11+ Maths Worksheets -

Zc 11 + Practice Worksheets 100 Maths Worksheets for children aged 10-11 4² - 2² - 1² = 11

X - 11 = 0

£11.00 shared in a ratio 9:2

( 15 + 6) - 10 = 11

Includes: Place value Addition and Subtraction Multiplication and Division Factors and Multiples Special Numbers Algebra Fractions, Decimals and Percentages Ratio and Proportion Probability Money Shape Transformations Measurement Time Multi-step Problems Handling Data

Answers Included © C. Diamond – not for resale

1

Contents 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Place value Addition Subtraction Multiplication Division Factors and Multiples Special Numbers Number Sequences Algebra Fractions Decimal Fractions Percentages Fractions Decimals and Percentages Ratio and Proportion Probability Mean, median, mode and range Shape Transformations Measurement Time Money Multi-step problems Handling Data Answers End

Page 3 9 11 13 16 21 23 27 29 34 42 47 51 52 54 56 57 71 75 81 85 89 98 103 114

2

Place value 1 What is the value of the blue digits? 1.

467,921

2.

61,309

3.

235,262

4.

13,263

5.

49,736

6.

170,134

7.

5,179,241

8.

3,825,721

60,000

Write these numbers out in words. 9.

23,145

Twenty three thousand,______________________

10. 3,215 11. 41,631 12. 903,282 Write these numbers in figures. 13. 14.

Twelve thousand, two hundred and sixteen Forty six thousand, two hundred and forty three

15. Six hundred and ten thousand, two hundred and two 16.

Fifty nine thousand, seven hundred and thirty three

3

Place value 2 1. Multiply these numbers by 10. a. 40

b. 700

c. 0.9

2. Multiply these numbers by 1000. a. 67

b. 2.6

c. 12.56

3.

Multiply these numbers by 20.

a.

45

b. 300

c.

3.1

c.

2.6

c.

1·1

4. Multiply these numbers by 50. b. 30

b. 200

5.

Multiply these numbers by 60.

b.

80

6.

Which of these numbers is not a multiple of 15? Circle the correct letter.

b. 400

a. 60 b. 45 7.

c. 90

d. 50

e. 105

Which of these numbers is not a multiple of 25? Circle the correct letter. b. 100 b. 170

c. 250

d. 375

e. 900

4

Place value 3 1. Divide these numbers by 10. a. 300

b. 900

c. 3.0

2. Divide these numbers by 100. a. 9,000

b.

50

c. 6.0

3. Divide these numbers by 20. a.

200

b. 1,200

c.

10

c.

10

4. Divide these numbers by 50. a. 400

b. 750

5. Divide these numbers by 1000. a. 500

b. 205

c. 40.1

6. How many times must you subtract 0·02 from these numbers to make 0? a.

2

b. 20

c. 0.2

7. How many times must you add 0.05 to 0 to make 5? 8. How many hundreds equal 40 tens? 9. How many thousands equal 60 hundreds?

5

Place Value 4 1. Round 678 to the nearest 10. 2. Round 9,875 to the nearest 100. 3. Round 672,351 to the nearest 1000. 4. Round 45.876 to the nearest tenth. 5. Round 678,456 to the nearest: a. 10 _________ b. 100 ____________ c. 1000 _________ d. 10 000 _____________ 6. Round 764.258 to the nearest: a. tenth _________ b. hundredth ___________ 7. Round 1,856,292 to the nearest: a. 10 _________ b. 100 _____________ c. 1000 _________ d. 10 000 _____________ 8. Round 148.2834 to the nearest: a. tenth _________ b. hundredth ___________ c. thousandth ____________________ 9. What is the value of 3 in these numbers: a. 431,456 _______________________________ b. 2.43 _______________________________ c. 0.356 _______________________________ d. 3,000,258 _______________________________ e. 2,307,489 _______________________________ f. 56.893 _______________________________ g. 457,463 _______________________________ 6

Place Value 5 1. What number is the arrow pointing to? Circle the correct letter. 6.8

6.9

a.

6.95

b.

6.89

c.

6.98

d.

7.78

e

6.99

7.0

7.1

2. What number is the arrow pointing to? Circle the correct letter. 0.82

a.

0.95

b.

0.905

c.

0.915

d.

0.9055

e.

0.9005

0.85

0.9

7

Place Value 6 1.

7.41673 What is this number correct to two decimal places? Circle the correct letter.

a.

7.40

b.

7.4

c.

7.05

d.

7.42

e.

7.41

2. Which of these numbers does not give the answer 5.22 when rounded to two decimal places. a. 5.2203 b. 5.2135 c. 5.2198 d. 5.2153 e. 5.2244 3.

987.79663 What is this number when rounded to 1 decimal place? Circle the correct letter.

a. 987.0 b. 9

c. 987.7 d. 987.8

e. 9.8 8

Addition 1 Answer these different types of addition questions. 1. a. b. c. d. e.

Look for pairs of numbers that add up to a multiple of 10: 17 + 13 + 45 = 30 + 45 = ____________________ 19 + 27 + 51 = ____________________________ 38 + 52 + 35 = ____________________________ 246 + 354 + 238 = _________________________ 411 + 543 + 279 = _________________________

2. What is the sum of 278 and 476? ______________ 3. If there are 3462 red pens and 2579 blue pens. How many pens are there altogether? ___________ 4. If 693 is increased by 892. What is the total? ___________________________ 5. What is 7352 plus 425? ______________________ 6. If Jane spends £31.28 and £48.56. How much does she spend altogether?____________ 7. a. 23 + 17 + 49 = _________________________ b. 19 + 27 + 51 = _________________________ c. 241 + 304 + 132 = _______________________ 8. Increase £5.99 by £3.50 ______________________ 9. Underline the correct answer to 934.78 plus 778.56? a. 1713.44 b. 1713.54 c. 1713.53 d. 1713.34 e. 1714.13 9

Addition 2 Answer these addition questions involving money. Round up calculations involving 99p to make them easier to work out in your head. Then adjust by 1p. 1. a. £1.99 + £3.50 = ___________________________ b. £2.76 + £5.99 = ___________________________ c. £38.28 + £7.99 = ___________________________ d. £206.19 + £35.99 = ________________________ e. £347.56 + £76.99 = _________________________ Round up or down these numbers to add them up then adjust to deal with the difference. 2. a. 4.49 + 3.60 ______________________________ b. 7.01 + 8.25 ______________________________ c. 55.98 + 7.26 ______________________________ d. 24.48 + 33.83 _____________________________

3. Underline the correct answer to 34·99 plus 56·49? a. 91.52 b. 91.58 c. 92.48 d. 92.51

e. 91.48

10

Subtraction 1 Answer these different types of subtraction questions. 1. a. b. c. d. e.

967 - 345 1002 - 678 782 - 326 2001 - 473 4103 - 543

= ____________________________ = ____________________________ = ____________________________ = ____________________________ = ____________________________

2. Deduct 578 from 1476 ____________________ 3. If a rope is 1453m long and a wall is 671m long, how much longer is the rope than the wall? ________ 4. If 9234 is decreased by 452, what is the amount remaining? __________________ 5. What is 6382 minus 425? ______________________ 6. If Matt has £301.50 and spends £48.36, how much does he have left?____________________ 7. Find the difference between 2345 and 1672. _____________________________________________ 8. Decrease £5.34 by £1.99 ______________________ 9. Underline the correct answer to 856.34 minus 277.59? a. 578.75 b. 577.76 c. 578.74 d. 578.65 e. 579.13

11

Subtraction 2 Answer these subtraction questions involving money. Round up calculations involving 99p to make them easier to work out in your head. Then adjust by 1p. 1. a. £10.99 - £4.50 = ________________________ b. £12.99 - £3.60 =

________________________

c. £38.62 - £8.99 =

________________________

d. £106.81 - £38.99 = ________________________ e. £246.99 - £73.43 = ________________________ Round up or down these numbers to subtract them then adjust to deal with the difference. 2. a. 12.49 - 3.21 ______________________________ b.

9.01 - 6.32 ______________________________

c. 78.98 - 7.84 ______________________________ d. 99.99 - 75.01 ______________________________

3. Underline the correct answer to 67·99 minus 24·68? a. 43.32 b. 43.31

c. 44.31

d. 45.51

e. 44.51

12

Multiplication 1 Answer these different types of multiplication questions. 1. a. 2 × 3 ×____ = 24 b. 5 × 4 ×____= 80 c.

4 × 2 ×____ = 48

d.

9 × 3 × 2 = _____

e.

___× 4 × 6 = 72

f.

2 × 4 ×____ = 160

2. Find the length of 5 bricks that are each 6.35cm long. ____________________________________________ 3. Multiply 2 litres 400ml by 3. ____________________ 4. What is the product of 7 and 15? _________________ 5. Find the cost of 6 apples at 37p each? _____________ 6. A game costs £4.25. How much would 5 games cost? Answer _____________________________________ 7. There are 300 oranges in a box. How many oranges are in 130 boxes? Answer _____________________________________ 8. There are 46 sweets in a bag. How many sweets are in 16 bags? Answer _____________________________________ 9. Underline the correct answer to 8 multiplied by 29.17? a. 27.36 b. 217.36 c. 218.36 d. 417.35 e. 233.36 13

Multiplication 2 Use the grid method to multiply these numbers. Example 234×26 = 6084 = 200 30 4 = 4000 1200 4680 20 4000 + 600 + 180 + 1404 600 80 + 80 + 24 6084 180 24 6 1200 4680 1404 1.

523×28 =

2.

615×36 =

3.

451×43 =

4.

Find the product of 164 and 81. ______________

5.

Multiply 670 by 35. _______________________

6.

Find the product of 247 and 56. ______________

14

Multiplication 3 Answer these different types of multiplication questions. 1.

4×4×4= ?

