYLLABUS D)

October/November 2016

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (ST/SW) 123264/3 © UCLES 2016

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ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1

(a) Evaluate 9.03 - (4.273 + 2.3) .

(b) Evaluate

2

Answer

......................................... [1]

Answer

......................................... [1]

Answer

......................................... [1]

8 6 - . 9 7

Given that 192 # 64.3 = 12 345.6 , write down the values of (a) 0.192 # 643 ,

(b)

12.3456 . 192 Answer .......................................... [1]

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3

(a)

In the diagram, five small squares are shaded. Shade one more small square, so that the diagram has exactly one line of symmetry.

[1]

(b)

In the diagram, three small squares are shaded. Shade one more small square, so that the diagram has rotational symmetry of order 4.

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[1]

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4

4

(a) The total cost of 3 pencils is $1.23 . Find the total cost of 5 pencils.

Answer $ ....................................... [1] (b) Arrange the following in order, starting with the smallest. 74%

-0.7

Answer

.

0.7

-

3 4

.................... , ..................... , ..................... , ................... [1] smallest

5 F

E

D

A

65° 74° B

C

In the diagram, ABC is a straight line and BF is parallel to DE. ˆ = 74° and DBF ˆ = 65°. FBA ˆ (a) Find CBD.

ˆ = ............................. [1] Answer CBD ˆ (b) Find reflex BDE.

ˆ = .............................. [1] Answer reflex BDE

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6

3.98 # 602.3 . 2.987

By making suitable approximations, estimate the value of Show clearly the approximations you use.

Answer .......................................... [2] 7 y 6 5 4 3

A

2 1 –2

–1

0

1

2

3

4

5

6

7

8 x

The diagram shows triangle A. Triangle A is mapped onto triangle B by an enlargement. The enlargement has centre (3, 3) and scale factor -2. Draw and label triangle B.

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6

8

(a) Write the number 513 000

in standard form. Answer .......................................... [1]

(b) Expressing your answer in standard form, evaluate (4 # 10 -5) # (6 # 10 -4) .

Answer .......................................... [2] 9 5 4 Frequency density 3 2 1 0

0

5

10

15

20 25 30 Time (t minutes)

35

40

45

50

The diagram shows part of the histogram which represents the distribution of times taken by some people to travel to work. (a) Complete the table. Time (t minutes) Frequency

0 1 t G 20

20 1 t G 30 30

30 1 t G 35

35 1 t G 50 30 [2]

(b) Complete the histogram.

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10

f(x) = 4 + 3x 1 (a) Find f b- 2 l. 2

Answer .......................................... [1] (b) Find f -1(5).

Answer .......................................... [2] 11

y varies inversely as the square of x. (a) When x = 2, y = 9. Find the value of y when x = 3.

Answer y = .................................... [2] (b) When x = n, y = p. Write down an expression for y, in terms of p, when x = 2n.

Answer .......................................... [1]

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12 A school recorded the number of absent students over a 50-day period. The results are given in the table. Number of absent students

0

1

2

3

4

5 or more

Number of days

25

15

6

3

1

0

(a) Write down the mode.

Answer .......................................... [1] (b) Calculate the mean.

Answer .......................................... [2]

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13 Triangle ABC is mapped onto triangle AlBlC l by a rotation, centre O, through 110° clockwise. Draw and label triangle AlBlC l . C

A

B

O

[3]

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14 (a) In the Venn diagram, shade the region which represents the subset ^A + Blh , C . 

B

A

C [1] (b) In a group of 36 students, 23 study Spanish, 17 study French, 4 study neither Spanish nor French. By drawing a Venn diagram, or otherwise, find the number of students who study both Spanish and French.

Answer .......................................... [2] 15 Solve the simultaneous equations.

3x + y =

9

2x + 3y = -8

Answer x = .......................................... y = .................................... [3]

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11

16 (a) Evaluate 32 + 31 + 30 .

Answer .......................................... [1] J4 N-2 (b) Evaluate K O . 3 L P

(c) Simplify ^16y

1 6h2

Answer .......................................... [1] .

Answer .......................................... [1] 17 (a) Some money is shared between Ali, Ben and Carl in the ratio 5 : 3 : 2. Ben receives $60. How much money is shared?

Answer $ ........................................ [1] (b) Express the ratio

3

1 hours : 14 minutes in the form k : 1. 2

Answer ..............................

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:

1 [2]

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18

1

2

3

4

Four cards are marked with the numbers 1, 2, 3 and 4. One card is chosen at random. A second card is then chosen, at random, from the remaining three cards. The sum of the numbers on the two chosen cards is calculated. (a) Complete the table to show the possible outcomes. First card

Second card

1

2

3

4

1 2 3 4 [1]

(b) What is the probability that the sum is less than 2? Answer .......................................... [1] (c) What is the probability that the sum is greater than 5? Answer .......................................... [1] 19 A box has a mass of 1.7 kg, correct to the nearest 0.1 kg. (a) Write down the lower bound for the mass of the box. Answer ..................................... kg [1] (b) The box holds 100 jars. Each jar has a mass of 140 grams, correct to the nearest 10 grams. Calculate the lower bound of the total mass of the box and 100 jars. Give your answer in kilograms.

Answer ..................................... kg [2]

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20 Solve the equation

2x - 1 x - 2 + =2. 4 3

Answer x = .................................... [3]

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21 [The volume of a sphere is

4 3 rr ] 3

During a storm, raindrops fall into a cylinder which stands on horizontal ground. The cylinder was empty before the storm started. The cylinder has radius 20 mm. Each raindrop is a sphere of radius 2 mm. After the storm, the depth of water in the cylinder is 16 mm. Calculate the number of raindrops that fell into the cylinder.

Answer .......................................... [3]

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22 The diagram shows triangle ABC. (a) Construct the locus of points, inside triangle ABC, that are equidistant from A and B.

[1]

(b) Construct the locus of points, inside triangle ABC, that are equidistant from AB and BC.

[1]

(c) On the diagram, shade the region inside triangle ABC which contains the points that are nearer to A than to B and nearer to BC than AB.

[1]

B

C

A

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23 5 1

5 2

The diagram shows a square piece of card, from which a triangle and two small squares are removed. All lengths on the diagram are in centimetres. (a) Calculate the area of the shaded card.

Answer ................................... cm2 [2] (b) Calculate the perimeter of the shaded card.

Answer .................................... cm [2]

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24 B C

y° 34°

t°

A

D x°

O

z° E In the diagram, A, B, C, D and E lie on the circle, centre O. BOE is a straight line. ˆ = 34° . DAB (a) Find x.

Answer x = .................................... [1] (b) Find y.

Answer y = .................................... [1] (c) Find z.

Answer z = .................................... [1] (d) Find t.

Answer t = .................................... [1]

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25 y 7 6 5 4

A

R

3 2 1 0

B 1

2

In the diagram, the line 3y + 2x = 13

3

4

5

6

7 x

meets the axes at A and B.

(a) Find the coordinates of A.

Answer (.................... , ..................) [1] (b) The shaded region R is defined by five inequalities. Two of these are x G 6 and y G 6 . Write down the other three inequalities. Answer ................................................ ................................................ .......................................... [2] (c) The point P is in the shaded region R. Given that AP is as large as possible, write down the coordinates of P. Answer (.................... , ..................) [1]

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26 Two sequences have

1, 3, 5

as their first three terms.

(a) In the first sequence, each term is 2 more than the term before it. (i) Find an expression, in terms of n, for the nth term.

Answer .......................................... [1] (ii) The kth term of this sequence is 841. Find the value of k.

Answer k = .................................... [1] (b) The nth term of the second sequence is 2n - 1 -

( n - 1) ( n - 4) . 2

(i) Find the fourth term of this sequence.

Answer .......................................... [1] (ii) Find the fifth term of this sequence.

Answer .......................................... [1] Question 27 is printed on the next page

© UCLES 2016

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20

27 30

Speed (m/s) 12 0

0

k

20 Time (t seconds)

The diagram shows the speed-time graph of a car which slows down from 30 m/s to 12 m/s in 20 seconds, and then continues at a speed of 12 m/s. (a) Find the retardation when t = 10.

Answer .................................. m/s2 [1] (b) Find the distance travelled by the car between t = 0 and t = 20.

Answer ...................................... m [2] (c) The distance travelled by the car between t = 20 and t = k is 60 m. Find the value of k.

Answer k = .................................... [2] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/12/O/N/16

Cambridge International Examinations Cambridge Ordinary Level

* 1 9 2 5 1 7 5 0 8 6 *

4024/21

MATHEMATICS (SYLLABUS D)

October/November 2016

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (ST/SW) 123265/4 © UCLES 2016

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Section A [52 marks] Answer all the questions in this section. 1

(a) In 2016, the price of a television is $1995. (i) Afzal pays the $1995 with a deposit of $399 and 12 equal monthly payments. Calculate Afzal’s monthly payment.

Answer $ ....................................... [1] (ii) What percentage of $1995 is $399?

Answer ...................................... % [1] (iii) The price of the television in 2016 is 5% more than the price in 2015. Calculate the price in 2015.

Answer $ ........................................ [2]

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(b) Afzal watched a programme that lasted 2 hours 53 minutes. It ended at 01 15. At what time did it start?

Answer .......................................... [1] (c) A company paid a quarter of a million dollars for an advertisement that lasted 38 seconds. Calculate the cost, correct to the nearest hundred dollars, for each second of the advertisement.

Answer $ ........................................ [2] (d) The programme showed an athlete running 100 metres, measured correct to the nearest metre. The time the athlete took was 11.3 seconds, measured correct to the nearest 0.1 second. Calculate the upper bound of the athlete’s average speed.

Answer .................................... m/s [2]

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2

(a) Evaluate

3

543 . 28.6 - 1.35

Answer .......................................... [1] (b) Factorise completely 9p 2 - 6pq .

Answer .......................................... [1] (c) Expand the brackets and simplify (3a + b)2 .

Answer .......................................... [1] (d) Express as a single fraction in its simplest form

4 3 . 2t + 1 3t + 1

Answer .......................................... [3]

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(e) Find the integer values of n such that 4(2 – n) 2 17 and n 2 -6.

Answer .......................................... [2] (f) Abebi, Bella and Chuku share $112. Abebi receives $x. Bella receives $12 less than Abebi. Chuku receives twice as much as Bella. Form an equation in x and solve it to find how much Chuku receives.

Answer $ ....................................... [3]

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3 D

C

Q

A

P

a°

B

In the diagram, ABCD is a parallelogram. ˆ = 90°. P and Q are points on AB and BC respectively, such that PB = BQ and DPQ ˆ BPQ = a°. (a) Find an expression, in terms of a, for each of the following angles. Give each answer in its simplest form. ˆ (i) PBQ

Answer .......................................... [1] ˆ (ii) APD

Answer .......................................... [1] ˆ (iii) DAP

Answer .......................................... [1] ˆ (iv) ADP

Answer .......................................... [1]

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(b) AB = 8 cm and AD = 4.7 cm. (i) Find PB.

Answer .................................... cm [1] ˆ = 54°, calculate the area of the parallelogram. (ii) Given also that DAB

Answer ................................... cm2 [2]

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4

[The volume of a sphere is

4 3 rr ] 3

[The surface area of a sphere is 4rr 2 ] 9 0.8

1.5 3.8 A hemispherical bowl is made of material that is 0.8 cm thick. The outside rim of the bowl has radius 9 cm. The bowl is attached to a base which is a solid cylinder, of radius 3.8 cm and height 1.5 cm. (a) Calculate the surface area of the inside of the hemispherical bowl.

Answer ................................... cm2 [2]

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(b) Calculate the total volume of material used to make the bowl and the base.

