Pmr Mat K2 Set 3

SULIT 50/2 NO. KAD PENGENALAN

50/2 Mathematics Paper 2 1

3 hours 4

Set 3 3

ANGKA GILIRAN

PENILAIAN MENENGAH RENDAH 2006 LEARNING TO SCORE MATHEMATICS Paper 2 [SET 3] I hour 45 minutes

Question DO NOT OPEN THIS QUESTION PAPER UNLESS 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 maximum marks allocated for each question are shown in brackets.

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 3 2 4 2 5 5 2 3 3 3 3 3 2 2 5 4 60

Marks Obtained

-2-

Learning To Score 2006: SET 3

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 3

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

=

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1 x base x height 2

1 x sum of parallel sides x height 2

r 2

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-4-

Learning To Score 2006: SET 3

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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-5-

Learning To Score 2006: SET 3

Answer all questions. 1

Calculate the value of 164 – 2 5 + 18 x 3



2 marks

Answer :

1

2

2

Calculate the value of 4.48 x 0.6 -  2 to two decimal place.

1 2



and express the answer correct 2 marks

Answer :

2

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-63

(a) Find the value of

Learning To Score 2006: SET 3

 1  3

(b) Calculate the value of

3



4.8 ÷

3

64

2

3 marks

Answer : (a)

(b)

3 3 4

In Diagram 1, shows a right angle triangle ABC. Given that sin x = 0.4

A x

.

B

h cm 18 cm C DIAGRAM 1 Find the value of h.

2 marks

Answer :

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-7-

5

Learning To Score 2006: SET 3

In Diagram 2, PQR is a straight line

S

y

8 cm

x P

Q

R

DIAGRAM 2

Given that sin x =

8 1 and tan y = , calculate the length in cm of PQ. 17 2

2 marks

Answer :

5

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-86

Learning To Score 2006: SET 3

Diagram 3 in the answer space shows two quadrilaterals, PQRS and P’Q’R’S’ , drawn on a grid of equal squares. P’Q’R’S’ is the image of PQRS under a reflection. On the diagram in the answer space, draw the axis of reflection.

2 marks

Answer :

P

Q

S P’

R

Q'

S’ R’

DIAGRAM 3

6

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-97

Learning To Score 2006: SET 3

Diagram 4 shows the three triangles, A, B and C, which are drawn on a Cartesian plane.

Answer : y

10 8

A

6 4

B

C

2 -4

x

-2

0

2

4

6

DIAGRAM 4

State (a) (i) the direction of the rotation, (ii) the coordinates of the centre of the rotation. (b) C is the image A under the transformation P. Describe in full transformation P.

4 marks

Answer : (a) (i) (ii)

7 8 (b)

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- 10 8

Learning To Score 2006: SET 3

Diagram 5 shows a pentagon.

20 m

24 m

12 m

DIAGRAM 5 On the grid in the answer space , draw Diagram 5 using the scale 1 : 400. The grid has equal squares with sides of 1 cm. 2 marks Answer :

8

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- 11 -

9

Learning To Score 2006: SET 3

Diagram 6 , in the answer space shows a square ABCD drawn on a grid of equal squares with sides of 1 unit. On the diagram , (a) construct the locus of point M moving at a distance of 4units from K. (b) construct the locus of a moving point S which is equidistant from the point R and T. (c) mark  for all the points that satisfy the loci in (a) and (b). 5 marks Answer :

A

B R

T K

C

D DIAGRAM 6

9

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Learning To Score 2006: SET 3

Set squares and protactors are not allowed for this question. 10

Diagram 7 shows triangle ABC.

C 5.5 cm B

30 0

A DIAGRAM 7 (a) Using only a ruler and a pair of compasses, construct Diagram 7 using the measurements given, beginning from the straight line DE provided in the answer space. (b) Based on the diagram constructed in (a), measure the distance in cm,between the point A and the point C. 5 marks Answer :

(a)

B

A 10 (b)

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- 13 11

Simplify

2 p

- q

2

+

p

- 2q

Learning To Score 2006: SET 3

2

[2 marks]

Answer:

11

2

12 Factorise completely each of the following expressions.

(a) 4 fg - 12 gh

(b) 3x 2 - 75 [3 marks] Answer: (a)

(b)

12

3

13 Express

2 3m

m3 6m 2 [3 marks]

Answer:

13

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14

Given

Learning To Score 2006: SET 3

5q  1 = 3 , express q in terms of r. qr [3 marks]

Answer:

14

3

15. Solve each of the following equations :

(a) 2 k = 5k - 12

(b)

2 5p = 3p 4 [3 marks]

Answer: (a)

(b)

15

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- 15 1

16

Evaluate

Learning To Score 2006: SET 3

1

33  9 3 2

64 3 [3 marks] Answer:

16

3

  5  , calculate the value of

17 Given 5 3 x 2 = 5 x

3

x.

[2 marks]

Answer:

17

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- 16 18. Solve the inequality

Learning To Score 2006: SET 3

8 - 3x  5 - x

Answer:

[2marks]

18

2

19. Table 1 shows the quantity of each type of books ordered by a school library.

Type of books Science Mathematics History Novel

Quantity 30 23 25 22 TABLE 1

The information for History is shown fully in the pie chart in the answer space. Complete the pie chart to represent all the information in Table 1 [5marks] Answer:

History

19

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- 17 20

Learning To Score 2006: SET 3

Use the graph paper provided to answer this question. Table 2 shows the values of two variables, x and y , of a function.

x y

–3 15

–2 5

–1 –1

0 –9

1 -1

2 5

3 15

TABLE 2

By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y –axis, draw the graph of the function.

[4 marks]

20

4

END OF QUESTION PAPER

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