Math P2 Pahang Spm 2008(ans)

SULIT 1449/2 Matematik Kertas 2 Mei 2008 2½ jam

1449/2

SEKOLAH-SEKOLAH MENENGAH NEGERI PAHANG PEPERIKSAAN PERCUBAAN SPM 2008

MATEMATIK Kertas 2 PERATURAN PERMARKAHAN

UNTUK KEGUNAAN PEMERIKSA SAHAJA

Question 1(a)

Solution and Mark Scheme

Marks K1

3

(b) K2

2

3.

⎛ 1 4 22 3 ⎞ ⎜ × × ×7 ⎟ ⎝2 3 7 ⎠ ⎞ ⎛ 1 4 22 ⎞ ⎛ 1 22 1155 = ⎜ × × 7 2 × h ⎟ + ⎜ × × × 7 3 ⎟ ⎝3 7 ⎠ ⎝2 3 7 ⎠ 154h = 1309 h = 8.5 cm

Kenalpasti sudut ∠ BFC or ∠ CFB 9 Tan ∠ BFC = 8 ∠ BFC = 41.630 or 410 38’

K1 K1 K1 N1

P1 4 K1K1 N1

4(a)

True

P1

(b)

If 3x = 1 then x = 0

K1

If x = 0 then 3x = 1

K1

(c)

2(3)n + n ; n = 1, 2,3, …

4

5

K1K1 4

5.

9v + 6w = 42 atau setara 10v = 40 atau setara v=4 w=1

K1 K1 N1 N1

6

7 (a)

4p2 -4p-15 =0 (2p+3)(2p-5) =0 −3 5 p= atau p = 2 2 4 m kl = 3 LM; x=2 -4 = -

(b)

K1 K1 N1N1 P1

K1

−4 x + 4 atau 3y = -4x + 12 3

(b)

9 (a)

k=4 v=6

P1 P1

⎛ x⎞ 1 ⎜⎜ ⎟⎟ = ⎝ y ⎠ (7 × −2) − (−6 × 3)

⎛ − 2 6⎞ ⎟⎟ ⎜⎜ ⎝ − 3 7⎠

⎛ 5⎞ ⎜⎜ ⎟⎟ ⎝1⎠

NI N1

22 ⎤ 22 ⎡ 120 ⎡ 105 ⎤ ⎢⎣ 360 × 2 × 7 × 7⎥⎦ atau ⎢⎣ 360 × 2 × 7 × 14⎥⎦

K1

44 77 + 3 3

1 cm. 3 ⎡ 120 22 2 ⎤ ⎡ 60 22 2 ⎤ ⎡ 105 22 2⎤ ⎢⎣ 360 × 7 × 7 ⎥⎦ or ⎢⎣ 360 × 7 × 7 ⎥⎦ or ⎢⎣ 360 × 7 × 14 ⎥⎦

68

2 2⎞ ⎛ 1 ⎜ 51 + 179 − 25 ⎟ 3 3⎠ ⎝ 3 1 616 2 205 cm 2 atau cm 3 3

6

K2

x= -1 y = -2

7 + 7 + 14 +

(b)

KI N1

y-intercept is 12 8 (a)

5

N1

4 (6) + catau setara 3

MN; y =

4

K1

NI K1

K1

N1

6

10(a)

(b)(i)

(ii)

11(a) (b)

(c)

16 25

⎛ 15 14 ⎞ ⎛ 10 9 ⎞ ⎜ × ⎟+⎜ × ⎟ ⎝ 25 24 ⎠ ⎝ 25 24 ⎠ 1 2 ⎛ 16 15 ⎞ ⎜ × ⎟ ⎝ 25 24 ⎠ 2 5

6s 6 − 12 8−0

K1 K1

N1 5 K1

N1

P1 K1 6 N1

-0.75

⎡1 ⎤ 156m = ⎢ (6 + u )6⎥ + 6u ⎣2 ⎦ u = 10

K1 N1

Question

12(a)

(b)

Solution and Mark Scheme

Marks

3

K1

-2

K1

2

Graph Axes drawn in correct direction, uniform scale for − 5 ≤ x ≤ 1 and − 2 ≤ y ≤ 7

P1

7 point and *2 points correctly plotted or curve passes through these points for − 5 ≤ x ≤ 1 .

