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ANSWER TO SCOREPENILAIAN MENENGAH RENDAH 2009
MATHEMATICSANSWERS FOR PAPER 1 (SET 1)
1. D 21. A2. A 22. D3. C 23. B4. D 24. C5. C 25. B6. A 26. B7. B 27. D
8. C 28. B9. C 29. A
10. B 30. C11. B 31. B12. B 32. A13. C 33. C14. B 34. B15. D 35. C16. D 36. B17. D 37. A18. B 38. C19. B 39. A20. A 40. D
MARKING SCHEME
1. The number 345,678 is written as 350,000 when it is rounded off to theA nearest ten = 345 680B nearest hundred = 345 700C nearest thousand = 346 000
D nearest ten thousand = 350 000
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2. Which of the following fractions has value greater than4
3?
A 87
0.875168
147
8
7=
B3
2 0.667 or
168
112
3
2=
C2
1 0.5168
84
2
1=
D7
5 0.714168
120
7
5=
3. 33100000
168= 3 +
100000
168
= 3 + 0.00168
= 3.00168
4. Town H = 8C (Coolest on a particular day)
5. m = 23n = 29m + n = 23 + 29
= 52
6. Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 29Answer: A = 2, 3, 18
7. Broken eggs perday = 9000100
1 = 90
Number of broken eggs produced in a week = 7 90
= 630
8. Total length of road constructed = 5.54 km + 6.78 km= 12.32 km
= 12 km 320 m
9. x = 180 55 (180 125)= 180 55 55= 180 110= 70
10
.
PTS = 180 140 = 140
p + q + r+s + PTS = (5 2) X 180p + q + r+s + 140 = 540
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p + q + r+s = 540 140 = 400
11.
3x + 2x + 3x + 115 + 122 + 75 = (6 2) X 1808x + 312 = 720
x =o720 312
8
o
= 51
12.
Interior angle of pentagon = ( )o
5 - 2 180
5= 108
Interior angle of hexagon = ( )o6 - 2 180
6= 120
The value ofm is = 360 - 108 - 120 = 132
13.
Perimeter is the total length of the boundaries.= PQ+QW+WV+VU+UR+RP
1. each side of square QRVW and equilateral triangle RVU is 12cm.2. PQR is a right angled triangle, therefore
PR = 5 + 12
= 25 + 144= 169= 13cm
3. Perimeter of the whole diagram = 5 + 12 + 12 + 12 + 12 + 13= 66cm
14. 1. Area of XYZ = 2
1x B x H
= x 14 x 15= 105cm
2. Area of VWZ =2
1x B x H
= x 10 x 6= 30cm
3. Area of shaded reqion = Area 1 Area 2= 105 30= 75 cm
15 Area of whole diagram177
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. = (10 cm 15 cm) (5 cm 4 cm)= 150 cm - 20 cm= 130 cm
16.
Which of the following geometric solid is a cone?
A
Cube
B
Cylinder
C
Sphere
D
cone
17. Volume of the cone =
hr2
3
1
= 21431 2
= 21163
1
= 16 7= 112 cm
Volume of the cylinder = Volume of the cone
Height of the cylinder = 4 h = 112
16h = 112
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h =
16
112
= 7 cm
18.
Length of base = 36= 6 cm
Total surface area of pyramid = (4 2
1 6 cm 5 cm) + 36 cm
= 60 cm + 36 cm= 96 cm
19.
PQ = 5 3= 25 9= 16
PQ = 16= 4 cm
Total surface area of the prism= 2 (
2
1 3 cm 4 cm) + (3 cm 12 cm) + (5 cm 12 cm) + (4 cm 12 cm)
= 12 cm + 36 cm + 60 cm + 48 cm= 156 cm
20.
PSX = RSX
21. x = 2
130360 00
179
Locus X
P
S
Q
R
Locus X
P
S
Q
R
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=2
2300
= 115
22.
