Pmr Mat K2 Set 1

SULIT 50/2 NO. KAD PENGENALAN

50/2 Mathematics Paper 2 July 2006 1

ANGKA GILIRAN

3 hours 4

JABATAN PELAJARAN PERAK

Set 1

PENILAIAN MENENGAH RENDAH 2006 LEARNING TO SCORE MATHEMATICS Paper 2 [SET 1] I hour 45 minutes

DO NOT OPEN THIS QUESTION PAPER UNLESS YOU ARE TOLD TO DO SO

1. This question paper consists of 20 questions. 2. Answer all questions. 3. Write your answers clearly in the spaces provided in the question paper. 4. Diagrams are not drawn to scale unless stated. 5. The marks allocated are shown in brackets.

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL

This question paper consists of 18 printed pages.

Allocated Marks 2 2 3 2 2 2 3 3 2 4 2 3 3 3 5 3 3 6 3 4 60

Marks Obtained

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Learning To Score 2006: SET 1

INFORMATION FOR CANDIDATES

1.

This question paper consists of 20 questions.

2.

Answer all questions.

3.

Write your answers clearly in the spaces provided in the question paper.

4.

Show your working. It may help you to get marks.

5.

If you wish to change your answer, neatly cross out the answer that you have done. Then write down the new answer.

6.

The diagrams provided in the questions are not drawn to scale unless stated.

7.

The marks allocated for each question are shown in brackets.

8.

A list of formulae is provided on pages 3 and 4.

9.

A booklet of four-figure mathematical tables is provided.

10. Calculators are not allowed. 11. This question paper must be handed in at the end of the examination.

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Learning To Score 2006: SET 1

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

RELATIONS õ an = a

1

a

m

2

a

m

3

(am)n = a

4

Distance =

5

Midpoint

m+n

 a n = a m-n mn

( x 2  x1 ) 2  ( y 2  y1 ) 2

 x1  x2 y1  y 2  ,  2   2

(x,y) = 

distance travelled time taken

6

Average speed =

7

Mean =

8

Pythagoras Theorem c2 = a2 + b2

sum of data number of data

SHAPE AND SPACE 1

Area of rectangle = length x width

2

Area of triangle =

3

Area of parallelogram = base x height

4

Area of trapezium =

5

Circumference of circle = d = 2 r

6

Area of circle

7

Curved surface area of cylinder = 2 rh

=

Unit Kurikulum Jabatan Pelajaran Perak

1 x base x height 2

1 x sum of parallel sides x height 2

r 2

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Learning To Score 2006: SET 1

8

Surface area of sphere = 4 r2

9

Volume of right prism = cross sectional area õ length

10

Volume of cuboid = length x width x height

11

Volume of cylinder =  r2 h

12

Volume of cone =

13

Volume of sphere =

14

Volume of right pyramid =

15

Sum of interior angles of a polygon = (n – 2) x 180

16

1 2 r h 3 4 3 r 3

arc length

1 x base area x height 3

=

angle subtended at centre

circumference of circle 17

area of sector

=

angle subtended at centre

area of circle 18

Scale factor,

360

360 k =

PA’ PA

19

Area of image = k2 x area of object

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Learning To Score 2006: SET 1

Answer all questions. 1

1  3 

Calculate the value for 3   2 

3  and express the answer as a fraction in its 4

lowest term. [ 2 marks] Answer:

1

2

2

Calculate the value of a decimal.

1  1  (0.5  0.1) and express the answer as 2

2 marks

Answer :

2

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Learning To Score 2006: SET 1

(a) Find the value of  0.33 . (b) Calculate the value of

3

 125  12

3 marks

Answer: (a)

(b)

3 3

4

In Diagram 1, ABCD is a square. Given that kos x °= A

x°

E

5 . 13

B

y° D

C

DIAGRAM 1 Find the value of sin y 0.

