PEPERIKSAAN PERCUBAAN SPM TAHUN 2012MARKING SCHEME FOR ADDITIONAL MATHEMATICS FORM 5 PAPER 1

NO. MARKING SCHEME MARKS FULL MARKS1 a) p, q

b) 2c) many to many

111

3

2 -11

f (-6) = 2 (-6) + 1 @ fg (-2) = 112-

2-6- ++）（

g(-2) = -6 @ fg (x) = 11

3-2 +

+xx

3

B2

B1

3

3

)3(2

5

+x , 3−≠x

5 = )3( +x 2y or y = 62

5

+x

2

B1

2

4k = - 5

0)1)(1(4)4( 2 =−−− k

142 +=+ xkx

3

B2

B1

3

5

2

13- ≤≤ x

( ) ( ) 0312 ≤+− xx

3

B2

B1

3

6andx

3

1= 5−=x

5))(143( =+ xx

1))(143(log5 =+ xx

3

B2

B1

3

-32

1

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7

3

1-=x

81

x-5 =+x

31

x-5log 2 =

+x

Change base: 2log2

x)-5(log2

2

2

4

B3

B2

B1

4

8 a) p=2

b) 9c) 1a −=

1

1

1

3

9 a) -8

P – 2 - ( - 6 ) = -14 - ( p – 2 ) @ 2-p2

14-6- =+ ）（

b) – 126

[ ])4(6)6(22

77

−+−=S

d = -10 – ( - 6 ) = -4

2

B1

2

B2

B1

4

10128

( )

−

=∞

2

11

64S

2

1=r

3

B2

B1

3

11 h =5 and h=15

h =5 or h=15

4033235816h516-21- =+−−+++ h

3

B2

B1

3

12 r =1 1

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2

1t =

5

)(1)4(43

rr

+−=− or 5

)8(1)(42

+= t

1

B1

3

13 b~~

6a4 −

PRQPQR +=

2

B12

14290

13 11i j− +% %

3 ( ji 73 +− ) - 2( ji 52 + )

3

B2

B1

3

15

3+=x

xy

31 += xy

x

m = 12

12

xx

yy

−−

= 13

3

03

36 ==−−

or c = 3

3

B2

B1

3

16a)

t

t 21−

Cot θ = θnta

1

b) 21 t−

2

B1

1

3

17 a) 3

b) 60 ,131.81 ,228.19 ,300ο ο ο ο

( 2 cos3 +θ )( 1 cos2 −θ ) = 0

3 ( 1 cos2 2 −θ ) + cosθ + 1 = 0

1

3

B2

B1

4

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18 a) rad 2 =θ

b) 32cm

r =4 or 8)2(4AB ==S

2r = ( 8 – r ) 2

1

3

B2

B1

4

19 k = 17

h = - 8

4 x + h = 0

hxdx

dy += 4

4

B3

B2

B1

4

20 5−

=

−

11 ）3-4（

10-

）3-5（

10-

= 5

4

1

）1（1

)3x（10

−

− −

3

B2

B1

3

21 a) 36.6

(16.8 X 2) + 3

b) 5

2

B1

1

3

22a) 8

8P = 40320

b) 4320

= 66P X 2

3P

23P

1

3

B2

B1

4

23 BJ 'L

=15

4)

3

2)(

5

3)(

3

2( =

1

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=45

19

=45

4

45

3

45

12 ++

= )5

2)(

3

1)(

3

2()

3

1)(

5

3)(

3

1()

3

2)(

5

3)(

3

2( ++

BJ 'L + LJ 'B + BL 'J

3

B2

B1

4

24n = 820

pqn2 =σ196.8 = n (0.4)(0.6)