Answer ................................... cm3 [5]

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5 O

A

B 120° 1.8 C

P

Q T

The diagram shows a semicircle with radii OP and OQ drawn. The circle, centre C, touches the radii at A and B and the semicircle at T. The radius of the circle is 1.8 cm. ˆ = 120°. BCA (a) Calculate the length of the minor arc AB.

Answer .................................... cm [2] (b) The shaded region lies between the circle and the radii OP and OQ. Calculate the perimeter of this shaded region.

Answer .................................... cm [3]

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(c) (i) Show that the radius of the semicircle is 5.4 cm.

[2] (ii) Calculate the length of BQ.

Answer .................................... cm [1]

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6 T

6 D

C

8 A 5 E

9

5

B

H

G 8 9

F

The four walls of a building are faces of a cuboid ABCDEFGH. ˆ = A DT ˆ = 90°. T is vertically above C and G, so ABT The cuboid has length 9 m, width 8 m and height 5 m. TC = 6 m. (a) Calculate the length of DT.

Answer ...................................... m [2] (b) The roof is formed by four triangles, ABT, BCT, CDT and DAT. Calculate the total surface area of the roof.

Answer ..................................... m2 [3] © UCLES 2016

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1 # area of base # perpendicular height] 3 Calculate the total volume of the building.

(c) [The volume of a pyramid is

Answer ..................................... m3 [2] (d) Calculate the angle of elevation of T from H.

Answer .......................................... [3]

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14

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7 D North

27

48° A 55° 19

C

51°

B The diagram shows the positions of four islands at A, B, C and D. A is due north of B. ˆ = 48°, CAB ˆ = 55° and BCA ˆ = 51°. DAC AC = 19 km and AD = 27 km. (a) Calculate the bearing of D from A. Answer .......................................... [1] (b) Calculate the bearing of A from C. Answer .......................................... [1] (c) Calculate the distance between A and B.

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(d) Calculate the distance between D and C.

Answer .................................... km [3] (e) A boat leaves D and sails, at a constant speed, in a straight line to A. It takes 3 hours and 36 minutes to sail from D to A. X is the point on DA that is closest to C. Calculate the time, correct to the nearest minute, the boat takes to travel from D to X.

Answer .......................................... [4]

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8

y=

3 x #2 5

The table shows some values of x and the corresponding values of y, correct to one decimal place where necessary. x

-1.5

-1

0

1

2

2.5

3

3.5

4

y

p

0.3

0.6

1.2

2.4

3.4

4.8

6.8

9.6

(a) Calculate p.

Answer .......................................... [1] (b) On the grid, • using a scale of 2 cm to 1 unit, draw a horizontal x-axis for - 2 G x G 4 , • using a scale of 1 cm to 1 unit, draw a vertical y-axis for 0 G y G 10 , • plot the points from the table and join them with a smooth curve.

© UCLES 2016

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[3]

17

(c) By drawing a tangent, estimate the gradient of the curve at the point where x = 2.5 .

Answer .......................................... [2] (d) (i) On the same grid, draw the straight line that passes through (-0.4, 0) and (2, 3.6). [1] (ii) Find the equation of this line in the form y = mx + c.

Answer .......................................... [2] (iii) Write down the x-coordinates of the points where the line intersects the curve. Answer x = ....................... and x = ....................... [1] (iv) These x-coordinates satisfy the equation 2 x = Ax + B . Find the values of A and B.

Answer A = ................ B = ................ [2]

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9

On Monday, Abdul sold 140 boxes of matches at 30 cents per box. (a) Calculate the income, in dollars, Abdul received on Monday.

Answer $ ........................................ [1] (b) On Tuesday, the price per box decreased by 10% and the number of boxes sold increased by 30%. Calculate the percentage change in the income.

Answer ...................................... % [3] (c) On Wednesday, the price of a box was y cents less than it was on Monday. Abdul sold 4y more boxes on Wednesday than he did on Monday. (i) Write down an expression, in terms of y, for the income received on Wednesday. Give your answer in dollars.

Answer $ ............................................................ [2]

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(ii) Given that this income is equal to $40, write down an equation in y and show that it simplifies to y 2 + 5y - 50 = 0 .

[2] (iii) Solve the equation

y 2 + 5y - 50 = 0 .

Answer y = ................... or ................... [3] (iv) Hence find the number of boxes sold on Wednesday.

Answer .......................................... [1]

© UCLES 2016

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20

10 (a) The times taken by 135 runners to complete a cross-country course were recorded. The results are summarised in the table. Time (t minutes) Number of runners

20 1 t G 30 15

30 1 t G 35 30

35 1 t G 40 40

40 1 t G 50 35

50 1 t G 70 15

(i) On the grid, draw a histogram to represent this information.

Frequency density

20

30

40 50 Time (t minutes)

60

70 [3]

(ii) Calculate an estimate of the mean time.

Answer ............................. minutes [3] © UCLES 2016

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(b) A bag contains R red beads and B blue beads. Two beads are chosen, at random, without replacement. The tree diagram shows the possible outcomes and their probabilities. First bead

3 5

2 5

Second bead 11 19

red

8 19

blue

12 19

red

7 19

blue

red

blue

(i) Calculate the probability that both beads are red.

Answer .......................................... [1] (ii) Calculate the probability that the two beads are different colours.

Answer .......................................... [2] (iii) What is the value of R? Answer .......................................... [1] (iv) Of the red beads, half have a yellow spot. Calculate the probability that, of the two chosen beads, neither has a yellow spot.

Answer .......................................... [2] © UCLES 2016

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22

11

(a) B

A C J- 6N AB = K O , L 11P AC .

In the diagram, (i) Find

J 12N AC = K O . L- 5P

Answer .......................................... [2] (ii) D is the point such that BD is parallel to AC. (a) Show that

J0N AD = K O , where k 2 0. LkP

J 6 N O. BD = K Lk - 11P

[1] (b) Find k.

Answer k = .................................... [2] (c) Find the difference between the lengths of AD and AC.

Answer .......................................... [1]

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23

(b) y B

2

A

1 –2

–1

0

1

2

3

4

5

6

7

8

9 x

Triangle A has vertices ( 12 , 1), (1, 2) and (2, 2). Triangle B has vertices ( - 12 , 1), (-1, 2) and (-2, 2). (i) Describe fully the single transformation that maps triangle A onto triangle B. Answer ....................................................................................................................................... .............................................................................................................................................. [2] J1 3N O. (ii) Triangle A is mapped onto triangle C by a transformation represented by the matrix K L0 1P (a) Calculate the coordinates of the vertices of triangle C.

Answer ( ........ , ........ ) ( ........ , ........ ) ( ........ , ........ ) [2] (b) Find the matrix which represents the transformation that maps triangle B onto triangle C.

Answer

© UCLES 2016

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J K K K L

N O O O P

[2]

24 BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/21/O/N/16

Cambridge International Examinations Cambridge Ordinary Level

* 2 4 2 8 2 7 2 3 6 8 *

4024/22

MATHEMATICS (SYLLABUS D)

October/November 2016

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (ST/SW) 123266/4 © UCLES 2016

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2

Section A [52 marks] Answer all questions in this section. 1

The basic price of the 2016 model of a car is $21 000. Sayeed and Rasheed each buy this model of car. (a) (i) Sayeed pays a deposit of $756. Calculate the deposit Sayeed pays as a percentage of the basic price.

Answer ...................................... % [1] (ii) He then pays 24 monthly payments of $922.25 . Calculate the total amount that Sayeed pays as a percentage of the basic price.

Answer ...................................... % [2]

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(b) Rasheed pays a deposit of $381 followed by 36 equal monthly payments. The total amount that he pays is 127% of the basic price of $21 000. Calculate Rasheed’s monthly payment.

Answer $ ........................................ [3] (c) $21 000 represented an increase of 5% on the basic price of the 2015 model. Calculate the difference between the basic prices of the 2015 and 2016 models.

Answer $ ........................................ [3]

© UCLES 2016

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4

2

(a) Simplify

3a 2 9a ' . 10bc 5b 2 c

Answer .......................................... [2] (b) Simplify

h-k . 5h - 5k

Answer .......................................... [2] (c) Factorise

9m 2 - 4n 2 .

Answer .......................................... [1]

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5

(d) Factorise

q ( p - 2 ) + 3 (2 - p ) .

Answer .......................................... [2] (e) (i) Find the two solutions of

5x - 1 = ! 9 .

Answer x = ................. or .................. [2] (ii) The solutions of are integers.

5x - 1 = ! 9

are also the solutions of

5x 2 + Bx + C = 0 , where B and C

Find B and C.

Answer B = ................. , C = ................. [2]

© UCLES 2016

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6

3

(a) Complete the table of values for

y=

x 2 (x - 10) . 20

x

0

1

2

3

4

y

0

-0.45

-0.6

-0.15

1.2

5 [1]

(b) Using a scale of 2 cm to 1 unit on both axes, draw the graph of y =

x 2 (x - 10) for 0 G x G 5. 20

y

0

x

[2] (c) By drawing a tangent, estimate the gradient of the curve at the point where x = 2.5 .

Answer .......................................... [2]

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7

(d) Use your graph to solve the equation

x 2 (x - 10) = 0 20

for

0 G x G 5.

Answer x = ................. or ................. [2] x 2 (x - 10) , together with the graph of a straight line L, can be used to solve the 20 x 3 + 10x - 80 = 0 for 0 G x G 5.

(e) The graph of y = equation

(i) Find the equation of line L.

Answer .................................................. [2] (ii) Draw the graph of line L on the grid. (iii) Hence solve the equation

x 3 + 10x - 80 = 0

[1] for

0 G x G 5.

Answer x = .................................... [1]

© UCLES 2016

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8

4

(a) C 41°

B 3

A

27°

D

In the framework ABCD, BD = 3 m. ˆ = 27°, BCD ˆ = 41°. DBC ˆ and DAB ˆ are right angles. BDA (i) Find AD.

Answer ...................................... m [2] (ii) Find CD.

Answer ...................................... m [3]

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9

(b) In triangle PQR, PQ = 3 m and QR = 5 m. The area of triangle PQR = 6 m2. ˆ Find the two possible values of PQR.

ˆ = ................. or ................. [3] Answer PQR

© UCLES 2016

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10

5 T

C A

D

P

B

In the diagram, A and B are the centres of two circles that touch at P. The line ACT touches the small circle at T and intersects the large circle at C. ˆ = 90°. D is the point on AB such that CDA (a) Complete the following, to show that triangle ACD is similar to triangle ABT. In triangle ACD and triangle ABT angle DAC

=

angle ................

(same angle)

angle CDA

=

angle .................

(.....................................................................)

angle ACD

=

angle .................

(two angles in a triangle are equal, so the third angles are equal)

Because the three pairs of angles are equal, the triangles are similar.

[2]

(b) Given that the radii of the circles are 7 cm and 3 cm, calculate CD.

Answer .................................... cm [3]

© UCLES 2016

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11

6

J2 0N O A=K L3 1P

J 1 B=K L- 1

2N O 3P

(a) Find A + 2B.

Answer

J K K K L

N O O O P

[2]

Answer

J K K K L

N O O O P

[2]

(b) Find AB.

JxN J 8 N (c) A K O = K O L2P L2yP Find x and y.

Answer x = ................. y = ................. [2] (d) Find B -1 .

Answer

© UCLES 2016

4024/22/O/N/16

J K K K L

N O O O P

[2]

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12

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a) x =

a2 + b2

(i) Calculate x when a = -0.73 and b = 1.84 .

Answer .......................................... [1] (ii) Express b in terms of x and a.

Answer b = .................................... [2] (b) B

C Q

A

x

D

P

R x+5

S

ABCD and PQRS are rectangles. AD = x cm and PS = (x + 5) cm. Each rectangle has an area of 17 cm2. (i) Write down an expression for PQ in terms of x.

