SULIT 1449/2(PP)

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PROGRAM PENINGKATAN PRESTASI AKADEMIK SPM 2013

ANJURAN

MAJLIS PENGETUA SEKOLAH MALAYSIA (KEDAH)

MODUL A

MATEMATIK KERTAS 2

PERATURAN PEMARKAHAN

UNTUK KEGUNAAN PEMERIKSA SAHAJA

Peraturan pemarkahan ini mengandungi 14 halaman bercetak

SULIT 1449/2(PP)

1449/2(PP) SULIT

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Section A [ 52 marks]

Question Solution and Mark Scheme Marks

1

2

40-2

-4

-6 -4

-2

6

4

2 x

y

y = - x - 1

y = 2x + 2

Straight dotted line x = 1 correctly drawn. K1 Region correctly shaded P2 3 Note: 1 Accept solid line x = 1 for K1 2 Award P1 to shaded region bounded by two correct lines,

including part of R. (Check one vertex from any two correct lines

2(a) ∠MFH P1

3 (b)

137tan =∠MFH or equivalent

K1

28.3° or 28° 18′ N1

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3 Question Solution and Mark Scheme Marks

3

049 2 =−x

( )( ) 02323 =+− xx or equivalent

32

=x or 0.67

32

−=x or –0.67

Note : 1. Accept without ‘= 0’

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

3. ( )( )0 67 0 67x x− ⋅ + ⋅ with 0 67, 0 67x x= ⋅ = − ⋅

award Kk2

K1

K1

N1

N1

4

4 14 3 2x y+ = − or 7 21 77x y+ = or equivalent K1 Note :

Attempt to equate one of the coefficients the unknowns, award K1 OR

( )

31 2 1 711 211 33 7 3

y xxx y or y or x or y− − − −−

= − = = =

or equivalent (K1)

Note :

Attempt to make one of the unknowns as the subject award K1.

3913 13 782

x or y− = = or equivalent K1

OR

3 113123 1(1) (3)(7) 7 1

2

xy

− = − − −

(K2)

Note : Attempt to write without equation, award (K1)

1x = − N1 4y = N1 4

Note :

14

xy

− =

as final answer, award N1

SULIT 1449/2(PP)

1449/2(PP) SULIT

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Question Solution and Mark Scheme Marks 5(a) 20

214

214

722

21

×××× K1

4

1540 N1

(b) 202

142

14722

21

×××× + ( )1 20 10 14 67902

AB× + × × = K1

25 N1

Note : 1. Accept π for K mark. 2. Correct answer from incomplete working, award Kk2.

6 (a) benar / true P1

5

(b) Jika n adalah nombor negatif maka 0n < . If n is a negative number then 0n < . benar / true

P1

(c) Set R ialah subset bagi set K Set R is subset of set K

P1

(d) Bilangan subset bagi suatu set yang mempunyai 7 unsur ialah 72

The number of subsets in a set with n elements is 72 .

K1

72 128= N1

7 (a) 5x = − P1

5

(b) 45SR PQM M= = P1

( )

*44 55

c= − + or ( )

*4 45 5

yx

−=

− − K1

8

54

+= xy N1

y-intercept = 8 N1 8 (a) 12 P1 1

(b) 12 010 0

or equivalent−−

K1

6 1 25

or ⋅ N1 2

Note: Accept answer without working for K1N1

(c) ( )1 1(18 28) 12 (( 28)(12 20) 4682 2

t+ + − + = or

equivalent method K2 Note:

1 1(18 28)(12) (( 28)(12 20)2 2

or t+ − +

equivalent, award K1 40 N1 3 6

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5 Question Solution and Mark Scheme Marks

9(a)

(b)

147222

360120

××× or 77222

360180

×××

14 + 14 + 14 + 147222

360120

××× + 77222

360180

×××

3280 or

3193 or 93.33

214722

360120

×× or 27722

360180

××

214

722

360120

×× − 27722

360180

××

3

385 or 31128 or 128.33

Note :

1. Accept π for K mark. 2. Correct answer from incomplete working, award Kk2.

K1

K1

N1

K1

K1

N1

6

10 (a)

{(P, M), (P, 4), (P, 5), (P, N), (Q, M), (Q, 4), (Q, 5), (Q, N), (3, M), (3, 4), (3, 5), (3, N), (R, M), (R, 4), (R, 5), (R, N)} Note :

1. Accept 8 correct listing from not more than 16 outcomes for P1

P2

(b)(i) {(3, 4), (3, 5)}

K1

162 or

81

N1

(ii) {(P, 4), (P, 5), (Q, 4), (Q, 5), (3, M), (3, N), (R, 4), (R, 5)}

168 or

21

K1

N1

NOTE : 1. Accept other method for K mark.

2. Accept answer without working from correct listing, correct tree diagram or correct grid for K1N1.

SULIT 1449/2(PP)

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Question Solution and Mark Scheme Marks 11 (a)

( ) ( )1 216 33 1 2 6

− − −× − − ×

1 215 156 1

15 5

−

P2 2

(b) 3 2 96 1 7

xy

= − −

P1

1 2 916 3 7(3)( 1) (2)(6

xor

y− −

= − −− −

* 9

7x Inversey matrix

= −

K1

13

x = − N1

y = 5 N1 4 6 Note:

1. 13

5

xy

− =

as final answer, award N1

2. Do not accept any solution solved no using matrix method.

3. Do not accept * 3 26 1

inversematrix

= −

or * 1 00 1

inversematrix

=

12 (a) x = -4, y = 3

x = -1.5, y = 8 K1 K1

12

(b) Graph Axes drawn in correct direction, uniform scales in -6<x< -0.75 and 0 < y < 16.