What does the ? stand for? Circle the correct letter. a. 3 × 4

b. 4²

c. 3 × 3 × 3 × 3

d. 4³

e. 32

2. Multiply 1 kg 700 g by 5. ____________________ 3. Find the cost of 8 cakes at 56p each? ____________ 4. There are 400 paper clips in a bag. How many paper clips are in 90 bags? Answer ____________________________________ 5. Underline the correct answer to 5 multiplied by 37.03? a. 155.5

b. 175.25 c. 185.15 d. 185.5 e. 175.15

6. Which of these numbers is not a multiple of 15? Circle the correct letter. a. 190

b. 45

c. 150

d. 105

e. 135

7. 5 × 5 × 5 = ? What does ? stand for? Circle the correct letter. a. 625

b. 3 × 5

c. 3 5

d. 5 3

e. 130

15

Division 1 Answer these different types of division questions. 1. How many 23p pencils can you buy for £1l.50? ___________________________________________ 2. 7200 ÷ 8 = __________________________________ 3. Divide 1800 by 45. ____________________________ 4. The product of two numbers is 608. If one of the numbers is 32, what is the other? Answer _____________________________________ 5. How many 25 cm strips can be cut from an 8 m tape? ___________________________________________ 6. What is the smallest number divisible by 2, 3 and 5? Answer ____________________________________ 7. There are 4000 marbles in a box. How many bags containing 50 marbles can they fill? Answer ____________________________________ 8. Partition 810 into 9 sets. Answer ____________________________________ 9. Underline the correct answer to 50·6 divided by 1·1? a. 45.01

b. 67

c. 45.6

d. 46

e. 450

16

Division 2 Answer these different types of division questions. 1. Underline number that is exactly divisible by 7 and 8? a. 336

b. 315

c. 290

d. 720

e. 450

2. What is the answer when 355 is divided by 5? Answer ___________________________________ 3. A box can hold 36 cakes. How many boxes are needed to hold 396 cakes? Answer ____________________________________ 4. The product of two numbers is 814. If one of the numbers is 11, what is the other? Answer ____________________________________ 5. What is the answer when 376 is divided by 4? Answer_____________________________________ 6. What is the smallest number divisible by 2, 5, and 7? Answer _______________________________ The number you get when you divide one number by another is called a quotient. 7. What is the quotient when 648 is divided by 18? Answer ____________________________________ 8. Underline the quotient for this division calculation: 4200 ÷ 60: a. 70 b. 7 c. 700 d. 100 e. 7000

17

Division 3 Answer these different types of division questions. Some of them have a remainder which needs to be taken into account. 1. How many 42p pens can you buy for £12.25? ___________________________________________ 2. 9900 ÷ 30 = _________________________________ 3. Divide 3200 by 800. ___________________________ 4. A coach can carry 25 people. How many journeys must it make to transport 412 people to the theatre? Answer ____________________________________ 5. Split 2200 into 8 equal amounts? Answer_____________________________________ 6. A cook bakes 270 cup cakes. She puts the same number of cakes on each plate. If she uses 15 plates, how many cakes are on each plate? Answer ____________________________________ 7. 8400 ÷ 40 = _________________________________ 8. Divide 9600 by 300. ___________________________

18

Division 4 Answer these different types of division questions. Some of them have a remainder which needs to be taken into account. 1. Iced buns come in packs of eight Mark has 152 iced buns. How many packs can he fill? Answer___________________________________ 2. What is the answer when 6.9 is divided by 0.3? Answer___________________________________ 3. What is the answer when 8.4 is divided by 0.2? Answer ___________________________________ 4. A mini bus can hold 12 passengers. How many mini buses are needed to transport 150 children? Answer ___________________________________ 5. What is 176 ÷ 6 to two decimal places? Answer ___________________________________ 6. What is the answer when 980 is divided by 4? Answer ___________________________________

19

Factors and Multiples 1 A factor is a whole number that will divide exactly into another number. Find the highest common factor (HCF) of these numbers. You will need find all the factors of each number and see which is the largest one they share. 1. Find the HCF of 27, 36 and 45. The factors of 27 are: 1,3,9,27 The factors of 36 are: _____________________ The factors of 45 are: _____________________ The HCF of 27, 36 and 45 is________________ 2. Find the HCF of 24, 32 and 48. The factors of 24 are: _____________________ The factors of 32 are: _____________________ The factors of 48 are: _____________________ The HCF of 24, 32 and 48 is________________ 3. Find the HCF of 60, 84 and 144. _________________________________________ _________________________________________ _________________________________________ Answer ___________________________________ 4. Find the HCF of 21, 56 and 84. _________________________________________ _________________________________________ _________________________________________ Answer ___________________________________ 5. Find the HCF of 24, 88 and 100. __________________________________________ __________________________________________ __________________________________________ Answer ___________________________________ 20

Factors and Multiples 2 A prime factor is a factor which is only divisible by itself or 1. Examples a. What are the Prime factors of 42? The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. 1, 2, 3 and 7 are all prime numbers so they are the prime factors of 21. 6, 14, 21 and 42 are not prime numbers. Answer 1, 2, 3 and 7. b. Express 28 in prime factors. 2 × 2 × 7 = 28 Answer 2, 2 and 7.

1. What are the prime factors of 70? ________________________________________ 2. What are the prime factors of 55? _________________________________________ 3. Express 45 in prime factors. _________________________________________ 4. Express 39 in prime factors. __________________________________________ 5. Express 54 in prime factors. __________________________________________ 21

Factors and Multiples 3 A multiple is the answer when a number is multiplied by another number. Find the lowest common multiple (LCM) of these numbers. If there are two numbers multiply them together. For three numbers start by writing down the first five multiples of the highest number. Check if one of these is a multiple of all the other numbers. If it’s not try more numbers until you find the LCM. 1. Find the LCM of 4, 5 and 10. The multiples of 10 are: 10,20,30,40,50 The multiples of 5 are: _____________________ The multiples of 4 are: _____________________ The LCM of 10, 5 and 4 is________________ 2. Find the LCM of 4, 6 and 9. The multiples of 4 are: _____________________ The multiples of 6 are: _____________________ The multiples of 9 are: _____________________ The LCM of , 4, 6 and 9 is________________ 3. Find the LCM of 10, 12 and 15. _________________________________________ _________________________________________ _________________________________________ Answer ___________________________________ 4. Which multiples of 8 are greater than 50 and less than 80. _________________________________________ 5. What is the LCM of 7 and 8? ___________________

22

Special Numbers 1 A square number is a number multiplied by itself. 3 × 3 = 3² means 3 squared = 9 The small number is known as the index number. A cube number is a number multiplied by itself twice. 3 × 3 × 3 = 3³ means 3 cubed = 27 Answer these questions involving square and cube numbers. 1.

1² + 5² = ______

2.

3² + 4² = ______

3.

6² + 2² = _______

4. 8² - 5² = ______

5.

4³ + 2³ = _______

6. 5³ - 2³ ________

A prime number has only two factors itself and 1. The first 20 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71. Answer these questions involving prime numbers. 7. James thinks of a prime number, he multiplies it by 3 and subtracts 4. His answer is 17. What number did James think of first? ___________ 8. What is the 21st prime number? _________________ 9. Underline the prime numbers? 17

27

49

79

81

97

93 23

Special Numbers 2 A square root of a number is the number that you multiply by itself to make that number. The square root of 16 is 4 because 4 × 4 = 16. The symbol for a square root is: √. So, the square root of 25 is written as √25. Answer these questions involving square roots. 1.

√4 = _______

2.

√36 = _______

3.

√64 = _______

4.

√100 = _______

5.

√81 = _______

6.

√49 = _______

7.

√9 +√16 = _______

8. √100 -√25 = ______

9. Add 6² to √81 = ____________________________ 10. Which prime number is the same as √25 + √4? ____ 11. Which square number is the same as √36 added to 5² added to the third prime number? ______________ 12. Subtract the square root of 64 from 9 squared _____ 13. Multiply √16 by 3² = _________________________ 14. Multiply √9 by √81= _________________________ 15. Divide √36 by √9 = _________________________ 24

Special Numbers 3 The values of some Roman Numerals are: 1= I 2= II 3= III 4= IV 5= V 6= VI 7= VII 8= VIII 9= IX 10= X 11= X1 12= XII 13= XIII 14= XIV 15=XV 16= XVI 17= XVII 18= XVIII 19= XIX 20 =XX 70 =LXX 30= XXX 40= XL 50= L 60= LX 80= LXXX 90= XC 100= C 500= D 1000=M You can make up make up numbers by combining numbers. For example 219 = 200 +10 + 9 CCXIX Answer these Roman numeral questions. 1.

XX1 = _________

2.

DX = ___________

3.

XLIV = _________

4.

CL = ___________

5.

DCI = _________

6.

DCCL= ___________

Answer these questions in Roman numerals. 7.

75 = __________

8.

99 = ____________

9.

555 = __________

10.

1040 = ____________

11.

Mark was born in the year MMIV. How old was he in 2011? _____________________

12. V11+ IX = _______

13. X11 + IV = _________

14. XXX – 1V =_______

15. C – L = ____________ 25

Special Numbers 4 A negative number on a number line is less than zero. -16

-20

-12

-8

-4

0

4

8

12

16

20

Answer these negative numbers questions. 1.

The average temperature was recorded for five days at Les Gets ski resort. Which is the coldest temperature? Underline the correct letter.

a. -5ºC 2. -0.6

b. 3ºC

c. -4ºC

d. 0ºC

e. -1ºC

What number does the arrow point to? -0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Underline the correct letter. a. 3.

-0.51

b. -0.45

c. -0.41

d. -0.55

e. -0.425

A scientist has two liquids. One freezes at -2ºC the other freezes at a temperature 9 degrees colder. At what temperature does the second liquid freeze? Underline the correct letter.

a. -7ºC b. -10ºC

c. -12ºC

d. -11ºC

e. 7ºC

26

Number Sequences 1 To find the missing number in a sequence, you need to find different numbers in the sequence. Some patterns go up and others go down. Some patterns go alternately or in pairs. Other patterns are: Odd numbers: 1, 3, 5, 7… Even numbers: 2, 4, 6, 8 … Prime numbers: 2, 3, 5, 7 … Double numbers: 4, 8, 16, 32 … Multiples: 5, 10, 15, 20… Halving numbers: 80, 40, 20, 10 … Square numbers: 4, 9, 16, 25 … 1 1 3 Fractions: 4 , 2 , 4 , 1… , Decimals: 0.1, 0.15, 0.2, 0.25 … 1 Some sequences have more than one rule: 5, 4, 7, 8, 9, 12, 11, 16… odd numbers and multiples of 4. 2, 2, 3, 4, 5, 8, 7, 16, 11… prime numbers and doubling. Complete these sequences. 1. 5, 6, 8,_____, 15, 20 2. 9, 11, 15, 23, 39, ____ 1

1

3

1

1

3. 6 4 , 7 2 , 8 4 , ____, 11 4 , 12 2, 4. 0.525, 1.05, 1.575, 2.1, 2.625, ____ 5. 5000, 500, 50, 5, 0.5, ____ 6.

14, 20, 17, 23, 20, 26, ____

7. 9, 2, 18, 4, 36, 6, ____ 27

Number Sequences 2 Complete these sequences. 1.

2, 5, 4, 7, 6, 9, ____

2. 4, 9, 16, 25, 36, ____ 3. 6, 13, 20, 27, 34, ____ 4.

1 8,

1 4,

19,

21, ____ 23, 1

5. 0.15, 0.30, 0.60, 1.20, 2.40, ___ How many dots are missing in the two missing patterns? Underline the correct letter. 6.

∙∙

a. 2, 8

∙ ∙ ∙ ∙ b. 9, 15

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

?

c. 6, 10

?

d. 5, 18 e. 6, 16

7.

∙ ∙ ∙ ∙∙ ∙∙ ∙∙ ∙∙∙ ∙∙∙ ∙∙∙∙ a. 12, 15

b. 12, 18

?

c. 15, 18

?

d. 18, 21 e. 15, 21

28

Algebra 1 Algebra is a part of mathematics in which symbols such as letters stand for numbers. You have to find the value of the missing number to solve the equation. An equation has an equals sign and both sides of the equals sign must balance. Example: 5 + b = 12 To make it balance b must equal 7. If there is a number next to a letter it is a short way of saying “multiplied by”. Example: 4c = 12 c=3

because 4 × 3 = 12

Equations sometimes have “divided by”. 12d Example: 12d ÷ 4 = 6 or 4 = 6 d= 2 Try solving these equations. 1. e – 7 = 10

Answer e = _____________

2. 18 ÷ f = 6

Answer f = _____________

3. 7g = 91

Answer g = _____________

4.

h 6 = 4

Answer h = _____________

5.

