soalan topikal (pmr)

1. 0 WHOLE NUMBERS / DIRECTED NUMBERS

1. –3 – ( –11) – ( –8 ) 9. 25 + (– 75) 5 × 2

2.– 120 6 × (–5) 10. 2 – × (– 6)

3.– 2 + (– )

4. – 1 –

5.– 2

6. – 6.18 – (– 2.07)

7.Calculate the value of 18 – (–0.2)

8.Calculate the value of 2.48 × 0.6 – (– 2 ) and express your answer correct to two

decimal places.

2.0 SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS

1

1. (a) Find the value of

(b)Calculate the value of

[ 3 marks] 2. (a) Find the value of


[ 3 marks] 3. (a)

Find the value of


[ 3 marks] 4. (a)

Find the value of

(b) Calculate the value of [ 3 marks]



6. (a)Find the value of





(b) Calculate the value of


(b) Calculate the value of


2

(b) Calculate the value of +[ 3 marks]


(b) Calculate the value of 42 ×

[3 marks]

12. (a) Find the value of 3

(b) Calculate the value of ( 4.2 ÷ 2 [3 marks]

13. (a) Find the value of .

(b) Calculate the value of 3 [3 marks]


(b) Calculate the value of . [3 marks]


(b) Calculate the value of . [3 marks]

3

3.0 ALGEBRAICS EXPRESSIONS

1. Simplify each of the following:a. x

[1 mark]c.

(15x – 24y²)

[1 mark]b 10p² ÷ 16pq

[1 mark]d. (18x – 36y²) ÷ 6

[1 mark]

2. Simplify each of the following:a.

[2 marks]

c. [2 marks]

b.

[2 marks]

d. ³ ³ [2 marks]

3. Simplify each of the followinga.

[2 marks]c. ²

[2 marks]b. ²

[2 marks]d.

[2 marks]

4. Expand each of the following:a.

[1 mark]c.

[2 marks]b. ²

[1 mark]d.

[1 mark]

5. Factorise completely each of the following expressions:a.

[1 mark]c.

[1 mark]b. ²

[1 mark]d. ²

[1 mark]

6Express as a single fraction in its simplest form.

[2 marks]

5

7.Express as a single fraction in its simplest form.

[2 marks]

8. Simplify each of the followinga.

3

35 x +

[2 marks]

b.

[2 marks]

9. Simplify each of the following:a.

[2 marks]

b.

[3 marks]

10.

The diagram shows a trapezium.a) Write an algebraic expression for the area of the trapezium.

[2 marks]b) If x = 2, find the area of the trapezium, in cm².

[1 mark]

6

5x cm

cm

cm

4.0 LINEAR EQUATIONS

1. Solve each of the following equationsa ) 7x = 49 c ) 4k + 7 = 8

b ) = -3

d ) 5y – 5 = 40

[4 marks ]

2. Solve each of the following equationsa )

= 10c )

- 4 = 6

b ) 3d + 2 = 20 d ) 7 – 4e = 19[8 marks ]

3. Solve each of the following equationsa ) 8f + 2 = 4f c ) 5g = 4 – 3g

b ) 6n – 8 = 5n + 7 d ) 2m – 3 = m + 3[8 marks ]

4. Solve each of the following equationsa ) 2 ( p – 4 ) = 16 c ) 2 ( r – 2 ) = 10 – 5r

b ) q + 3 = -3 ( q – 6 ) d ) = 4s

[8 marks ]

5. Solve each of the following equationsa ) -4 – 6x = 14 c ) 2z = 15 – 3z

b ) = 2

d ) 2 ( n – 1 ) = 8 – 3n

[8 marks]

6. Solve the following simultaneous equationsa ) 3x – 7y = 27

5y – 2x = -19c ) 4h – 3k = 5h + 1

5h + k = 23

b ) 7s – 3p = 53s + p = 9

d ) 5p – 2q = 203p + 2q = -4 [16 marks]

5.0 GEOMETRICAL CONSTRUCTIONS

7

1. Based on the diagram 1 below, construct the right angled triangle EFD such that EFD 30˚ and DF = 5cm in actual size.

Diagram 1

Answer : [5 marks]