Answer PQ = .......................... cm [1]

© UCLES 2016

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13

(ii) AB is 3 cm longer than PQ. Form an equation in x and show that it simplifies to 3x 2 + 15x - 85 = 0 .

[3] (iii) Solve the equation 3x 2 + 15x - 85 = 0 . Give your solutions correct to 3 significant figures.

Answer x = ................. or ................. [3] (iv) Find the perimeter of the rectangle PQRS.

Answer .................................... cm [2]

© UCLES 2016

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14

8

(a) P and Q are points on the circumference of a circle, centre O, radius R cm. ˆ = 48°. The minor arc PQ = 20 cm and POQ (i) Show that R = 23.9, correct to one decimal place. P

20

Q

48° R O

[3] (ii) Calculate the area of the minor sector POQ.

Answer ................................... cm2 [2] (iii) The minor sector POQ is removed from the circle and the remaining major sector is shaped to form an open cone of radius r cm. Q

P

r

48° R O

Calculate r.

Answer r = .................................... [2]

© UCLES 2016

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15

(b) [The curved surface area of a cone is πrl, where l is the slant height] Cone A has radius 7.5 cm and height 4 cm. (i) Calculate the curved surface area of cone A.

4 7.5 Cone A

Answer .................................. cm2 [3] (ii) Cone B is geometrically similar to cone A. The ratio curved surface area of cone A : curved surface area of cone B is 64 : 25 . Find the height of cone B.

Answer .................................... cm [2]

© UCLES 2016

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16

9 A 58°

North 65

B

110 70

D

70° C

ABCD is a level playing field. AB = 65 m, BC = 70 m and CA = 110 m. ˆ = 70°, DAC ˆ = 58° and C is due South of B. CDA (a) Calculate the bearing of A from C.

Answer .......................................... [4] (b) Calculate AD.

Answer ...................................... m [3]

© UCLES 2016

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17

(c) There are two vertical trees, AX and CY, each of height 17 m, one at each end of the path AC. (i) Calculate the angle of elevation of Y from B.

Answer .......................................... [2] (ii) A bird flies in a straight line from X to Y. It takes 24 seconds. Calculate the average speed of the bird. Give your answer in kilometres per hour.

Answer ................................. km/h [3]

© UCLES 2016

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18

10 (a) B D 6b C O

3a

A

ACB and OCD are straight lines. AC : CB = 1 : 2 . OA = 3a and OB = 6b . (i) Express AB in terms of a and b.

Answer .......................................... [1] (ii) Express AC in terms of a and b.

Answer .......................................... [1] (iii)

BD = 5a - b . Showing your working clearly, find OC : CD .

Answer ................... : ................... [4]

© UCLES 2016

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19

(b) y 5

A –5

5 x

0

B

–5 (i) Describe fully the single transformation that maps triangle A onto triangle B. Answer ................................................................................................................................. [2] (ii) Triangle A is mapped onto triangle C by the shear H in which the y-axis is invariant, and H(2, 1) = (2, 3). (a) On the grid, draw and label triangle C.

[2]

(b) State the shear factor of H. Answer .......................................... [1] (c) Find the matrix that represents H.

Answer

© UCLES 2016

4024/22/O/N/16

J K K K L

N O O O P

[1]

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20

11

(a) Six hundred candidates took a mathematics examination which consisted of two papers. Each paper was marked out of 100. The diagram shows, on the same grid, the cumulative frequency curves for Paper 1 and Paper 2. 600

500

Paper 2 Paper 1

400 Cumulative frequency 300

200

100

0

0

10

20

30

40

50 60 Marks

70

80

90

100

(i) Use the cumulative frequency curve for Paper 1 to find an estimate of (a) the median, Answer .......................................... [1] (b) the interquartile range,

Answer .......................................... [2] (c) the number of candidates who scored more than 45.

Answer .......................................... [1] © UCLES 2016

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21

(ii) A candidate scored 60 on Paper 1. Using both graphs, estimate this candidate’s mark on Paper 2.

Answer .......................................... [1] (iii) State, with a reason, which you think was the more difficult paper.

Answer

Paper ............... because ............................................................................................

.............................................................................................................................................. [1]

Question 11(b) begins on the next page

© UCLES 2016

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22

(b) Amira has three $1 coins and two 20c coins in her purse. She picks out coins at random, one after the other. The coins are not replaced. The tree diagram shows the possible outcomes and their probabilities when picking out two coins.

First coin

Second coin x

3 5

2 5

$1

$1 2 4

20c

3 4

$1

1 4

20c

20c

(i) Find x. Answer .......................................... [1] (ii) Find the probability that the total value of the two coins picked out is 40 cents.

Answer .......................................... [1] (iii) Find the probability that the total value of the two coins picked out is $1.20 .

Answer .......................................... [2]

© UCLES 2016

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23

(iv) At a car park, the charge is $1.40 . Amira picks out three coins, one after the other. Find the probability that the total value of the three coins is $1.40 .

Answer .......................................... [2]

© UCLES 2016

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24

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2016

4024/22/O/N/16

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/11

Paper 1

October/November 2017

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 5 printed pages. © UCLES 2017

[Turn over

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

October/November 2017

Abbreviations cao dep FT isw oe SC nfww soi

correct answer only dependent follow through after error ignore subsequent working or equivalent Special Case not from wrong working seen or implied

Question

Answer

Marks

1(a)

17 24

1

1(b)

0.52

1

2(a)

80

1

2(b)

(±)

1

1 3

3(a)

24

1

3(b)

120

1

4

Partial Marks

Initial statement containing 1000 and 0.02

M1 If M0, award C1 for 50 000 nfww.

50 000

A1

5(a)

1

5(b)

1 X X

6

11

2 M1 for 1 1 × 10 + 7 2

7(a)

16.6

1

7(b)

x−7 oe 3

1

© UCLES 2017

Page 2 of 5

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

Question 8

Answer 80

Marks 2

October/November 2017 Partial Marks

4 if y = “k”× x2 used 5 1 y or M1 for 5 2 = 2 oe ( 1 ) 10

B1 for “k” =

2

or FT M1 for y = (their k) × 100 when y = “k” × x2 used 9(a)

x>4

1

9(b)

–3 and –2

1

10(a)

–2

1

10(b)

–1

1

10(c)

0

1

11(a)

1.2 × 10 – 4

1

11(b)

5.29 × 10 7

2 C1 for figs. 529; or for 5.3 × 10 7 or B1 for 55 × 10 6 ; or for 0.21 × 10 7; or for figs 529

12

Correct method to eliminate one variable

M1 Either equating one set of coefficients, or equating expressions in either [m]x or in [m]y, or substituting for x or for y.

Both x = –2 and y = 5 nfww.

A2 A1 for either x = –2 or y = 5 nfww. After A0, C1 for a pair of values that satisfies either original equation.

13(a)

Correct line

1

13(b)

7 cao 15

1

13(c)

240

1

14(a)

0.106

1

14(b)

5.678 to 5.68[0]

1

14(c)

3180

1

15(a)

5 – 6t

1

15(b)

4 x 2 y −1 4 x2 or 3 3y

2

© UCLES 2017

Page 3 of 5

4 2 , x , denominator y (or y –1 in 3 numerator) correct. or B1 for 8 x 6 y 3

C1 for two of

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

October/November 2017 Partial Marks

16(a)

( 5, 3 )

1

16(b)

164 nfww

2 M1 for [0 – 10] 2 + [7 – (–1)] 2 or for [10 – 0] 2 + [–1 – 7] 2

17(a)

Correct curve from (4, 77) to (6, 90) via (5, 87)

1

17(b)(i)

2.8

1

17(b)(ii)

67 or 68

1

18(a)

14

1

18(b)

36

1

18(c)

72 nfww; or FT 90 – their(b)/2 nfww

2 B1 for angle OB2 = 18°, where B is the bottom point. or M1 for correct angle clearly identified.

19(a)

5a ( 5a – 1 )

1

19(b)

( 3b – 4 )( 3b + 4 )

1

19(c)

( 2x + 3 )( 2y + t )

2 B1 for one of the partial factorisations: 2y(2x + 3); t(2x + 3); 2x(2y + t); 3(2y + t)

20(a)

Acceptable quadrilateral with visible arcs

1

20(b)(i)

Acceptable bisector of angle ABC

1

20(b)(ii)

Acceptable perpendicular bisector of BC

1

20(c)

Acceptable PQ – dep. on correct types of loci in (b).

1

21(a)

( 18, 6 )

1

21(b)

Both y > 6 and y <

x 3

1

21(c)

h = 22 and k = 7

2 C1 for one correct

22(a)

v oe 10

1

22(b)

20 nfww

3 M1 for 1 × (40 + 80) × v oe 2 or B1 for two of 15v, 40v, 5v. M1 for their 60v = their(1200)

© UCLES 2017

Page 4 of 5

4024/11

Cambridge O Level – Mark Scheme PUBLISHED

Question 23(a)

Answer

Marks B

A

October/November 2017 Partial Marks

1

C

23(b)(i)

4

1

23(b)(ii)

1 1 1 4 4 4 , , , , , oe and isw −1 1 2 −1 1 2

2 C1 for 4 or 5 correct members

6a + 2b oe

1

3

1

24(b)(ii)(a)

3b; or FT kb

1

24(b)(ii)(b)

–3a

1

25(a)

11, 36

1

25(b)(i)

2N +1

1

25(b)(ii)

( N + 1 ) 2 oe

1

25(c)

169

2 B1 for their (b)(i) = 25; or for N = 12

26(a)

 −6 − 6    oe 3  3

2 C1 for 2 or 3 correct elements;

26(b)

 −2 − 6     3 7

2 C1 for 2 or 3 correct elements

26(c)

1 2

1

24(a) 24(b)(i)

© UCLES 2017

; or 0.5 ; only

 6 2 or for 3 or 4 correct elements of    −1 3  or B1 for the correct matrix in the Wkg. and simplified, incorrectly, to give the response in the Ans.Space.

Page 5 of 5

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/12

Paper 1

October/November 2017

MARK SCHEME Maximum Mark: 80

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 5 printed pages. © UCLES 2017

[Turn over

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

October/November 2017

Abbreviations cao dep FT isw oe SC nfww soi

correct answer only dependent follow through after error ignore subsequent working or equivalent Special Case not from wrong working seen or implied

Question

Answer

Marks

1(a)

9 35

1

1(b)

200

1

2(a)

7, 8, 5 all three

1

2(b)

18 × their (min. frequency) FT provided min. frequency < 20

1

3

1 oe nfww 2

2

4(a)

1 ; or 0.125 8

1

4(b)

4x

1

5(a)

68

1

5(b)

14 33; or 2.33 p.m.

1

6(a)

3.84

1

6(b)

4

1

7(a)

78°

1

7(b)

70°

1

8(a)

0

1

8(b)

1.5

1

9(a)

7.5

1

9(b)

3 nfww

1

© UCLES 2017

Page 2 of 5

Partial Marks

30 k oe if y = used 6 x or FT M1 for y = (their k) / 10 when y = “k” / x used 1 or M1 for × 30 = y × 10 6

B1 for “k” =

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

Question 10

Answer

Marks

October/November 2017 Partial Marks

Two or three of 40, 6, 3000

M1

Final answer 0.08 cao nfww

A1 C1 for 0.08 without any working.

