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Matematik
Kertas 2
Ogos
2007
1 34
jam
SEKTOR SEKOLAH BERASRAMA PENUH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN SELARAS PMR SBP
2007
Kertas soalan ini mengandungi 17 halaman bercetak
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 Inggeris3. 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
SoalanMarkah
Penuh
Markah
Diperoleh
1 2
2 2
3 2
4 3
5 2
6 3
7 2
8 3
9 3
10 3
11 3
12 3
13 6
14 3
15 3
16 2
17 2
18 5
19 4
20 4
Jumlah
Nama : ……………………………..
Tingkatan : 3 ………...……………
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The following formulae may be helpful in answering the questions. The symbols given are the ones
commonly used.
RELATIONS
1m n m n
a a a
2 m n m na a a
3 ( )m n mna a
4 Distance = 2 2
2 1 2 1( ) ( ) x x y y
5 Midpoint
( , ) x y =
2
21 x x,
2
21 y y
6 Average speed =distance travelled
time taken
7sum of data
Mean =
number of data
8 Pythagoras Theorem2 2 2
c a b
SHAPE AND SPACE
1 Area of rectangle = length width
2 Area of triangle = 1 base height2
3 Area of parallelogram = base height
4 Area of trapezium =1
sum of parallel sides height2
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5 Circumference of circle = 2d r
6 Area of circle = 2r
7 Curved surface area of cylinder = 2 rh
8 Surface area of sphere = 24 r
9 Volume of right prism = cross sectional area length
10 Volume of cuboid = length width height
11 Volume of cylinder = 2r h
12 Volume of cone = 21
3r h
13 Volume of sphere = 34
3r
14 Volume of right pyramid =1
3 base area height
15 Sum of interior angles of a polygon = ( 2) 180n
16arc length angle subtended at centre
circumference of circle 360
17area of sector angle subtended at centre
area of circle 360
18 Scale factor, k =PA
PA
19 Area of image = 2 area of objectk
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For
Examiner’s
Use
Answer all questions.
1 Calculate the value of )3158(212 .
[2 marks]
Answer:
2 Calculate the value of 15.6)5
1(4 and express the answer as a decimal.
[2 marks]
Answer:
2
2
2
1
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3 Calculate the value of
4
3
7
21
7
3and express the answer as a fraction in its
lowest term.
[2 marks] Answer:
4 (a) Find the value of 3 064.0
(b) Calculate the value of
2
2
13
64
27
[3 marks]
Answer :
(a)
(b)
2
3
3
4
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For
Examiner’s
Use
5 Simplify ).3(1262
k k [2 marks]
Answer
6 Find the value of
3
1
2
3
1
3
34
[3 marks]
Answer:
2
5
3
6
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7 Given that 432 hhhm
. Find the value of m.
[2 marks]
Answer :
8 Solve each of the following equations.
(a)2
14
n
(b) 18)2(37 uu
[3 marks]
Answer:
(a)
(b)
3
8
2
7
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For
Examiner’s
Use9 List all the integer values of x which satisfy both the inequalities
427 x and 23 x .
[3 marks]
Answer :
10 Given that
R
Re L
4 , Express R in terms of e and L
[3 marks]
Answer :
3
9
3
10
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11 In diagram 1, EFGH is a rectangle.
Given that tan x = 1. Find(a) The length of EF .
(b) The value of cos y . [3 marks]
Answer:
12 Expressh
h
hk
k h
3
32
as a single fraction in its simplest form.
[3 marks]
Answer:
H G J
x◦
y◦
2cm
Diagram 1
6 c m
3
11
3
12
F E
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For
Examiner’s
Use
Set squares and protractors are not allowed for this question.
13 Diagram 2 in the answer space shows an incomplete rhombus.
(a) Using only a ruler and a pair of compasses, beginning from the diagram provided
construct the rhombus ABCD completely .
(b) Based on the diagram constructed in (a), construct a perpendicular line from D to
AB and measure the length of the line drawn.
[6 marks]
Answer :
(a)
(b)6
13
A B
Diagram 2
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For
Examiner’s
Use16 In diagram 4 R’ is the image of R under transformation U.
Describe in full transformation U .
Answer:
[2 marks]
2
16
R R’
Diagram 4
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17 Diagram 5 shows a hexagon J drawn on a grid of equal squares with sides of 1 unit.
On the grid in the answer space, redraw the hexagon J using the scale 1: 3
1
.
The grid has equal squares with sides of 1 unit.
[2 marks]
Answer:
2
17
Diagram 5
J
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For
Examiner’s
Use18 Diagram 6 in the answer space provided shows a square ABCD. P,Q, R and S are the
midpoints of AB, BC, CD and AD respectively.
X, Y, and Z are the three points that move in the diagram.
(a) X is the point which moves such that it is equidistant from the straight lines ABand AD. By using the letters in the diagram, state the locus of X.
(b) On the diagram, draw
(i) the locus of point Y , such that OY = OP.
(ii) the locus of point Z that is constantly 2 cm from the line SQ.
(c) State the number of intersection of the locus of Y and the locus of Z.
[5 marks]
Answer:
(a)
(b)
(c)
5
18
A B
C D
O
P
R
QS
Diagram 6
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