2. Using only a pair of compasses and ruler, construct

8

DE

5cm

F

30˚

(a) A perpendicular bisector of QS(b) UVW = 120˚

Answer [5 marks]a)

b)

3. Using only a pair of compasses and ruler, construct (a) a perpendicular line to RS which passes through X(b) A parallel line to MN which passes through X

Answer : [6 marks](a)

(b)

9

Q

S

U

V

N

M X

S

R

X

4. Using only a pair of compasses and a ruler, construct a triangle PQR with side PQ = 4cm, QR = 4.5cm and PQR 45˚.

Answer : [5 marks]

5. Using only a pair of compasses and ruler, construct a parallelogram TUVW where TU = 3cm, UV = 4cm and TUV = 60˚.

Answer : [5 marks]

6.0 LOCI IN TWO DIMENSIONS

10

1. The diagram below shows a square ABCD. X, Y and Z are three moving points in the diagram.(a) X is a moving point such that it is always equidistant from line AB and line BC. By using the

letters in the diagram, state the locus of X.(b) On the diagram draw

(i) The locus of Y such that YA = AD.(ii) The locus of Z such that it is equidistant from point A and point D.

© Hence, mark with the symbol the intersection of the locus of Y and the locus of Z.

[5 marks]

2. The diagram below shows a square JKLM, containing grid columns and rows with each side measuring 1 unit. P, Q and R are three moving points in the diagram.(a) P is a moving point such that it is always equidistant from point J and point L. By using the

letters in the diagram, state the locus of P.(b) On the diagram draw

(i) The locus of Q such that it is constantly 2 units from line JK.(ii) The locus of R such that it is constantly 4 units from point K.

(c) Hence, mark with the symbol the intersection of the locus of Q and the locus of R.

[5 marks]

3 The diagram below shows a triangle STU . X and Y are two moving points in the diagram.

11

AB

A D

C

J

K L

M

(a) On the diagram draw(i) The locus of X such that it is equidistant from line SU and line ST.(ii) The locus of Y such that its perpendicular distance from line SU is always 2 cm.

(b) Hence, mark with the symbol the intersection of the locus of X and the locus of Y.

[3 marks]

4. The diagram below shows four identical parallelogram ABEF, BCDE, EFGH and DEHI. M, P and Q are three moving points in the diagram.(a) M is a moving point such that it is always equidistant from line DF. By using the letters in

the diagram, state the locus of M.(b) On the diagram draw

(i) The locus of point P such that PD = DC,(ii) The locus of point Q such that QE = EF

(c) Hence, mark with the symbol the intersection of the locus of P and the locus of Q.

[6 marks]

5. The diagram below shows a trapezium QRST. Y and Z are two moving points in the diagram.

12

S

UT

D

G

A

B

C

E

F

I

H

(a) On the diagram, draw(i) The locus of Y such that YT =4 cm(ii) The locus of Z such that it is equidistant from line QT and line RS.

(b) Hence, mark with the symbol the intersection of the locus of Y and the locus of Z.

[3 marks]

6. The diagram below shows two squares PQTU and QRST of the same size . K, X and Y are three moving points in the diagram.(a) K is a moving point such that it is equidistant from line PU and line RS. By using the letters in

the diagram, state the locus of K.(b) On the diagram draw

(i) The locus of point X such that XT = TS,(ii) The locus of point Y such that its distance from point Q and point U are the same.

© Hence, mark with the symbol the intersection of the locus of X and the locus of Y.

[5 marks]

7. 0 TRANSFORMATIONS

13

S

Q

R

Q

T

P Q R

U T S

1. In Diagram 1, Q is the image of P under a rotation of 90° clockwise about the centre M. On the diagram in the answer space, mark the point M.

[2 marks]Answer:

Diagram 1

2. Diagram 2, in the answer space shows a triangle T drawn on a grid of equal squares.On the diagram in the answer space, draw the image of triangle T under an enlargement with centre P and scale factor 3.