14 years 6 months nfww

2 M1 for (3 × (14 years 3 months) + 15 years 3 months) oe

12(a)

25

1

12(b)

1 ; or 0.2 5

1

13(a)

40

1

13(b)

rectangle: base 40 to 50; frequency density (height) 3

1

rectangle: base 50 to 80; frequency density (height) 1

1

–2 and –1

3

15(a)

5

1

15(b)

72, 70, 38 all three

2 C1 for 72 and 70; or for three angles totalling 180°.

16(a)

3.6 × 108

1

16(b)(i)

4.5 × 10– 6

1

16(b)(ii)

(±) 3 × 10–8

1

17(a)

77

1

17(b)

20

2 M1 for a wholly correct method, such as 15000 − 12000 × 100 15000

18(a)

236

2 M1 for 2 × 5 × 11 + 2 × 5 × 6 + 11 × 6 oe or C1 for 302

18(b)

30

1

11

14

© UCLES 2017

Page 3 of 5

5 x k (i.e. collecting x terms, where ... represents any inequality symbol, or = ) and k = 12, 4, 3, 1 or 48. Or equiv., with zero on one side and both terms on the other. B1 for x > –2.4; or for –2.4 < x If 0 scored, then C1 for one correct solution 12 or for x = – oe in the answer space. 5

B1 for (–)5x ... (–)k ; or (–)1 ... (–)

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

Question 19(a)

Answer

October/November 2017

Marks

Partial Marks

Probabilities 0.7 and 0.3 on the correct branches

1

19(b)(i)

0.49 oe

1

19(b)(ii)

0.42 oe

1 FT from their diagram, provided their diagram probabilities are less than 1, and 0 < ans. < 1.

20(a)

–2

1

20(b)

y = –2x + 4 or FT y = (their(a)) x + 4 or y = (their(a)) (x + 3) + 10

1

20(c)

(3, –2)

2 C1 for one correct coordinate

21(a)

9  7    −15 −16 

2 C1 for two or three correct elements,  11 −3  or for 3 or 4 elements of  .  −15 −8 

21(b)

1  −4 −1 −   oe, e.g. 7  5 3

22(a)

3a(3a – 2)

1

22(b)

(2 – 5t )(2 + 5t)

1

22(c)

(x + 3d)(2c – y)

2 B1 for one of the partial factorisations: x(2c – y), 3d(2c – y), 2c(x + 3d), –y( x + 3d ), y(x + 3d )

23(a)

97 to 99 inclusive

1

23(b)

Acceptable line

1

23(c)

Full circle, centre C, radius 5 cm

1

23(d)

4.3 to 4.9 cm, dep. on two labelled intersections of an acceptable line and arc.

1

24(a)

21

1

24(b)

18 oe 20

1

24(c)

420

2 M1 for a correct, complete, method to find the area. e.g. 12 × (30 + 12) ×(60 – 40);

 74  5 − 7

 3 −7 1 7

2

 −4 −1 B1 for (det A =) –7 or B1 for   seen  5 3

12 × (60 – 40) + (60 – 40) × 30 –

© UCLES 2017

Page 4 of 5

1 2 1 2

× (60 – 40) × (30 – 12); × (60 – 40) × (30 – 12)

4024/12

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

October/November 2017 Partial Marks

25(a)

7x + 5y > 35 oe and x < 4 oe and y < 5 oe

2 C1 for two inequalities correct; or for x ... 4 and y ... 5 (with “...” ≠ “ < ”).

25(b)

3 nfww

2

26(a)

49, 19, 30

1

26(b)(i)

3n + 4 oe and isw

1

26(b)(ii)

(n + 2)2 oe

1

26(c)

n2 + n; or n(n + 1)

2 M1 for attempt at their(bii) – their(bi), provided both parts are different expressions in n, and the answer space also contains an expression in n, or is empty: or for a valid method.

27(a)

7

JJJG 3 M1 for OP = ( −3) 2 + (4) 2 JJJG B1 for PQ = 2

27(b)(i)

 −3 + 2 k    oe 4  

1

27(b)(ii)

4 12 oe

© UCLES 2017

10 oe; 7 7 or for eqn. of OA is y = x oe 2

B1 for x-coord. of A is

JJJJG JJJG 2 B1 for expressing OM as a multiple (by 4) of OT JJJG  6  or B1 for T is (6, 4); or for OT =    4

Page 5 of 5

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4024/21

Paper 2

October/November 2017

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 6 printed pages. © UCLES 2017

[Turn over

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

October/November 2017

Abbreviations cao dep FT isw oe SC nfww soi

correct answer only dependent follow through after error ignore subsequent working or equivalent Special Case not from wrong working seen or implied

Question

Answer

Marks

Partial Marks

1(a)(i)

503.5[0] final answer

3 M2 for 12.50 × 38 × 1.06 oe or 12.50 × 38 × 0.06 oe or M1 for 12.50 × 38 or 12.50 × 1.06 oe soi or 12.50 × 0.06 oe soi

1(a)(ii)

12

2 M1 for (525 – 462) ÷ 525 oe After M0, SC1 for answer 88

1(a)(iii)

2400 nfww

2 M1 for 1.03x = 2472 soi

1(b)

192

3 M1 for 520 × 0.74 M1 for (their 384.8 – 260) ÷ 0.65

2(a)

14.35 or 14.4

3 B1 for use of correct midpoints soi M1 for (2.5 × 35 + 7.5×42 + 15×30 + 25×28 + 40 × 15) ÷ 150

2(b)

Correct histogram with linear scale on frequency density axis

3 B2 for all 5 bar heights correct with frequency density axis scaled OR B1 for at least 3 correct heights drawn or 3 correct frequency densities calculated B1 for 5 bars correct width and position

2(c)

18 to 20

2 M1 for (15 + 14) ÷ 150

3(a)

040

1

3(b)

BC = 252 + 38 2 − 2 × 25 × 38cos(360 − 220)

BC = 59.36 to 59.37

© UCLES 2017

M2 or M1 for 252 + 382 – 2 × 25 × 38 × cos(360 – 220) A1

Page 2 of 6

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question 3(c)

Answer

Marks

204.1 to 204.3[2…]

October/November 2017 Partial Marks

4 B3 for 24.1 to 24.3[2…] OR

38 × sin(360 − 220) 59.4 sin B sin(360 − 220) = or M1 for 38 59.4

M2 for sin B =

and M1 for 180 + their B 4(a)

5 oe 9

1

4(b)(i)

25 oe 81

1

4(b)(ii)

40 oe 81

2

4(c)

4 oe nfww 9

3

5(a)

–3 , 2 nfww

3 M1 for y2 + 5y = 4y + 6 M1 for (y + 3)(y – 2) [ = 0]

5(b)

t=

2 p −1 1− 2 p or t = final answer 4+ p −4 − p

their 5 (9 − their 5) × soi or 9 9 their 5 4 × 9 9

M1 for

5 4 4 3 × + × 9 8 9 8 4 3 5 4 or M1 for × or × 9 8 9 8

M2 for

3 M1 for p(2 – t) = 4t + 1 or better M1FT for 2p – 1 = 4t + pt M1FT for completion to explicit formula for t Max 2 marks if final answer incorrect

3x − 2 final answer x+4

3 B1 for (3x – 2)(x – 4) seen B1 for (x + 4)(x – 4) seen

6(a)(i)

ˆ =] 38 [ ACB

1

6(a)(ii)

ˆ = ] 38, [ AEF angles in same segment are equal

1 Strict FT their (i)

6(a)(iii)

ˆ = ] 112 [ CDE

1

6(a)(iv)

ˆ = ] 106 [ BCD

2 FT 180 – their CDE + their ACB ˆ = 180 – their 112 soi M1 for ACD

5(c)

© UCLES 2017

Page 3 of 6

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

October/November 2017

Marks

Partial Marks

6(b)

156

3 B1 for sum of angles in pentagon = 540 soi M1 for 8x + 124 = their 540 oe

6(c)

105.5

2 B1 for two of 65.5, 131.5 and 57.5 seen After B0, SC1 for answer 108.5

7(a)(i)

y = –2x + 5 oe

2 B1 for y = –2x + c oe or for y = mx + 5 oe 5+3 or M1 for gradient = oe 0−4

7(a)(ii)

y = –2x – 1 oe FT their gradient from (a)(i)

2 B1 for answer y = their (–2)x + k, where k ≠ their 5 or M1 for 3 = their (–2) × –2 + k oe

7(b)(i)

3.5

1

7(b)(ii)

Correct smooth curve through 8 correct points

3 B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted

7(b)(iii)

Clear correct tangent drawn at (1, 1)

M1

–2.4 to –1.6

A1

7(b)(iv)

8(a)

8(b)

0.6 to 0.8 and 4.2 to 4.4

2 FT reading from their graph at y = 2 B1 for one correct or for y = 2 soi

[x2 =] 62 + 122

M1 or [ x =] 62 + 122

[x = ] 13.41[6…] or 13.42

A1

478.7 to 479.4

3

1  M1 for  × 4 × π × 62 seen 2  M1 for π × 6 × 13.4 seen

After 0 scored, SC1 for consistent use of r = 3 in formula for [hemi]sphere and cone 8(c)

904.7 to 905 nfww

3

1  4 M1 for  ×  × π × 63 seen 2  3 1 M1 for × π × 62 × 12 seen 3

After 0 scored, SC1 for consistent use of r = 3 in formula for [hemi]sphere and cone 8(d)(i)

8(d)(ii)

© UCLES 2017

4310 or FT 9 × their (b)

2

6 M1 for   soi 2

1 × their (c) 8

2

1 M1 for   soi  2

113 or FT

Page 4 of 6

2

3

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

October/November 2017

Marks

Partial Marks

9(a)

7 cao

2

9(b)(i)

2500 x

1

9(b)(ii)

2500 2500 − = 15 x x + 20

M1 Or equivalent unsimplified equation

2500(x + 20) – 2500x = 15x(x + 20)

M1 FT elimination of their fractions with algebraic denominators

Correct simplification leading to 3x2 + 60x – 10 000 = 0 AG

A1

9(b)(iii)

48.59 and –68.59 final answer

M1 for

3 B1 for B1 for

12 × 1750 oe 3000

60 2 − 4 × 3 × −10000 soi

−60 ± their123600 2×3

9(b)(iv)

36 minutes 27 seconds

3

10(a)(i)

Triangle B at (2, –3), (3, –3), (3, –5)

2 B1 for translation of correct triangle B

10(a)(ii)

Triangle C at (3, 3), (3, 9), (6, 3)

2 B1 for two vertices correct or for  3 0  1 2 1     oe  0 3  1 1 3 

10(a)(iii)

 13 0  oe  1 0 3 

1

10(a)(iv)

Enlargement Centre (3, –1.5) 1 SF − 3

3 B1 for each

10(b)(i)

 4   8

2 B1 for one component correct  6  8 or M1 for 2   −   oe  3   −2 

2500 their 48.59 + 20 2500 or M1 for their 48.59

M2 for

 −4  After 0 scored, SC1 for answer    −8 

10(b)(ii)

© UCLES 2017

2 B1 for one component correct JJG JJG 3 1 or M1 for − (their SR) or (their SR) soi 4 4

9   0

Page 5 of 6

4024/21

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

Marks

October/November 2017 Partial Marks

∠ARB = ∠PRQ, [vertically] opposite ∠RAB = ∠RQP, alternate [angles] ∠RBA = ∠RPQ alternate [angles] ∆ARB and ∆QRP similar, equal angles

3 B1 for one pair of angles stated with reason or for two pairs with no reasons or incorrect reasons

11(b)(i)

[AQ = ] 8.72 or 8.717[…]

2

11(b)(ii)

[AR = ] 7.37[2…]

2

11(b)(iii)

[Area ARB = ] 18.8 to 19.2[…]

2

11(a)

B1 for a further correct pair of angles with reason

or FT their AR

11(b)(iv)

0.942

5 5 or sin 35 = oe AQ AQ

M1 for cos35 =

AR AR or sin 55 = oe 9 9

M1 for Or

19.6 to 19.7 nfww

7.37

M1 for cos55 =

3

1 × their 7.37 × 9 × sin 35 oe 2

1 2 × their 7.37 × 92 − ( their 7.37 ) 2 PR oe their RQ PR their RB oe or = their RQ their AR where their RQ = (their 8.72 – their

M1 for tan 35 =

5.16 7.37)

1.34

M1 for their area ARB + 1 × their RQ × their PR 2

© UCLES 2017

Page 6 of 6

Cambridge Assessment International Education Cambridge Ordinary Level

MATHEMATICS (SYLLABUS D)

4042/22

Paper 2

October/November 2017

MARK SCHEME Maximum Mark: 100

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

® IGCSE is a registered trademark.