2i + 7 = 19

Answer i = _____________

6.

3j – 5 = 16

Answer j = _____________

29

Algebra 2 To help solve equations it is often useful to use the inverse operation on both sides of the equation. For add, subtract. For subtract, add. For multiply, divide. For divide, multiply. Examples: k – 8 = 14 add 8 to both sides of the equation. k - 8 + 8 = 14 + 8 3k = 42 3m ÷ 3 = 42 ÷ 3

k = 14 + 8

Answer k = 22

divide both sides by 3 m = 42 ÷ 3

Answer m = 14

Try solving these equations. 1. n + 12 = 7

Answer n = _______________

2. p ÷ 6 = 6

Answer p = _______________

3. q - 11 = 44

Answer q = _______________

4.

r 7 = 14

Answer r = _______________

5.

8s = 96

Answer s = _______________

6.

5t - 5 = 5

Answer t = _______________

7.

2u + 6 = 24

Answer u = _______________

8.

2v = 6 4 3w - 4 = 20

Answer v = _______________

9.

Answer w = _______________

30

Algebra 3 Some equations need two inverse operations before the mystery number is left on its own on one side of the equation. Examples: 6x + 2 = 4x + 6 6x + 2 - 2 = 4x + 6 - 2 6x - 4x = 4x + 4 - 4x 2x = 4

Answer x = 2

Try solving these equations. 1.

4y - 4 = 3y + 5

Answer y = ___________

2.

5z + 2 = z +14

Answer z = ___________

3. 8a - 9 = 2a - 3

Answer a = ___________

4.

3b 2 =b+2

5.

4c +15 = 45 - 2c Answer c = ___________

6.

5d -15 = 3d - 7

7.

3e + 8 = 9e - 16 Answer e = ___________

8. 9.

f +4=f-8 4 35 ÷ 7 = 60 ÷ g

Answer g = ___________

10.

6h ÷ 3 = 3h - 7

Answer h = ___________

Answer b = ___________

Answer d = ___________

Answer f = ___________

31

Algebra 4 Some equations have brackets; you must complete the calculations inside the brackets first. Try solving these equations. 1.

2i + 2 = 5i - (9 + 4)

Answer i = __________

2.

7 + (4j - 2j) = 5j - 2

Answer j = __________

3. 3(k + 1) = 4k - 4

Answer k= __________

Some equations contain two or more unknowns. Try solving these equations. 4. If 3x = y , which of the following is not true. a.

6x = 2y

c.

y x= 3 y x=3

d.

y+x=3

e.

9x = 3y

b.

5.

(3a - 5b) + c = d

If a = 4 , b = 2 and c = 7 what is the value of d? Answer d = __________ 32

Algebra 5 Try solving these equations. 1. If 3x + 2y = z, underline the incorrect statement below. a.

6x + 4y = 2z

b.

2y = z - 3x

c.

4y = 2z - 6x

d.

3x + 2y - z = 0

e.

2y = z +3x

2.

If 4a = b Which of the following is not true? Underline the letter.

a. b.

b = 4a 1 b 4

= a

c.

4=b+a

d.

8a = 2b

e. 2a + 2a = b

33

Fractions 1 Find a fraction of these numbers, divide the numbers by the denominator and then multiply the answer by the numerator. Example: Find

3 of 48. 4

48 ÷ 4 = 12

1 of 48 = 12 4

Multiply by 3

12 × 3 = 36

3 of 48 = 36 4 1.

3 8 of 32 = ________________________________

2.

3 5 of 25 = ________________________________

3.

2 of 42 = ________________________________ 3

4.

5.

6.

5 12 of 84 = _______________________________ 12 4 of 72 = ________________________________ 9 5 of 64 = ________________________________ 8

34

Fractions 2 Equivalent fractions are fractions that are equal to each other. For example two eighths is exactly the same as a quarter. To find a fraction equivalent to another multiply the numerator and the denominator by the same number. Example: 9 15

18 30

=

=

27 45

=

36 60

Answer these questions about equivalent numbers. 1.

Write the missing numbers:

a.

3 = 5

27 c. 45 =

2.

___

35

___

5

b.

8 9

d.

24 = 42

=

___

36

___

7

Circle the two equivalent fractions. 5 12 12

7 9

3 5

15 24

35 45

21 18

3 8

35

Fractions 3 A mixed number is a mixture of a whole number and a fraction. 2 23 Example: = 37 7 23 7 is an improper fraction it is top heavy, the numerator is larger than the denominator. Improper numbers can be changed into mixed numbers by dividing numerator by the denominator. The answer becomes the whole number. The remainder becomes the numerator of the fraction. In the example 23 ÷7 = 3 remainder 2 Answer these mixed number questions. 1. 2. 3. 4.

25 Change 9 43 Change 6 37 Change 8 57 Change 10

into a mixed number. ____________ into a mixed number. ____________ into a mixed number. ____________ into a mixed number. ____________

To change a mixed number into an improper fraction, multiply the whole number by the denominator and add on the numerator. 5.

3

Change 6 7 into an improper fraction ___________ 1 94

6.

How many quarters is

7.

How many eighths is 4 8 ?

7

? ___________________ ___________________

36

Fractions 4 Add these fractions together. You will need to convert the fractions to the same denominator before you can add them.

1.

3 + 4

2 3

=

2.

5 6

+

1 4

=

3.

1 + 2

4 9

=

4.

2 7

5 3

=

+

5.

1+ + 1 + 1 = 3 4 2

6.

1+ + 1 + 1 = 2 5 4

7.

3+ + 1 + 5 = 3 4 6

9 12 +

8 12

=

17 12

5

= 112

37

Fractions 5 Subtract these fractions. You will need to convert the fractions to the same denominator before you can subtract them. 2 3

-

3 5

=

2.

9 10

-

1 2

=

3.

3

-

5 6

=

8 -

3 45

=

1. 2

4. 1

5. 5 4

6.

17 20+

7.

3 68

2

- 23

=

-

3 4

=

-

2 43

=

40 15

-

9 15

=

31 15

1

= 2 15

38

Fractions 6 Sometimes you will need to convert the fractions to the same denominator to work out other fraction questions. Example: Arrange these fractions in order, largest first. 1 2

3 4

1 3

5 6

=

6 9 4 10 12 12 12 12 =

5 3 1 1 6 4 2 3

Arrange these fractions in order smallest first. 1.

3 7 1 9 5 10 2 20

2.

1 3 4 8

3.

5 4 9 3 7 14 28 4

4.

5 6

1 2

Put these fractions in order of size, starting with the largest. Underline the correct letter. 3 4

7 8

8 12

5 6

7 3 8 4

a.

3 5 8 7 4 6 12 8

b.

5 8 6 12

d.

5 7 3 8 6 8 4 12

e.

7 5 3 8 8 6 4 12

c. 7 8 3 8 12 4

39

5 6

Fractions 7 To simplify fractions, you need to reduce them to their lowest terms. To do this you need to find a number that will divide exactly into both the numerator and the denominator. Repeat until the fraction is as simple as possible. Example Reduce

48 ÷ 8 = 6 48 to its simplest terms. 72 ÷ 8 = 9 72

6 ÷3=2 9 ÷3=3

Simplify these fractions.

1.

9 63

2.

32 40 =

3.

24 27 =

4.

75 = 120

=

32 5. What is the fraction 72 in its lowest terms? Underline the correct letter. a. 4 9

b. 1 2

c. 16 18

d.

16 36

e.

3 9 40

Fractions 8 Answer these fraction questions. Example Jill has 16 cherry cakes and 8 chocolate cakes. What fraction of the cakes are chocolate? Altogether there are 24 cakes. 8 24

simplified is

1 3

1. Tom has 25 second class stamps and 10 first class stamps. What fraction of the stamps are first class?

2. Jane buys 42 apples. 24 are green. What fraction of the apples are green?

3. Peter has 18 black socks and 6 brown socks. What fraction of the socks are brown?

4. Fiona has 21 grapes and 15 plums What fraction of the fruit are plums? Underline the correct letter. a.

5 7

b. 1 3

c.

5 12 18

d.

3 7

e.

5 6 41

Decimal Fractions 1 Change these common fractions into decimal fractions. 1.

1 = 0.1 10

2.

1 5

=

3.

1 2

4.

3 5

=

=

You can convert any common fraction into a decimal fraction by dividing the numerator by the denominator. Change these common fractions into decimal fractions. 5.

56 = 0.56 100

6.

95 = 1000

7.

1 8

=

8.

3 4

=

9.

23 = 100

10.

4 5

=

11.

1 = 20

12.

3 5

=

13.

3 = 8

14.

6 20

=

Change these decimal fractions into mixed numbers 15. 4.5 =

16. 3.9

=

17. 6.09 =

18. 5.023

= 42

Decimal Fractions 2 To arrange decimals in order line them up under each other. Example 4.04

4.44

4.404

4.004

4.44 4.404 4.044 4.04 4.004

4.044

Arrange these decimals in order largest first. 1. 7.140 _______ 2. 8.082 _______

7.410 _______ 8.820 _______

7.014

7.441

_______ 8.088

7.004

_______

8.002

_______

_______

8.802

_______

_______

Arrange these decimals in order smallest first. 3. 0.053 _______ 4. 9.06 _______

5. 1.110 _______

0.503 _______ 9.6

0.535

_______

9.666

_______

1.10 _______

0.353

9.66

_______

1.001

_______

_______

9.006

_______

1.011

0.005

_______

_______

1.101 _______

_______ 43

Decimal Fractions 3 To add or subtract decimal fractions line them up under each other. 3 14 1

Example

5.55 + 7.67 13.22

4.56 - 2.77 1.79

1 1

Answer these addition and subtraction questions. 1. Add 7.692 and 8.34 Answer ______________ 2. What is the total of 9.465 and 12.178 Answer ______________ 3. Take 5.982 from 8.20 Answer ______________

4. Find the difference between 0.4 and 0.04 Answer ______________

5. How much must you add to 64.9 to equal 70? Answer ______________

44

Decimal Fractions 4 To multiply decimal fractions it can be helpful to ignore the decimal points to begin with. Example

0.3 × 0.4 3 × 4 = 12 Replace the 2 decimals places = 0.12

Answer these multiplication questions. 1. 0.4 × 0.4 = ________________________________ 2. 0.5 × 0.5 × 0.5 = ___________________________ 3. 1.6 × 0.4 = ________________________________ 4. 0.2 × 0.2 × 0.2 = ___________________________ 5. 1.5 × 1.5 = ________________________________ 6. 3.2 × 4 = _________________________________ 7. 100 × 0.07 =_______________________________ 8.

0.2 × 0.1 = ______________________________

9. 10 × 0.5 × 0.5 = ____________________________ 10. Multiply 0.05 by 24 _________________________ 11. Circle the correct answer: 0.2 × 0.3 × 0.4 2.4

0.24

0.0024

0.024

24

45

Decimal Fractions 5 To divide decimal fractions it can be helpful to use repeated addition. Example

3 ÷ 0.5 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 = 3 Therefore 3 ÷ 0.5 = 6 Answer these division questions. 1.