P = 180 - (50 + 70)= 180 - 120= 60
x = 180 - (90 + 60)= 180 - 110= 30
or
x = 180 - (110 + 40)= 180 - 150= 30
or
x = 70 - 40= 30
23. TOU = 40UOV = 60WOP = 50ROS = 30
Answer = B
24. Area of the shaded part =
27
7
22-
25.3
7
22
=
49722
-
25.12722
= 154 cm - 38.5 cm= 115.5 cm
25.
PT = 20 - 16= 400 256= 144
PT = 144
= 12 cm
QR = 12 + 5180
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= 144 + 25= 169
QR = 169= 13 cm
26. CDBE
= ACAB
6
BE=9
6
BE =9
36
= 4 cm
27.
x + 3y = 9 .. i2x 3y = 6 .ii
i + ii; 3x = 15
x =3
15
= 5
28. 4
3y
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p = 9
30.
OP = 22 68 + = 3664 += 100= 10 units
OQ = 22 310 +
= 9100 += 109OQ 10
OR = 22 29 += 481+= 85
OR 10
OS = 22 68 +
= 3664 += 100= 10 units
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OT = 22 511 += 25121+= 146
OT 10
OP = OS
31.
Perimeter of the shaded region
= ( 147
222
4
1 ) + ( 77
222
4
1 ) + 7 cm + 21 cm
= 22 cm + 11 cm + 7 cm + 21 cm= 61 cm
32.
Mimi : RM 150 + ( 8 X RM 35 + 3 X RM 40 + 3 X RM 38 )= RM 664
Roger : RM 150 + ( 7 X RM 35 + 2 X RM 40 + 3 X RM 38 )= RM 589
Difference = RM 664 - RM 589= RM 75
33.
A : B B : C7 (3) 4 (3) 6 (2) 5 (2)
21 : 12 12 : 10
A : B : C = 21 : 12 : 10
34.
** Convert to 24Hours system
0740 + 0630 + 0020 = 1430
Time Daud arrive = 2.30 p.m.
35.
Total students = 160
x =160
32 360 = 72
y =160
36 360 = 81
153
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36.
0
5
10
15
20
25
30
A B C
BOYS
GIRLS
Diagram 24
The bar chart shows the nmber of students in three classes. Which of the following statementis true?A The total number of students in three classes is 125
A = 45, B = 40, C = 45A + B + C = 120
B The total number of girls in Class A and Class B are the same.
C The number of boys in this school is greater than the number of girls.Boys = 20 + 15 + 20
= 55
Girls = 25 + 25 + 15
= 65The number of boys in this school is less than the number of girls.
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D The number of girls in class C is greater than the number of girls in class B.
The number of girls in class B = 25The number of girls in class C = 15The number of girls in class C is less than the number of girls in class B.
37
.
Mode = B = 13
Choose the answer which is less than 13.Suitable answer is A = 12
38.
Total frequency = 30
Median =2
1615 datadata thth +
=2
33+
= 2
6
= 3
39.
y = 3x2 2xSubstitute x = -2Then, y = 3x2 2x
y = 3(-2)2 2(-2)y = 3 (4) + 4
y = 12 + 4y = 16
40.
y = x + 6The graph intersect y-axis at 6.(-6, 0) and (0, 6) certify the functiony =x + 6
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ANSWER TO SCOREPENILAIAN MENENGAH RENDAH 2009
MATHEMATICS
ANSWERS FOR PAPER 1 (SET 2)
1. B 21. C2. D 22. A3. C 23. B4. A 24. A5. C 25. B6. D 26. A7. B 27. C
8. D 28. C9. D 29. D10. B 30. C11. A 31. B12. B 32. C13. C 33. D14. D 34. C15. B 35. B16. A 36. C17. B 37. B18. D 38. C
19. C 39. D20. A 40. B
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MARKING SCHEME
1. Which of the following numbers when rounded off to the nearest hundred thousand becomes8700000 ?
A 8754321 = 8800000B 8654321 = 8700000 C 8643210 = 8600000D 8554321 = 8600000
2. 250 (4.5 30) (2.5 19) (0.5 18) = 58.50
3.(6
1 300) 20 = 30. Percentage durians left =
300
30 100% = 10%
4. P = -12 6= -18
Q = 18
5. Original price = RM 24.00
Selling price =11
2412
RM
= 22RM
Swee Lan uses2
1 of her savings.
