Kalkulator Maths Spm 2017.pptx

SEKOLAH MENENGAH KEBANGSAAN TAMAN MUTIARA 09700 KARANGAN KEDAH DARUL AMAN

MODULE OF CALCULATOR EXPLORATION PROGRAMME DEVELOP BY : PN ROSNANI SURIAYANTI BT MUSA

TOPIK PENGGUNAAN KALKULATOR 1. GRAF FUNGSI 2. PERSAMAAN LINEAR 3. PERSAMAAN INDEKS 4. PERSAMAAN KUADRATIK 5. ASAS NOMBOR 6. MATRIKS 7. BENTUK PIAWAI 8. PERSAMAAN LINEAR SERENTAK 9. UBAHAN 10. KECERUNAN GARIS LURUS

GRAF FUNGSI: MELENGKAPKAN JADUAL 1 Lengkapkan jadual

-2 -1

-0.5

1 2 3

4 4.5

7 0 -2 -2 3 12 25 33 (2005.2.12) ALPHA

2

Y

ALPHA

SOALAN 2005

=

ALPHA

X

X

ALPHA

CALC CALC -2 SEMAK

=

X? 7 KIRA

-1

X? =

CALC 4

3

0 X?

=

25

GRAF FUNGSI: MELENGKAPKAN JADUAL 2 Lengkapkan jadual

SOALAN 2006

(2006.2.12)

- 4 - 3 -2 -1 1 1.5 2 - 6 - 8 -12 -24 24 16 12 ALPHA

Y

ALPHA

= 24 a b/c

CALC CALC -4

=

X? -6

-3

X

X? =

CALC 1.5

ALPHA

3 8

-8 X?

=

16

GRAF FUNGSI: MELENGKAPKAN JADUAL 3 Lengkapkan jadual (2007.2.12)

- 3 - 2.5 -2 -1 33 21.63 14 7

0 6

1 5

2

2.5

-2

-9.63 SOALAN 2007

ALPHA

Y

ALPHA

6

--

= X

ALPHA

SHIFT

CALC CALC -2

=

X? 14

-1

X? =

CALC 2

7 X?

=

-2

PERSAMAAN LINEAR : MENCARI NILAI 1

10 – 3 (2 – w) = 9 w + 2 , hitungkan nilai w (2005.1.22) Diberi

10 -- 3 ALPHA

=

SHIFT SHIFT

( 9

2 ALPHA

SOLVE SOLVE a b/c

--

ALPHA

X

+ 2

X

X?

)

0

X=

0.333333

X=

1/3

PERSAMAAN LINEAR : MENCARI NILAI 2 Diberi,

- 4 k = - 2 ( 3 – k ) , maka k = (2006.1.22)

5

a b/c

2 -- 4 -2

SHIFT SHIFT

SHIFT

(

ALPHA

3 --

SOLVE

X

ALPHA

ALPHA

X

=

)

X?

……….

SOLVE

X=

a b/c

X = 1/5/12

a b/c

X = 17/12

1.416667

PERSAMAAN LINEAR : MENCARI NILAI 3 Diberi , cari nilai

(

ALPHA

ALPHA

=

SHIFT SHIFT

x

(2007.1.22)

X

2

+

1

ALPHA

SOLVE SOLVE a b/c

) X --

a b/c

5

1

X?

0

X=

0.666666

X=

2/3

PERSAMAAN INDEKS : MENCARI NILAI Diberi , cari nilai

3

^

x

(2005.1.24)

ALPHA

9 a b/c 3

SHIFT SHIFT

X

^

ALPHA

(

SOLVE SOLVE a b/c

=

2

ALPHA

X?

X

)

0

X=

0.666666

X=

2/3

PERSAMAAN LINEAR SERENTAK 1

EQN 1

MAT 2

VCT 3

Hitungkan nilai p dan nilai q yang memuaskan persamaan linear serentak berikut

2 p – 3 q = 13 4p+q =5 (2005.2.2)

MODE

2 -3

13

4

MODE

MODE

a1? b1? c1? a2?

