Spb Maths Answer Spm 2009

SULIT

1449/2(PP) 1449/2

1449/2(PP) Peraturan Pemarkahan Matematik Kertas 2 Ogos 2009

BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KLUSTER KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2009

MATEMATIK Kertas 2 PERATURAN PEMARKAHAN

UNTUK KEGUNAAN PEMERIKSA SAHAJA

AMARAN Peraturan Pemarkahan ini SULIT dan Hak Cipta Sekolah Berasrama Penuh. Kegunaannya khusus untuk pemeriksa yang berkenaan sahaja. Sebarang maklumat dalam peraturan pemarkahan ini tidak boleh dimaklumkan kepada sesiapa. Peraturan Pemarkahan ini juga tidak boleh dikeluarkan dalam apa jua bentuk penulisan dan percetakan.

Peraturan Pemarkahan ini mengandungi 9 halaman bercetak 1449/2(PP)

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Section A [ 52 marks ] No

Marking Scheme

1

Marks

K1 K1 4 N1N1

2

K1

or equivalent

K1

or equivalent ,

N1 N1

3

Line x = 8 drawn

K1

Shaded region

P2

4

Deduct 1mark for solid line x = 8 3

8 4

 UTS

P1

Tan  UTS =

or equivalent K2

 UTS = 60.26

5

0

0

or

60 15

’

N1

P1

(i) (ii) 12  2(5)  c

or

y  12 2 x5

y  2x  2

(iii) 2  2  5   c

or

y2 2 05

K1 N1

K1

S  0, 8 

6

4

N1 5

=

K1

Vcylinder =

K1

Vprism

Vsolid

K1

= =

OR

N1

OR 668.57

4

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2

No

7

Marking Scheme

(a)

30 22 90 22  2   4 or  2 5 360 7 360 7

K1

30 22 90 22  2  4   2 5  5  3  4 360 7 360 7 21

(b)

20  21.95 21

K1

N1

30 22 90 22   4  4 or  55 360 7 360 7 30 22 90 22   4 4   5 5 360 7 360 7 23

Marks

K1

K1

5  23.83 6

N1 6

8

(a)

(b)

(c)

9

P1

Implication 1: If the bearing of P from Q is 070 then the bearing of Q from P is 250 .

K1

Implication 2: If the bearing of Q from P is 250 then the bearing of P from Q is 070 .

K1 K1 N1

3n 2  1 , n  1,2,3,...

5 K1

(a)

3 1  12 4

N1

(b)

K2

8 2  12 3

N1 5

10

(a)

55  60 30

K1 N1

110 (b)

32

P1

(c)

(70  70)  60 110

K2

 76

4 11

or

76.36

N1

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3

No

11

Marking Scheme

a)

=

s

(b)

Marks

K1

3 2

N1

 1  2  x    4       4   y   11  3

K1

 x  1  4 2   4        y  2  3 1  11 

K1

x = 3

N1

1 y 2

N1

6

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4

Section B [48 marks] No

12

Marking Scheme

(a)

x y

-3 30

2 0

Marks

K1K1

(b) Graph ( Refer graph on page 6) K1 Axes drawn in the correct direction , the uniform scale is in the range given. K2 9 coordinates plotted correctly in the range given. Smooth curve drawn continuously in the range without a straight line at any part and passed through 9 correct coordinates . y  34.25  0.5

(c)

(i)

(d)

(ii) x  3.25  0.1 ,  0.55  0.1 , 3.8  0.1 Identify the equation y   2 x  20 or equivalent. Draw the line y   2 x  20

N1

P1 P1 K1 K1

x= N2

Notes : 2 values correct - N1

12

13

(a) (i) (4, 3)

P2

(ii) (5, 8)

P2

(b) (i) Reflection in the line BC or

x y4.

P2

(b) (ii) Enlargement with scale factor 2 about centre B or (4, 0)

P3

(b) (ii) 2 2  37  x

K2

37

A = 111

N1

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5

12

Graph for Question 12 y

35

30

25

20 y  2 x  20

15

10

5 y  x 3  13 x  18

4

3

2

1

0

2

4

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6

1

2

3

4

x

No

Marking Scheme

14

(a)

Class Interval

Frequency

Cumulative Frequency

I

30-34

0

0

II

35 - 39

2

2

III

40 - 44

4

6

IV

45 - 49

7

13

V

50 - 54

7

20

VI

55 - 59

6

26

V11

60 - 64

4

30

V111

65-69

2

32

Class interval Frequency

: :

Cumulative Frequency :

(b)

Marks

( III to VIII) correct ( I to VIII ) correct Allow 2 mistakes –P1

P1 P2

( I to VIII ) correct

P1

0  32  2  37  4  42  7  47  7  52  6  57  4  62  2  67 32

K2

2659 32

51.84 or N1

(c)

Ogive (Refer graph on page 8) Axes drawn in the correct direction , uniform scale for 34.5  x  69.5 and

0  y  32 .

K1

Horizontal axis labeled using upper boundary or use the values of upper boundary for plotting

K1

8 points plotted correctly or the ogive passed through them.

K1

The ogive completed and passed through 8 points correctly.

(d)

Any correct information Eg: 20 students obtained 54.5 marks and below

N1

N1 12

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7

Cumulative Frequency

35

30

25

20

15

10

5

0 34.5

39.5

44.5

49.5

54.5

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8

59.5

64.5

69.5

Marks

No

15

Marking Scheme

Marks

(a) Correct shape of rectangle BCGH

K1

Dotted line

K1

3 cm Correct measurement

0.2 cm

N1

3 cm 4 cm Correct shape of two rectangle and a circle K1 Circle drawn by using compasses K1

(b)(i)

4 cm



The centre of the circle marked

K1

Correct measurement

N2

0.2 cm

3 cm (b)(ii)

Correct shape of a pentagon and a triangle K1

5cm

Isosceles triangle with height 5 cm

K1

Correct measurement

N2

0.2 cm

6 cm

3 cm

12

7 cm

16

P1P1

(a) (b

K1 K1 3600 n.m

(c) 1800 or cos 40

N1 seen

K1 K1

K1K1 K2 499.14 knot N1

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9

12