This document consists of 8 printed pages. © UCLES 2017

[Turn over

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

October/November 2017

Abbreviations cao dep FT isw oe SC nfww soi

correct answer only dependent follow through after error ignore subsequent working or equivalent Special Case not from wrong working seen or implied

Question 1(a)

Answer

Marks

A by 240

Partial Marks

4 B3 for 4980 and 5220 seen or difference = 240 Or M1 for 4500 ÷ 5 and 12 × 340 oe and M1 for 0.12 × 4500 and 24 × 195 oe and M1 for the difference between their 5220 and their 4980

1(b)

10.61 cao

3 M2 for 240 ÷ 100 × 5.2 × 0.85 soi Or M1 for 240 ÷ 100 × 5.2 or their 12.48 × 0.85 or 5.2 × 0.85

1(c)

42

3 B2 for 280 Or M1 for 1.15 x = 322 soi and M1 for 322 – their 280

2(a)(i)

12 40 85 107

1

2(a)(ii)

Correct cumulative frequency curve

2 B1FT for at least 5 correct plots

2(b)(i)

47 to 49

1FT

2(b)(ii)

28 to 32

2FT B1 for 63 to 65 or 32 to 35

© UCLES 2017

Page 2 of 8

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 2(c)

Answer

Marks

49.3

October/November 2017 Partial Marks

3 M1 for (12×10 + 28×30 + 45×50 + 22×70 + 13×90) and B1 dep for their Σfx ÷ 120

3(a)

3(b)(i)

5    6  cao 8  

1

 440    cao  540 

2

B1 for one element correct 3(b)(ii)

The amount Anya makes for men’s Tshirts and women’s T-shirts

1

3(c)(i)

( 290

2

630 537.5[0])

B1 for two correct values seen in a row of 3 elements or column of 3 elements isw 3(c)(ii)

48.7%

3 M1FT for their (440 + 540) and their (290 + 630 + 537.5) and M1 for (their 1457.5 – their 980) ÷ their 980 oe

4(a)(i)

Triangle B at (4, –1), (4, –4), (5, –4)

2 B1 For triangle B the correct size and orientation

4(a)(ii)

Triangle C at (1, 4), (3, 4) (3, –2)

2 B1 for correct size and orientation, incorrect position or for triangle with two vertices correct or for triangle at (–3, 0), (–5, 0), (–5, 6)

4(b)(i)

Triangle Q at (3, 1), (9, 1), (6, 3)

2 B1 for coordinates (3, 1), (9, 1) and (6, 3) soi or for triangle with two vertices correct

4(b)(ii)

(Stretch) factor 3

2

y-axis invariant or parallel to x-axis B1 for either © UCLES 2017

Page 3 of 8

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 5(a)

Answer

Marks

14 − x Final answer ( x − 2)( x + 1)

Partial Marks

2

M1 for 5(b)

October/November 2017

–4 or 1.5 oe

4( x + 1) − 5( x − 2) or better soi ( x − 2)( x + 1)

3 B1 for 2x2 + 5x –12 [= 0]

and

M1 for (2x – 3)(x + 4) [= 0] OR M1 for FT factorising their 3-term quadratic equation Or for correct FT substitution into formula oe

and A1FT for solutions from their quadratic equation 5(c)(i)

3p + 2n = 4.8[0] or 3p + 2n = 480 5p + 4n = 9[.00] or 5p + 4n = 900

5(c)(ii)

0.6[0] 1.5[0]

1 3FT M1 for a correct method to eliminate one variable A1 for either p = 0.6[0] or n = 1.5[0] www After A0 , B1FT for a correct substitution to find the other variable After 0, SC1 for a pair of values that satisfy either equation

6(a)(i)

1

1

6(a)(ii)

10, 12, 14, 15, 16, 18, 20

1

6(a)(iii)

7 oe 11

1

6(b)(i)

8

2 M1 for 14 + 10 + 24 – x = 40 oe or for correct Venn diagram with algebraic expressions. Or B1 for Venn diagram with at least 3 numbers correct

© UCLES 2017

Page 4 of 8

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 6(b)(ii)

Answer

Marks

October/November 2017 Partial Marks

2FT

28 oe 45

M1 for

their 8 their 7 [×2] × k k −1

 their 8  Or SC1 for    10  7(a)(i)

–4.5 –4.5

7(a)(ii)

Correct smooth curve

where k > their 8

2

1 Both correct 3FT B2FT for 8 or 9 points correctly plotted Or B1FT for 6 or 7 points correctly plotted Or B1 for the correct scales drawn

7(a)(iii)

2 Accept a correctly formed ∆y ÷ ∆x isw

–2.4 to –1.6 dependent on tangent drawn

B1 for tangent drawn at (3, 1.5) 7(a)(iv)(a)

–2 cao

7(a)(iv)(b)

–2.4 to –2.3 and 4.3 to 4.4

FT reading their graph at y = their –2 Tolerance ± 1 small square B1 FT for one correct

7(b)(i)

4

1

7(b)(ii)

3

1

7(b)(iii)

324

1

y oe 2 angle at centre = twice angle at circumference oe

2

8(a)(i)

B1 for 8(a)(ii)

90 – y oe

y 2

2

[Angle between] radius and tangent = 90°,

B1 for 90 − y

[sum of angles in a triangle]

© UCLES 2017

Page 5 of 8

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 8(a)(iii)

Answer 2y oe or 2(90 – their (a)(ii)) or 180 – 2 their (a)(ii)

Marks

October/November 2017 Partial Marks

2FT FT dependent on expressions in y

Angle in semicircle = 90° B1 for 2y 8(b)

EFC

1

8(c)

Any two of • ∠OCG is common oe • ∠ADC = ∠OGC [= 90°] • ∠DAC = ∠GOC [= y] with no incorrect reason or fact stated

2

B1 for one pair of angles 8(d)

Trapezium

1

8(e)(i)

1 : 4 oe

1

8(e)(ii)

1 : 8 oe

1

7.54

2

9(a)

M1 for π × 0.42 × 15 9(b)

53.7

4 M1 for

1 × 4.52 × sin 110 oe 2

M1 for

250 110 × π × 4.52 or × π × 4.52 360 360

M1 for their 9.514 + their 44.18 oe 9(c)

2 minutes 20 seconds

2 M1 for figs 175 ÷ 45 soi

© UCLES 2017

Page 6 of 8

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

Question 9(d)

Answer

Marks

146.5°

October/November 2017 Partial Marks

4 B3 for 33.5° 450sin 62 720 sin Q sin 62 M1 for = 450 720

M2 for sin Q =

Or

Or AND

M1 for 180 – their Q 10(a)

4

3x 2 + 16 x − 460 = 0 correctly derived

B1 for ( x + 4)(3x + 4) oe

and

M1 for expanding brackets and collecting like terms and M1 for their area = 476

and

A1 for correct simplification leading to 3x2 + 16x – 460 = 0 10(b)

10 and −

3

46 oe ( −15.3 ) 3

B2 for (x – 10)(3x + 46) Or M1 for such as ( x + a)(3x + b) with ab = – 460 or 3a + b = 16 A1FT for solutions from their factors 10(c)

[Height = ] 14 [Length = ] 34

2FT B1FT for either, or for both correct but in the wrong places

10(d)

61.6 or 16(their +ve root + 1)×0.35

3FT M2 for (their 476 – their 10 × their 30) × 0.5 × 0.7 oe Or M1 for their 476 – their 10 × their 30 oe

© UCLES 2017

Page 7 of 8

4042/22

Cambridge O Level – Mark Scheme PUBLISHED

Question

Answer

11(a)

Need to see 2.58 rounded from a correctly obtained 2 581 or better.

October/November 2017

Marks

Partial Marks

3 Method 1 M2 for AY = 3.65cos45 or (3.65 ÷ 2) ÷ sin 45 or 3.65 ÷ 2 AY M1 for e.g. = cos 45 or sin 45 = 3.65 AY Method 2 M1 for such as AY2 + AY2 = 3.652 or 3.652 + 3.652 = AC2 soi M1 for AY 2 =

3.652 oe 2

A1 for AY = 2.580[9…] 11(b)

7.93

2 M1 for 7.52 + 2.582

11(c)

 0.5 × 3.65  26.6° or 2sin −1    their 7.93 

3FT

 0.5 × 3.65  M2 for 2sin −1    their 7.93  their 7.932 + their 7.932 − 3.652 or cos […] = 2 × their 7.932 Or 0.5 × 3.65 their 7.93 or 3.652 = their7.932 + their7.932 – 2 ×their 7.932 × cos […]

M1 for sin[...] =

11(d)(i)

11.18 or 11.2

2 M1 for tan 77 =

11(d)(ii)

80.7°

XY oe 2.58

2FT M1 for tan […] =

© UCLES 2017

Page 8 of 8

their 11.2 3.65 ÷ 2

Cambridge International Examinations Cambridge Ordinary Level

* 9 7 7 2 7 9 3 1 5 4 *

4024/11

MATHEMATICS (SYLLABUS D)

October/November 2017

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NF/SW) 136665/1 © UCLES 2017

[Turn over

2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Evaluate

1 38 - 23

.

Answer .......................................... [1] (b) Evaluate 0.4 # 1.3 .

Answer .......................................... [1] 2

(a) Evaluate 92 - 90 .

Answer .......................................... [1] 1

(b) Evaluate 9 - 2 .

Answer .......................................... [1]

© UCLES 2017

4024/11/O/N/17

3 3

(a) Find the simple interest on $200 for 3 years at 4% per year.

Answer $ ........................................ [1] (b) Two brothers share $200 in the ratio 2 : 3. Calculate the larger share.

Answer $ ........................................ [1] 4

By writing each number correct to 1 significant figure, calculate an estimate for the value of 987.65 . 0.0193

Answer .......................................... [2]

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4 5

(a) The diagram shows part of a figure that has AB as its line of symmetry. Complete the figure. A

B

[1] (b) In the diagram, six small squares are shaded. Shade two more small squares so that the completed diagram has rotational symmetry of order 4.

[1] 6

As part of her training, Samantha runs for 2 hours. For the first 1 12 hours she runs at an average speed of 10 km/h. She runs 7 km in the remaining 12 hour. Calculate her average speed for the 2 hours.

Answer ................................. km/h [2]

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5 7

f(x) = 3x + 7 (a) Find f(3.2).

Answer .......................................... [1] (b) Find f -1(x).

Answer f -1(x) = ............................ [1] 8

y varies directly as the square of x. 1 1 Given that y = when x = , find y when x = 10. 5 2

Answer y = .................................... [2]

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6 9

(a) Solve the inequality 12 - 2x 1 x .

Answer x ........................................ [1] (b) Find the integer values of n that satisfy - 8 1 2n G - 4 .

Answer .......................................... [1] 10 One week the temperatures, in degrees Celsius, at midnight were recorded. The results are given below. -1

-3

2

5

-2

1

-2

Use these results to find (a) the mode, Answer .......................................... [1] (b) the median,

Answer .......................................... [1] (c) the mean.

Answer .......................................... [1]

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7 11

(a) Write the number 0.000 12 in standard form. Answer .......................................... [1] (b) Giving your answer in standard form, evaluate 5.5 # 107 - 2.1 # 106.

Answer .......................................... [2] 12 Solve the simultaneous equations.

