No. PERATURAN PEMARKAHAN TOTAL 53y 54x file3472/2 add maths spm trial 2012 scheme of marking 1 sulit...

3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING

1 SULIT

No. Question PERATURAN PEMARKAHAN TOTAL

MARKS 1

2

2

4 3 5 or 2 3 3 5 or 4 3 2 3 3x y x y xyx y x y xy+ = − + =

+ = − +

5 34yx −

= OR 5 43xy −

=

* 2 *5 3 5 32 3 3 5

4 4y yy y− −⎡ ⎤ ⎡ ⎤− + =⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

OR

* *2 5 4 5 42 3 3 5

3 3x xx x− −⎡ ⎤ ⎡ ⎤− + =⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

23 8 5 0y y+ + =

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

2(3)y

− ± −=

OR 22 9 10 0x x− + =

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

2(2)x

− − ± − −=

5 , 13

y y= − = −

5 , 22

x x= =

1 1 1 1

1 1

6

2

(a) 2 42p−= − or ( )2 4 4k − + = −

10p =

4k =

(b) 4 4x y− =

( )1 44yf y− −

=

(c) ( )1 2 2f g− = −

1 1 1 1 1 1

6


2 SULIT

3

y = 3

2π x - 2

y = - 2 cos 32 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= =

( )( )78 2 2T π=

256π

(b) ( )10

10

2 2 12 1

Sπ −

=−

10 6428.532 cmS =

RM 64. 29

1 1 1 1 1 1

6


3 SULIT

5 (a) 1

2DEBm = −

1 92

y x= − +

(b) 1 9 2 62x x− + = −

( )6,6B

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

3 3E

+ +⎛ ⎞= ⎜ ⎟⎝ ⎠

( )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 1

8

6

(a) 4m =

(b) (i) 10 112+

Median 10.5=

(ii) 2 2078fx∑ = or 323

x =

22078 32

18 3σ ⎛ ⎞= −⎜ ⎟

⎝ ⎠

1.291σ =

(c) New median 13.5=

1 1 1 1 1 1 1

7


4 SULIT

7

a)

2

yx

114 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

y hx kx= −

(i) h m=

5h = −

(ii) intk y− = −

128k = −

(iii) 931y =

1 1 1 1 1 1 1 1 1 1

10 8

(a) 4cos7

AOD∠ =

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 2

AODΔ =

( ) ( )2 *1Area sector BOD 4 0.9632

=

1 1 1 1 1 1 1 1


5 SULIT

Area ( )( ) ( ) ( )* 2 *1 15.745 4 4 0.9632 2

= −

3.786 cm2

1 1

10 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− = −

49

n =

89

m =

1 1 1 1 1 1 1 1 1 1

10

10

(a) 23 3x x x+ = − −

( )( )3 1 0x x+ + = ( 1,2)P −

( 3,0)Q −

1 1 1


6 SULIT

(b) Area ( )( )1 2 22

Δ = or 2 332 3x x⎡ ⎤

− −⎢ ⎥⎣ ⎦

Sub limit 0 and 2 3

* 31 in 2 3x x⎡ ⎤

− −⎢ ⎥⎣ ⎦

Total area ( )( )2 31 32 2

2 2 3x x⎡ ⎤

= + − −⎢ ⎥⎣ ⎦

196

unit2

(c) ( )22 23y x x= − −

Volume ( )0

2 3 4

3

9 6x x x dxπ−

= + +∫

4 5

3 332 5x xx

⎡ ⎤+ +⎢ ⎥

⎣ ⎦

Use limit 0 and * 3− in 04 5

3

3

332 5x xx

−

⎡ ⎤+ +⎢ ⎥

⎣ ⎦

8.1 π unit2

1 1 1 1 1 1 1

10

11

(a)(i) 0.3 and 0.7p q= = ( ) ( )2 46

2( 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


7 SULIT

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

38.2 0.2534

k −=

39.21k =

1 1 1

10

12

(a) 12/106.50 1005.00

I = ×

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 20

I + + +=

+ + +

122.65

(c) 12 100 122.6540P

× =

RM 49.06

(d) 12/08115 120100

I = ×

138

1 1 2 1 1 1 1 1 1

10

13

(a) ( )( )134 8 9 sin2

QPS= ∠

70.81QPS∠ = °

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

9.883 cmQS =

1 1 1 1


8 SULIT

(c) Use 109.19QRS∠ = °

sin sin109.19

6 9.883SQR∠ °

=

35.82QSR∠ = °

(d) Area ( )( )1 9.883 6 sin35.822

QSRΔ = °

Area PQRS ( )( )1 9.883 6 sin35.82 342

= °+

51.35 cm2

1 1 1 1 1 1

10

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


9 SULIT

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 21 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


10 SULIT

2

yx

x 1 2 3 4 5 6 7 0

40

20

60

100

80

120

140

Appendix 1 (Answer no 7)


11 SULIT

y

x 5 10 15 20 25 30 35 0

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

No. PERATURAN PEMARKAHAN TOTAL 53y 54x file3472/2 add maths spm trial 2012 scheme of marking 1 sulit...

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Transcript of No. PERATURAN PEMARKAHAN TOTAL 53y 54x file3472/2 add maths spm trial 2012 scheme of marking 1 sulit...