P1

All 6 points and *2 points correctly plotted or curve passes through these points -6 < x < -0.75 and 0 < y < 16.

K2

A smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for -6 < x < -0.75 and 0 < y < 16.

N1

Note : 1. 6 or 7 points correctly plotted, award K1.

2. Ignore curve out of range.

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7

.

.

. .

. . . . .

0 -6 -5 -4 -3 -2 -1

2

0

4

6

8

10

12

14

16

Graf untuk Soalan12 Graph for Question 12

SULIT 1449/2(PP)

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(c) (i) 4.6 < y < 5.0 P1

(ii) -1.0 < x < = - 0.8 P1

(d) y = 2x + 12 or garis lurus y = 2x + 12 dilukis

K1 K1

-4.8 < x < -4.65 , -1.35 < x < -1.20 N1N1

13(a)(i) (2 , 6) P2

12

Note: (4, 5) or (4, 5) marked , award P1

(ii) (7, 8) P2

Note: (9 , 7) or (9 , 7) marked, award P1

(b)(i)(a) W: Rotation, 90° clockwise at (10 , 10)

P3

Note :

1. P2 : Rotation 90° clockwise or Rotation, at (10 , 10) / Putaran 90°

ikut arah jam atau Putaran pada (10,10)

2. P1: Rotation// Putaran

(b) V: Enlargement at centre (13 , 10), with scale factor 31 P3

Note:

P2: Enlargement at centre (13 , 10), or Enlargement with scale factor

31 // Pembesaran pada (13 , 10) atau pembesaran dengan faktor

skala 31

P1: Enlargement// Pembesaran

(ii) 21 1803

= ×

K1

20

N1

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9Question Solution and Mark Scheme Marks

14(a)(i)

Marks : (II to VII)

Mid point : (II to VII)

Frequency : (I to VII)

Note : Allow two mistake in frequency for P1.

P1

P1

P2

4

(b)(i) 40 – 49

P1

4

(ii)

( ) ( ) ( ) ( ) ( ) ( ) ( )* * * * * * *

* * * * * * *

2 24.5 5 34.5 8 44.4 6 54.5 4 64.5 3 74.5 2 84.52 5 8 6 4 3 2

× + × + × + × + × + × + ×

+ + + + + +

or 30

1555

Note: 1. Allow *midpoint for K1

6

311 or 6551 or 51.83

Note: Correct answer from incomplete working, award Kk2

K2

N1

(c) Axes drawn in correct direction and uniform scale for 5.845.24 ≤≤ x and 0 ≤ y ≤ 8. *7 points correctly plotted Note : *5 or *6 points correctly plotted or bar passes through using at least 6 correct mid-point, award K1. Correct bar passes all 7 correct points for using given scales 5.845.24 ≤≤ x

P1

K2

N1

4

Marks Markah

Mid-point Titik tengah

Frequency Kekerapan

20 – 29 24.5 2 I

30 – 39 34.5 5 II

40 – 49 44.5 8 III

50 – 59 54.5 6 IV

60 – 69 64.5 4 V

70 – 79 74.5 3 VI

80 – 89 84.5 2 VII

SULIT 1449/2(PP)

1449/2(PP) SULIT

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Graf untuk Soalan14 Graph for Question 14

8 7 6 5 4 3 2 1 0

24.5 34.5 44.5 54.5 64.5 74.5 84.5 Mark

frequency

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11

Question Solution and Mark Scheme Marks

15

Note : (1) Accept drawing only (not sketch). (2) Accept diagrams with wrong labels and ignore wrong 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

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Question Solution and Mark Scheme Marks

15(a)

P

J K

L

MN

3.5 cm

3.5 cm

7 cm

8 cm

Correct shape with rectangles JKMN , JKLP and PLMN All solid lines.

K1

3

JK > KM > KL=LM

K1 dep K1

Measurement correct to ± 0 2⋅ cm (one way) and all angles

at vertices of rectangles = 90° ± 1°

N1 dep K1K1

15(b)(i)

J

P L

K

FR

S

QE4 cm

3 cm

3 cm

2 cm

2 cm

8 cm

Correct shape with rectangle PLKJ, SQ perpendicular to EQ All solid lines

K1

4

PL > LF > EQ > LK = KF > RF = QR = QS

K1 dep K1

Measurement correct to ± 0 2⋅ cm (one way) and all angles at the

vertices of rectangles = 90° ± 1°

N2 dep

K1K1

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13 Question Solution and Mark Scheme Marks

15(b)(ii)

S

G

V

M

L

K

F

1 cm

2 cm

7 cm

5

Correct shape All solid lines Note : Ignore *SV

K1

5

12

S and V joined with dashed line to form rectangles SVFG

K1 dep K1

FG > LM > MG K1 dep K1K1

Measurement correct to ± 0 2⋅ cm (one way) and all angles at the vertices of rectangles = 90° ± 1°

N2 dep K1K1K1

16(a)

105 o E ∕∕ 105 o T) Note :

105 o or θo E ∕∕ θo T, award P1

P2

12

(b)(i) 390060

35 o N // U

K1

N1N1

(ii) 60 cos35 4669oθ × × = 20

K2

N1 (c) ( )

60030cos6010575 ××+

15.59

K2K1

N1 Note :

* cos 45 + * (75 105 )+ , award K1

SULIT 1449/2(PP)

1449/2(PP) SULIT

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