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SMKDarulaman j*k

http://edu.joshuatly.com/ http://www.joshuatly.com/

SMKDarulaman j*k

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN

PEPERIKSAAN PERCUBAAN SPM 2010 1449/1 MATHEMATICS ANSWER FOR PAPER 1

1 B 11 C 21 C 31 D

2 A 12 D 22 A 32 B

3 D 13 A 23 A 33 B

4 B 14 B 24 B 34 D

5 C 15 C 25 B 35 C

6 B 16 B 26 D 36 B

7 C 17 D 27 A 37 D

8 C 18 C 28 D 38 C

9 A 19 A 29 A 39 D

10 B 20 A 30 C 40 A

ANALISIS

A 10

B 11

C 10

D 9

NOTA: MARKAH PELAJAR = 100140

)21( ×+ KK

SMKDarulaman j*k

SULIT 1449/2(PP)

[Lihat halaman sebelah 1449/2(PP) SULIT

1449/2 (PP) Matematik Kertas 2 Peraturan Pemarkahan 19 September 2010

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH

NEGERI KEDAH DARUL AMAN.

PEPERIKSAAN PERCUBAAN SPM 2010

UNTUK KEGUNAAN PEMERIKSA SAHAJA

Peraturan pemarkahan ini mengandungi 19 halaman bercetak

MATHEMATICS

Kertas 2

PERATURAN PEMARKAHAN

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

2

Section A [ 52 marks]

Question Solution and Mark Scheme Marks

1(a)

(b)

Note : P ∪ R correctly shaded, award K1

K1

K2

3

P R

Q

P R

Q

P R

Q

SMKDarulaman j*k

SULIT 1449/2(PP)

3

2

24 3 7 0− − =x x

( ) ( )1 4 7 0+ − =x x or equivalent

OR

2( 3) ( 3) 4(4)( 7)

2(4)

− − ± − − −=x (K1)

1= −x

7 31 1 75

4 4= ⋅x or or

Note : 1. Accept without ‘= 0’.

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

3. Accept correct answer from the correct term without factorisation for Kk2.

K1 K1

N1

4

3

3 212

p q− = or 3 2 18p q+ = or equivalent

Note: Attempt to equate the coefficient of one of the unknowns award K1

4 12q− = or 4 32p = or equivalent OR

14 2p q= + or 14

2

pq

−= or equivalent (K1)

2(9 )

3

qp

−= or 3

92

q p= − or equivalent (K1)

Note: Attempt to make one of the unknowns as the subject, award K1

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

4

OR

( ) ( )

1 2141

33 911 1 2 22

p

q

= − − −

or equivalent (K2)

8p =

3q = − Note : Accept

1. 8

3

p

q

= −

as final answer, award N1

2.

( ) ( )

1 2141

33 911 1 2 22

− − −

or equivalent seen, award (K1)

N1

4(a)

(b)

PTQ∠ or QTP∠

2 2

12tanθ

6 8=

+ or equivalent

50 19⋅ ° or 50 11'° or 50 12'°

P1

K1

N1

3

5(a)(i)

(ii)

(b)

False // Palsu

True // Benar

If 2 0x > , then 0 or 0x x> < //

Jika 2 0x > , maka 0 atau 0x x> <

P1

4

SMKDarulaman j*k

SULIT 1449/2(PP)

5

(c)

If 0 or 0x x> < , then 2 0x > //

Jika 0 atau 0x x> < , maka 2 0x >

5 and 9 are odd numbers // 5 dan 9 adalah nombor ganjil

P1

K1

5

6(a)

(b)

0 2 5x= − − or equivalent

5

2x = − or

12

2− or 2 5− ⋅

mQR = 2−

6

4

y

x

− =−

*mQR or 6 = *mQR (4) + c or equivalent

2 14y x= − + or equivalent

K1

N1

P1

K1

N1

5

7(a)

(b)

p = 14 q = – 4

2 3 13

4 1 5

x

y

− =

1 3 131

4 2 2(2)(1) ( 3)(4)

x

y

= −− −

or

*

13

2

x inverse

y matrix

=

2x =

3y = −

P1

K1

N1

2

4 6

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

6

Note:

1. Do not accept *

2 3 1 0

4 1 0 1

inverseor

matrix

=

.

2. 2

3

x

y

= −

as final answer, award N1.

