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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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