1. This document is a marking scheme for a trial examination paper for the Malaysian Certificate of Education (SPM) mathematics additional paper in 2009. 2. The marking scheme provides the full and sub marks awarded for each question on the paper. For multiple part questions, it outlines the marks given for each part. It also includes the expected solutions and working for many of the questions. 3. The paper consisted of 3 sections - Section A with 7 questions, Section B with 10 questions, and Section C with 5 questions. Most questions had multiple parts testing different math skills like algebra, geometry, calculus, and problem solving.

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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3472/2 @ 2009 Hak Cipta JPWPKL SULIT

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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3472/2 @ 2009 Hak Cipta JPWPKL SULIT

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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3472/2 @ 2009 Hak Cipta JPWPKL SULIT

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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3472/2 @ 2009 Hak Cipta JPWPKL SULIT