3. Do not accept any solutions solved not using matrix method.

8

21 22

3 5 63 7

× × ⋅ ×

222

5 47

× ×

2 21 22 223 5 6 5 4

3 7 7 × × ⋅ × + × ×

2739

7 or

2391

7 or 391 3⋅

Note :

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

K1

N1

4

9(a)

(b)(i)

{(S,C), (S,O), (S,R), (S,E), (C,S), (C,O), (C,R), (C,E), (O,S),

(O,C), (O,R), (O,E), (R,S), (R,C), (R,O), (R,E), (E,S), (E,C),

(E,O), (E,R)}

Note :

1. Accept correct tree diagram or grid for P2

2. Accept 10 correct listings for P1

{(C,S), (C,O), (C,R), (C,E)} 4

20 or

1

5

P2

K1

N1

2

SMKDarulaman j*k

SULIT 1449/2(PP)

7

(ii)

{(S,C), (S,R), (C,S), (C,R), (O,E), (R,S), (R,C), (E,O)} 8

20 or

2

5

Note : Accept answer without working from correct listing, tree diagram or grid.

K1

N1

4

6

10(a)

(b)

90 22

2 14360 7

× × × or 120 22

2 7360 7

× × ×

90 22

2 14360 7

× × × + 120 22

2 7360 7

× × × + 14 + 7 + 7 or equivalent

194

3 or

264

3 or 64 67⋅

290 2214

360 7× × or 2120 22

7360 7

× ×

290 22

14360 7

× × − 2120 227

360 7× × or equivalent

308

3 or

2102

3 or 102 7⋅

Note :

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

K1

N1

K1

N1

6

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

8

11(a)

(b)

(c)

45915.3

30=

11 28

10

− or

17

10

−

7

110

− or 1 7− ⋅

Note : Without working, award K1N1

( ) ( ) ( )1 111 28 10 11 12 11 8 459

2 2v

× + × + × + × + × =

or equivalent method Note:

1. ( )111 28 10

2× + × or ( )11 12× or ( )1

11 82

v× + ×

or equivalent, award K1

2. Accept 195 or 132 for K1 22

P1

K1

N1

K2

N1

6

SMKDarulaman j*k

SULIT 1449/2(PP)

9

12(a)

(b)

(c)(i)

(ii)

(d)

7

2

Note : K only meant for table value. Graph Axes drawn in correct direction, uniform scales in 3 5 4x− ⋅ ≤ ≤ and 8 28y− ≤ ≤ . All 7 points and *2 points correctly plotted or curve passes through these points for 3 5 4x− ⋅ ≤ ≤ and 8 28y− ≤ ≤ . A smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for 3 5 4x− ⋅ ≤ ≤ . Note : 1. 7 or 8 points correctly plotted, award K1.

2. Ignore curve out of range.

10 0 11 0y⋅ ≤ ≤ ⋅

3 20 3 10x− ⋅ ≤ ≤ − ⋅

Identify equation 2 9y x= − + or equivalent. Straight line 2 9y x= − + correctly drawn.

Values of x : 2 65 2 55x− ⋅ ≤ ≤ − ⋅

3 05 3 15x⋅ ≤ ≤ ⋅ Note : 1. Allow N marks if values of x shown on the graph. 2. Values x obtained by calculation, award N0.

K1

P1

K2 (does not

depend on P)

N1

(depends on P and K )

P1

K1

N1

(dep 2nd K1)

N1 (dep 2nd K1)

2

4

2

4

12

Note:

1. Allow P mark if value of x and y are shown on the graph.

2. Value of x and y obtained by calculation, award P0.

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

10

y = – 2x + 9

22 3 7y x x= − − ××××

××××

×××× ××××

– 2 – 1 O 1

20

15

10

5

– 5

– 10

2 3 4 x

25

30

y

– 3 – 4

SMKDarulaman j*k

SULIT 1449/2(PP)

11

13(a)(i) (6, 1) P2

Note: (6, 1) marked or (1, 4) seen or (1, 4) marked, award P1

(ii) (8, 5) P2 4

Note: (8, 5) marked or (3, 8) seen or (3, 8) marked, award P1

(b)(i)(a) W: Reflection in the line x = 1 P2

Note :

