spm mm ans (kedah)

8/14/2019 Spm Mm Ans (Kedah)

1/18

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH

NEGERI KEDAH DARUL AMAN

PEPERIKSAAN PERCUBAAN SPM 2008 1449/1MATHEMATICS

ANSWER FOR PAPER 1

1 C 11 D 21 C 31 C

2 B 12 C 22 A 32 C

3 D 13 A 23 D 33 A

4 B 14 D 24 D 34 D

5 C 15 C 25 B 35 B

6 B 16 A 26 B 36 D

7 A 17 B 27 D 37 A

8 C 18 C 28 A 38 B

9 D 19 D 29 B 39 C

10 B 20 A 30 A 40 A

ANALISIS

A 10

B 10

C 10

D 10

NOTA: MARKAH PELAJAR = 100140

)21(

+KK


2/18

1449/2 (PP)

Matematik

Kertas 2

Peraturan

Pemarkaha

n

17 Sept2008

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH

NEGERI KEDAH DARUL AMAN.

PEPERIKSAAN PERCUBAAN SPM 2008

UNTUK KEGUNAAN PEMERIKSA SAHAJA

MATHEMATICS

Kertas 2

PERATURAN PEMARKAHAN


3/18

Peraturan pemarkahan ini mengandungi 17 halaman bercetak

Section A

[ 52marks]

Question Solution and Mark Scheme Marks

1(a)

(b)

Note:

SetPQ correctly shaded, award K1

K1

K2 3

P Q R

PQ

R

PQ

R


4/18


2 3 21p q or2

2 143

p q or equivalent

5 25p or 5 103 q or equivalent

OR

4

2

qp

or 4 2q p or equivalent (K1)

5 25p or5

103 q or equivalent (K1)

OR

1711

31 4

1 1 2 2 13

p

q

or equivalent (K2)

5p

6q

Note :

Accept

1. 56

pq

as final answer, award N1

2.

111

31

1 1 2 2 13

or equivalent seen, award (K1)

K1

K1

N1

N1 4


5/18


3 23 10 0x x

3 5 2 0x x or equivalent

2x

5

3x 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 5

2 0, with , 2

3 3

x x x

for KK2

K1

K1

N1

N1 4

4 Identify UPT or TPU

tan2 2

7

5 4UPT

or equivalent

66 8 or 66 48'

P1

K1

N1 3

5(a)

(b)

3

2y

Gradient SR = 4

*6 41

y

x

or *6 4 1 c or equivalent

4 10y x

or equivalent

10

N1

P1

K1

N1

N1 5


6/18


6(a)

(b)

Non-statement P1

Implication 1 : Ifxp >yp , thenx >y K1

Implication 2 : Ifx >y, thenxp >yp K1

(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 14

360 7 or

60 222 7

360 7

14 +90 22

2 14360 7

+60 22

2 7360 7

+ 7 + 7

172

3 or

157

3 or 57 33

290 2214

360 7 or 2

180 227

360 7 or 2

60 227

360 7

290 22 14360 7

2180 22

7360 7

+ 260 22

7360 7

308

3 or

2102

3 or 102 67

Note :

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

K1

K1

N1

K1

K1

N1 6


7/18


8(a)

(b)

1 2

3 5

2

15

1 2 1 3 1 3

3 5 3 5 3 8

Note :1 2

3 5 or

1 3

3 5 or

1 3

3 8 , award K1

(with condition of not more than 3 pairs)

165

360 or

55

120 or

11

24 or 0 458

K1

N1

K2

N1 5

9(a)

(b)

10k

3p

4 2 41

3 1 24 1 2 3

x

y

2x

1y

Note :

1.

*inverse 4

matrix 2

x

y

or

4 21

3 14 1 2 3

seen,

award K1

2. Do not accept

*inverse 1 2

matrix 3 4

or

*inverse 1 0

matrix 0 1

.

3.2

1

x

y

as final answer, award N1.

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

P1

P1

K2

N1

N1 6


8/18


10(a) 9 P1

(b)

9 3 3 9

5 0 0 5or

K1

6 11 1 25 5or or N1

Note: Without working, award K1N1

(c) 1 1

3 9 5 5 9 9 21 16 1532 2

t t or equivalent K2

12 N1 6Note : Allow one mistake in distance expression for any two or

one correct areas for K1.

11 40

1 223 3 5

3 7

40 1 22

3 3 53 7

232 8 232 9

Note:

1. Accept for K mark

2. Correct answer from incomplete working, award KK2

K1

K1

K1

N1 4



9/18

12(a)

(b)

(c)(i)

(ii)

(d)

10

5

Note : Konly meant for table value

Graph

Axes drawn in correct direction, uniform scales in 3 5 x 4and 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 for3 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 ofx : 1 8 1 7x

2 7 2 8x

Note : 1. Allow P mark or N mark if values ofy andx

shown on graph

2. Values ofy andx 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 ofx on the

graph must correct


10/18

y

O 1 2 3 4

5

10

1234

5

10

15

25

35

20

30

15

22 5 8 y x x

3 2y x


11/18


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) orequivalent. P3

Note :

1. P2: Rotation 90 anticlockwise orRotation 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) orEnlargement scale factor 3.

2. P1: Enlargement.

(c)198

*(3)K1

198198 198 22

*(3)or K1

176 N1 3

OR198

1618

OR198

89

or 2198

83

, award K2

12



12/18

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 for29 5 99 5x and 0 y 40

*8 points correctly plotted

Note :

*6 or *7 points correctly plotted or curve passes through usingat 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


13/18

0

5

10

15

20

25

30

35

40

39.5 49.5 59.5 69.5 79.5 89.5 99.529.5

Marks

Cumulative

Frequency


14/18


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, nomark 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 theactual lines:

(i) Dotted line : If outside the diagram, award the Nmark.

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 1mark from the N mark obtained, for each part attempted.



15/18

15(a)

Correct shape with rectanglesJFGR ,JKPNand

square NPQR

All solid lines.

JFFGGQ = QR =RN >NJ

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

K1

K1

dep K1

N1 depK1K1

3


R Q G

N P

J K F


16/18

15(b)

Correct shape with the triangleFEV, rectangleJKPNand

hexagonABFEKJ

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

K1dep K1

N2 dep

K1K1 4


A B

E

N P

J K

F

V


17/18

15(c)

Correct shape with rectanglesBCGF, GWVUandFULK

All solid lines

Note : IgnorePQ

Pand Q joined with dotted line to form squarePQGUorrectanglePQWV

CW>BC> VL > VW=BK>KL > UL =LP=PV=BF=FK

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

K1

K1

dep K1

K1 dep

K1K1

N2 dep

K1K1K1

5

12

U

B C

G

P

LK

F

WV

Q


18/18


16(a)

(b)(i)

(ii)

(c)

(36N, 70W)

Note: 70oW or (65N, W/ 70E), award P2

36N or (180

110), award P1

50 36 60 or equivalent

5160

140 60 cos50 or equivalent

5399 52

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

spm mm ans (kedah)

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