2y = x + 12 3y = 11 - 2x

Answer x = .................................... y = .................................... [3]

© UCLES 2017

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8 13 In a survey, some people were asked which of three types of tea, labelled X, Y and Z, they preferred. The diagram shows part of a pie chart that illustrates the results. The angle of the sector that represents the people who preferred Y is 168°. (a) Complete the pie chart.

Z

X 120°

Y

[1] (b) Find the fraction of people who preferred Y. Express your answer in its simplest form.

Answer .......................................... [1] (c) Given that 80 people preferred X, calculate the number of people in the survey.

Answer .......................................... [1]

© UCLES 2017

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9 14 The table shows the square roots, given correct to 4 significant figures, of some numbers from 31.0 to 32.9. 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

31

5.568

5.577

5.586

5.595

5.604

5.612

5.621

5.630

5.639

5.648

32

5.657

5.666

5.675

5.683

5.692

5.701

5.710

5.718

5.727

5.736

For example, the square root of 32.5 is 5.701. Use the table to find (a) the difference between the square root of 32.5 and the square root of 31.3,

Answer .......................................... [1] (b) an estimate of the square root of 32.25,

Answer .......................................... [1] (c) the number which has a square root of 56.39.

Answer .......................................... [1] 15 (a) Simplify 8 - 3(2t + 1).

(b) Simplify

^2x yh 2

Answer .......................................... [1]

3

6x 4 y 4

.

Answer .......................................... [2]

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10 16 The coordinates of P and Q are (0, 7) and (10, -1). (a) Find the coordinates of the midpoint of PQ.

Answer ( .................. , .................) [1] (b) The length of PQ is

N units, where N is an integer.

Find N.

Answer N = ................................... [2]

© UCLES 2017

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11 17 The lengths of 90 leaves of a plant were measured. The results are given in the table. The diagram shows part of the cumulative frequency curve. Length (t cm)

01tG1 11tG2 21tG3 31tG4 41tG5 51tG6

Frequency

7

17

29

24

10

3

100

Cumulative frequency

80

60

40

20

0

0

1

2

3 4 Length (t cm)

(a) Complete the cumulative frequency curve.

5

6

7

[1]

(b) Use the curve to estimate (i) the median, Answer .................................... cm [1] (ii) the number of leaves with a length less than 3.5 cm.

Answer .......................................... [1]

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12 18 27

28

29 30

1

2 3

x° O

The diagram represents a vertical, circular fairground wheel which turns about its centre O. The wheel has 30 seats, equally spaced around the circumference, numbered consecutively from 1 to 30. The diagram, which is not drawn to scale, shows seven of the seats, labelled with the seat number. The seat number 29 is at the top of the wheel. (a) What is the number of the seat which is at the bottom of the wheel?

Answer .......................................... [1] (b) Calculate the angle x°, as shown on the diagram.

Answer .......................................... [1] (c) Work out the angle of elevation of seat 2 from the bottom of the wheel.

Answer .......................................... [2]

© UCLES 2017

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13 19 (a) Factorise 25a2 - 5a.

Answer .......................................... [1] (b) Factorise 9b2 - 16.

Answer .......................................... [1] (c) Factorise 4xy + 3t + 6y + 2tx.

Answer .......................................... [2]

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14 20

C

A

B

The diagram shows the lines AB and BC. The point D is on the opposite side of AC to B. AD = 5 cm and CD = 6.5 cm. (a) Construct quadrilateral ABCD.

[1]

(b) On the diagram, construct the locus of points, inside the quadrilateral, that are (i) equidistant from AB and BC,

[1]

(ii) equidistant from B and C.

[1]

(c) The line PQ consists of the points, inside the quadrilateral, which are equidistant from AB and BC, and nearer to C than to B. Mark and label the line PQ on the diagram.

© UCLES 2017

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[1]

15 21 y

C A

B

x

O

The diagram shows the triangle ABC formed by the lines y = 6, x = 23 and y =

x . 3

(a) Find the coordinates of A.

Answer ( .................. , ..................) [1] (b) The region inside the triangle is defined by three inequalities. One of these is x 1 23 . Write down the other two inequalities. Answer .......................................... .......................................... [1] (c) The point P (h, k), where h and k are integers, lies inside triangle ABC. Find the values of h and k.

Answer h = .................................... k = .................................... [2]

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16 22 The diagram is the speed-time graph of a train which travels between two stations.

v Speed (m/s)

0

0

30

Time (t seconds)

70

80

(a) Find an expression, in terms of v, for the retardation of the train.

Answer .................................. m/s2 [1] (b) The distance between the two stations is 1.2 km. Find v.

Answer v = .................................... [3]

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17 23 (a) In the Venn diagram, shade the region which represents the subset Al + B + C . 

A

B

C

[1] (b) P = { 1, 4 } Q = { -1, 1, 2 } x R = ' | x ! P, y ! Q 1 y (i) Find n ^P , Qh .

Answer .......................................... [1] (ii) List the members of R.

Answer .............................................................................. [2]

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18 24 E

D

F 2b A

C

B

6a

In the diagram, ABC and AFE are straight lines. AB = 6a and BF = 2b. (a) Express AF in terms of a and b.

Answer .......................................... [1] (b) AE = 9a + kb. (i) Find k.

Answer k = .................................... [1] (ii) ED is parallel to BC, CD is parallel to BF and BC = AB. Find, in terms of a and/or b, (a) CD,

Answer .......................................... [1] (b) DE .

Answer .......................................... [1]

© UCLES 2017

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19 25 Mary makes pendants, of the same design, from small beads. The sequence of diagrams shows the pendants she makes.

Diagram 1

Diagram 2

Diagram 3

Diagram 4

(a) Complete the table. Diagram number

1

2

3

4

Number of rows

3

5

7

9

Number of beads

4

9

16

25

5

[1] (b) Find an expression, in terms of N, for (i) the number of rows in Diagram N,

Answer .......................................... [1] (ii) the number of beads in Diagram N.

Answer .......................................... [1] (c) Julia asks Mary to make her a pendant with 25 rows. How many beads are used to make this pendant?

Answer .......................................... [2]

© UCLES 2017

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20 J0 - 2N OO A = KK 1 3 L P

26

J 3 B = KK L- 1

2NO O 0P

(a) Express A - 2B as a single matrix.

Answer

[2]

Answer

[2]

(b) Find A2.

(c) B-1 = kA where k is a rational number. Find k.

Answer k = .................................... [1] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/11/O/N/17

Cambridge International Examinations Cambridge Ordinary Level

* 8 0 3 6 2 0 6 3 4 8 *

4024/12

MATHEMATICS (SYLLABUS D)

October/November 2017

Paper 1

2 hours Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages. DC (NF/SW) 136664/1 © UCLES 2017

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2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER 1

(a) Evaluate

6 3 - . 7 5

Answer .......................................... [1] (b) Evaluate

90 . 0.45

Answer .......................................... [1] 2

The masses, in kilograms, of 20 parcels sent by a dispatch centre are given in the table. 4.2

5.3

5.1

7.8

8.2

7.5

3.2

5.7

4.1

5.9

8.4

5.6

8.0

3.2

4.8

6.9

6.2

3.2

5.4

4.7

(a) By using tally marks, or otherwise, complete the grouped frequency distribution for these masses. Mass (m kilograms)

Tally marks

Frequency

31mG5 51mG7 71mG9 [1] (b) The results are to be shown in a pie chart. Calculate the angle of the sector representing the group with the smallest frequency.

Answer .......................................... [1]

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3 3

y is inversely proportional to x. Given that y =

1 when x = 30, find y when x = 10. 6

Answer y = .................................... [2] 4 J1N (a) Find f KK OO . L2P

f ^xh =

x 4

Answer .......................................... [1] (b) Find f -1 ^xh.

Answer f -1 ^xh = ........................... [1]

© UCLES 2017

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4 5

The timetable for buses from A to E, calling at B, C and D, is given below. A

08 12

08 42

and every 30 minutes until

17 12

B

08 33

09 03

and every 30 minutes until

17 33

C

08 48

09 18

and every 30 minutes until

17 48

D

09 05

09 35

and every 30 minutes until

18 05

E

09 20

09 50

and every 30 minutes until

18 20

(a) How many minutes does each journey from A to E take?

Answer ............................ minutes [1] (b) Sharon has an appointment at D at 3.30 p.m. What is the latest time she can catch a bus from B?

Answer .......................................... [1] 6

(a) P

3.8

3.9

The diagram shows a scale from 3.8 to 3.9, divided into five equal parts. What is the value at the mark labelled P?

Answer .......................................... [1] (b) A

X

Y

B

The points X and Y lie on the line AB such that AX : XY : YB = 3 : 2 : 4. AB = 18 cm. Find XY.

Answer .................................... cm [1] © UCLES 2017

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5 7

B

A

D

35°

C

102° E

G

F

In the diagram, ABC is parallel to DEFG. t = 35° and BFG t = 102°. BC = BE, ACE t . (a) Find CBF t = .............................. [1] Answer CBF t . (b) Find ABE

t = .............................. [1] Answer ABE 8

Thirty students were asked on how many days they ate pasta last week. The results are given in the table. Number of days

0

1

2

3

4

5

Frequency

9

6

7

4

2

2

(a) Find the mode. Answer .......................................... [1] (b) Find the median.

Answer .......................................... [1]

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6 9

The area of a rectangle is given as 8 cm2, correct to the nearest cm2. (a) Write down the lower bound for the area of the rectangle.

Answer ................................... cm2 [1] (b) The width of the rectangle is given as 2 cm, correct to the nearest cm. Calculate the lower bound for the length of the rectangle.

Answer .................................... cm [1] 10 By making suitable approximations, calculate an estimate for

40.32 # 35.7 . 2980

Show clearly the approximations you use and give your answer correct to 1 significant figure.

Answer .......................................... [2]

© UCLES 2017

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7 11

The mean age of Ali, Ben and Chris is 14 years 3 months. Dai’s age is 15 years and 3 months. Calculate the mean age of the four people.

Answer ......... years ......... months [2] ax = 5

12 (a) Find a 2x .

Answer .......................................... [1] (b) Find a -x .

Answer .......................................... [1]

© UCLES 2017

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8 13 The distribution of the lengths of time spent on the internet on a Monday by each member of a group of students is given in the table. Time (t minutes)

10 1 t G 30

30 1 t G 40

40 1 t G 50

50 1 t G 80

Frequency

k

50

30

30

The histogram represents some of this information.

5 4 Frequency density

3 2 1 0

0

10

20

30

40 50 60 Time (t minutes)

70

80

90

(a) Find k.

Answer k = .................................... [1] (b) Complete the histogram.

© UCLES 2017

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9 14 Find the two solutions of

3x x -1 1 which are negative integers. 4 3

Answer x = .............. and ............. [3] 15

The diagram shows a figure made from five identical triangles. The figure has rotational symmetry. (a) Write down the order of rotational symmetry. Answer .......................................... [1] (b) Each marked angle is 110°. Find the angles of one of the triangles.

Answer ............. , ............ , ............ [2]

© UCLES 2017

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10 16 (a) Write the number 360 million in standard form. Answer .......................................... [1] p = 5 # 109

(b)

q = 9 # 10-16

Expressing each answer in standard form, find (i) p # q,

Answer .......................................... [1] (ii)

q.

Answer .......................................... [1] 17 (a) Find 110% of 70.

Answer .......................................... [1] (b) When new, a car was worth $15 000. After one year it was worth $12 000. Calculate the percentage reduction in its value.

Answer ...................................... % [2]

© UCLES 2017

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11 18

5 11

6

An open rectangular tray has inside measurements length 11 cm

width 6 cm

height 5 cm.

(a) Calculate the total surface area of the four sides and base of the inside of the tray.

Answer ................................... cm2 [2] (b) Cubes are placed in the tray and a lid is placed on top. Each cube has an edge of 2 cm. Find the maximum number of cubes that can be placed in the tray.