SOALAN 2005

UNKNOWNS ? 2 3

1

1 5

X Y

b2? c2?

2 -3

PERSAMAAN LINEAR SERENTAK 2 Hitungkan nilai x dan nilai y yang memuaskan persamaan linear serentak EQN 1

MAT 2

VCT 3

berikut SOALAN 2008

(2008.2.2) MODE

1 3 ab/c 2

-3 4

MODE

MODE

a1? b1? c1? a2?

UNKNOWNS ? 2 3

1

-1 16

x

y

b2? c2? 3 -4

PENYELESAIAN PERSAMAAN KUADRATIK Selesaikan persamaan kuadratik EQN 1

MAT 2

VCT 3

SOALAN 2005

(2005.2.1)

Tukar pada bentuk am MODE

MODE

MODE

DEGREES ? 2 3

2 -9 -5

a? b? c?

UNKNOWNS ? 2 3

1

X1

5

X2

-0.5

a b/c

X2=-1/2

( k – 5 ) ( 2 k + 1 ) , k = 5, k =

PENGIRAAN NOMBOR ASAS 2, 8, 10 (2005.1.4)

SD REG BASE 1 2 3

MODE

MODE

3

BIN

110001 - 1011

=

CARA LAIN : MODE

d 1

h 2

b 3

LOGIC

0 4

3

MODE LOGIC

LOGIC

3

110001

b 110001 --

LOGIC

LOGIC

b 110001 – b 1011

LOGIC

=

3

1011

PENGIRAAN NOMBOR ASAS 2, 8, 10

516 SD d REG h BASE b 0 1 22 3 3 4

MODE

MODE

3

OCT

LOGIC

LOGIC

LOGIC

4

7654

0 7654 LOGIC

o 7654

LOGIC

d 12

LOGIC =

1

12

PENGIRAAN NOMBOR ASAS 2, 8, 10

1110 SD REG BASE 1 2 3

MODE 14 BIN OCT

=

MODE

3

16

PENGIRAAN MATRIKS 1.1

Dim EQN A ABMAT Mat Edit (mxn) 12 C m? 21 22 11 n? Mat VCT 11 222 3 1 00330 30

MODE

SHIFT

MODE

MAT

1

MODE 1

2

=

Mat A (mxn) n?

2

=

Mat A 11

3 1 4

= = =

Mat A 12 Mat A 21 Mat A 22

6

=

Mat A 11

AC

2

(2005.1.39)

Mat A (mxn) m?

BINA MATRIKS A

PENGIRAAN MATRIKS 1.2

Mat Dim A B 11 (mxn) 12 21 22 BEdit m? n? C Mat 1 2 2 31 0 00 -1 03

(2005.1.39)

SHIFT

MAT

1

2

Mat B (mxn) m?

2

=

Mat B (mxn) n?

2

=

Mat B 11

-1 = 0 = -1 =

Mat B 12 Mat B 21 Mat B 22

4

Mat B 11

=

BINA MATRIKS B

AC

PENGIRAAN MATRIKS 1.3

5 9

2Mat Dim 2Mat A Mat Ans ABEdit A– 22 12 21 Mat C BAns Mat 11 1 22 3 8 2 9 5403

2 8

(2005.1.39)

BINA PENGIRAAN 2

SHIFT

-- SHIFT =

MAT MAT

3

1

2 Mat A

3 2

Mat Ans 11 Mat Ans 12 Mat Ans 21 Mat Ans 22

2 Mat A – Mat B 7 2 9 8

J A W A P A N

HASIL DARAB DUA MATRIKS 1

EQN Mat (mxn) 12 C 21 22 31 32 11 Dim Edit A A Mat ABMAT (mxn) 11 222 3

n? VCT Mat m? 1 00 003032

MODE SHIFT

MODE MAT

2

MODE

1

1

(2008.1.39)

Mat A (mxn) m?

3

=

Mat A (mxn) n?