[2 marks]Answer:

Diagram 2

3. Diagram 3, shows two triangles P and Q, drawn on a Cartesian plane. Q is the image

14

P

Q

P

Q

●P T●P T

of P under a rotation.State:(a) the direction of the rotation(b) the coordinates of the centre of the rotation

[2 marks]Answer:

Diagram 3

4. Diagram 4 is drawn on square grids. Draw the image of triangle KLM under a rotation of

15

0 2 4 6 8 10 12 x

y

12

10

8

6

4

2

P

Q

0 2 4 6 8 10 12 x

y

12

10

8

6

4

2

P

Q

T

90° clockwise about T.[3 marks]

Answer:

Diagram 4

5. Diagram 5 in the answer space is drawn on a grid of equal squares. On the diagram, draw

16

●K

L

M

●K

L

M

the image of trapezium PQRS under the translation and label it as P’ Q’ R’ S’.

[3 marks]Answer:

Diagram 5

6. In Diagram 6,

17

- 6 - 4 - 2 0 2 4 6

6

4

2

- 2

- 4

- 6

P

S

R

Q

y

x

- 6 - 4 - 2 0 2 4 6

6

4

2

- 2

- 4

- 6

P

S

R

Q

y

x

(a) draw and label the image P’Q’R’S’ of quadrilateral PQRS after a reflection in line KL.

(b) mark the point T’ which is the image of T under the same reflection.(c) state the coordinates of T’.

[3 marks]Answer:

Diagram 6

18

- 6 - 4 - 2 0 2 4 6

6

4

2

-2

-4

-6

P Q

R

S

T

L

K

x

y

●- 6 - 4 - 2 0 2 4 6

6

4

2

-2

-4

-6

P Q

R

S

T

L

K

x

y

●

7. Diagram 7 in the answer space shows a quadrilateral OPQR drawn on a grid of equal squares of sides 1 unit.(a) If OPQR is reflected in the line OR, draw and shade the image of OPQR in the grid

below.(b) If OPQR is mapped onto OJKL by an enlargement about the centre O with scale

factor 3, draw the quadrilateral OJKL in the same grid below.[3 marks]

Answer:

Diagram 78. In Diagram 8, triangle K’L’M’ is the image of triangle KLM under transformation T.

Describe in full transformation T.[2 marks]

Answer:

Diagram 8

19

PQ

R

O

PQ

R

O

- 3 0 3 6

6

3

-3

K

L

M

M’

K’

L’

x

y

- 3 0 3 6

6

3

-3

K

L

M

M’

K’

L’

x

y

9. Diagram 9 in the answer space shows triangle PQR drawn on a Cartesian plane.

(a) If triangle ABC is the image of triangle PQR under a translation draw the

triangle ABC.(b) The vertex R is the image of the vertex Q under a reflection about the line HG.

Draw on the same diagram, the axis of reflection.(c) If C’ is the image of C under a reflection in the line HG, mark the point C’ in

the diagram. State the coordinates of C’. [3 marks]

Answer:

Diagram 9

20

0 2 4 6 8

6

4

2

Q

R

P

y

x0 2 4 6 8

6

4

2

Q

R

P

y

x

10. Diagram 10 in the answer space shows a polygon ABCDEF and a straight line QR drawn on a grid of equal squares. Starting from the line QR, draw the polygon PQRSTU which is congruent to polygon ABCDEF.

[2 marks]Answer:

Diagram 10

21

AB

C D

EF

Q

R

AB

C D

EF

Q

R

8.0 STATISTICS

1. FOODS NUMBER OF PUPILSCURRY PUFF 25

MUFFIN 15APPLE PIE 10

PIZZA 8NOODLE 12

The table shows the favourite foods of a group of pupils. Draw a bar chart to represent the data.

[3 marks]

2.

The bar chart shows the number of students in five societies and clubs. Given that the total number of Chinese students is 220, calculate the total number of Malay students.[2 marks]

3.

22

MALAYCHINESE

NUMBER

OF

STUDENTS

Key :

P Q R S T

Types of Cars Number of Women Number of Man

Kancil 15 5

Persona 18 22

Waja 20 32

The frequency table shows the number of car owners in a housing park. Represent the data using a horizontal dual bar chart.

[3 marks]

4. The table shows the number of book in the three shelves in a library.

Shelf Number of book

Shelf 1 120

Shelf 2 60

Shelf 3 100

Table 1

The information for Shelf 1 is shown fully in the pictograph in the answer space. Complete the pictograph to represent all the information in Table 1.

