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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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