4 ÷ 0.4 = ______________________________

2.

9 ÷ 1.5 = ______________________________

3.

4 ÷ 0.5 = ______________________________

4.

4 ÷ 0.8 = ______________________________

5.

9 ÷ 1.8 = ______________________________

6.

20 ÷ 2.5 =_______________________________

7. Circle the correct answer: 32 ÷ 0.4 40

8

4

80

800

8. Circle the correct answer: 1000 ÷ 0.25 40 50 400 500 4000 5000 9. Circle the correct answer: 42 ÷ 0.07 60

0.6

600

6

6000 46

Percentages 1 100% = 100 = 100 25% = 25 = 100 75% = 75 = 100

1 1 4 3 4

10 = 1 100 10 50% = 50 = 1 100 2 20% = 20 = 1 100 5

10% =

To find one per cent of a number divide that number by 100. To find 30% of a number divide that number by 10 then multiply by 3. Example Find 40% of £380 380 ÷ 10 = 38 (10%) 32 × 4 = 152 Answer £152 1. What is 10% of 230cm? _____________________ 2. What is 90% of £610? _______________________ 3. What is 30% of 360m? ______________________ 4. Find 70% of £5. ___________________________ 5. Circle the number below which is 21% of 560. 112 117.6

117 112.6 117.2

6. Circle the amount below which is 95% of £950. £935 £940.50 £902.50

£945.75 £920.50

7. Circle the number below which is 88% of 220. 193.6

109

190

192.4 193.2

47

Percentages 2 To increase a number by a percentage, work out the percentage and add it on to the original number. Example Increase £340 by 20% 340 ÷ 10 = 34 (10%) 34 × 2 = 68 £340 + £68 = £408 To decrease a number by a percentage, work out the percentage and subtract it from the original number. 1. Reduce £120 by 60% _______________________ 2. A book cost £8 its price is increased by 20%. What is its new price? _______________________ 3. 25% of the sweets in a jar of 380 sweets were red. How many red sweets were there? _____________ 4. In a sale all goods were reduced by 20%. What will be the new price of items costing: a. £28 ______

b. £166 ______

c. £1.20 ______

5. The cost of a meal is increased by 5%. It was originally £10.60. What is its new price? _______________________ 6. 25% of the children in a class of 36 were absent. How many were present? ____________________ 7. Circle the number below which is 21% less than 440. 93.24

347.6

346.76

356

336.76 48

Percentages 3 Answer these questions. What percentage of the shapes are shaded? Example

The shape has 25 rectangles. Each rectangle is 4% of the whole. 2 rectangles are shaded. 4% × 2 = 8% 1.

% shaded__________________________________ 2.

% shaded __________________________________ 3.

% shaded __________________________________ 49

Percentages 4 Answer these percentage questions.

1. What percentage of the diagram is shaded? _____

2. What percentage of the shape is shaded? _______

50

Fractions, Decimals and Percentages Answer these questions. 1. Circle the number which is closest to 4? 3.59 4.01 3.997

4.1 3.98

2. Which has the greatest value? Circle the correct letter. a. 40 % of 250

b.

d. 0.3 of 280

1 3

of 290

c.

1 4

of 399

e. 30% of 335

3. Which of these fractions is not equivalent to

5 ? 6

Circle the correct letter. a.

10 12

b.

20 24

c.

30 36

d.

40 42

e.

100 120

9

4. What is 2 100 as a decimal? Circle the correct letter. a. 2.9

b. 9.2

c. 2.09

d. 2.009

e. 0.29

5. In a packet of 40 sweets 8 are toffees. What percentage of sweets are toffees? Circle the correct letter. a. 40% b. 20%

c. 80% d. 30% e. 25%

6. Which fraction has the highest value? Circle the correct letter. a. 6 b. 3 c. 7 d. 7 10 4 9 8

e. 85 100 51

Ratio and Proportion 1 Ratio is used to compare two or more numbers or quantities. Ratio is written as a colon between Examples a.

xxxxoooxxxxooo These noughts and crosses are in the ratio 4:3

b. Beads are threaded in a ratio 2:3:5. 2 red for every 3 blue and 5 white. There are 200 beads. How many of each colour? Find the total number of parts 2+3+5=10. Divide the total number by the number of parts. 200 ÷ 10 = 20. 20 × 2 = 40 red, 20 × 3 =60 blue, 20 ×5 = 100 white Answer these ratio questions. 1.

Jim has 50 toy cars in the ratio 4 red for every 6 other colour. How many red cars does he have? Answer__________________________________

2.

Mum shares £7.20 in the ratio 2:3:4 into 3 pots. How much is in the third pot? ________________

3. The ratio of 9 year olds and 10 year olds in a class is 3:4. If there are 35 children in the class, how many 9 year olds are there? _______________________

52

Ratio and Proportion 2 xxxxoooxxxxooo If the ratio of noughts and crosses 4 crosses to every 3 noughts then the proportion of crosses is 4 in every 7, and the proportion of noughts is 3 in every 7. Answer these proportion questions. Example Sweets are shared out in the ratio 2:5 between Jim and Joe. If there are 28 sweets, what proportion does Joe receive? 2+5=7

28 ÷ 7 = 4 Joe’s proportion = 4 × 5 = 20

1. Red and black grapes are in the ratio 5:7 There are 180 grapes. How many are red? Answer___________________________________ 2. £3.60 is shared between Sean, Alf and Tony in the ratio 1:2:3. How much does Alf get? Answer __________________________________ 3. £9.80 is shared between Lola, Chris, Jane and Sue in the ratio 2:3:7:8. How much does Lola get? Answer __________________________________ 4. In a nursery school there are 108 children. There are 2, 3 and 4 year olds in the ratio 2:7:9 How many 4 year olds are there? Answer _________________________________ 53

Probability 1 The probability of something happening can be expressed as a fraction. Examples a. When a regular die is rolled then the chance of any number being rolled is 1 in 6 or

1 6

b. When a coin is tossed twice then the chance of 2 heads is 1 in 4 or

1 4

Make sure you check all the possible combinations. For b. they are tails tails, tails heads, heads tails, heads heads. Answer these probability questions. 1. What is the probability that you roll an even number from throwing a fair dice? Answer___________________________________ 2. What is the probability a girl will throw double 1 if she throws two fair dice once each? Answer___________________________________ 3. In a bag there are 2 red balls and 3 blue balls. Circle the probability: 0

2 3

b. Of picking a green ball. 0

2 3

a. Of picking a red ball.

2 6 2 6

3 6

2 5

3 5

3 6

2 5

3 5

54

Probability 2 The probability of picking any card from a pack of playing cards is 1 in 52 as there are 52 cards in a pack. There are four suits, hearts, spades, clubs and diamonds. Each suit has 13 cards ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King. Answer these probability questions 1. What is the probability that you will pick a Queen from a pack of playing cards? Answer___________________________________ 2. What is the probability a boy will pick spade from a pack of 52 playing cards? Answer___________________________________ 3. In a bag there are 5 red balls 7 blue balls and 4 green balls. Circle the probability: a. Of picking a red ball. b. Of not picking a blue ball.

5 12 5 16

5 7 9 16

5 11 9 11

5 16 4 9

3 4 3 4

4. What is the probability that you will throw a 1or 2 when throwing a fair dice? Answer___________________________________

55

Mean, Median, Mode and Range 1 4 9 5 3 5 1 3 5 To find the average or mean number from a set of numbers add all the numbers together dividing by how many numbers are in a set. The numbers at the top add up to 36 then divide by 9 = 4 The mode is the number that comes most often = 5 The median is the middle number when they are put in order of size. 1 1 3 3 4 5 5 5 9 = 4 The range is the difference between the largest and smallest numbers. 9 - 1= 8 Answer these questions. 1. Find the mean of 12, 15, 23, and 46. ____________ 2. The average of four numbers is 6. What is the total of the four numbers? ___________ 3. Find the mode of 1,1,2,5,2,3,4,2. _______________ 4. Find the median of 2,4,8,1,3,7,6. _______________ 5. Jim is 6 years 4 months, Paul is 7 years 6 months, Tom is 8 years 2 months. What is the mean age of the three children? __________________________ 6. Four children have a mean age of 6. Three of the children are aged 4, 10, 7. What is the age of the fourth child?_____________ 7. Here is the weight of five parcels: 0.9 kg 1.4 kg 2.9 kg 1.9 kg 0.3 kg What is the range? __________________________

56

Shape 1 Angles are measured in degrees. There are 360 degrees (360º) in a circle. A circle is divided into four right angles (90º) An acute angle is less than 90º, an obtuse angle is . A between 90º and 180º, a reflex angle is greater than 180º. Two lines are perpendicular if they are 90º to each other. Two lines are parallel if they are the same distance apart all along their length. Answer these angle questions.

1. What is the size of angle x __________

53 ͦ

x

2. Subtract one right angle from 360 ͦ ___________

3. Which line is perpendicular to A B? __________ C

E

G

I

K

A

B D

F

H

J

L

4. Which two lines are parallel to each other? ____

5. Which of these angles is obtuse? _____________ A

B

C

D

E

57

Shape 2 All triangles have 3 angles which add up to 180 .ͦ There are 6 different types of triangle. a. An equilateral triangle has 3 equal sides and angles. b. An isosceles triangle has 2 equal sides and angles. c. A scalene triangle has 3 different sides and angles. d. A right-angled triangle has one right angle. e. An acute-angled triangle has 3 acute angles. f. An obtuse-angled triangle has one obtuse angle. Label these triangles each with a different name. 1.

2.

____________________ 3.

__________________

4.

____________

5.

_____________

_________________

6. What is the size in degrees of angle x? ________ x 36 ͦ

25 ͦ

7. Which of these could also be an equilateral triangle? Circle the correct letter. a. obtuse-angled triangle b. right-angled triangle. c. acute-angled triangle

d. scalene triangle 58

Shape 3 Answer these questions about triangles. b

1.

c

a

A scalene triangle has three angles, a, b and c. Angle a is 20 ͦ smaller than c. Angle c is 50 ͦ smaller than b. What is the size of angle a? Circle the correct letter. a. 25 ͦ

b. 20 ͦ

c. 30 ͦ

d. 40 ͦ

e. 32 ͦ

2. Which triangle has three acute angles?

A

B

C

D

E

Answer _______________ 3. What is the approximate size of angle x? Circle the correct letter. x a. 90 ͦ

b. 75 ͦ

c. 120 ͦ

d. 140 ͦ e. 105 ͦ

59

Shape 4 Quadrilaterals are 2D shapes with 4 sides and 4 angles. There are 6 different types of special quadrilaterals. 1. A square has 4 equal sides, 4 right angles and 4 lines of symmetry. 2. A rectangle has 2 pairs of parallel sides, 4 right angles and 2 lines of symmetry. 3. A rhombus has 4 equal sides, 2 equal acute angles and 2 equal obtuse angles. 4. A parallelogram has 2 pairs of parallel sides, 2 equal acute angles and 2 equal obtuse angles. 5. A kite has 2 pairs of sides that are adjacent. It has one pair of opposite equal angles and one line of symmetry. 6. A trapezium has a pair of parallel sides and 2 pairs of angles. 1. Label these shapes. a

b

___________

d

______________

e

_____________

______________

c

___________

f

_____________

2. How many of the shapes above have four sides all the same length? __________________________

60

Shape 5 A polygon is any 2D shape with three or more straight lines. A regular polygon has all sides and angles the same. An irregular polygon has different sides and angles. a. b. c. d. e. f. g.