K2

smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for −5 ≤x ≤ 3 .

N1

4

Note: 7 or 8 points correctly plotted, award K1 (c)(i) (ii)

(d)

4.65 ≤ y ≤ 4.80

P1

− 0.2 ≤ x ≤ − 0.4 − 3.85 ≤ x ≤ − 3.65

P1 P1

Identify equation y = - x

K1

Straight line y = - x correctly drawn

K1

3

Values of x : − 3.85 ≤ x ≤ − 3.7 0.7 ≤ x ≤ 0.9

N1

3

Note: Values of y and x obtained by computations, award P0N0

12

Question

Solution and Mark Scheme

Marks

13(a)

Correct shape with rectangles KLPS and PQRS . All solid lines. KL > DL > LI

K1

Measurements correct to ± 0.2 cm (one way) and All angles at vertices of rectangles = 90o ± 1o

K1 3

N1

Question

Solution and Mark Scheme

Marks

(b)

Question

Correct shape with rectangle MJHI and trapezium ABMH . All solid lines.

K1

JB > JI = MH > BM > MJ = HI

K2

Measurements correct to ± 0.2 cm (one way) and All angles at vertices of rectangles = 90o ± 1o

N2

Solution and Mark Scheme

5

Marks

(c)

Correct shape with rectangles HGIL and MHJI and square ADHG. All solid lines.

K1

JL > DL = AI > DG = HG > GL = HI=MJ

K1

Measurements correct to ± 0.2 cm (one way) and All angles at vertices of rectangles = 90o ± 1o

K1

N2

5 12

Question

Solution and Mark Scheme

Marks

14(a)

120o E θ E , award P1

Note: 120o or (b)

P2

40 x 60 x cos 450

K2

1697.06

N1

2

3

Notes: cos 45 used correctly, award K1 (c)

(d)

4500 or 750 60 75 - 45

K1

300S

N1

K1

10800 750 =

3

K1 10800 T

K2

14.4

N1

4

12

Question

Solution and Mark Scheme

Marks

15(a)(i)

P1

( 8, -1) Note: point (8 , -1) marked on the diagram award P1

(ii)

(5 , 5)

P2

Note: point (5 , 5) marked on diagram, award P1 ( 9, 5 )

(iii)

P2

Rotation 180o , centre (3,3)

(iv)

5

P3

Note: 1. P2: Rotation 180o, Rotation 180o , centre G 2. P1: Rotation 180o (v) Enlargement centre N(6,1) with scale factor 3

P3

Note: 1. P2: Enlargement centre N or Enlargement scale factor 2 2. P1: Enlargement

(ii)

160 22

K1

40

N1

8 12

Question

Solution and Mark Scheme

Marks

16(a)

Mass(kg) 30 35 40 45 50 55

-

34 39 44 49 54 59

Frequency

Midpoint

5 6 9 8 7 5

32 37 42 47 52 57

I II III IV V VI

Class interval :

(III to VI)

P1

Frequency

:

(I to VI)

P2

Midpoint

:

(I to VI)

P1 4

Note: Allow one mistake in frequency for P1.

(b)

32(5) + 37(6) + 42(9) + 47(8) + 52(7) + 57(5) 5+6+9+8+7+5

K2

44.63

N1 3

Notes: Allow two mistakes for K1. ( c)

Axes drawn in correct direction, uniform scale for 29.5 ≤ x ≤ 59.5 and 0 ≤ y ≤ 9

P1

Using lower boundry or upper boundry or midpoint or class interval for x-axis.

K1

* 6 bar correctly drawn Note: * 5 bar correctly drawn, award N1

N2

(d)

4

K1 example: Most of the telephone bill is between 40 to 44

1 12

Graph for Question 16 Graf untuk Soalan 16

9

8

7

6

5

4

3

2

1

29.5

34.5

39.5

44.5

49.5

54.5

END OF MARK SCHEME

59.5