TRIAL MATE SPM 2010 Kedah Paper 2 Answer

8/8/2019 TRIAL MATE SPM 2010 Kedah Paper 2 Answer

1/19

SULIT 1449/2(PP)

[Lihat halaman sebelah

1449/2(PP) SULIT

1449/2 (PP)

Matematik

Kertas 2

Peraturan

Pemarkahan

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


2/19

SULIT 1449/2(PP)

1449/2(PP) SULIT

2

Section A

[ 52marks]

Question Solution and Mark Scheme Marks

1(a)

(b)

Note :

PR correctly shaded, award K1

K1

K2 3

P R

Q

P R

Q

P R

Q


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SULIT 1449/2(PP)


1449/2(PP) SULIT

3


2 24 3 7 0 !x x

1 4 7 0 !x x or equivalent

OR2( 3) ( 3) 4(4)( 7)

2(4)

s !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

N1 4

3 33 21

2p 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! or14

2

pq

! or equivalent (K1)

2(9 )

3

qp

! or

39

2q p! or equivalent (K1)

Note:

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


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SULIT 1449/2(PP)

1449/2(PP) SULIT

4


OR

1 2141

3

3 911 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 91

1 1 2 22

or equivalent seen, award (K1)

N1

N1

4(a)

(b)

T or

T

2 2

12tan

6 8!

or equivalent

50 19 r or 50 11'r or 50 12'r

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

P1

P1

4


5/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

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

P1

P1

K1

N1

N1

2

4

6


6/19

SULIT 1449/2(PP)

1449/2(PP) SULIT

6


Note:

1. Do not accept

*

2 3 1 0

4 1 0 1

inverseor

atrix

!

.

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

v v v

222

5 47 v v

2 21 22 223 5 6 5 43 7 7

v v v v v - -

2739

7 or

2391

7 or 391 3

Note :

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

K1

K1

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 P22. Accept 10 correct listings for P1

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

4

20 or

1

5

P2

K1

N1

2


7/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

7

Question Solution and Mark Sche me Marks

(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)

90 222 14

360 7v v v or

120 222 7

360 7v v v

90 222 14

360 7v v v +

120 222 7

360 7v v v + 14 + 7 + 7 or equivalent

194

3 or

264

3 or 64 67

290 22 14360 7

v v or 2120 22

7360 7

v v

290 22 14360 7

v v 2120 22 7

360 7v v or equivalent

308

3 or

2102

3 or 102 7

Note :

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

K1

K1

N1

K1

K1

N1 6


8/19

SULIT 1449/2(PP)

1449/2(PP) SULIT

8


11(a)

(b)

(c)

45915.3

30!

11 28

10

or

17

10

71

10 or 1 7

Note : Without working, award K1N1

1 1

11 28 10 11 12 11 8 4592 2

v

v v v v v ! - -

or equivalent method

Note:

1. 1 11 28 102

v v or 11 12v or 1

11 82

vv v

or equivalent, award K1

2. Accept 195 or 132 for K1

22

P1

K1

N1

K2

N1 6


9/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

9


12(a)

(b)

(c)(i)

(ii)

(d)

7

2

Note : Konly meant for table value.

Graph

Axes drawn in correct direction, uniform scales in 3 5 4x e e

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 e e .

Note : 1. 7 or 8 points correctly plotted, award K1.

2. Ignore curve out of range.

4.0 < y < 5.0

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 e e

Note : 1. Allow N marks if values of xshown on the graph.

2. Values x obtained by calculation, award N0.

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

Note:

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

2.

Value ofx and y obtained by calculation,award P0.


10/19

SULIT 1449/2(PP)

1449/2(PP) SULIT

10

y = 2x+ 9

22 3 7y x x! v

v

v

v

v

v

vvv

2 1 O 1

20

15

10

5

5

10

2 3 4 x

25

30

y

3 4


11/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

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 centreK or (6, 10) with scale factor3

2 P3

Note :

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

Enlargement scale factor3

2

2. P1 : Enlargement.

(ii) * 2388

2

v

K1

* 23

88 882

v

K1

110 N18

12


12/19

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

v v v v v v v

Note :

1. Allow *midpoint for K12. Allow 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

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


13/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

13


(c)

(d)

Axes drawn in correct direction and uniform scale for

29 5 99 5x

and 0e y e 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 passesthrough 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


14/19

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

v

Marks

Frequency

45

v

v

v

v

v

v

99.5

v


15/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

15


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, nomark is awarded.

(7) If other scales are used with accuracy of s 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 e 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 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 1mark from the N mark obtained, for each part attempted.


16/19

SULIT 1449/2(PP)

1449/2(PP) SULIT

16

Question Solution and Mark Sche me Marks

15(a)

Correct shape with pentagonABHGF

All solid lines.

BA"AF"HG >BH

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

at vertices of rectangles = 90rs 1r

K1

K1

dep K1

N1 dep

K1K1 3

F

G H

BA


17/19

SULIT 1449/2(PP)


1449/2(PP) SULIT

17


15(b)(i)

Correct shape with rectanglesPNML, FPLG, GLJHandFPJH

All solid lines

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

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

vertices of rectangles = 90rs 1r

K1

K1dep K1

N2 dep

K1K1 4

N M

L J

HGF

P


18/19

SULIT 1449/2(PP)

1449/2(PP) SULIT

18


15(b)(ii)

Correct shape with rectangles QNPD andADEF

All solid lines

Note : Ignore straight lineKG

Kand G joined with dashed line to form rectanglesADKG and

GKEF

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

EP = AG = DK

Measurement correct to s 0 2 cm (one way) and all angles at

the vertices of rectangles = 90rs 1r

K1

K1

dep K1

K1 dep

K1K1

N2 dep

K1K1K15

12

N P

Q

GK

FE

DA


19/19

SULIT 1449/2(PP)


19


16 (a)

(b)

(c)

(d)

(75rS, 100rE) // (75rS, 100rT)

Note: 1. 100rE or 100rT , award P2

2. 100r or E or T, award P1

6420

60 or 107

642075

60

32S

80 20 60 cos75 v v r or 100 60 cos75v v r

Note: 80 20 or 100 or using cos75r correctly, award K1

1552 91

180 60

550

v or equivalent

Note:

*

180 60

550

v, award K1

19 64 hours or 19 hours 38 minutes

END OF MARK SCHEME

P3

K1

K1

N1

K2

N1

K2

N1

3

3

3

3

12

TRIAL MATE SPM 2010 Kedah Paper 2 Answer

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