A quadrilateral is a 4 sided shape. A pentagon is a 5 sided shape. A hexagon has 6 sides. A heptagon has 7 sides. An octagon has 8 sides. A nonagon has 9 sides. A decagon has 10 sides.

Answer these questions about polygons. 1. Name as many shapes as you can in this pattern.

Answer________________________________________ ______________________________________________ ______________________________________________ 2. A 50p coin is based on which polygon? _________

61

Shape 6 To find the area of a rectangle, multiply its length by its width. 7cm 3cm

4cm

7cm × 3cm = 21cm²

6cm

(4cm ×6cm)÷2 =

24 2 =12cm² =

To find the area of a triangle multiply its base by its height and divide the answer by 2. 12m

Answer these area questions. 1.5m

1. What is the area of the pond? 6m

Answer __________________

3m

3m pond

1.5m

2. What is the area of a rectangle with a length of 9cm 1

and a width of 2 2 cm?_______________________ =

3. What is the area of a triangle with a height of 12cm and a base of 7cm? _________________________ 4. What is the area of this shape in cm²? Answer___________________________________ 60mm 40mm 20mm 90mm 62

Shape 7 To find the perimeter of a shape you need to add all the measurements of the sides together. Answer these perimeter questions. 1. If you have a rectangle with length 15cm and width 1

5 2 cm. What is the perimeter?________________ =

2. What is the perimeter of a square whose area is 36cm²? __________________________________ 3. The perimeter of a rectangle whose length is twice its width is 90 cm, find its width. Answer __________________________________ 4. What is the perimeter of an isosceles triangle whose 1

1

longest 2 sides are 9 2 cm and base 6 2 cm? _______ =

=

5. Which 2 shapes have the same perimeter? _______ 2.5cm

2.5cm 4cm

A 2.5cm

3.5cm

2.5cm 4cm

B

4cm

2cm

C

3.5cm

2.5cm 3.5cm

3cm

3.5cm

2 cm 2cm

2cm 3.5cm

D 2cm

2cm

2cm

E

3.5cm

3.5cm

2cm

63

Shape 8 Answer these area and perimeter questions. 1. The diagram shows the plan of a room. What is the area of the floor? Circle the correct letter. 1m 5m 3.5m 3m

a. b. c. d. e.

18m² 29m² 18.5m² 19.5m² 180m²

6m

2. Which expression gives the area of the shape? Circle the correct letter. a. f × g + h

h

h

b. 2(f × g) + h c. (f × h) + (f ×g) 2 d. f(g + h) ÷ 2 e. f × g + h × 2

g f

3. Jane uses a square and equilateral triangles all with sides 7cm long to make a shape. What is the perimeter of the new shape? ______________

64

Shape 9 Answer these area and perimeter questions. 1. Which of the shapes have a different perimeter to the other four shapes? ______________ 6cm

3.5cm 3cm

A

C

1.5cm 5cm

B

D

5cm

E

3cm

4cm

2. The shaded area of the shaded area in the regular hexagon is 8cm². B B What is the total area of the regular hexagon in mm²? Circle the correct letter. a. 1400mm² b. 2400mm² c. 24mm² d. 800mm² e. 240mm²

3. What is the perimeter of 2 squares with a total area of 32cm²? ____________

65

Shape 10 Answer these area and shape questions. 1. What is the area of the shape? Circle the correct letter.

x y a.

x(x + y)

b.

2x + xy

c.

xy + xy

d.

2xy

e.

x +2

x

y

2. James has some equilateral triangles and rectangles. 50mm 40mm

40mm

What is the perimeter of the shape he made?__________

66

Shape 11 A net is what you would draw, cut out and fold to make a 3D shape. There are 11 different nets of a cube in total. Answer these questions about nets. 1. Circle the net which could be used to form a cube. a

b.

c.

2. Which nets will make a square based pyramid and a triangular prism? Label the correct nets. a. b. c.

_______________ _________________ ____________ d. e.

___________________ _________________

67

Shape 12 The volume of a 3D Shape is the amount of space it takes up. To find the volume of a cube or cuboid multiply the length by the breadth by the height. 6cm 6cm × 6cm × 6cm = 216cm³ 6 cm 6cm Find the volume of the shapes below. 1.

2 cm 2cm 7cm Answer ________________________________

2. 2cm 3cm This cuboid is made from 1cm cubes. Answer

____________

3.

This cuboid is made up from cubes with a volume of 8 cubic centimetres. Answer______________ 68

Shape 13 Answer these questions about 3D shapes. 1. Which of these nets fold to make this cube?

A

B

C

D

Answer ________________________________ 2.

How many small cubes have been used to make ? this larger cube? ___________________________

3. How many cubes make up the solid shape?_______

69

Shape 14 A shape is symmetrical when it can be split into two equal mirror images by a line of symmetry. Shapes can have more than one line of symmetry. Rotational symmetry is when you turn a shape around to see how often it maps onto, or fits exactly on top of itself. The number of times a shape maps is its order of symmetry. Example This triangle maps 3 times there are 3 lines of symmetry. Answer these symmetry questions. 1. How many lines of symmetry has a regular octagon? Answer__________________________________ 2. What is the order of rotational symmetry of a regular heptagon? ________________________ 3. Look at these shapes. A

B

C

D

E

Which shapes have:

a. b. c. d. e.

No line of symmetry? _______________________ One line of symmetry?_______________________ Two lines of symmetry? _____________________ Order 6 of rotational symmetry? _______________ Maps onto itself 4 times? _____________________

4. Which of these shapes has no lines of symmetry?__ A

B

C

D

E

70

Transformations 1 A shape can be rotated round a given point or centre of rotation. It can be rotated clockwise like the hands of a clock or anticlockwise which is the other way round. 1. Here is a patterned plate.

Which picture shows the plate when it has been rotated clockwise through 90º?

A

B

C

D

E

Answer________________________________ 2. Here is a tile

Which picture shows the tile when it has been rotated through 270 º anticlockwise?

A

B

C

D

E

Answer________________________________ 71

Transformations 2 Often in questions about transformations, the points of shapes are given as coordinates such as (-2, 4). The first number is always the x amount along the x- axis, the second number is always the y amount and you have to go up or down the y- axis. 1. The points M, N and O are marked on the grid. When a fourth point P is added they make a rectangle. What are the coordinates of P?______ y 5 4 3 N

O

2 1 0

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

-1 M -2 -3 -4 -5

2. Shapes can be rotated about a given point. Draw the rectangle then rotate it 90º clockwise about point O. What are the new coordinate for N?_________ 3. Shapes can be reflected in a given mirror line. Draw the reflection of the original rectangle along the y axis. What are the new coordinate for M?___________ 72

x

Transformations 3 1. The points Q, R and S are marked on the grid. When a fourth point T is added they make a rhombus. What are the coordinates of T?______ y 5

Q

4 3

R

2 1

S

0 -9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

-1 -2 -3 -4 -5

2. Shapes can be translated along and up or down a given number of squares. Draw the rhombus then translate it 10 squares left. What are the new coordinates of S?__________ 3. Draw the original rhombus when it is reflected about the X axis. What are the new coordinates of R?__________ 4. Draw the rhombus from question 3 when it is translated 5 squares left and 2 squares up. What are the new coordinates of Q?__________

73

x

Transformations 4 1. Plot the vertices (1,-3) (6,-2) (5,-5) on the grid and then join up the vertices. y 5 4 3 2 1 0 -8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

x

-1 -2 -3 -4 -5

2. Reflect the shape you made in the line x = 0 Write in the new coordinates. Answer_________________________________ 3. Translate the original shape 1 square to the right and 4 squares up. Write in the new coordinates. Answer_________________________________ 4. Plot these points and join them in order. (-8,1) (-7,4) (-3,4) (-3,1) Rotate this shape clockwise 90º around point (-3,1) Write in the new coordinates. Answer_________________________________ 74

Measurement 1 Examples Metric units of measurement use tens, hundreds (approximate) and thousands. Length – 1centimetre (cm) = 10 millimetres (mm) 1 pencil width 1 stride 1metre (m) = 100 cm = 1000 mm 1 kilometre (km)= 1000m Weight – 1 gram (g) = 1000 milligrams (mg) A Smartie 1 kilogram (kg) = 1000 g A bag of sugar 1 tonne (t) = 1000 kg A small car Capacity –1 litre (l) = 1000 millilitres (ml) A carton of juice Answer these measurement questions. 1. 3m = ______________cm 2. 5.3litres = ___________ml 3. Circle the most likely metric measurement for the length of a house brick. 40cm

1m

5000mm

0.10m

20cm

4. Circle the most likely capacity of cola can. ¼ litre

500ml

10ml

330ml

1 litre

5. Circle the most likely weight of a pound coin. 10g

50g

3000mg

1 10

kg

20g

6. What is the approximate weight of a 20p coin?____ 75

Measurement 2 Imperial units of measurements were used before metric ones. They are still in use so it is important to know them and their metric equivalents. Metric examples Length – 1 mile = 1760 yards (yds) Almost 2 km 1 yard = 3 feet Just over 1 m 1 foot = 12 inches A small ruler Weight– 1 stone = 14 pounds Just over 6 kg 1 pound (lb) = 16 ounces (oz) 400 grams Capacity- 1 gallon = 8 pints 4 litres 1 pint = 20 fluid ounces ½ litre Answer these measurement questions. 1. Which is longer 30 miles or 32 km? ____________ 2. 6.5 metres is about the same as: 10 feet 7 yards 20 feet

12 feet

30 feet

3. A jug holding 4 pints would hold about ____litres. 4. 5 stone is about ______ kg. 5. Which of the following statements is true? a. b. c. d.

An apple can weigh 6oz ___________________ A paper clip is about 1g ___________________ A pint of water will fill 20 mugs ____________ A 6 year old child could be 6 feet tall _________

76

Measurement 3 When reading a measuring scale it is important to work out what one division of a scale is worth. Answer these questions on measuring scales. 1. These 4 jugs all hold 500ml. __500ml __ __ __ __ __ __ __ __ __

__500ml __ __ __ __ __ __ __ __ __

__500ml

__500ml

__ __ __ __

A

B

C

D

How much water is in each jug?

A________________

B __________________

C________________

D __________________

2. 0kg

1kg

2kg

3kg

4kg

5kg

0kg

1kg

2kg

3kg

4kg

E F a. What is the mass shown by pointer E in kilograms and grams? _____________________________________ b. How many grams must be added to pointer F to make 5 kg?__________________________________ 77

5kg

Measurement 4 Answer these measurement questions. 1. What is the weight of this package? Circle the correct letter.