P=0.4 or q=0.6

3

B2

B1

3

250.2580

=0.5 – 0.1612 -0.0808

0.0808

3

B2

B1

3

( )f z

z0 1.4m

0.1612

0.0808

0.5 – 0.1612 -0.0808

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

No. Question PERATURAN PEMARKAHAN TOTAL

MARKS

1

2

2

4 3 5 or 2 3 3 5 or

4 3 2 3 3

x y x y xy

x y x y xy

+ = − + =+ = − +

5 3

4

yx

−= OR 5 4

3

xy

−=

* 2 *5 3 5 3

2 3 3 54 4

y yy y

− − − + = OR

* *2 5 4 5 4

2 3 3 53 3

x xx x

− − − + =

23 8 5 0y y+ + =

( ) ( )3 5 1 0y y+ + = or 2(8) (8) 4(3)(5)

2(3)y

− ± −=

OR22 9 10 0x x− + =

( ) ( )2 5 2 0x x− − = or 2( 9) ( 9) 4(2)(10)

2(2)x

− − ± − −=

5 , 1

3y y= − = −

5 , 2

2x x= =

1

1

1

1

1

1

6

2(a)

24

2

p− = − or ( )2 4 4k − + = −

10p =

4k =

(b) 4 4x y− =

( )1 4

4

yf y− −=

(c) ( )1 2 2f g− = −

1

1

1

1

1

1 6

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

3

y = 3

2π x - 2

y = - 2 cos 3

2 x

- 2

2

2ππ

y

x

(a) Draw cosine shape

Negative cos

1.5 cycle

Amplitude 2

(b) Equation : 3

22

y xπ

= −

Draw line 3

22

y xπ

= −

No of solutions : 3

1

1

1

1

1

1

1

7

4 (a) 2 or 2a rπ= =

( ) ( ) 7

8 2 2T π=

256π

(b)( )10

10

2 2 1

2 1S

π −=

−

10 6428.532 cmS =

RM 64. 29

1

1

1

1

1

16

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

5 (a)1

2DEBm = −

19

2y x= − +

(b)1

9 2 62

x x− + = −

( )6,6B

(c)( ) ( ) ( ) ( )0 2 6 1 9 2 6 1

,3 3

E+ +

=

( )2,8E

(d) ( ) ( ) ( ) ( )2 2 2 26 6 0 9x y x y− + − = − + −

4 2 3 0x y− + =

1

1

1

1

1

1

1

18

6 (a) 4m =

(b) (i) 10 11

2

+

Median 10.5=

(ii) 2 2078fx∑ = or 32

3x =

2

2078 32

18 3σ = −

1.291σ =

(c) New median 13.5=

1

1

1

1

1

1

1 7

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

7 a)

2

y

x114 99 85 68.75 53 38.89

b) Plot 1 point and use a correct scale

Plot all points correctly

Line of best fit

c) 2

yhx k

x= −

(i) h m=

5h = −

(ii) intk y− = −

128k = −

(iii) 931y =

1

1

1

1

1

1

1

1

1

110

8(a)