Number of books in the shelves

Shelf 1

Shelf 2

Shelf 3

Represents ……… books.

[3 marks]

5. The diagram shows the number of book borrowed from a school library by 14 students.

23

(a) Using the data, complete the frequency table below.

Number Frequency

23456

(b) State the median.[3 marks]

6. The table below shows the ages of a group of foreign workers in a rubber estate.

Ages Number of workers

25 327 429 731 x33 5

The median age of the worker is 29 years old. Find the possible value of x. [3 marks]

7. The bar chart shows the incomes of a private company in Malaysia throughout a duration of five month.

State the greatest increase in income between any two consecutive months.

[3 marks]

9. 0 SCALE DRAWINGS & SOLID GEOMETRY ( NETS )

24

3 2 4 3 5 6 24 2 5 5 3 2 6

45

40

35

30

25

20

15

10

5

Jan Mac Apr Mei Jun

INC

OM

ES

(R

M M

ILL

ION

)

1. Diagram 1 shows a trapezium. On the grid in the answer space, draw Diagram 1 using the scale 1 : 300. The grid has equal square with sides of 1 cm.

Diagram 1

(3 marks)

Answer:

2. Diagram 2 shows a right pyramid with a square base and 4 cm height.25

12 m

18 m

6 m

Diagram 2

Draw a full scale the net of the pyramid on the grid in the answer space. The grid has equal squares with sides of 1 cm.

(3 marks)Answer:

3. Diagram 3 shows a polygon.

26

4 cm

3 cm3 cm

4 cm

3 cm3 cm

Diagram 3

On the grid in the answer space, redraw the polygon using the scale 1 : 50. The grid has equal square with sides of 1 cm.

(3 marks)Answer:

27

6 m

5 m

2 m

5 m

4. Diagram 4 shows a right prism.

Diagram 4

Draw a full scale net of the prism on the grid in the answer space. The grid has equal squares with sides of 1 unit.

(3 marks)

Answer:

28

3 units5 units

4 units

3 units5 units

4 units

5. Diagram 5 shows a composite figure draw on a grid of equal squares.

Diagram 5

Redraw the figure in the answer space according to the scale 1 : 2.

(3 marks)

Answer:

29

6. Diagram 6 shows the net of a cuboid drawn in the square grid of 2 cm.

Diagram 6

When the cuboid is constructed, what would be its volume?(3 marks)

Answer:

30

7. Diagram 7 shows a cube.

Diagram 7Draw three different nets of the cube.

(3 marks)

Answer:

31

1 unit

8. Diagram 8 shows a right pyramid with a square base.

Diagram 8

Draw a full scale the net of the pyramid on the grid in the answer space. The grid has equal squares with sides of 1 unit

. (3 marks)

Answer:

32

5 units

6 units

10.0 INDICES

1. Simplify

(a) y3 × y b) (p q ) × q

_______ y

[ 4 marks ]

2. (a) Find the value of 4 ÷ 4

(b) Simplify (pq ) × p [ 4 marks ]

3. Simplify :(a) (3x y) × (x ) ÷ x y [ 3 marks ](b) [ (xy) × 2xy ] [ 2 marks ]

4. Find the value of

(a) 3 ÷ 3 (b) (5 × 3 )

[ 3 marks]

5. Find the value of (10 ) × (10 ) .

[ 2 marks ]

6. (a) Given that 3 = 81, calculate the value of x

(b) Given that 2 = 32, calculate the value of p [ 4 marks]

7. (a) Given that (p ) = (p )(p ) , find the value of n. [ 3 marks ]

33

8.

Evaluate .

[ 3 marks ]

9. Find the value of 81 × 27 × 3

[ 3 marks ]

10. Evaluate 16 8 × 4

[ 3 marks]

34

11.0 ALGEBRAIC FORMULAE

1. Given that , express c in the terms of A and b.[2 marks]

2. Given that , express p in terms of q and r.[2 marks]

3. Given that , express y in terms of x .[3 marks]

4.Given that , express y in terms of x.

[3 marks]

5.Given that , express y in terms of k.

[2 marks]

6.Given that , express k terms of n and m.

[3 marks]

7.Given that express y in terms of x.