200

400

g 0

a. b. c. d. e.

600

450 grams 325 grams 280 grams 375 grams 350 grams

2. The jug contains lemonade. 0.15 litres of lemonade is poured into a large glass. __500ml How many millilitres of __ lemonade are left in the jug? __ 400ml __ Circle the correct letter. a. b. c. d. e.

450 millilitres 350 millilitres 325 millilitres 275 millilitres 300 millilitres

__ 300ml __ __ 200ml __ __ 100ml __

78

Measurement 5 Answer these measurement questions. 1. Jack weighs himself, the dial on the scales points to here: 37

38

39

kg What is Jack’s weight in kilograms and grams? Answer______________________________________ 2. A map is drawn to the scale of 1:4,000. What distance in metres would be represented by 5 cm on the map? ________________________ 3. Apples cost 70p per kilogram. What is the total cost of the apples shown on the scale? ______________________________ 6 5

7

4

0 3

kg 2

1

4. A map is drawn to the scale of 1: 20,000. What distance in metres would be represented by 10 cm on the map? _______________________

79

Measurement 6 Answer these measurement questions. 1. The scale on a map is 1: 125,000 What actual distance is represented by 4 cm on the map? Circle the correct letter. a. b. c. d. e.

2.5km 1.25 km 5 km 4.5 km 1 km

2. The scale on a map is 1: 125 000 What actual distance in metres is represented by 10 cm on the map? Answer_________________________________ 3. A tree is 11 feet 6 inches high? Which is closest to its height in metres? Circle the correct answer. a. 3.4m b. 3m c. 2.5m d. 4.5m e. 2.9m f. 4.2m 4. What is the approximate length in feet. of 5 metres?____________________________ 80

Time 1 Time can be in analogue time, using a clock with hands or digital time using a clock with figures. It can be based on the 12-hour clock where each day is split into a.m. and p.m. So 7:00 a.m. is 7 o’clock in the morning and 7:00 p.m. is 7 o’clock in the evening. 24-hour clock times always have four digits so 7 in the morning is written 07:00 and 7 in the evening is written 19:00. Answer these time questions. 1. Change 2:38 p.m. to 24 hour clock time. ______ 2. Write this 24 hour clock time using a.m. or p.m. 16:19 _________________________________ 3. What is the time 35 minutes before 03:20? Answer ________________________________ 4. 300 minutes is _____hours _____minutes. 5. The time on an analogue clock shows 4:56 a.m. How would this be written as a 24-hour clock time? __________________________________ 6. 4 hours 25 minutes is _______________minutes. 7. How many hours are there in 3 days 6 hours? Answer_________________________________ 8. How many minutes are there in 6½ hours?_____ 81

Time 2 Answer these time questions. 1. The time is ‘quarter to nine in the evening’. What is the time as a 24-hour clock time? Circle the correct letter. a. 9:45 b. 19:45 c. 21:15 d. 21:45 e. 20:45 2. A TV programme starts at 17:25 and finishes at 19:48. How many minutes does the programme last? Answer_________________________________ 3. Write this 24 hour clock time using a.m. or p.m. 18:55 Answer________________________________

4. What is the time fifty minutes before 01:16? Answer________________________________ 5. One of these clocks is nine minutes slow, the other is 14 minutes fast. What is the correct time? 12:33 Answer__________________________________ 82

Time 3 To answer questions about months and calendars it is important to remember how many days are in each month. The rhyme about months can help. 30 days have September, April, June and November. All the rest have 31 Except February alone Which has 28 days clear And 29 each leap year. Answer these calendar questions. 1. Jill was in a play every night from 27th June until 16th July. How many days was the play on? _____

2.

September

S

M

T

5 12

6 13

7

W 1 8

T 2 9

F 3 10

S 4 11

Use this part of a calendar to find the date of the second Sunday in October. ________________

3. How many days are there in total in May, June and July? _______________________________

83

Time 4 Timetables generally use the 24-hour clock. To find the difference between two times, it can be useful to count the hours first and then the minutes. Example If a train leaves at 11:34 and arrives at 15:12, how long did the journey take? 11:34 14:34 = 3 hours 14:34 15:12 = 38 minutes The journey took 3 hours 38 minutes. Answer these time questions. 1. Here is part of a bus timetable. Bus A Stop 1 08:17 Stop 2 08:25 Stop 3 08:40 Stop 4 09:06 Stop 5 09:33

Bus B 09:41

Both buses travel at the same speed. What time will bus B arrive at Stop 5?_________________________ 2. What time is six hours 35 minutes before 02:19? __________________________________________ 3. What time is nine hours 54 minutes later than 19:12?_____________________________________ 4. A TV programme starts at 19:36 and ends at 20:55. How long does it last?_______________________ 84

Money 1 Money can be involved in many different types of questions. Answer these money questions. 1. Solomon has two £2 coins, three £1 coins, nine 50p coins, three 10p coins, four 5p coins and seven 2p coins. How much money does he have? Answer___________________________________ 2. Jonah buys two games. The total cost is £27.67. The first game costs £12.15. How much does the second game cost? Answer___________________________________ 3. A toy costs £2.45. How much do 8 toys cost? Answer___________________________________ 4. Mary buys a small vanilla ice cream and a large strawberry ice cream. Ice cream Chocolate Vanilla Strawberry Peach & Cream

Small £1.36 £1.09 £1.59 £2.19

Large £2.68 £2.15 £2.98 £3.46

How much change will she get from a £10 note? Answer___________________________________

85

Money 2 Answer these money questions. 1.

Sharon bought 6 apples and paid for them with a £5 note. She was given £3.38 change. What is the price of one apple? Answer_______________________________

2.

Karl is saving to buy a game costing £44.99 He is saving £3.50 a week and already has £19.60 in savings. How many more weeks until he will have to save for until he has enough money? Answer_________________________________

3.

Pens cost £x each and pencils cost £y each. What is the cost of 6 pens and 6 pencils? Circle the correct letter. a. b. c. d. e.

4.

6xy 6x + y 6+x+y x + y + 12 6x + 6y Paul bought 15 pens and paid for them with a £10 note. He was given £8.35 change. How much did one pen cost? Answer _________________________________ 86

Money 3 Answer these money questions. 1. Which has the greatest value? Circle the correct letter a. b. c. d. e.

2 5

of £4.00 20% of £5.00 25% of £3.00 0.2 of £6.00 1 5 of £5.00

2. A chair has its price reduced by 30% in a sale. The sale price is £182. What was the original price of the chair? Circle the correct letter. a. £260 b. £250 c. £190 d. £280 e. £230 3. A shop sells 16 types of chocolates. On average, the shop sells 18 boxes of each sort of chocolates a day. The typical cost of a box of chocolates is £3. Which of the answers below gives the best estimate of the shop’s total daily money taken for selling chocolate? Circle the correct letter. a. £8600 b. £300 c. £860 d. £80

e. £1200

4. 5. A dress costing £90 was reduced in price by 40%. . What is the new price of the dress? Answer ________________________________ 87

Money 4 Answer these money questions. 1. A trip to a theme park costs £34 per child. 24 children are going on the trip. The children have raised £460 towards the cost of the trip. How much money do they need to cover the cost of the trip? Circle the correct letter. a. £356 b. £134 c. £426

d. £516

e. £366

2. A book costs £3.20. How many books can be bought for £488? Answer_________________________________ 3. Molly spends 48p on crisps each week day. How much does she spend in a week? Answer__________________________________ 4. Games costs £4.99. a. How much will 145 games cost? _____________ b. If Tom buys 7 games. How much change will Tom get from £50?________________________ c. If Peter buys 16 games. How much change will he get from £100?_________________________ d. If a game is on sale with 20% off. How much will it cost now? ________________ 88

Multi-step problems 1 Answer these questions which combine either multiplication or division with addition or subtraction. Remember to read the problem carefully. Decide which number operation you need for each step. Estimate the answer. Work out the answers to the calculation. Check that the answer is similar to your estimate. 1. The teacher had 210 felt pens. He gave 18 pens to each of eight groups. How many felt pens did the teacher have left? Answer ___________________________________ 2. Find the difference in millilitres between half a litre and two and seven tenths litres? Answer ___________________________________ 3. Jake bought 10 metres of rope. He gave a £20 note and received £5.20 change. How much did a metre cost? Answer __________________________________ 4. The youth club has 49 members. They are divided into three teams. One team has 17 members the rest are divided into 2 equal teams. How many are in each of these teams? Answer ___________________________________ 5. There are 1.75kg of biscuits to share between 5 people. 50 grams of biscuits get lost. How many grams of biscuits does each person get? Answer____________________________________

89

Multi-step problems 2 Answer these questions which combine either multiplication or division with addition or subtraction. 1. Jenny has a 5m of ribbon, she cuts 1.82m and then a further 2.07m. How much ribbon is left in metres? Answer _________________________________ 2. A container holds 5 litres of custard. The empty container weighs 1.25kg. A litre of custard weighs 1.2kg. Find the total mass of the full container in kilograms. Answer __________________________________ 3. How much change from £10 does Wilfred have if he buys a key ring for £2.49 and a fridge magnet for £3.57? Answer ___________________________________ 4. The fair starts at 6:00p.m. 237 people go to the fair between 6:00p.m. and 7:00p.m. 135 people go to the fair between 7:00p.m. and 8:00p.m. whilst 189 people leave. How many people are at the fair at 8:00p.m.? Answer ___________________________________ 5. Shirley buys three melons costing £1.25 each and two pineapples costing £2.15 each. How much did she spend altogether? Answer ___________________________________ 90

Multi-step problems 3 Answer these questions which combine either multiplication or division with addition or subtraction. 1. This machine multiplies a number by 7 and then adds 12. 15

?

What number comes out of the machine? Answer ___________________________________ 2. Tomatoes cost 55p per kilogram and onions cost 90p per kilogram. Sarah buys 3 kg of tomatoes and 2 kg of onions. How much does Sarah spend? Answer ___________________________________ 3. A box of biscuits weighs 480 grams and contains 35 biscuits. The empty box weighs 60 grams. What is the weight in grams of one biscuit? Answer ___________________________________ 4. Sally thinks of a number. She adds 4 to the number, then multiplies her answer by 3. She then subtracts 11. Her final answer is 25. What was the number Sally first thought of? Answer ___________________________________

91

Multi-step problems 4 1. Mo buys 80 plums each plum costs 5p. How much does he spend on plums in pounds? Answer ___________________________________ 2. This machine multiplies a number by 3 and then subtracts 5.5. ?