4cos

7AOD∠ =

55.15AOD∠ = °

0.963AOD∠ = rad

(b) ( )*4 0.963BD∩ =

2 27 4 or 5.745AD AD= − =

Perimeter ( )*4 0.963 5.745 3= + +

12.597 cm

(c) ( ) ( )*1Area 5.745 4 or

2AOD∆ =

( ) ( )2 *1Area sector BOD 4 0.963

2=

1

1

1

1

1

1

1

1

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

Area ( ) ( ) ( ) ( )* 2 *1 15.745 4 4 0.963

2 2= −

3.786 cm2

1

110

9 (a) (i) DE DA AE= +uuur uuur uuur

(ii) CG CA AG= +uuur uuur uuur

8 4DE q p=− +uuur

% %

5 2CG q p=− +uuur

% %

(b) (i) 4BE q p=− +uuur

% %

4BF nq np=− +uuur

% %

(ii) 5 2CF mq mp=− +uuur

% %

(c) BF BC CF= +uuur uuur uuur

( )4 4 5 2nq np q mq mp− + = + − +% % % % %

Sub 2m n= in 4 5n m− = −

4

9n =

8

9m =

1

1

1

1

1

1

1

1

1

110

10 (a) 23 3x x x+ = − −

( ) ( )3 1 0x x+ + =

( 1, 2)P −

( 3,0)Q −

1

1

1

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

(b) Area ( ) ( )12 2

2∆ = or

2 33

2 3

x x − −

Sub limit 0 and 2 3

* 31 in

2 3

x x − −

Total area ( ) ( )2 31 3

2 22 2 3

x x = + − −

19

6 unit2

(c) ( ) 22 23y x x= − −

Volume ( )0

2 3 4

3

9 6x x x dxπ−

= + +∫

4 53 3

32 5

x xx

+ +

Use limit 0 and * 3− in 04 5

3

3

33

2 5

x xx

−

+ +

8.1 π unit2

1

1

1

1

1

1

110

11 (a)(i) 0.3 and 0.7p q= =

( ) ( )2 462( 2) 0.3 0.7P X C= =

0.3241

(ii) ( )3P X <

( ) ( ) ( ) ( ) ( ) ( )2 4 1 5 0 66 6 62 1 00.3 0.7 0.3 0.7 0.3 0.7C C C+ +

0.7443

(b) (i) ( ) 0.55P z < −

29.12 %

1

1

1

1

1

1

1

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

(ii) ( ) 0.4P z k> = 0.253z =

38.2

0.2534

k − =

39.21k =

1

1

110

12(a) 12/10

6.50100

5.00I = ×

130

(b) 116.67PI = or 120QI = or 125RI =Note: all correct 2, one or two correct 1.

116.67(30) 120(50) 125(70) 130(20)

30 50 70 20I

+ + +=+ + +

122.65

(c) 12 100 122.6540

P × =

RM 49.06

(d) 12 / 08115

120100

I = ×

138

1

1

2

1

1

1

1

1

110

13(a) ( ) ( )1

34 8 9 sin2

QPS= ∠

70.81QPS∠ = °

(b) ( ) ( ) ( )2 28 9 2 8 9 cos 70.81QS = + − °

9.883 cmQS =

1

1

1

1

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

(c) Use 109.19QRS∠ = °

sin sin109.19

6 9.883

SQR∠ °=

35.82QSR∠ = °

(d) Area ( ) ( )19.883 6 sin 35.82

2QSR∆ = °

Area PQRS ( ) ( )19.883 6 sin 35.82 34

2= ° +

51.35 cm2

1

1

1

1

1

110

14 a) (i) 35x y+ ≤

(ii) 30 60 1200x y+ ≥ (iii) 12 2 120x y+ ≥

b) Draw one line correctly

Draw all line correctly

Shaded the region R correctly

c) (i) 10

(ii) Use point ( )5,30

Profit ( ) ( )850 5 1150 30= +

RM 38750

1

1

1

1

1

1

1

1

1

1

10

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

15

(a) ( ) ( )23 0 18 0 15v = − +

15 ms-1

(b) 6 18dv

tdt

= −

3t =

-112 msv = −

(c) 23 18 15 0t t− + <

( ) ( )5 1 0t t− − <

1 5t< <

(d) 3 29 15 S t t t c= − + +

0, 0 0S t c= = ∴ =

( ) ( ) ( ) ( ) ( ) ( )3 2 3 2

1 41 9 1 15 1 or 4 9 4 15 4S S= − + = − +

Total distance 1 42 S S= +

34 m

1

1

1

1

1

1

1

1

1

1

10

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

10 SULIT

2

y

x

x1 2 3 4 5 6 70

40

20

60

100

80

120

140

Appendix 1 (Answer no 7)

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3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

11 SULIT

y

x5 10 15 20 25 30 350

10

5

15

25

20

30

40

35

45

Appendix 2 (Answer no 14)

40

R

x + y = 35

12x + 2y = 120

30x + 60y =1200

50

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