1. 50/2
Matematik
Kertas 2
Ogos
2006
1 3
4 jam
SULIT 1 50/2
SEKTOR SEKOLAH BERASRAMA PENUH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN PMR SELARAS SBP
2006
Kertas soalan ini mengandungi 17 halaman bercetak
[Lihat sebelah
50/2 © 2006 Hak Cipta Sektor SBP SULIT
MATEMATIK
Kertas 2
Satu jam empat puluh lima minit
JANGAN BUKA KERTAS SOALAN INI
SEHINGGA DIBERITAHU
1. Tuliskan nama dan tingkatan anda pada
ruang yang disediakan
2. Kertas soalan ini adalah dalam bahasa
Inggeris
3. Kertas soalan ini mengandungi 20
soalan.
4. Jawab semua soalan.
5. Jawapan hendaklah ditulis pada ruang
yang disediakan dalam kertas soalan.
Kertas soalan ini hendaklah diserahkan
pada akhir peperiksaan.
6. Tunjukkan langkah-langkah penting. Ini
boleh membantu anda untuk
mendapatkan markah.
7. Rajah yang mengiringi soalan tidak
dilukiskan mengikut skala kecuali
dinyata.
8. Markah yang diperuntukkan bagi setiap
soalan ditunjukkan dalam kurungan.
9. Anda tidak boleh menggunakan
kalkulator.
Guru Pemeriksa
Soalan
Markah
Penuh
Markah
Diperoleh
1 2
2 2
3 3
4 3
5 3
6 3
7 3
8 3
9 2
10 3
11 2
12 3
13 3
14 3
15 5
16 3
17 2
18 5
19 3
20 4
Jumlah
Nama : ……………………………..
Tingkatan : 3 ………...……………

2. SULIT 2 50/2
The following formulae may be helpful in answering the questions. The symbols given are the ones
commonly used.
RELATIONS
1 m n m n
a a a +
× =
2 m n m n
a a a −
÷ =
3 ( )m n mn
a a=
4 Distance = 2 2
2 1 2 1( ) ( )x x y y− + −
5 Midpoint
( , )x y = 

 +
2
21 xx
, 

+
2
21 yy
6 Average speed =
distance travelled
time taken
7
sum of data
Mean =
number of data
8 Pythagoras Theorem
2 2 2
c a b= +
SHAPE AND SPACE
1 Area of rectangle = length × width
2 Area of triangle =
1
base height
2
× ×
3 Area of parallelogram = base height×
4 Area of trapezium =
1
sum of parallel sides height
2
× ×
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3. SULIT 3 50/2
5 Circumference of circle = 2d rπ π=
6 Area of circle = 2
rπ
7 Curved surface area of cylinder = 2 rhπ
8 Surface area of sphere = 2
4 rπ
9 Volume of right prism = cross sectional area × length
10 Volume of cuboid = length × width × height
11 Volume of cylinder = 2
r hπ
12 Volume of cone =
21
3
r hπ
13 Volume of sphere =
34
3
rπ
14 Volume of right pyramid =
1
3
× base area × height
15 Sum of interior angles of a polygon = ( 2) 180n − × o
16
arc length angle subtended at centre
circumference of circle 360
= o
17
area of sector angle subtended at centre
area of circle 360
= o
18 Scale factor, k =
PA
PA
′
19 Area of image = 2
area of objectk ×
[Lihat sebelah
50/2 SULIT

4. For
Examiner’s
Use
SULIT 4 50/2
Answer all questions.
1 Calculate the value of
3 3 3
1
16 8 4
 
÷ − ÷
 
and express the answer as a fraction in its lowest
term.
[2 marks]
Answer:
2 Calculate the value of
3
5.48 ( 6)
4
− × − − and express the answer as a decimal.
[2 marks]
Answer:
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2
2
2
1

5. For
Examiner’s
Use
SULIT 5 50/2
3 (a) Find the value of 3
0.343−
(b) Calculate the value of ( )
2
3
( 3) 169− +
[3 marks]
Answer:
(a)
(b)
4 In Diagram 1, JKL and LMN are right angled triangles.
Given that
3
cos
5
x = .
Find (a) the length of LM
(b) tan y
[3 marks]
Answer :
(a)
(b)
[Lihat sebelah
50/2 SULIT
3
3
3
4
K
J
L M
N
25 cm
15 cmx°
y°
10 cm
DIAGRAM 1

6. For
Examiner’s
Use
SULIT 6 50/2
5 In Diagram 2, triangle P′ is the image of the triangle P under a transformation V.
Describe in full the transformation V.
[3 marks]
Answer:
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3
5
DIAGRAM 2
0 2 4 6 8 10 12
12
10
8
6
4
2
P
P′
x
y