1. P1 : Reflection // Pantulan.

(b) V: Enlargement at centre K or (6, 10) with scale factor3

2 P3

Note :

1. P2 : Enlargement at centre K or (2, 1) or

Enlargement scale factor 3

2

2. P1 : Enlargement.

(ii) * 23

882

×

K1

* 23

88 882

× −

K1

110 N1 8

12

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

12

14(a)

(b)

Frequency : (I to VIII)

Cumulative frequency : (I to VIII)

Upper Boundary : (I to VIII)

Note : Allow one mistake in frequency for P1

* * * * * * *

( 34 5 2) ( 44 5 3) ( 54 5 8) ( 64 5 10) ( 74 5 11) ( 84 5 4) ( 94 5 2)

2 3 8 10 11 4 2

⋅ × + ⋅ × + ⋅ × + ⋅ × + ⋅ × + ⋅ × + ⋅ ×+ + + + + +

Note :

1. Allow *midpoint for K1 2. Al low two mistakes for the multiplication of midpoint

and *frequency, for K1 65 75⋅ Note :

Correct answer from incomplete working, award Kk2

e.g. 2630

65 7540

= ⋅ (without table)

P2

P1

K2

N1

4 3

Marks Markah

Frequency Kekerapan

Cumulative Frequency Kekerapan Longgokan

Upper Boundary Sempadan

Atas

20 – 29 0 0 29.5 I

30 – 39 2 2 39.5 II

40 – 49 3 5 49.5 III

50 – 59 8 13 59.5 IV

60 – 69 10 23 69.5 V

70 – 79 11 34 79.5 VI

80 – 89 4 38 89.5 VII

90 - 99 2 40 99.5 VIII

SMKDarulaman j*k

SULIT 1449/2(PP)

13

(c)

(d)

Axes drawn in correct direction and uniform scale for 29 5 99 5x⋅ ≤ ≤ ⋅ and 0 ≤ y ≤ 40 Note :

Do not accept wrong label *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 through 8 correct points for using given scales 29 5 99 5x⋅ ≤ ≤ ⋅ Any true statement from the ogive

Note :

Do not accept answer without an ogive

P1

K2

N1

K1

4

1

12

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

14

0

5

10

15

20

25

30

35

40

29.5 39.5 49.5 59.5 69.5 79.5 89.5

××××

Marks

Frequency

45

××××

99.5 ××××

SMKDarulaman j*k

SULIT 1449/2(PP)

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.

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

16

15(a)

Correct shape with pentagon ABHGF All solid lines. BA > AF > HG > BH Measurement correct to ± 0 2⋅ cm (one way) and all angles at vertices of rectangles = 90° ± 1°

K1

K1 dep K1

N1 dep K1K1

3

F

G H

B A

SMKDarulaman j*k

SULIT 1449/2(PP)

17

15(b)(i)

Correct shape with rectangles PNML, FPLG, GLJH and FPJH All solid lines

FN > FH > HJ = FP > MN = FG > LJ = GH = LM

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

K1

K1 dep K1

N2 dep K1K1

4

N M

L J

H G F

P

SMKDarulaman j*k

SULIT 1449/2(PP)

1449/2(PP) SULIT

18

15(b)(ii)

Correct shape with rectangles QNPD and ADEF All solid lines Note : Ignore straight line KG K and G joined with dashed line to form rectangles ADKG and GKEF

QN = QA > AF > EF = AD > KE = GF > NP = QD >

EP = AG = DK

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

K1

K1 dep K1

K1 dep K1K1

N2 dep K1K1K1

5

12

N P

Q

G K

F E

D A

SMKDarulaman j*k

SULIT 1449/2(PP)

19

16 (a)

(b)

(c)

(d)

(75°S, 100°E) // (75°S, 100°T) Note: 1. 100°E or 100°T , award P2

2. 100° or E or T , award P1

6420

60 or 107�

6420

7560

−

32�S

( )80 20 60 cos75+ × × ° or 100 60 cos75× × °

Note: ( )80 20+ or 100 or using cos75° correctly, award K1

1552 91⋅

180 60

550

× or equivalent

Note: ( )*180 60

550

×, award K1

19 64⋅ hours or 19 hours 38 minutes

END OF MARK SCHEME

P3

K1

N1

K2

N1

K2

N1

3

12

SMKDarulaman j*k

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