Answer .......................................... [1]

© UCLES 2017

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12 19 Each time an archer fires an arrow, the probability that she hits the target is 0.7 . She fires two arrows. (a) Complete the tree diagram. First arrow

Second arrow 0.7

0.7

hit

hit miss hit miss miss

[1] (b) Find the probability that (i) she hits the target twice,

Answer ������������������������������������������ [1] (ii) she hits the target exactly once.

Answer .......................................... [1]

© UCLES 2017

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13 20 The coordinates of P and M are (-3, 10) and (0, 4). (a) Find the gradient of the line PM.

Answer .......................................... [1] (b) Find the equation of the line PM.

Answer .......................................... [1] (c) M is the midpoint of PQ. Find the coordinates of Q.

Answer ( .................. , .................) [2]

© UCLES 2017

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14 J 3 J1 1NO K 21 (a) Express 3 K O - 2 KK 5 4 L P L0

- 3NO O as a single matrix. 2P

J 3 1NO (b) Find the inverse of KK O. L- 5 - 4P

© UCLES 2017

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Answer

J K K KK L

N O O OO P

[2]

Answer

J K K KK L

N O O OO P

[2]

15 22 (a) Factorise 9a2 - 6a.

Answer .......................................... [1] (b) Factorise 4 - 25t 2 .

Answer .......................................... [1] (c) Factorise 6cd - xy + 2cx - 3dy.

Answer .......................................... [2]

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16 23 A

B C

The diagram shows the triangle ABC. (a) Measure angle ABC. Answer .......................................... [1] (b) On the diagram, construct the perpendicular bisector of AB.

[1]

(c) On the diagram, construct the locus of points that are 5 cm from C.

[1]

(d) The points P and Q lie on the perpendicular bisector of AB and are 5 cm from C. Mark and label the points P and Q on the diagram and measure PQ. Answer PQ = ........................... cm [1]

© UCLES 2017

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17 24 The diagram is the speed-time graph of part of a train’s journey.

30 Speed (m/s) 12

0

0

40

10

60

Time (t seconds)

(a) Calculate the speed when t = 5.

Answer ................................... m/s [1] (b) Calculate the acceleration.

Answer .................................. m/s2 [1] (c) Calculate the distance travelled from t = 40 to t = 60.

Answer ...................................... m [2]

© UCLES 2017

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18 25

y 7

5

A

B

C

0

4

5

x

In the diagram, the equation of the line AC is 7x + 5y = 35. (a) Write down the three inequalities that define the region inside triangle ABC.

Answer .......................................... .......................................... .......................................... [2] (b) The line y = kx, where k is an integer, passes through triangle ABC. Find the greatest possible value of k.

Answer k = .................................... [2]

© UCLES 2017

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19 26 The sequence of diagrams shows patterns made from some black beads and some white beads. Each diagram has two rows more than the previous diagram. Diagram 1

Diagram 2

Diagram 4

Diagram 3

(a) Complete the table for Diagram 5. Diagram number

1

2

3

4

Total number of beads

9

16

25

36

Number of white beads

7

10

13

16

Number of black beads

2

6

12

20

5

[1] (b) Write down an expression, in terms of n, for (i) the number of white beads in Diagram n,

Answer .......................................... [1] (ii) the total number of beads in Diagram n.

Answer .......................................... [1] (c) Find an expression, in terms of n, for the number of black beads in Diagram n. Give your answer in its simplest form.

Answer .......................................... [2]

© UCLES 2017

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20 27

y

P

Q

T

x

O

In the diagram, (a) Find

J- 3N OP = KK OO L 4P

J2N PQ = KK OO . L0P

OP + PQ .

Answer .......................................... [3] (b) T is the point where PT = kPQ . (i) Express OT as a column vector in terms of k.

Answer

J24N (ii) M is the point such that O, T and M lie on a straight line and OM = KK OO . L16P Find the value of k.

[1]

Answer k = .................................... [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/12/O/N/17

Cambridge International Examinations Cambridge Ordinary Level

* 7 5 3 3 4 2 4 5 0 6 *

4024/21

MATHEMATICS (SYLLABUS D)

October/November 2017

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 19 printed pages and 1 blank page. DC (CW/AR) 136659/1 © UCLES 2017

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2

Section A [52 marks] Answer all questions in this section. 1

(a) (i) Jasmine earns $12.50 for each hour she works. She works for 38 hours each week. She is given a pay increase of 6%. Calculate the total amount Jasmine earns each week after the pay increase.

Answer $ ......................................... [3] (ii) Abdul earns $525 each week. He moves to a new job where he earns $462 each week. Calculate the percentage reduction in his earnings in his new job.

Answer ...................................... % [2] (iii) Maria is given a pay increase of 3%. After the pay increase, she earns $2472 each month. Calculate her monthly pay before the pay increase.

Answer $ ........................................ [2]

© UCLES 2017

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3

(b) The exchange rate between dollars ($) and pounds (£) is $1 = £0.65 . The exchange rate between euros (€) and pounds is €1 = £0.74 . Dan changes €520 into pounds. He spends £260 and then changes the rest into dollars. Work out how many dollars he receives.

Answer $ ........................................ [3]

© UCLES 2017

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4

2

Sunil recorded the lengths, in minutes, of the 150 phone calls he made one month. His results are summarised in the table. Length of call (t minutes) Frequency

01tG5

5 1 t G 10

10 1 t G 20

20 1 t G 30

30 1 t G 50

35

42

30

28

15

(a) Calculate an estimate of the mean length of a call.

Answer ............................. minutes [3] (b) On the grid below, draw a histogram to represent this data.

Frequency density

0

0

10

20

30

40

50

Length of call (t minutes) [3] (c) Find an estimate for the percentage of Sunil’s calls that were longer than 25 minutes.

Answer ...................................... % [2]

© UCLES 2017

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5

3 B

North

25 A 220°

38 C The diagram shows the positions of three towns, A, B and C. B is due north of A and the bearing of C from A is 220°. AB = 25 km and AC = 38 km. (a) Find the bearing of A from C. Answer ........................................... [1] (b) Show that BC = 59.4 km correct to 3 significant figures.

[3] (c) Calculate the bearing of C from B.

Answer ........................................... [4] © UCLES 2017

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6

4

Adam has a bag containing 9 balls, numbered from 1 to 9. (a) Adam takes a ball at random from the bag and replaces it. Find the probability that the ball has an odd number.

Answer ........................................... [1] (b) Adam takes a ball from the 9 balls in the bag, notes the number and replaces it. He then takes a second ball from the bag, notes the number and replaces it. (i) Work out the probability that both numbers are odd.

Answer ........................................... [1] (ii) Work out the probability that one number is odd and the other is even.

Answer ........................................... [2] (c) Adam now takes two balls from the 9 balls in the bag, without replacement. Work out the probability that the two numbers are either both odd or both even.

Answer ........................................... [3]

© UCLES 2017

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7

5

(a) Solve

y 2 = . 2y + 3 y + 5

Answer y = ................. or ................. [3] (b) Make t the subject of the formula p =

4t + 1 . 2-t

Answer ........................................... [3] (c) Simplify fully

2

3x - 14x + 8 . x 2 - 16

Answer ........................................... [3]

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6

(a)

B

C 68° O 52°

F

D

A E A, B, C, D and E are points on the circumference of the circle, centre O. AC is a diameter and AC is parallel to ED. AC and BE intersect at F. t = 52° and CBE t = 68°. BAC t . (i) Find ACB

t = ........................................... [1] Answer ACB t . (ii) Find AEF Give a reason for your answer. t = ....................... because ............................................................................... [1] Answer AEF t . (iii) Find CDE

t = ........................................... [1] Answer CDE t . (iv) Find BCD

t = ........................................... [2] Answer BCD

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(b) 124° 3x°

2x°

x°

2x°

Work out the size of the largest angle in the pentagon.

Answer ........................................... [3] (c) y° 57° 65°

131°

The angles in the quadrilateral are given correct to the nearest degree. Find the lower bound for the value of y.

Answer ........................................... [2]

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Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a) (i) The points (4, -3) and (0, 5) lie on the line L. Find the equation of line L.

Answer ........................................... [2] (ii) The line M is parallel to line L and passes through the point (-2, 3). Find the equation of line M.

Answer ........................................... [2] (b) The table below shows some values of x and the corresponding values of y for y = x + x

0.5

1

1.5

2

3

4

5

y

3.5

1

0.5

0.5

1

1.75

2.6

(i) Complete the table.

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(ii) Using a scale of 2 cm to 1 unit on both axes, draw a horizontal x-axis for 0 G x G 7 and a vertical y-axis for 0 G y G 4. Draw the graph of y = x +

3 - 3 for 0.5 G x G 6. x

[3] (iii) By drawing a tangent, estimate the gradient of the curve at (1, 1).

Answer ........................................... [2] (iv) Use your graph to solve the equation x +

3 = 5. x

Answer x = ................. or ................. [2]

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8

[Volume of a cone =

1 2 rr h] 3

[Curved surface area of a cone = rrl ] [Volume of a sphere =

4 3 rr ] 3

[Surface area of a sphere = 4rr2]

x 18

6

The diagram shows solid A which is made from a hemisphere joined to a cone of equal radius. The hemisphere and the cone each have radius 6 cm. The total height of the solid is 18 cm. (a) Show that the slant height, x cm, of the cone is 13.4 cm, correct to 1 decimal place.

[2] (b) Calculate the total surface area of solid A.

Answer ................................... cm2 [3]

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(c) Calculate the volume of solid A.

Answer ................................... cm3 [3] (d) Solid A is one of a set of three geometrically similar solids, A, B and C. The ratio of the heights of solid A : solid B : solid C is 2 : 6 : 1. (i) Calculate the surface area of solid B correct to 3 significant figures.

Answer ................................... cm2 [2] (ii) Calculate the volume of solid C correct to 3 significant figures.

Answer ................................... cm3 [2]

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9

(a) A pump takes 12 minutes to add 3000 litres of water to a pond. How long will it take the same pump to add 1750 litres of water to a pond?

Answer ............................. minutes [2] (b) A tank holds 2500 litres of oil. A small pump can add oil to the tank at a rate of x litres per minute. A large pump can add oil to the tank at a rate of (x + 20) litres per minute. (i) Write down an expression, in terms of x, for the number of minutes the small pump takes to fill the empty tank.

Answer ........................................... [1] (ii) It takes 15 minutes longer to fill the empty tank using the small pump than it does with the large pump. Form an equation in x and show that it simplifies to 3x2 + 60x - 10 000 = 0.

[3]

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(iii) Solve the equation 3x2 + 60x – 10 000 = 0. Give each answer correct to 2 decimal places.

Answer  x = ...................... or ...................... [3] (iv) Find the length of time the large pump takes to fill the empty tank. Give your answer in minutes and seconds, correct to the nearest second.

Answer .............. minutes .............. seconds [3]

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10 (a) Triangle A is shown on the grid. y 10 9 8 7 6 5 4 3 2 A

1 –6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

8

x

–1 –2 –3 –4 –5 –6 (i) Triangle A is mapped onto triangle B by a rotation of 180° about point (2, -1). Draw and label triangle B on the grid. (ii) Triangle A is mapped onto triangle C by the transformation J3 0N OO . represented by the matrix KK 0 3 L P Draw and label triangle C on the grid.

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[2]

[2]

17

(iii) Write down the matrix that represents the transformation that maps triangle C onto triangle A.

Answer

J K K K L

N O O O P

[1]

(iv) Describe fully the single transformation that maps triangle C onto triangle B. .................................................................................................................................................... ............................................................................................................................................... [3] (b) The diagram shows triangle PRS. R

Q

P S Q is the midpoint of PR. J6N J 8N PQ = KK OO and PS = KK OO . L3P L- 2P (i) Find SR.