2 marks

Answer :

4 2 Unit Kurikulum Jabatan Pelajaran Perak

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Learning To Score 2006: SET 1

Diagram 2 is drawn on a Cartesan plan. On the diagram, draw and label the image triangle KLM under a rotation about R through 90° clockwise. 2 marks

Answer :

R 5

2

DIAGRAM 2

6.

In Diagram 3, PQRS is a rhombus. Draw its image if it is enlarged with a scale factor of 3 with centre O. 2 marks

Answer:

O

6

DIAGRAM 3

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2

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Learning To Score 2006: SET 1

Diagram 4 shows a cuboid.

10 cm 3 cm 5 cm

DIAGRAM 4 Draw on the grid in the answer space the scale net of the cuboid if the shaded region is not included. The grid has equal squares with sides of 1 unit. 3 marks

Answer :

7

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Learning To Score 2006: SET 1

Table 1 shows the frequency distribution of the heights of students in Form 2A1.

Height 140 – 144 145 – 149 150 – 154 155 – 159 160 – 164 Total

Frequency 5 11

x 12 5 40 TABLE 1

Find (a) the value of x . (b) the percentage of pupils who are less than 150 cm tall.

3 marks

Answer :

(a)

(b)

8

3 9

Simplify

p 2  q 2  ( p  q) 2

2 marks

Answer :

9

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10

(a) (b)

Learning To Score 2006: SET 1

Solve the inequality  x  3  5 List all the integer value of x which satisfy both the inequalities

2m  1 and 9 

 3m 3 2

4 marks

Answer : (a)

(b)

10

4

11

1  3

4

n Given that    3 , calculate the value of n.

.

[2 marks]

Answer:

11

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12

1 2

Learning To Score 2006: SET 1

3 2

Simplify (81n t )  t  (3nt 2 ) 2 4

. [3 marks]

Answer:

12

3 13 Given that

5 1  , express p in terms of s . 2( p  1) s [3 marks]

Answer:

13

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Learning To Score 2006: SET 1

Solve each of the following equations: (a) m  5  2m (b) h  3  3  2( h  6)

[3 marks]

Answer: (a)

(b)

14

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Learning To Score 2006: SET 1

15 Diagram 5 in the answer space shows a square PQRS. M and N are two moving points in the diagram. By constructing suitable loci, draw points M and N within the square that are 5 cm from R and equidistant from P and R. Hence, measure the distance, in cm, between the point M and the point N. [5 marks] Answer:

S

R

P

Q

15 DIAGRAM 5

5

16

Express

1 1 y  as a single fraction in its simplest term. x xy

16

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Learning To Score 2006: SET 1

Factorize completely the following expressions. (a)

m  m3

(b)

2rs  2rt  s  t

[3 marks]

Answer: (a)

(b)

17

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Learning To Score 2006: SET 1

Set squares and protectors are not allowed to be used in section (a) of this question.

Diagram 6 in the answer space shows a straight line TU. (a) Using only a ruler and a pair of compasses, construct (i) STU = 60, (ii) a triangle STU such that STU = 60 and TU = 5cm, (iii) hence, construct the perpendicular line to the straight line ST which passes through the point U. (b)

Based on the diagram constructed in (a), measure the perpendicular distance between point U and the straight line ST. [6 marks]

Answer: (a)

(i),(ii)

T

S Diagram 6

(b)

(i) (ii)

18

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Learning To Score 2006: SET 1

Table 2 shows the number of visitors to the Taiping Zoo in a week. On the circle in the answer space, with o, as the centre of the circle, construct a pie chart to represent all the information given in the table. Day Monday Tuesday Wednesday Thursday Friday

Numbers of visitors 12.5% 10% 22.5% 10% 45% TABLE 2

[4 marks]

O

19

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20

Learning To Score 2006: SET 1

Use the graph paper provided to answer this question.

x y

–5 -8

–3 0

– 0.5 2

0.5 2

3 4

4 7

5 12

TABLE 2

Table 2 shows the values of two variables, x and y, of a function. By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 2 units on the y –axis, draw the graph of the function. [4 marks]

20

4

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