1. SULIT 3472/2
JABATAN PELAJARAN WILAYAH PERSEKUTUAN KUALA LUMPUR
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2009
SKEMA PEMARKAHAN
MATEMATIK TAMBAHAN
Kertas 2
3472/2 @ 2009 Hak Cipta JPWP SULIT

2. SULIT
SECTION A
Solution Sub Full
Question
Mark Mark
1. x 5 2y 5 x 1
y
2 2
3x y 5 2y 1
5 x 1
3x 2 x 1
10 y 2 55 y 74 0 2
5x2 5x 2 0
2
55 ( 55) 4 10 74 1
y 2
2 10 5 5 45 2
x
25 1
y 3.153 , 2.347
x 0.306 , 1.306
x 1.306 , 0.306
y 2.347 , 3.153 1
5
2.
2(5.5) 5(15.5) 11(25.5) h(35.5) 6(45.5)
(a) 30.25 ..........
2 5 11 h 6 1, 1
h = 16 ........................ 1
(b) fx 2 2(5.5 2 ) 5 15.5 2 11 25.5 2 16 35.5 2 6 45.5 2 ..... 1
41000
30.25 2 ................................................................... 1
40
= 10.485 1
.........................................................................................
1 7
(c) 10.485 ..............................................................................................
3.
(a) P(-8, 0) and Q(0, 4) ………………………………………. 1
S( -4, 2) …………………………………………………… 1
1 0 0 4 2 0
(b) Area of OQSR =
2 0 4 2 0 0
1
= (0 0 0 0) (0 16 4 0) ………..
2 1
= 10 ………………………………………… 1
3( 2) 2 x 3(0) 2 y ………………………
(c) 4, or 2 1
5 5
T =(-7, 5) ………………………………………………
1
6
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3. SULIT 3472/2
4. (a) List of perimeters ; 4x, 8x, 16x,
T2 T3
2 ……………………………………………………… 1
T1 T2
1
This is Geometric Progression and r = 2 …………………………..
1
(b) 10240 4 x(2) 9 .......................................................................
x = 5................................................................................ 1
(c) List of numbers of squares: 1, 4, 16,
1(44 1) 1(45 1) 1(410 1)
Find S 4 or S5 or S10 ...... 1
4 1 4 1 4 1
410 1 44 1
S10 S4 ...........................................
4 1 4 1 1
= 349440............................................................... 1 7
5.
dy 1
(i) 8 x 3 …………………………………………..
dx
8 x 3 13 …………………………………………… 1
x 2
A(2, 5) …………………………………………… 1
(ii) 13(5) + 2 = k ………………………………………… 1
k = 67 ……………………………………….. 1
(iii) y 5 13( x 2) or c 21 …………………….. 1 7
y = 13x – 21 ………………………………………. 1
6. (a) cos 2 x 1 2 sin 2 x or cos 2 x 2 cos 2 x 1 1
2 sin 2 x sin 2 x
or
2 cos 2 x cos 2 x
and
1
tan 2 x
(b) Refer to attachment
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4. SULIT
BAHAGIAN B
Sub Full
Question Solution
Mark Mark
7.
Refer to attachment
8.
(a) (i) BD BA AD or ………………….
8 y 4 x ………………………………….…… 1
1
(ii) BC BD DC
8 y 4x 4 y
4 y 4 x …………………………………….……
1 3
(i) AP AK KP
1
AB n AD ………………………………..…… 1
3
8
y 4n x …………………………………….…… 1
3
(ii) Let AP m AC
8 …………………………… 1
y 4n x m( AB BC )
3
m 4 y 4 x …………………………… 1
8
Then 4m and 4m 4n ………………… 1 7
3
2 2 ……………………… 1,1
m and n 10
3 3
9.
15 …………………………………… 1
(a) KML 2 sin
8
KML 2 0.6751
…………………………………… 1 2
1.3503 rad
(b) Arc LAK = 8( KML ) …………………………………… 1
= 10.8024 cm
Arc KBL = 5( ) ……………………………………
1
Perimeter = 10.8 + 5
= 26.51 cm …………………………………… 3
1
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5. SULIT 3472/2
(c) Find area of segment
1 2
8 1.3503 sin 1.3503 ……..…………....................…. 1, 1
2
11.9844 cm 2
or
Area of sector MKAL - Area ∆ KML
1 1 1, 1
= (8)²(1.3503) - (10) ( 8 2 5 2 ……..…………........….
2 2
= 43.21 cm2 - 31.225 cm²
Area of semicircle KBL =
= 11.985 cm²
1 2 ……..…………........….
Area of semicircle KBL = 5 1
2
= 39.27 cm²
5
Area of shaded region = (area of semicircle) – (area of segment) 1
= 27.29 cm² 1 10
10. (a) x(c) – 5 ) = 0 -----------------------------------------------------
( 3x 1
5 4
Q , …………………………………………………… 1 2
3 9
5
1 4 5 2
(b) 1 3 x 1 dx ……..……….................…. 1, 1
2 9 3 0
or
5
x
3 1 x2 2x 1 dx ……..……….................….
