Maths Spm Melaka Answer

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2009

JAWAPAN MATHEMATICS 1 1449/1 1

D

11

B

21

B

31

A

2

B

12

B

22

D

32

D

3

D

13

B

23

A

33

B

4

C

14

C

24

C

34

B

5

A

15

B

25

A

35

D

6

D

16

D

26

B

36

D

7

A

17

B

27

B

37

C

8

C

18

A

28

D

38

B

9

D

19

A

29

C

39

A

10

C

20

D

30

B

40

D

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PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2009

JAWAPAN MATHEMATICS 2 1449 / 2

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MARKAH MAKSIMUM BAGI KERTAS INI : 100 MARKAH No

Peraturan Pemarkahan

y

1

Markah

y = 3x + 9 y=x Line y = 9 (solid or dashed) Region correctly shaded x Note: Any 2 vertex shaded correctly award 1 mark

1 2

3

2

3x – 2y = 12 @equivalent 6y = − 18 @ equivalent y=−3 x=2 3p2 – 2p – 5 = 0 (3p ─5) ( p +1) = 0 5 p = , p = −1 3

3

4

1 1 1,1

1 × (10 + 16) × 9 ×10 2

4

1 1 1 1

4

1

2

22 ⎛ 7 ⎞ ×⎜ ⎟ ×9 7 ⎝2⎠

1 2

1 22 ⎛ 7 ⎞ × (10 + 16) × 9 ×10  × ⎜ ⎟ × 9 2 7 ⎝2⎠ 1647 1 @ 823 @ 823.5 2 2

5

All prime numbers are odd numbers and a regular hexagon has an interior angle of 120o (b) If p < 10, then p < 7 False (c) 2n2 – (n + 1); n = 1,2,3,4,… Note : 2n2 – (n + 1) , n = 1,2,3,4 only @ 2n2 – (n + 1) award 1 mark

1 1 4

(a)

1 1 1 2 5

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No

Peraturan Pemarkahan

(a) 6

7

(b)

(a)

(b)

8

x=3

Markah

1

3 − 7 = − (9) + c 2 3 13 y= − x+ 2 2 3 13 0= − x+ 2 2 13 x= 3

22 22 120 60 × 2 × ×14 @ × 2 × × 7 @ equivalent 7 7 360 360 120 22 60 22 × 2 × ×14 + × 2 × × 7 + 14 + 7 + 7 360 7 360 7

194 2 @ 64 @ 64.67 3 3 120 22 180 22 2 60 22 2 × ×14 2 atau × ×7 @ × × 7 @ equivalent 360 7 360 7 360 7 120 22 180 22 2 60 22 2 × ×14 2 ─ × ×7 + × × 7 @ equivalent 360 7 360 7 360 7 154

⎛2 1⎞ ⎜5 3⎟ ⎟ ⎜ ⎝2 2⎠ ⎛ −1 − 2⎞ 1 ⎛ 4 2⎞ 1 ⎟⎟ @ ⎜ ⎟ award 1 mark Note : ⎜⎜ 1 × (−1) − 2 × 3 ⎜⎝ − 3 1 ⎟⎠ 2 ⎝ 5 3⎠

1 1 1 1

5

1 1 1 1 1 1

6

(a)

(b)

⎛ 3 − 2 ⎞⎛ u ⎞ ⎛ 4 ⎞ ⎜⎜ ⎟⎟⎜⎜ ⎟⎟ = ⎜⎜ ⎟⎟ ⎝ − 5 3 ⎠⎝ v ⎠ ⎝ − 7 ⎠ ⎛ u ⎞ 1 ⎛ 4 2 ⎞⎛ 4 ⎞ ⎟⎟⎜⎜ ⎟⎟ ⎜⎜ ⎟⎟ = ⎜⎜ ⎝ v ⎠ 2 ⎝ 4 3 ⎠⎝ − 7 ⎠ u= 1 1 v=− 2

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2

1 1 1 1

6

No

9

Peraturan Pemarkahan

(a) 6 saat 20 − 2 (b) 4−0 9 2 1 (c) × (2 + 20) × 4 + (10 − 4) × 20 + 2 Note : 1 × (2 + 20) × 4 @ (10 − 4) × 20 @ 2

1 1 1 1 × (20 + 30) × (t − 10) = 239 2

(b)