Her savings was 222 RM= 44RM
6. A 238 = remainder 2
158 = remainder 3
B 339 =
159 = remainder 4C 8325 = remainder 1
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5525 =
D 15345 =
9545 =
Common multiple of 3 and 5 is 45
7.5 rolls of rope x
13
2m = 17.5 m
5 rolls of rope x 1.69m = 8.45mLength of remaining rope = 17.5m 8.45m = 9.05m
8. 2400 + 0445 05152330
9. x +x + 35 + 62 + (180 - 147) = 180
2 x + 130 = 1802 x = 180 - 1302 x = 50x = 25
10.
Scale factor, k=PQ
Q'P'
k= 22
4=
11. Interior angle of regular hexagon = 6
180)26(
=
1206
720=
The value ofy =2
120180
=
302
60=
12.
3x +x = 180
x = 4180
= 45
Number of sides =
45
360
= 8 sides
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13.
1 m = RM 13.60
The Perimeter of Rectangular Compound
= 2 (25m) + 2 (75m)
= 50m + 150m
= 200m
Cost of fencing
= 200 RM 13.60
= RM 2720
14
. 2
1 14 h = 168
7h = 168
h =7
168
= 24 cm
15. 2
1 3 EF = 6
EF = 6 3
2
= 4 cm
Area of the whole diagram
= 6 cm 2 + (12 cm 4 cm)
= 6 cm 2 + 48 cm 2
= 54 cm 2
16.
Right prism
17.
Volume of cuboid: Volume of right prism = base area x height= 21 6 11 66 h = 1386
= 1386 h =66
1386
h = 21
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18. Aminah ages = 4
34
Bala ages =12
1013
12
19
12
94
12
19
4
34 =+=+
Chee Meng ages =
24
1146
24
1115
12
223
2
5
12
718
2
5
12
1013
12
94
2
5
12
1013
4
34
2
12 ==
=
=
+=
+
19.
J = K = 70
M = 90
JLM = 180 - (90 + 70)
= 180 - 160
= 20
20.
E = 100
x = 180 - (100 + 30)
= 180 - 130
= 50
21. Area of the shaded region=2
1 8
=2
1 64
= 32
22.
PQ = 10 - 8= 100 - 64= 36
PQ = 36= 6 cm
Area of the coloured region
= (5 ) (2
1 8 cm 6 cm)
= 25 - 24
23.
x = 180 - 120= 60
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or
x =2
120
= 60
24. Height of triangle =22
1517 = 225289= 64= 8 m
Area of triangle =2
1 15 m 8 m
= 60 m
Number of paint tins = 60 m 5 m= 12
25.
180 - 70 = 110
Line XY non-parallel to line PQ.
26.
2x 3y = -17
2 (-4) 3y = -17
-8 3y = -17
3y = 17 8
= 9
y =3
9
= 3
27.
x -3 (a)x < 2 . (b)-3 x < 2
28.
C (-7, 8) and E (5, -2)
Let thex-coordinate of D bex : 2 57 + =x
191
70O
70O
X
Y
P
Q
70O
70O
X
Y
P
Q
70O
70O
X
Y
P
Q
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2
2=x
Thus, x = -1
Let they-coordinate of D bey :2
)2(8 +=y
26
=y
Thus, y = 3
Then, the coordinate of D is ( -1, 3 )
29.
OJ = 5 units OM = 6 units
OK = 3 + 4 OL = 8 + 6= 25 = 100
OK = 5 units OL = 10 units
Hence, distance of OJ = distance of OK
30.