0 3 1, 1
5
5
3 x2 x dx
0 3
5
x3 5 2 3
x ……..…………....................…. 1
3 6 0
3 2
5 5
5 1
3 3 ……..…………....................….
3 6
125 1
/ 0.7716 ……..…………....................…. 5
162
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6. SULIT
1
……..…………....................…. 1
(c) V ( x 1) 4 dx
0
1
( x 1)5 1
V ……..…………....................….
5 0
1 ……..…………....................…. 1 3
5 10
11. (a) (i) h = 52 1
k 52 ……..…………........................................….
(ii) 1.2 ……..…………........................................…. 1
5
k 58 ……..…………........................................…. 1 3
48 52
(b) P( z 1.2)
5 or ……....................................…. 1
P ( 0 .8 z 1 .2 ) 2
0.673 ……..………….................................................…. 1
(c) (i) P( X 56)
P( z 0.8)
……..…………........................................…. 1
0.7881
No of students = 200 (0.7881)
= 157 / 158 ……....................................…. 1
(ii) P( X m) 0.05
m 52 ……....................................….
1.645 1,1
5
m 60.225
……....................................…. 5
m 60 / 61 1
10
SECTION C
12. dv
(a) a 10 6t
dt
1
10 6t 0
5
t
3
2 1
5 5
Then v 8 10 3
3 3
1 1 3
v
3
(b) When v = 0 , 8 – 10t + 3t² = 0 1
(3t – 4)(t – 2)= 0
1 2
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7. SULIT 3472/2
4
t 2 or
3
(c) s v dt 8t 5t 2 t3
1
s 8(2) 5(2) 2 (2) 3 2
When t=2, 1
4m.
(d) When t 4, s 8(4) 5(4) 2 (4) 3
s 16m
2 3 Either
4 4 4 4
When t ,s8 5 one
3 3 3 3 1
112
s // 4.148m
27
Total dis tan ce 4.148 (4.148 4) 16 4 1
3
440 1
16.296m // 16.3 //
27 10
13.
AC 6.66 1
(a) AC 6.770 cm
sin 68.36 sin 66.13
3 3
AB AC 6.770 10.155 cm 1
2 2
1 1,1
CB 10.155 3.385 cm
3 4
(b) BAD 45.51o 1
CD 6.66
CD 5.1955 cm 1
sin 45.51 sin 66.13
BD 2 3.385 2 5.1955 2 2 3.385 5.1955 cos113.87 1
4
BD 7.2584 cm 1
1
(c) Area 6.66 10.155 sin 45.51 1 2
2
24.124 cm 2 1 10
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8. SULIT
14.
Refer to attachment
10
15 100
(a) (i) Price A 56 RM 40 1,1
140
I 08 I 08 I 03
I 00 I 03 I 00
110 105 1
(ii) I 08 100
100 100
115.5 1 4
(b) (i) x = 30 1
(140 35) (110 25) (120 30) (10 y )
123 1,1
(ii) 100
y 105 1
123
252 1
(iii) Price of toy = 100
309.96 1 6
10
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9. y Question 14
(a) 50x + 40y 4000 1
SULIT 5x + 4y 400 3472/2
100
10x + 30y 600 1
x + 3y 60
90
3y 4x + 60 1
5x+4y=400 (b) Draw correctly any straight line 1
80 All three straight lines are correct 1
Shaded region 1
(c) (i) 15 x 48 1
70 (ii) Use 30x + 10y where (x,y)
as point in the shaded region 1
3y=4x+60 Maximum point = (31, 61) 1
Maximum profit = RM 1540 1
10
60
50
40
30
R
20
x+3y=60
10
x
0 10 20 30 40 50 60 70 80
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10. SULIT
y
Question 6(b)
3
2
1
0
3 2
2 2
1
3
2
Graph cosine…………………….1
2 cycle between 0 to 2 …………1
Maximum and minimum values….1
3 x
cos 2 x 1
2
3 x
cos 2 x 1
2
x
The equation of straight line is y 1 ………………………………………...1
Draw the straight line, correct gradient or passed through y-intercept at 1………1
No of solutions = 4………………………………………………………………..1
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11. SULIT 3472/2
y
y – 2.8 – 2.1 – 1.5 – 0.7 0.7 1.5
x
Question 7 x
4 Table …………………….1
y
Graph against x………1
x
Plot all the points correctly …………2
3 (if 1 point is plotted wrongly ……….1)
Line of best fit ………1
2
1
0
x
1 2 3 4 5 6 7 8
–1
–2
–3
–4 y p
x q ………….1
x q
q = -3.55 (accept -3.65 to -3.45)……1
p
gradient found .........................1
q
p 2.556 (accept 2.628 2.484) ……1
From graph, x = 6.6
y = 7.92 ……..1 10
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