8.6 What number must be put in the machine? Answer ___________________________________

3. Carl is saving to buy a hand held console costing £130. He saves £10.50 a week and already has £40 in savings. How many weeks will he have to save for before he has enough money to buy the console? Answer ___________________________________ 4. A zoo has 16 penguins. On average, each penguin eats 14 small fish a day. Each fish costs 50p. Which of the following, estimates the total cost of fish for the zoo each day? Underline the correct letter. a. £160 b. £1600 c. £112 d. £11.20 e. £94 92

Multi-step problems 5 1. Felix multiplied a number by 6 instead of dividing it by 6. His answer was 1188. What should his answer have been? Answer _____________________________________ 2. Tom bought 8 apples and paid for them with a £2 coin. He was given 24p change. What was the price of one apple? Answer _____________________________________ 3. Wendy is saving to buy a computer game costing £45. She saves £3.50 a week and already has £18 in savings. How many weeks will she have to save for before she has enough money to buy the game? Answer _____________________________________ 4. A red box holds 6 tins; a blue box holds 2 tins. Which of the following, does not contain the same amount of tins as the other four? Underline the correct letter. a. 2 red boxes and 6 blue boxes. b. 4 red boxes. c. 3 red boxes and 3 blue boxes. d. 12 blue boxes. e. 8 blue boxes and 1 red box. 5. Alex and John share 121 sweets in a ratio 4:7. How many more sweets does John get than Alex? Answer _____________________________________ 93

Multi–Step problems 6 Answer these multi-step questions. 1. There are 96 sweets in a packet. 12 of the sweets are strawberry. ¼ are toffee. What fraction is neither strawberry nor toffee? Answer___________________________________ 2. Bill and Ted each think of a number. Bill’s number X is multiplied by 3 and added to Ted’s number, Y to give a total of 33. What are Bill and Ted’s numbers? Circle the correct letter. a. b. c. d. e.

X = 5 and Y = 4 X = 9 and Y = 6 X = 7 and Y = 3 X = 8 and Y = 6 X = 3 and Y = 9

3. The mean of six numbers is 9. Four of the six numbers are 7, 9, 15 and 11. The other two numbers are the same. What is the value of both these numbers? Answer___________________________________ 4. Jackie thinks of a number. She adds 15 to the number, then halves it. She ends up with the answer 56. What number did Jackie think of? ______________

94

Multi-step problems 7 Answer these multi-step problems. 1. Here is a recipe for Berry Milk Shake. Berry Milkshake Serves 6 1.2 litres milk 0.4 kg strawberries 0.2kg raspberries 0.3kg blueberries 3 scoops ice cream 150 grams icing sugar

This recipe is for 6 people. Sarah makes enough for 4 people. a. How many ml of milk does Sarah use? Answer__________________________________ b. How many kg of fruit does Sarah use? Answer__________________________________ 2. Sarah makes some more Berry Milkshake, she uses 0.6 kg of icing sugar. How many scoops of ice cream does she use? Answer__________________________________

95

Multi- Step Problems 8 1. Write the missing digits to make this correct.

4

×

6

_______________________

8

9

4

_______________________

2. There were 36 jars in a box. The shopkeeper has 48 boxes of jars. How many jars does he have? Answer________________________________

3. Three eighths of a number is 42. What is the number? Answer ______________________________

4. Kerry collects 5p coins. She has £14.65 How many 5p coins does she have? Answer ________________________________ 7

5. Calculate 9 of 1413. ____________________

96

Multi- Step Problems 9 Answer these multi-step problems. 1. Shane is n years old and 7 years older than Sam. Sam is 3 years older than Max. How old is Max? Circle the correct letter. a. b. c. d. e.

10 n + 10 n-7 n-10 n+7

2. What is the missing number in the grid?________ 9 18 36

18 36 72

36 72

3. Jane goes swimming every 10th day and goes to the gym every 4th day. On New Year’s Day Jane swims and goes to the gym. How many more days will she do both on the same day until 21st of May. It is not a leap year. Answer_________________________________ 4. Which of the following is correct? (15×19)-34 a. 645 b. 251 c. 318

d. 241

e. 249 97

Handling Data 1 Data can be organised in many different ways. A common way in a graph, these can have bars, lines or pictures. Answer these questions about graphs. 1. The bar chart shows the ages of a group of people. 10 Number of 8 People 4 0

0-5

6-10

11-15

16-20

21-25

26-30

Ages

Which of the following statements is true? Circle the correct letter. a. 8 people are aged 20 years? b. 12 people are older than 20? c. 25 people are aged between 11 and 25? d. 35 people are younger than 21? e. 7 people are aged between 11 and 15? 2. This conversion chart changes litres to gallons. Approximately how many litres is 25 gallons?_____ A Conversion Chart Gallons to Litres 15 Gallons 10

5 0

10

20

30

40

50

60

Litres 98

Handling Data 2 Answer these graph questions. 1. The graph shows the distance a train travels against time. 30 Time

in minutes

20 10 0 10

20

30 40 Kilometres

50

60

a. Use the graph to predict how long it will take the train to travel 80 km. Answer__________________________________ b. What was the trains speed in km/h? Answer__________________________________ 2. The dotted red line shows the average temperature for a week in June. 20

×

Temperature

ºc

×

Mon

Tue

Wed

× ×

×

10 0

×

Thu Days

Fri

× Sat

Sun

How many days that week was the temperature above average? Answer_____________________________________ 99

Handling Data 3 A pie chart is a circle divided into sections to show how something is shared. It is important to remember that there are 360º in a circle. A 90º section would take 14 of the data. A 45º section would take 18 of the data. 1 A 120º section would take 3 of the data. Answer these pie chart questions. 1. This pie chart shows the proportion of biscuits found in a tin. There are 180 biscuits in a tin. 10% Key chocolate 15% ginger 40% wafer other ? How many biscuits from the other category were in the tin? __________________________________ 2. The pie chart shows the number of pens in a pot. Key 20% black blue 45% red ? 40 pens were red. How many were black? Answer__________________________________ 100

Handling Data 4 Answer these pictogram questions remember to pay attention to the number of items represented by each picture. 1. The pictogram shows the number of cakes sold at the bakers over 6 days. Key represents 50 cakes Number of cakes Monday Tuesday Wednesday Thursday Friday Saturday How many cakes were sold on the three best days?______ 2. The pictogram shows the different types of fruit. Key

represents 20 fruits Number of Fruits

Apples Pears Plums Peaches Bananas Mangoes How many more apples are there than peaches?_____

101

Handling Data 5 Venn diagrams use circles to organise data. If an item can be included in 2 or more sections it is put in the overlap section. If it does not fit any circle it is placed outside the circles. Answer these Venn diagram questions. 1. 42 children are at the park. This Venn diagram shows how many of them played football(F) and how many played in the playground(P). F

P

11

14 12

5

How many children do not play football?_______ 2. Which number is incorrectly placed in the Venn diagram below? ___________________ muliples of 7

multiples of 3 21

19 25

7 35

33 84

63

102

Answers Place Value 1 page 3 1. 60,000 2. 300 3. 5,000 4. 60 5. 40,000 7. 5,000,000 8. 800,000 9. Twenty three thousand, one hundred and forty five 10. Three thousand two hundred and fifteen 11. Forty one thousand, six hundred and thirty one 12. Nine hundred and three thousand two hundred and eighty two 13. 12,216 14. 46,243 15. 610,202 16. 59,733

6.

70,000

Place Value 2 page 4 1. 3. 5.

a. a. a.

400 b. 900 b 4,800 b.

7,000 6,000. 24,000

c. c. c.

90 60 0.205 4

c. c. c. 9.

9 62 66

2. 4. 6.

a. a. d

67,000 1500 50

b. b. 7.

2,600 c. 12,560 10,000 c. 130 b 170

a. a. a.

b. 0.5 c. 0.06 b. 15 c. 0.2 b 1,000 c. 10

Place Value 3 page 5 1. 3. 5. 7.

a. a. a. a.

30 10 0.5 100

b. b b. 8.

0.3 2. 0.5 4. 0.0401 6. 6

90 8 100

Place Value 4 page 6 1. 5. 6. 7. 8. 9.

680 2. 9,900 a. 678,460 b. a. 764.3 b a. 1,856,290 b. a. 148.3 b. a. 30,000 b. e. 300,000 f.

3. 672,000 4. 45.9 678,500 c. 678,000 d. 680,000 764.26 1,856,300 c. 1, 856,000 d. 1,860,000 148.28 c. 148.283 0.03 c. 0.3 d. 3,000,000 0.003 g. 3

.

Place Value 5 page 7 1.

c

2.

b

Place value 6 page 8 1.

d

2. b

3.

d

Addition 1 page 9 1. a. 75 4. 1585

b. 97 c. 125 d. 838 e. 1233 2. 5. 7777 6. £79.84 7. a. 89 b. 97 c. 677

754 3. 6041 8. £9.49 9. d

103

Addition 2 page 10 1 a. £5.49 2. a. 8.09

b. £8.75 b. 15.26

c. £46.27 c. 63.24

d. £242.18 d. 58.31

e. £424.55 3. E

Subtraction 1 page 11 1. a. 622 4. 8782

b. 324 c. 456 d. 1528 5. 5957 6. £253.14 7. 673

e. 3560 8. £3.35

2. 9.

898 a

3. 782m

Subtraction 2 page 12 1. a. £6.49 2. a.. 9.28

b. £9.39 b. 2.69

c. £29.63 c. 71.14

d. £67.82 d. 24.98

e. £173.56 3. b

Multiplication 1 page 13 1. a. 4 4. 105

b. 4 c. 6 5. £2.22

d. 54 e. 3 f. 20 6. 21.25 7. 39,000

2. 31.75cm 3. 7 litres 200ml 8. 736 9. e

Multiplication 2 page 14 1. 523 × 28 =14,644 500 10000 20

20 400

3 60

4000

160

24

2. 615 × 36 = 22,140 600 18000 30

10 300

5 150

3600

60

30

50 2000

1 40

150

3

8

6

3. 451 × 43 = 19,393 400 16000 40 3

4.

13,284

1200

5. 23,450

=

10000 4000 10460 + 400 + 160 + 4184 + 60 + 24 14644 10460 4184 1

=

18000 3600 18450 + 300 + 60 + 3690 + 150 + 30 22140 18450 3690 1 1 1

=

16000 1200 18040 + 2000 + 150 + 1353 + 40 + 3 19393 18040 1353

6. 13,338

104

Multiplication 3 page 15 1. d

2. 8 kg 500g

3. £4.48

4. 36,000

5.

c

6. a

7. d

Division 1 page 16 1. 50

2.

900

3. 40

4. 19

5.

32

6. 30

7. 80

8. 90

9. d

Division 2 page 17 1.

a.

2. 71

3. 11

4. 74

5.

94

6. 70

7. 36

8. a

Division 3 page 18 1.

29

2. 330

3. 4

4.

17

5.

275

4. 13

5.

29.33

6. 18

7. 210

8. 32

Division 4 page 19 1.

19

2.

23

3. 42

6.

245

Factors and Multiples 1 page 20 1. The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36 The factors of 45 are: 1, 3, 5, 9, 15, 45 The HCF of 27, 36 and 45 is 9 2. The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24. The factors of 32 are: 1,2. 4, 8, 16, 32 The factors of 48 are: 1,2,3,4,6, 8, 12,16,24,48 The HCF of 24, 32 and 48 is 8 3. The factors of 60 are: 1, 2, 3, 4,5, 6, 10,12, 15, 30, 60. The factors of 84 are: 1,2 3, 4,6,7,12,14,21, 28, 42,84 The factors of 144 are:1,2,3,4,6,12,24,36,48,72,144 The HCF of 60, 84 and 144 is 12 4. The factors of 21 are: 1, 3, 7,21. The factors of 56 are: 1, 2,4,7,14, 28, 56 The factors of 84 are 1,2,3,4,6,7,12,14,21,28,42,84 The HCF of 21, 56 and 84 is 7 5. The factors of 24 are: 1, 2, 3, 4, 6, 8,12, 24 . The factors of 88 are: 1, 2,4, 8,11, 22, 44, 88 The factors of 100 are 1, 2,4,5,10, 20, 25, 50, 100 The HCF of 24, 88 and 100 is 4

105

Factors and Multiples 2 page 21 1. 1,2,5 and 7

2.