Answer

J K K K L

N O O O P

[2]

Answer

J K K K L

N O O O P

[2]

(ii) T is the point on SR such that ST : TR = 1 : 3. Find PT .

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11 A

B

R D

P

C

Q

ABCD is a rectangle. P and Q are points on DC. AQ and BP intersect at R. (a) Prove that triangle ARB is similar to triangle QRP. Give a reason for each statement you make. ................................................................................................................................................................... ................................................................................................................................................................... ................................................................................................................................................................... ................................................................................................................................................................... .............................................................................................................................................................. [3]

(b) 9

A

B

55°

35°

5 R D

P

Q

C

In rectangle ABCD, AB = 9 cm and AD = 5 cm. t = 55°, CBP t = 35° and AQ is perpendicular to BP. DAQ (i) Calculate AQ.

Answer .................................... cm [2]

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(ii) Calculate AR.

Answer .................................... cm [2] (iii) Calculate the area of triangle ARB.

Answer ................................... cm2 [2] (iv) Calculate the total area shaded in the rectangle.

Answer ................................... cm2 [3]

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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

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Cambridge International Examinations Cambridge Ordinary Level

* 2 1 9 8 1 4 2 6 5 3 *

4024/22

MATHEMATICS (SYLLABUS D)

October/November 2017

Paper 2

2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials:

Geometrical instruments Electronic calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

This document consists of 23 printed pages and 1 blank page. DC (CW/AR) 136654/1 © UCLES 2017

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Section A [52 marks] Answer all questions in this section. 1

(a) Sara buys a new car. The cash price of the car is $4500. She can pay for the car using option A or option B. Option A

Option B

1 of the cash price 5 then 12 monthly payments of $340

Pay 12% of the cash price then 24 monthly payments of $195

Pay

Which option is cheaper and by how much?

Answer Option .......... is cheaper by $ ................. [4] (b) Sara’s car uses 5.2 litres of petrol for each 100 km she drives. Petrol costs $0.85 per litre. Sara drives 240 km. Calculate the cost of the petrol used for this journey. Give your answer correct to the nearest cent.

Answer $ ......................................... [3]

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(c) Sara pays a total of $322 for her car insurance. This total is made up of a basic charge plus 15% sales tax. Calculate the amount of sales tax that Sara pays.

Answer $ ......................................... [3]

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2

A company asked their employees how long they took to travel to work one day. The table summarises the times for 120 employees. Time (t minutes)

0 1 t G 20

20 1 t G 40

40 1 t G 60

60 1 t G 80

80 1 t G 100

Frequency

12

28

45

22

13

(a) (i) Complete the cumulative frequency table below. Time (t minutes)

tG0

Cumulative frequency

0

t G 20

t G 40

t G 60

t G 80

t G 100 120 [1]

(ii) On the grid, draw a smooth cumulative frequency curve to represent these results. 120

100

80 Cumulative frequency 60

40

20

0

0

20

40 60 Time (t minutes)

80

100 [2]

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(b) Use your curve to estimate (i) the median time,

Answer ............................. minutes [1] (ii) the interquartile range of the times.

Answer ............................. minutes [2] (c) Calculate an estimate of the mean time taken for the employees to travel to work.

Answer ............................. minutes [3]

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3

Anya makes T-shirts. The matrix, M, shows the number of T-shirts of different types she makes in one week. Small Medium Large J10 25 30N Men OO M = KK 20 40 25 L P Women (a) Anya sells all of these T-shirts to a shop. She charges $5 for each small T-shirt, $6 for each medium T-shirt and $8 for each large T-shirt. Represent these amounts in a 3 # 1 column matrix N.

Answer N =

[1]

Answer P =

[2]

(b) (i) Work out P = MN.

(ii) Explain what the elements in matrix P represent.

Answer ....................................................................................................................................... ............................................................................................................................................... [1]

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(c) The shopkeeper sells all sizes of men’s T-shirts at $10 each. He sells all sizes of women’s T-shirts at $9.50 each. He sells all of these T-shirts. (i) Work out (10

J10 9.50) KK L20

25 40

30N OO . 25P

Answer ........................................... [2] (ii) Work out the percentage profit the shopkeeper makes when he sells all of the T-shirts.

Answer ....................................... % [3]

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4

(a) Triangle A is shown on the grid. y 10 9 8 7 6 5 4 3 2 A

–6

–5

–4

–3

1 –2

–1

0

1

2

3

4

5

6

7

8

x

–1 –2 –3 –4 –5 –6 J 7N (i) Triangle A is mapped onto triangle B by a translation of KK OO . L- 5P Draw and label triangle B on the grid.

[2]

(ii) Triangle A is mapped onto triangle C by an enlargement scale factor -2, centre (-1, 2). Draw and label triangle C on the grid.

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[2]

9

(b) Triangle P is shown on the grid. y 10 9 8 7 6 5 4 3 2

P

1 –2

–1

0

1

2

3

4

5

6

7

8

9

10 x

J3 0N OO . The stretch S is represented by the matrix KK 0 1 P L Triangle P is mapped onto triangle Q by the stretch S. (i) On the grid above, draw and label triangle Q.

[2] (ii) Describe fully the stretch S. .................................................................................................................................................... ............................................................................................................................................... [2]

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5

(a) Express as a single fraction in its simplest form

4 5 . x-2 x+1

Answer ........................................... [2] (b) Solve 2x(x + 1) = 3(4 - x) .

Answer x = ................. or ................. [3]

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(c) Anil and Yasmin buy some pens and notebooks from the same shop. Anil buys 3 pens and 2 notebooks for $4.80 . Yasmin buys 5 pens and 4 notebooks for $9.00 . (i) Form a pair of simultaneous equations to represent this information.

[1] (ii) Solve the simultaneous equations to find the cost of a pen and the cost of a notebook.

Answer

Cost of pen = $ .................

Cost of notebook = $ .................[3]

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6

(a)  = {x : x is an integer and 10 G x G 20} A = {x : x is an odd number} B = {x : x is a multiple of 5} (i) Find n(A + B).

Answer ........................................... [1] (ii) Find A′ , B.

Answer ........................................... [1] (iii) A number, r, is chosen at random from . Find the probability that r ! A , B.

Answer ........................................... [1]

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(b) In a survey, 40 people were asked what they had read that day. • • •

A total of 10 people had read a book A total of 24 people had read a newspaper 14 people had read neither a book nor a newspaper

(i) By drawing a Venn diagram, or otherwise, find the number of people who had read both a book and a newspaper.

Answer ........................................... [2] (ii) Two of the 10 people who had read a book are selected at random. Work out the probability that they had both read a book and a newspaper.

Answer ........................................... [2]

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Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7

(a) The variables x and y are connected by the equation y = 3 + x -

x2 . 2

Some corresponding values of x and y are given in the table below. x y

-3

-2

-1

0

1

2

3

4

-1

1.5

3

3.5

3

1.5

-1

(i) Complete the table.

5

[1]

(ii) Using a scale of 2 cm to 1 unit, draw a horizontal x-axis for -3 G x G 5. Using a scale of 1 cm to 1 unit, draw a vertical y-axis for -5 G y G 5. Draw the graph of y = 3 + x -

x2 for -3 G x G 5. 2

[3] (iii) By drawing a tangent, estimate the gradient of the curve at (3, 1.5).

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(iv) The points of intersection of the graph of y = 3 + x -

x2 and the line y = k are 2

the solutions of the equation 10 + 2x - x 2 = 0 . (a) Find the value of k.

Answer ........................................... [1] (b) By drawing the line y = k on your graph, find the solutions of the equation 10 + 2x - x 2 = 0 . Answer ........................................... [2] (b) This is a sketch of the graph of y = pax, where a 2 0. The graph passes through the points (0, 4) and (2, 36). y

(2, 36) (0, 4) x

O (i) Write down the value of p.

Answer ........................................... [1] (ii) Find the value of a.

Answer ........................................... [1] (iii) The graph passes through the point (4, q). Find the value of q.

Answer ........................................... [1]

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8 A B E

O y°

D

F X

G

C The diagram shows two circles each with centre O. A, B, C and D are points on the circumference of the large circle. E, F and G are points on the circumference of the small circle. CGD and CFB are tangents to the small circle. Lines AEOC and FG intersect at 90° at X. t = y° . GOX (a) Find each of these angles, as simply as possible, in terms of y. Give reasons for your answers. (i)

t GEO

t = ............................ because .............................................................................. Answer GEO ............................................................................................................................................... [2] (ii)

t GCX

t = ............................ because .............................................................................. Answer GCX ............................................................................................................................................... [2] (iii)

t DAB

t = ............................ because .............................................................................. Answer DAB ............................................................................................................................................... [2] © UCLES 2017

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(b) Complete the sentence. Triangle EGC is congruent to triangle ................. .

[1]

(c) Prove that triangle ADC is similar to triangle OGC. Give a reason for each statement you make.

................................................................................................................................................................... ................................................................................................................................................................... ................................................................................................................................................................... .............................................................................................................................................................. [2]

(d) What special type of quadrilateral is AOGD? Answer ........................................... [1] (e) Find the ratio (i) area of triangle OGC : area of triangle ADC,

Answer ..................... : ...................... [1] (ii) area of triangle OGC : area of quadrilateral ABCD.

Answer ..................... : ...................... [1]

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9

(a) The ventilation shaft for a tunnel is in the shape of a cylinder. The cylinder has radius 0.4 m and length 15 m. Calculate the volume of the cylinder.

Answer ..................................... m3 [2] (b) The diagram shows the cross-section of the tunnel.

O 4.5

110°

A

B

The cross-section of the tunnel is a major segment of a circle, centre O. t = 110°. The radius of the circle is 4.5 m and AOB Calculate the area of the cross-section of the tunnel.

Answer ..................................... m2 [4]

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(c) The length of the tunnel is 1750 m. A car drives through the tunnel at an average speed of 45 km/h. Work out the time the car takes to travel through the tunnel. Give your answer in minutes and seconds.

Answer

....... minutes ....... seconds [2]

(d) The diagram shows the position of the tunnel entrance, T, and two road junctions, P and Q, on horizontal ground. North Q 720

T P

62°

450

Q is due north of P and T is on a bearing of 062° from P. PT = 450 m and QT = 720 m. Calculate the bearing of T from Q.

Answer ........................................... [4]

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10 A rectangular picture, ABCD, is placed inside a rectangular frame. 2

A

B x

2 D

2

2 C

The length, AB, of the picture is three times its height, x cm. The width of the frame is 2 cm. (a) The total area of the picture and the frame is 476 cm2. Form an equation in x and show that it simplifies to 3x2 + 16x - 460 = 0 .

[4] (b) Solve the equation 3x2 + 16x - 460 = 0 .

Answer

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x = ...............  or ............... [3]

21

(c) Find the height and length of the frame.

Answer

Height = ..................... cm Length = ..................... cm [2]

(d) The frame is made from wood. The wood is 5 mm thick. The mass of 1 cm3 of the wood is 0.7 g. Calculate the mass of wood used in the frame.

Answer ....................................... g [3]

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11 X

P

D

C Y

A

B

A vertical mast, XY, is positioned on horizontal ground. The mast is supported by four cables attached to the mast at P and to the ground at points A, B, C and D. Y is the centre of the square ABCD. PY = 7.50 m. (a) Given that AB = 3.65 m, show that AY = 2.58 m correct to 3 significant figures.

[3] (b) Calculate the length of one of the cables used to support the mast.

Answer ...................................... m [2]

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t . (c) Calculate APB

Answer ........................................... [3] (d) The angle of elevation of X from A is 77.0°. (i) Calculate the height, XY of the mast.

Answer ...................................... m [2] (ii) Calculate the angle of elevation of X from the midpoint of AB.

Answer ........................................... [2]

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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2017

4024/22/O/N/17