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SULIT 1449/2(PP)

[Lihat sebelah 1449/2(PP) SULIT

1449/2 (PP) Matematik Kertas 2 Peraturan Pemarkahan 17 Sept 2008

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN.

PEPERIKSAAN PERCUBAAN SPM 2008

UNTUK KEGUNAAN PEMERIKSA SAHAJA

Peraturan pemarkahan ini mengandungi 17 halaman bercetak

MATHEMATICS

Kertas 2

PERATURAN PEMARKAHAN


SULIT 1449/2(PP)

1449/2(PP) SULIT

2

Section A [ 52 marks]

Question Solution and Mark Scheme Marks

1(a)

(b)

Note: Set P Q correctly shaded, award K1

K1

K2

3

P Q R

P Q R

P Q R


SULIT 1449/2(PP)


3 Question Solution and Mark Scheme Marks

2

3 21p q or 22 143

p q or equivalent

5 25p or 5 103

q or equivalent

OR

42

qp or 4 2q p or equivalent (K1)

5 25p or 5 103

q or equivalent (K1)

OR

1 71131 41 1 2 2 1

3

pq

or equivalent (K2)

5p

6q Note : Accept

1. 56

pq

as final answer, award N1

2.

111311 1 2 2 1

3

or equivalent seen, award (K1)

K1

K1

N1

N1

4


SULIT 1449/2(PP)

1449/2(PP) SULIT

4

Question Solution and Mark Scheme Marks 3

23 10 0x x

3 5 2 0x x or equivalent

2x

53

x or 1 67

Note : 1. Accept without ‘= 0’

2. Accept three terms on the same side, in any order.

3. Do not accept solutions solved not using factorisation.

4. Accept 5 52 0, with , 23 3

x x x

for KK2

K1

K1

N1

N1

4

4

Identify UPT or TPU

tan 2 2

75 4

UPT

or equivalent

66 8 or 66 48 '

P1

K1

N1

3

5(a)

(b)

32

y

Gradient SR = 4

*64

1y

x

or *6 4 1 c or equivalent

4 10y x or equivalent

10

N1

P1

K1

N1

N1

5


SULIT 1449/2(PP)


5


Non-statement P1

Implication 1 : If x p > y p , then x > y K1

Implication 2 : If x > y, then x p > y p K1

6(a)

(b)

(c) If k is a multiple of 9, then it is multiple of 3 P1

True dep P1

(d) Premise 2 : 384 is divisible by 12

or

384 boleh dibahagi tepat dengan 12 K1 4

7(a)

(b)

90 222 14360 7

or 60 222 7360 7

14 + 90 222 14360 7

+ 60 222 7360 7

+ 7 + 7

172

3 or 157

3 or 57 33

290 22 14360 7

or 2180 22 7360 7

or 260 22 7360 7

290 22 14

360 7 2180 22 7

360 7 + 260 22 7

360 7

3083

or 21023

or 102 67

Note :

1. Accept π for K mark. 2. Correct answer from incomplete working, award KK2.

K1

K1

N1

K1

K1

N1

6


SULIT 1449/2(PP)

1449/2(PP) SULIT

6


8(a)

(b)

1 23 5

215

85

31

52

31

52

31

Note : 1 23 5 or 1 3

3 5 or

85

31 , award K1

(with condition of not more than 3 pairs)

360195 or

12065 or

2413 or 0.5417

K1

N1

K2

N1

5

9(a)

(b)

10k

3p

4 2 413 1 24 1 2 3

xy

2x

1y Note :

1. * inverse 4

matrix 2xy

or

4 213 14 1 2 3

seen,

award K1

2. Do not accept * inverse 1 2

matrix 3 4

or * inverse 1 0

matrix 0 1

.

3. 21

xy

as final answer, award N1.

4. Do not accept any solution solved not using matrices.

P1

P1

K2

N1

N1

6


SULIT 1449/2(PP)


7


10(a) 9

P1

(b) 9 3 3 95 0 0 5

or

K1

6 11 1 25 5

or or

N1

Note: Without working, award K1N1

(c) 1 13 9 5 5 9 9 21 16 1532 2

t t or equivalent K2

12 N1 6

Note : Allow one mistake in distance expression for any two or

one correct areas for K1.

11

40 7

1 22 3 3 53 7

40 7 1 22 3 3 53 7

232 8 232 9

Note: 1. Accept π for K mark 2. Correct answer from incomplete working, award KK2

K1

K1

K1

N1

4


SULIT 1449/2(PP)

1449/2(PP) SULIT

8


12(a)

(b)

(c)(i)

(ii)

(d)

10

5

Note : K only meant for table value Graph Axes drawn in correct direction, uniform scales in 3 5 x 4 and – 34 y 11 7 points and *2 points correctly plotted or curve passes through these points for 3 5 x 4

Smooth and continuous curve without any straight line and passes through all 9 correct points using the given scales for 3 5 x 4 Note : 1. 7 or 8 points correctly plotted, award K1

2. Ignore curve out of range

2 5 2 7y

2 45 2 40x

Identify equation 3 2y x or equivalent Straight line 3 2y x correctly drawn

Values of x : 1 8 1 7x

2 7 2 8x Note : 1. Allow P mark or N mark if values of y and x shown on graph

2. Values of y and x obtained by computations, award P0 or N0

(> 2 decimal places)

K1

K1

P1

K2 (does not

depend on P)

N1 (depends on

P and K)

P1

P1

K1

K1

N1 (dep 2nd K1)

N1 (dep 2nd K1)