7. For
Examiner’s
Use
SULIT 7 50/2
6 (a) Diagram 3 in the answer space shows J′ is the image of J under a certain
translation. State the translation.
(b) On the diagram in the answer space, draw the image of quadrilateral ABCD under
a 90° anticlockwise rotation about the point (4, 3).
[3 marks]
Answer :
(a)
(b)
[Lihat sebelah
50/2 SULIT
3
6
J′
J
DIAGRAM 3
0 2 4 6 8 10
10
8
6
4
2
x
y
•
•
C
B
A
D

8. For
Examiner’s
Use
SULIT 8 50/2
7 Express
2
6
4 12
d d
e de
−
− as a single fraction in its simplest form.
[3 marks]
Answer :
8 The data below shows part of the number of goals scored by the 32 teams in the first
rounds of the World Cup 2006.
1 2 0 3 0 2 1
2 1 2 1 1 0 2
0 3 1 2 3 3 3
2 0 0 1 0 0 0
2 0 1 3 1 1 1
3 0 2 1 2 3 1
(a) Using the above data, complete the tally chart in the answer space.
(b) State the mode.
[3 marks]
Answer :
(a) Score Tally Frequency
0
1
2
3
(b)
9 Simplify 2
(2 3) 3(3 4 )a a− − +
[2 marks]
Answer :
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3
8
3
7

9. For
Examiner’s
Use
SULIT 9 50/2
10 List all the integer values of m which satisfy both the inequalities 7 2 3m− ≥ and
2 4m > − .
[3 marks]
Answer:
11 Given
2 1
4
64
n
= . Calculate the value of n.
[2 marks]
Answer:
[Lihat sebelah
50/2 SULIT
2
9
3
10

10. For
Examiner’s
Use
SULIT 10 50/2
12 Simplify
1 3
4 22 2
(4 )qp q p
−
÷ .
[3 marks]
Answer :
13 Given that
2
2
18
2
F m
T
= . Express T in terms of F and m.
[3 marks]
Answer:
50/2 SULIT
3
12
2
11

11. For
Examiner’s
Use
SULIT 11 50/2
14 Solve each of the following equations.
(a) 7 5 2u u+ =
(b)
3
(4 8) 7
2
w w− + =
[3 marks]
Answer:
(a)
(b)
15 Diagram 4 in the answer space shows a rhombus. S, X and Y are three moving points in
the diagram.
(a) S is the point which moves such that its distance from point A and point C are the
same. By using the letters in the diagram, state the locus of S.
[Lihat sebelah
50/2 SULIT
3
13
3
14

12. For
Examiner’s
Use
SULIT 12 50/2
(b) On the diagram, draw
(i) the locus for the point X that is constantly 2 cm from the line AC,
(ii) the locus for the point Y that is constantly 4 cm from the point A
(c) Hence, state the number of intersection points of the locus of X and the locus of Y.
[5 marks]
Answer:
(a)
(b)
`
(c)
16 Factorise completely :
(a) 2
4 8m m n−
(b) 2
(3 ) 4 2y y y− − +
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5
15
D
C
B
A
DIAGRAM 4

13. For
Examiner’s
Use
SULIT 13 50/2
[3 marks]
Answer:
(a)
(b)
17 Diagram 5 in the answer space shows polygon ABCDEFG and straight line PQ drawn
on a grid of equal squares.
Starting from the line PQ, draw polygon PQRSTUV which is congruent to polygon
ABCDEFG.
[2 marks]
Answer:
18 Set squares and protractors are not allowed for this question.
[Lihat sebelah
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3
16
2
17
P
R
Q
DIAGRAM 6
S
60°
DIAGRAM 5
BA
C
D
E
F
G
P
Q

14. For
Examiner’s
Use
SULIT 14 50/2
(a) Using only a ruler and a pair of compasses, construct quadrilateral PQRS as
shown in Diagram 6 using the straight lines PS and SR provided in the answer
space.
(b) Based on the diagram constructed in (a), construct QT, angle bisector of the
∠ PQR such that point T lies on the line PS. Measure the length QT.
[5 marks]
Answer:
19 The pictograph below shows the number of cakes sold by a school canteen within a
week.
Monday
Tuesday
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5
18
RS
P

15. For
Examiner’s
Use
SULIT 15 50/2
Wednesday
Thursday
Friday
Key : represents 10 cakes
Draw a line graph in the answer space to represent all the information in the pictograph
above.
[3 marks]
Answer:
20 Use the graph paper given to answer this problem.
Table 1 shows the value of two variables, x and y of a function.
x −4 −3 −2 −1 0 1 2
[Lihat sebelah
50/2 SULIT
3
19
3
19
Day
Numberofcake
MON TUE WED THU FRI
120
100
80
60
40
20

16. For
Examiner’s
Use
SULIT 16 50/2
y 5 0 −3 −4 −3 0 5
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 unit on the y-axis,
draw the graph of the function on the graph paper provided in the answer space.
[4 marks]
Answer:
(Refer to graph on page 17)
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4
20
TABLE 1