2

=

Mat A 11

2 = 3 = -3 =

Mat A 12 Mat A 21 Mat A 22

0

=

Mat A 31

4

=

Mat A 32

1

=

Mat A 11

BINA MATRIKS A

AC

0

HASIL DARAB DUA MATRIKS 2

Dim A BBEdit Mat (mxn) 21 C m? n? Mat 11 1 22 3 1 000300 1

(2008.1.39) SHIFT

MAT

1

2

Mat B (mxn) m?

2

=

Mat B (mxn) n?

1

=

Mat B 11

1

=

Mat B 21

-4 =

Mat B 11

AC

0

BINA MATRIKS B

HASIL DARAB DUA MATRIKS 3

=

Dim Mat Dim AA Ans A BxBEdit MatC BMat Ans Mat Ans Mat Mat Ans 11 21 31 xEdit 11 2 22 -3 03 -10 0343 1 2 3 4

- 10 -3 0

(2008.1.39)

SHIFT

X

MAT

SHIFT

=

3

1

MAT

3

Mat A 2

Mat A x Mat B

Mat Ans 11 - 10 Mat Ans 21 Mat Ans 31

JAWAPAN -3 0

MATRIKS: MENCARI PENENTU 1

EQN Mat 12 21 (mxn) 22 11 Dim A A Mat ABMAT Edit 11 C 11 222 3

VCT n? m? Mat 0030 1 -4 300

Cari nilai m dan nilai n MODE SHIFT

MODE MAT

MODE

1

1

2

=

Mat A (mxn) n?

2

=

Mat A 11

-4 = 2 = -5 =

Mat A 12 Mat A 21 Mat A 22

3

Mat A 11

AC

=

0

(2007.2.9)

2

SOALAN 2007

Mat A (mxn) m?

MATRIKS: MENCARI PENENTU 2

Det A Det A Mat Mat BTrn A C Mat Ans Dim Edit 1 22 3 43-2 00 0

Cari nilai m dan nilai n SHIFT

MAT

SHIFT

MAT

3

(2007.2.9) SOALAN 2007

1

Det

1

Det Mat A

0

0

=

Det Mat A -2

m = -2

n=3

SELESAI PERSAMAAN MATRIKS Menggunakan kaedah matriks, hitung nilai x dan nilai y yang memuaskan persamaan matriks berikut: SOALAN 2007

(2007.2.9b)

PENYELESAIAN

x Mat B 0

1. Masuk mode Matriks 2. Input Matriks A 3. Input Matriks B SHIFT

=

3

MAT

1

- 1.5

1

- 2.5

2

SHIFT

MAT

3

1

SHIFT

MAT

3

2

=

0.5

x

1.5

BENTUK PIAWAI

Fix 1

Sci 2

Norm 3 (2009.1.3) MODE

MODE

MODE

MODE

MODE

2

3

4.5

X

10

^

15

+

5.1

X

10

^

14

=

BENTUK PIAWAI

Fix 1

Sci 2

Norm 3 (2010.1.3) MODE

MODE

MODE

MODE

MODE

1

0.034 10

( ^

7

1.7 )

X =

2

BENTUK PIAWAI

Fix 1

Sci 2

Norm 3 (2012.1.3) MODE

MODE

MODE

MODE

MODE

2

4

(

746.5 10

X ^

10 -7

^ =

-3

)

GUBAHAN Jadual manakah mewakili yᴕx² Fix 1

Sci 2

Norm 3

A. B.

X

1

2

4

y

64 16

4

X

2

5

y

25 25 12

Y

ᴕ

3

x²

Y

=

K

K

=

y/x²

A.

C.

x²

3

y

18 50 98 3

4

y

16

54

128

ALPHA

Y

Ab/c

x²

)

X

CALC

64

=

X?

1

=

7

2

ALPHA

Y?

5

X D. (

X

ANSWER K

( )

KECERUNAN GARIS LURUS Mencari kecerunan antara titik A dan B pada satu garis lurus A(6,0) dan B(3,4) MODE

MODE

2

1

Maukkan nilai : 6 n=

,

,

4

M+

DI SCREEN CALCULATOR

SHIFT B

M+

DI SCREEN CALCULATOR

3 n=

0

2 =

2

DI SCREEN CALCULATOR

FINAL ANSWER = -4/3