2

4

2

4

12

Values of x on the graph must correct


SULIT 1449/2(PP)


9

y

x O 1 2 3 4

5

10

1 2 3 4

5

10

15

25

35

20

30

15

х

х

х

х

х

х х

х

х

22 5 8y x x

3 2y x


SULIT 1449/2(PP)

1449/2(PP) SULIT

10


13(a)(i) (5, 4) P1

(ii) (5, – 2) P2 3

Note : (1, 0) or (5, – 2) marked on diagram, award P1

(b)(i) W: Rotation 90 anticlockwise at centre (– 1, 2) or equivalent. P3

Note :

1. P2: Rotation 90 anticlockwise or Rotation at centre (– 1, 2),

2. P1: Rotation.

(ii) V: Enlargement centre (– 5, 5) with scale factor 3 P3 6

Note :

1. P2: Enlargement centre (– 5, 5) or Enlargement scale factor 3.

2. P1: Enlargement.

(c) 23*198 K1

23*198198 or 198 – 22 K1

176 N1 3

OR 198 1618

OR 19889

or 219883

, award K2

12


SULIT 1449/2(PP)


11


14(a) (b)

(c)

(i)

Upper boundary : (II to VIII)

Frequency : (II to VIII)

Cumulative frequency : (II to VIII)

Note : Allow one mistake in frequency for P1

(ii) 74 5 Axes drawn in correct direction and uniform scale for 29 5 99 5x and 0 y 40 *8 points correctly plotted Note : *6 or *7 points correctly plotted or curve passes through using at least 6 correct upper boundary, award K1 Smooth and continuous curve without any straight line passes all 8 correct points for using given scales 29 5 99 5x

First Quartile = 56 0 0 5 or Third Quartile = 75 5 0 5 Interquartile range = * *75 5 56.0 = 19 5 0 5

P1

P2

P1

P1

P1

K2

N1

K1

K1

N1

5

4

3

12

Upper Boundary Sempadan

Atas

Frequency Kekerapan

Cumulative Frequency Kekerapan Longgokan

29 5 0 0 I

39 5 2 2 II

49 5 3 5 III

59 5 8 13 IV

69 5 10 23 V

79 5 11 34 VI

89 5 4 38 VII

99 5 2 40 VIII


SULIT 1449/2(PP)

1449/2(PP) SULIT

12

0

5

10

15

20

25

30

35

40

39.5 49.5 59.5 69.5 79.5 89.5 99.5 29.5

Marks

Cumulative Frequency


SULIT 1449/2(PP)


13


15

Note : (1) Accept drawing only (not sketch). (2) Accept diagrams with wrong labels or without labels. (3) Accept correct rotation of diagrams. (4) Lateral inversions are not accepted. (5) If more than 3 diagrams are drawn, award mark to the correct ones only. (6) For extra lines (dotted or solid) except construction lines, no mark is awarded. (7) If other scales are used with accuracy of 0.2 cm one way, deduct 1 mark from the N mark obtained, for each part attempted. (8) Accept small gaps extensions at the corners. For each part attempted :

(i) If 0 4 cm, deduct 1 mark from the N mark obtained.

(ii) If > 0 4 cm, no N mark is awarded. (9) If the construction lines cannot be differentiated from the actual lines: (i) Dotted line : If outside the diagram, award the N

mark. If inside the diagram, award N0. (ii) Solid line : If outside the diagram, award N0.

If inside the diagram, no mark is awarded.

(10) For double lines or non-collinear or bold lines, deduct 1 mark from the N mark obtained, for each part attempted.


SULIT 1449/2(PP)

1449/2(PP) SULIT

14


15(a)

Correct shape with rectangles JFGR , JKPN and square NPQR All solid lines. JF FG GQ = QR = RN > NJ Measurement correct to 0 2 cm (one way) and all angles at vertices of rectangles = 901

K1

K1

dep K1

N1 dep K1K1

3

R Q G

N P

J K F


SULIT 1449/2(PP)


15


15(b)

Correct shape with the triangle FEV , rectangle JKPN and hexagon ABFEKJ All solid lines

AB EV EF = JA = NP > BF = NJ = VP

Measurement correct to 0 2 cm (one way) and all angles at the vertices of rectangles = 901

K1

K1 dep K1

N2 dep K1K1

4

A B

E

N P

J K

F

V


SULIT 1449/2(PP)

1449/2(PP) SULIT

16


15(c)

Correct shape with rectangles BCGF, GWVU and FULK All solid lines Note : Ignore PQ P and Q joined with dotted line to form square PQGU or rectangle PQWV CW > BC > VL > VW = BK > KL > UL = LP = PV = BF = FK Measurement correct to 0 2 cm (one way) and all angles at the vertices of rectangles = 901

K1

K1

dep K1

K1 dep K1K1

N2 dep K1K1K1

5

12

U

B C

G

P

L K

F

W V

Q


SULIT 1449/2(PP)


17


16(a)

(b)(i) (ii)

(c)

(36N, 70W) Note: 70oW or (65N, W / 70 E ), award P2 36N or (180 110), award P1 50 36 60 or equivalent 5160

140 60 cos50 or equivalent 5399.42

Note : Usage of cos 50 or 30 110 , award K1 180 60 cos36 or 8737 38

Note : Usage of cos 36 or 70 110 , award K1 180 60 cos36 *

800

10 92 or 10 hours 55 minutes

P3

K1

N1

K2

N1

K2

K1

N1

3

5

4

12

END OF MARK SCHEME


SULIT 1449/2(PP)

1449/2(PP) SULIT

18