AC = 12 + 9= 225
AC = 15 = radius
Length of arc AD = Angle at the centre circumference360
= 150 2r
360= 150 2
7
22 15
360= 39.29 cm
Thus, the perimeter = 39.29 + 15 + 9 + 12= 75.29 cm.
31.
x : 624 = 12 : 13
624
x
= 1312
X = 12/13 624
= RM 576
32. 6
3=42
21
33
.
30 % of the total number of computer sold over the four month period is 1950
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34.
10 square grids = 20 0001 square grid = 2 000
So , for February, 6 square grids = 12 000
35.
2y + 5y = 140
7y = 140
y =7
140
y = 20
Mangosteens = 5y
5y = 5 20
= 100
Number of mangosteens
= 252360
100
= 70
36.
Total income = RM1 400 + RM1 800 + RM1 350 + RM1 700= RM6 250
37
.
Min =5
46235 ++++
=5
20
= 4
38.
y = x + 2 because (0, 2) and (-2, 0) satisfy the equation and the graph intersect y-axis at 2.
39.
y = -2x2 + 1
Substitute x = -1Then, y = - 2x2 + 1
y = - 2(-1)2 + 1y = - 2 (1) + 1y = -2 + 1y = -1 so s = -1
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Substitute x = 2Then, y = - 2x2 + 1
y = - 2(2)2 + 1y = - 2 (4) + 1y = -8 + 1y = -7 so t = -7
s + t = (-1 ) + (- 7)= 1 7= 8
40.
B (intersect at point G)
2009 FORECAST PAPER 2SET 1
Answer Scheme
1. 42
6 10= 7 10
194
B C
A D
E
FG
H
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= 17
[ 2 marks]
2.
=4.0
44.110
10OR =
4
4.26
=4
4.14 = 3.6
= 3.6
[ 2 marks]
3. a)3
33
6
1
216
1
=
=6
1
b) = ( ) 21327+
= ( )214
= 196
[ 3 marks]
4. a) 2 ( r 2 ) = 10 5r2r 4 = 10 5r
7r = 14r = 2
b) s + 6 = 4s
2s + 6 = 8s
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s 8s = 6 7s = 6
s =7
6
[ 3 marks]
5.
Image correctly drawn - 2 marks[ 2 marks]
6.TransformationPis a translation
6
8.
[2 marks]
7. a) x8 xy4 = )2(4 yxx
b) k6 183 + k = 3 (2k + k 6) = 3 (2k 3) (k+ 2)
[ 2 marks]
196
L
M
A B
C
D
C
D
B
A
L
M
A B
C
D
C
D
B
A
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8. a) 8x + 6
b) ( ) ( )443 xx
164
4123
+++
x
xx
[ 3 marks]
9. (3) 5(2 )
5
n n
mn
=
3 10 5
5
n n
mn
+=
8 10
5
n
mn
=
[ 3 marks]
10. a) x < 14 - 8 x < 6
b) - 3x < 11 - 2 and -3
1x 7 - 8
- 3x < 9 -3
1x - 1
- x < 3 - x - 3 x > - 3 x 3
x = - 2, - 1, 0, 1, 2, 3
[ 3 marks]
11. km 452 =+54
2 = km54 = km
[ 3 marks]
12. a) 2412 qpqp
= 2142 + qp
= 36qp
= 63
p
q
b) = 3 2
197
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Number of cars
= 9 [ 3 marks]
13.
Key :
WomenMan
Uniform scale 1 markEach set of bars 1 mark
[ 4 marks]
14. a)
Number Frequency
2 43 34 25 36 2
All the frequency correct 2 marks3 or 4 correct 1 mark
b) 5.32
43=
+
[3 marks]
15.= 634
2
1
= 36 cm [2 marks]
16. a) PR ( 2 marks )
198
Locus X
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Kancil
Persona
Waja
Types of cars
Q
S
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b) i. locus x correctly drawn ii. locus y correctly drawn c) intersection point correctly marked
[5 marks]
199
OP R
P
Locus y
Intersectionpoint
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17.
a) uniform correct scale on y-axis 1 mark
b) 9 points correctly marked - 2 marksc) graph correctly drawn - 1 mark[4 marks]
200
y35
30
25
20
15
10
5
0
-5
-10
-15
-3 -2 -1 1 2 3 4 x
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T
Q
18.