1, 5 and 11

3. 3, 3 and 5

4. 3 and 13

5. 3, 3, 3 and 2

Factors and Multiples 3 page 22 1. The multiples of 10 are: 10, 20, 30, 40, 50. The multiples of 5 are: 5,10.15, 20, 25, 30 The multiples of 4 are: 4, 8, 12, 16, 20, 24 The LCM of 4, 5 and 10 is 20 2. The multiples of 4 are: 4, 8, 12, 16, 20. 24,28, 32, 36 The multiples of 6 are: 6,12.18, 24, 30, 36 The multiples of 9 are: 9, 18, 27, 36, 45, The LCM of 4, 6 and 9 is 36 3. The multiples of 10 are: 10, 20, 30, 40, 50.60 The multiples of 12 are: 12,24,36, 48, 60, 72 The multiples of 15 are: 15, 30, 45, 60, 75, 90 The LCM of 10, 12 and 15 is 60 4. 56, 64, 72

5. 56

Special Numbers 1 page 23 1. 26

2. 25

3. 40

4. 39

5. 72

6. 117 7. 7

8. 73

9. 17 79 97

Special Numbers 2 page 24 1. 2 9. 45

2. 6 10. 7

3. 8 11. 6²

4. 10 12. 73

5. 9 6. 7 13. 36 14. 27

7. 7 15. 2

8. 5

Special Numbers 3 page 25 1. 21. 2. 510 3. 44 4. 150 5. 601 6. 750 7. LXXV 8. XCIX 9. DLV 10. MXL 11. 7 12. 16 13. 16 14. 21 15. 50 Special Numbers 4 page 26 1. a

2. b

3. d

Number Sequences 1 page 27 1. 11

2. 71

3. 10

4. 3.15

5. 0.05

6.

23

7. 72

Number Sequences 2 page 28 1. 8

2. 49

3.

41

4.

1 2

5.

4.8

6. c 7. e

106

Algebra 1 page 29 1. 17

2. 3

3.

13

4.

24

5.

6

6. 7

.

Algebra 2 page 30 1. -5

2. 36

3.

55

4.

98

5.

12

5

6.

4

6. 2

7. 9

8. 12

9. 8

Algebra 3 page 31

1. 9

2. 3

3. 1

4. 4

5.

7. 4

8. 16

9. 12 10. 7

Algebra 4 page 32 1. 5

2. 3

3. 7

4. d

5. 9

Algebra 5 page 33 1. e

2. c

Fractions 1 page 34 1. 12 2. 15

3. 28

4. 35

5. 32

6. 40

Fractions 2 page 35 21

1 a. a.35

32 36

b..

3 5

c.

d.

4 7

7 9

2.

35 45

Fractions 3 page 36 7

1. 2 9

2. 7

1 6

5

7

3. 4 8

4. 5 10 5.

45 7

6. 37

7. 39

Fractions 4 page 37 1

5

1. 1 12

2. 1 12

3.

20

17 18

4. 1 21

1

5. 112

6.

19 20

11

7. 1 24

Fractions 5 page 38 1

1. 2 15

2.

2 5

3.

1

2

26

4. 3 5

7

5. 2 12

6.

1 10

7.

17

1 24

5 6

Fractions 6 page 39 1.

9 20

1 2

3 5

7 10

2.

1 3 1 5 4 8 2 6

3.

4 9 5 3 14 28 7 4

4.

e

107

Fractions 7 page 40

1.

1 7

2.

4 5

3.

5 8

8 9

4.

1 4

4. c

5. a

Fractions 8 page 41

1.

2 7

2.

4 7

3.

Decimal Fractions 1 page 42 1. 0.1 2. 0.2 3. 0.5 4. 0.6 8. 0.75 9. 0.23 10. 0.8 11. 0.05 23 9 15. 4 12 16. 3 9 17. 6100 18. 51000

5. 0.56 12. 0.60

6. 0.095 13. 0.375

7. 0.125 14. 0.3

10

Decimal Fractions 2 page 43 1. 7.441 7.410 7.140 7.014 7.004 3. 0.005 0.053 0.353 0.503 0.535 5. 1.001 1.011 1.10 1.101 1.110

2. 8.820 8.802 8.088 8.082 8.002 4. 9.006 9.06 9.6 9.66 9.666

Decimal Fractions 3 page 44 1. 16.032

2. 21.643

3. 2.218

4. 0.36

5. 5.1

Decimal Fractions 4 page 45 1. 0.16 8. 0.02

2. 0.125 9. 2.5

3. 0.64 10. 1.2

4. 0.008 11. 0.024

5. 2.25

6. 12.8

7. 7

Decimal Fractions 5 page 46 1. 10

2.

6

3.

8

4.

5

5.

5

6. 8

7. 80

8. 4000

9. 600

Percentages 1 page 47 1. 23cm 2. £549

3. 108m

4. £3.50

5. 117.6

6. £902.50

7. 193.6

c. £0.96

5. £11.13

Percentages 2 page 48 1. £48 6. 27

2. £9.60 3. 95 7. 347.6

4. a. £22.40

b. £132.80

Percentages 3 page 49 1. 15%

2. 25%

3. 30%

108

Percentages 4 page 50 1. 35%

2. 40%

Fractions, Decimals and Percentages page 51 1. 3.997

2. e

3. d

4. c

5. b

6. d

Ratio and Proportion 1 page 52 1. 20

2.

£3.20

3. 15

Ratio and Proportion 2 page 53 1. 75

2.

£1.20

3. 98p

4. 54

Probability 1 page 54 1 2

1.

2.

1 36

2 5

3. a.

b. 0

Probability 2 page 55 1.

1 13

1 4

2.

3. a.

5 16

b.

9 16

4.

1 3

Mean, Median, Mode and Range page 56 1. 24

2.

24

3. 2

4. 4

5. 7 years 4 months

6. 3

7. 2.6kg

Shape 1 page 57 1. 37 ͦ

2.

270 ͦ

3. GH

4.

DC and LK

5. E

Shape 2 page 58 1. isosceles 2. right-angled triangle 5. obtuse-angled triangle 6. 119 ͦ

3. equilateral 7. c

4.

scalene

Shape 3 page 59 1. c

2. D

3. c

109

Shape 4 page 60 1. a. trapezium b. square e. kite f. rectangle 2. 2

c. rhombus

d.

parallelogram

Shape 5 page 61 1. octagon hexagon quadrilateral

rectangle trapezium

rhombus

2. heptagon

Shape 6 page 62

1. 18m²

2.

22.5m²

3. 42cm²

4.

30cm²

Shape 7 page 63 1. 41cm

2.

24cm

3. 15cm

4.

1

25 2 cm

5. AC

Shape 8 page 64 1. c

2.

c

3. 49cm

Shape 9 page 65 1. c

2.

b

3. 24cm

Shape 10 page 66 1. a

2.

360mm

Shape 11 page 67 1. b

2.

b square based pyramid

d triangular prism

Shape 12 page 68 1. 28cm³

2.

36cm³ 3. 320cm³

Shape 13 page 69 1. C

2. 64

3. 42

110

Shape 14 page 70 1. 8

2. 7

3. a. C b. D c. A d. B e. E

4. E

Transformations 1 page 71 1. B

2. D

Transformations 2 page 72 1. (-3, -2)

2. (-3,5)

3. (6,-2)

Transformations 3 page 73 1. (5, 3)

2. (-3,1)

3. (9,-3 )

4. (2,-3)

Transformations 4 page 74

y

1.

5 4 3 2 1 0 -8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

x

-1

×

-2 -3

×

-4 -5

×

2. (1, 3) (6,2) (5,5) 3. (2,1) (6,-1) (7,2) 4. (-3,1) (-3,6) (0,5) (0,1)

111

Measurement 1 page 75 1. 300cm

2. 5300ml

3. 20cm

4. 330ml

5. 10g

6. 5g

Measurement 2 page 76 1. 30 miles 2. 20 feet 3. 2 litres 4. 30 kg 5. a. true b. true c. false d. false Measurement 3 page 77 1. A. 200ml B. 125ml C. 250ml D. 375ml 2. a. 2 kg 400g b. 3400g Measurement 4 page 78 1. d

2. c

Measurement 5 page 79 1. 37kg 800g 2. 200m

3. £3.15

4. 2000m

Measurement 6 page 80 1. c. 5km 2. 12 500m

3.

a

4.

15feet

Time 1 page 81 1. 14:38 2. 4:19 p.m. 3. 02:45 4. 5 hours 0 minutes 6. 265 minutes 7. 78 hours 8. 390 minutes

5. 04:56

Time 2 page 82 1. e 2. 2hours 23 minutes .

3. 6:55p.m.

4.

00:26

5. 12:19

Time 3 page 83 1. 20 days 2. 10th October.

3. 92 days.

Time 4 page 84 1. 10:57 2. 7:44

3. 05:06

4.

1 hour 19 min.

Money 1 page 85 1. £12.14 2. £15.52

3. £19.60

4. £5.93

Money 2 page 86 1. 27p 2. 8 weeks

3. e.

4. 11p

112

Money 3 page 87 1. a. 2. a.

3. c.

4. £54

Money 4 page 88 1. a. 2. 152

3. £2.40

4. a. £723.55

b. £15.07 c. £20.16 d. £4.00

Multi-step problems 1 page 89 1. 66

2. 2200ml

3. £1.48

4. 16

5.

340g

Multi-step problems 2 page 90 1. 1.11m

2. 7.25kg

3. £3.94

4. 183

5.

£8.05

Multi-step problems 3 page 91 1. 117

2. £3.45

3. 12g

4. 8

Multi-step problems 4 page 92 1. £4.00

2. 4.7

3. 9 weeks

4. c.

Multi-step problems 5 page 93 1. 33

2.

22p

3. 8 weeks

4. e.

5. 33

Multi-step problems 6 page 94 1.

5 8

2. b.

3. 6

4. 97

Multi-step problems 7 page 95 1. a. 800ml

b. 0.6kg

2. 12 scoops

Multi-step problems 8 page 96 1. 149 × 6 894

2. 1728

3. 112

4. 293

5. 1099

Multi-step problems 9 page 97 1. d.

2. 144

3. 3

4. b

Handling Data 1 page 98 1. c.

2. 110 – 115 accepted

113

Handling Data 2 page 99 1. a. 30 min.

2. 160 km/h

3. 4 days

Handling Data 3 page 100 1. 63

2. 70

Handling Data 4 page 101 1. 1025.

2. 35

Handling Data 5 page 102 1. 19.

2. 63

114