11

1

{(M,P) , (M,R), (M,E),(M,4), (A,P) , (A,R), (A,E),(A,4), (D,P) (D,R), (D,E),(D,4), (U,P) , (U,R), (U,E),(U,4), 3,P) , (3,R), (3,E),(3,4)} (a)

{(M,P) , (M,R), (D,P) (D,R)} 2 2 ATAU × 5 4 4 1 @ 20 5 {(A,4) , (U,4), (3,E),} 2 1 1 1 ATAU × + × 5 4 5 4 3 20

(a) ∠ UMP (b)

tan θ =

2

1 × (20 + 30) × (t − 10) (1 mark) 2

t = 13 saat 10

Markah

6

1 1 1 1 1

5 1

9 61

or equivalent

θ = 49.05◦ @ 49o 3'

2 1 4

12

(a) (b)

−18.75 , − 35

1 ,1

Refer to graph Uniform scale and correct axis Plot all points correctly Smooth curve

(i) − 9.0 ≤ y ≤ −8.0 (ii) − 2.5 ≤ x ≤ − 2.4 , 3.1 ≤ x ≤ 3.2 (d) y = 3x – 15 Draw line y = 3x – 15 − 2.8 ≤ x ≤ − 2.7 , 2.4 ≤ x ≤ 2.5 (c)

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1 2 1 1 1 1 1 1,1

12

No

13

Peraturan Pemarkahan

(a)

Markah

1 1

(i) 4 (ii) (0, 4) (iii) (−4, 3)

2 2

(b) (i) (a) U : Reflection in the line x = −1 Note : 1. Reflection only award 1 mark (b)

V : Enlargement with scale factor =

1 2

3

at centre P (ii)

16 ⎛1⎞ ⎜ ⎟ ⎝2⎠ 16 ⎛1⎞ ⎜ ⎟ ⎝2⎠ 48

14

2

2

1 - 16

1 1

(a)

Number of telephone calls 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44

Midpoint

Frequency

12 17 22 27 32 37 42

1 2 7 8 10 9 3

Column I (all class interval correct) Column II (all midpoint correct) Column III (all frequency correct)

1 1 2

Note : Allow two mistakes in column III for 1 mark (b)

(12 × 1) + (17 × 2) + (22 × 7 ) + (27 × 8) + (32 × 10) + (37 × 9) + (42 × 3) 40 = 29.88

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2 1

12

No

Peraturan Pemarkahan

(c)

Markah

Refer to graph Uniform scale and correct axis 9.5 ≤ x ≤ 44.5 and 0 ≤ y ≤ 10

7 Bars drawn correctly Using boundaries or midpoint or class interval as x – axis correctly

Notes :

5 or 6 bars drawn correctly, award K1 Other scale being used, deduct1 mark

(d)

22

1 2 1

12

15

6 cm

(a)

• •

5 cm

2cm

6 cm

(b)

• •

Correct shape Correct measurements • Accurate angle ± 0.1o and size ± 0.2 cm Note: Deduct 1 marks for double line or small gap or extension

5 cm

2cm

Correct shape Correct measurements • Accurate angle ± 0.1o and size ± 0.2 cm Note: Deduct 1 marks for double line or small gap or extension

2cm

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1 1 1

1 1 2

No

Peraturan Pemarkahan

(c)

• • • •

Correct shape Dashed line Correct measurements Accurate angle ± 0.1o and size ± 0.2 cm Note : Deduct 1 marks for double line or small gap or extension

5 cm

Markah

1 1 1 2

2 cm 5 cm 16

12

(a) (50o S , 140oE) Note : 50o S or 140oE only award 1 mark

2

4052 ..86 60 cos 50° Note : using cos 60 correctly award 1 mark

2

(b)

105.1 – 40 65.1o E

1 1

(c)

(180 – 50 – 50 ) × 60 or 80 × 60 4800

(d)

(50 + 50 ) × 60 (50 + 50) × 60 + 4052 .86 900 11.17 + 11 2217 hours

1 1 1 1 1 1 12

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y

5×

−3

−2

×

−1

0

Graph for Question 12

×

1

2

3

×

5

4

×

−5

×

−10

−15

×

×

−20

−25

× −30

x

×

−35

−40

−45

×

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x

Graph for Question 14 No. of students

10

9

8

7

6

5

4

3

2

1

0 9.5

14.5

19.5

24.5

29.5

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40

34.5

39.5 44.5 No. of phone calls