Construction of point S 1 markConstruction of rectangle PQRS 1 markConstruction of perpendicular line 1 markStraight line drawn from R 1 markLabel T correctly marked 1 mark
[5 marks]
19.
201
P
QR
S
Q
P
P
R
R
O
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Image correctly drawn 2 marks[2 marks]
20.a) tan xo =
6
8
=3
4
b) length ofMPQ = 8+9 = 17 cm
[3 marks]
202
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Set 2 Paper 2 ( Forecast Question )Answer Scheme
1.=2
3
15
10
15
21
=2
3
15
11
=10
11or 1
10
1
[2 marks]
2.= 9.1
5
13
= 9.1
135
= 3.5
[3 marks]
203
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3.
Diagram 3Tcorrectly marked
[2 marks]
4.
Diagram 4
Quadrilateral WXYZ correctly drawn [2 marks]
5.
204
- 6 - 4 - 2 0 2 4 6 8
8
6
4
2
-2
x
y
P
Q R
Q R
P
T
- 6 - 4 - 2 0 2 4 6 8
8
6
4
2
-2
x
y
P
Q R
Q R
P
T
P
Q
R
S
W
X
Z
Y
P
Q
R
S
W
X
Z
Y
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Diagram 5
Image correctly drawn [2 marks]
6. kp 53 = 35
+= kp
[2 marks]
7. a) 4 6x = 14 6x = 18
x = 3
b) 3m 10 = 8m 3m8m = 10
5m = 10m = 2
[4 marks]
8. = abbbab 8104736 ++ = 14ab 7b 3
[2 marks]
9.
205
L M
K
K
L
M
L M
K
K
L
M
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O
S R
QP
Any 2 lines correctly drawn 1 markAny 3 lines correctly drawn 2 marksAll the line correctly drawn 3 marks
[3 marks]
10.
intersection of locus y and z
Diagram 10
206
Locus y
Locus z
Locus x
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Locus x correctly drawn 1 markLocus y correctly drawn 1 markLocus z correctly drawn 1 markIntersection point correctly marked 1 mark
[4 marks]
11. a) = _2x 6 + 5x + 10x= 3x + 4
b) = n mmnmn 33 + = n mmn 34 +
[3 marks]
12.=
2
32 +a3
4 a
=6
)4(2)32(3 + aa
=6
8296 ++ aa
=6
174 +a
[3 marks]
13.a) JLM
b) KNLM = JN
JM
6
LM=3
5
LM =3
5x 6
= 10cm [3 marks]
14. 2k + 2 - 42k - 6
k - 3 4 - k > 0
207
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- k > - 4k < 4
k = - 3, - 2, - 1, 0, 1, 2, 3
[3 marks]
15. a) May
(b)1
3502
175= [3 marks]
208
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16.Answer :
-2 -1 0 1 2 3 4 x
y- axis correctly marked 1 mark7 points correctly marked 2 marks ( 6 points 1 mark )All the 7 points joined 1 mark
Smooth curve - 1 mark[5 marks]
209
Y
10
8
6
4
2
-2
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17.
90 correctly constructed at B 1 markBC correctly constructed 1 mark60 correctly constructed at A 1 markAD correctly constructed 1 markCD correctly joined 1 mark [5 marks]
18. = 2844
3 mmh37 mh
= 3287443 + mh = 9381 mh
=3
981
h
m
[3 marks]
19. = 23
2
3
2
1
2
1
2323 = 22 23 = 9 4= 36
[3 marks]
210
B
C
A
6 cm
3 cm
D
60
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20.tan xo=
3
4
tan x =9
QR
9
QR=3
4
QR =3
4x 9
= 12
PR = 9 2 + 12 2 = 225= 15cm
[3 marks]