[3 marks]

8.Given that E = , express n in terms of E and m.

[2 marks]

9.Given that , express y in terms of v and W.

[3 marks

10. Given that , express x as the subject for the formula.

[3 marks

12 .0 LINEAR INEQUALITIES

35

1. List all the integer values of x which satisfy both the inequalities

1 and 3 – 2x < 7

[ 3marks]

2. Find all the integers values of x which satisfy the inequalities 5x – 8 12 and 3x + 4 > 1

[3 marks]

3. Solve each of the following inequalities

(a) 3w – 12 < 0 (b) 1 + x 7 – x

[3 marks]

4. Solve the inequality 8 – 3x < 7 – x

36

[3 marks]

5. (a) Solve the linear inequality 4 + 3x < 10

(b) Given x is an integer, find all the values of x which satisfy both the linear inequalities

+ 2 5 and 6 – x < 0

[3 marks]

6. (a) Solve the inequality 2 + x 5

(b) List all the integer values of x which satisfy both the inequalities

- 3 1 and 3 - x < 0

[4 marks]

7. (a) Solve the inequality 3 + y - 1

37

(b) List all the integer values of x which satisfy both the inequalities 2y + 1 -1 and 6 - 2y > 0

[ 4 marks]

8. Solve the inequality 8 – 3x 5 - x

[ 2 marks]

13.0 GRAPHS OF FUNCTIONS

1. Use the graph paper provided to answer this question.Table 1 shows the values of two variables, x and y of a function.

38

x -2 -1 0 1 2 3 4y 4 -2 -6 -8 -8 -6 -2

Table 1

Draw the graph of the function using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis.

Answer:


x 0 1 2 3 4 5 6

39

y 25 27 27 25 21 15 7

Table 2


Answer:


x -2 -1 0 1 2.5 3 4y 21 8 1 0 10 16 33

40

Table 3

Draw the graph of the function using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis

Answer:

[4 marks]


x -2 -1 0 1 2 3y -30 3 10 9 18 55

Table 4

41


Answer:

[4 marks]


x -2 -1.5 0 1 2 3y -23 -10 1 1 9 37

Table 5

Draw the graph of the function using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units

42

on the y-axis

Answer:

[4 marks]

6.

Use the graph paper provided to answer this question.

Table 6 shows the values of two variables, x and y of a function

x -2 -1 0 1 2 3 4y 5 2 1 2 5 10 17

Table 6

The x-axis and the y-axis are provided on the graph paper.

43

(a) By using the scale of 2 cm to 4 units, complete and label the y-axis.(b) Based on table 6, plot the points on the graph paper.(c) Hence, draw the graph of the function

Answer:

[4 marks]

7. Use the graph paper provided to answer this question.

Table 7 shows the values of two variables, x and y of a function

x -3 -2 -1 0 1 2 3y -22 -3 3 5 3 -3 -13

Table 7

The x-axis and the y-axis are provided on the graph paper.44

y

x-2 -1 0 1 2 3

(a) By using the scale of 2 cm to 5 units, complete and label the y-axis.(b) Based on table 7, plot the points on the graph paper.(c) Hence, draw the graph of the function

Answer:

[4 marks]

8. Use the graph paper provided to answer this question. Table 8 shows the values of two variables, x and y of a function

x -2 -1 0 1 2 3y 5 0 1 2 -3 -20

Table 8

45

y

x-3 -2 -1 0 1 2 3

The x-axis and the y-axis are provided on the graph paper.(a) By using the scale of 2 cm to 4 units, complete and label the y-axis.(b) Based on table 8 , plot the points on the graph paper.(c) Hence, draw the graph of the function

Answer:

[4 marks]

9. Use the graph paper provided to answer this question.Table 9 shows the values of two variables, x and y of a function

x -4 -3 -2 -1 0 1 2y -2 -1 0 1 2 3 4

46

y

x-3 -2 -1 0 1 2 3

Table 9The x-axis and the y-axis are provided on the graph paper.(a) By using the scale of 2 cm to 1 units, complete and label the x-axis.(b) Based on table 9, plot the points on the graph paper. Hence, draw the graph

of the function(c) From the graph, determine the value of y when x = -2.5 and value of x when y =

1.5 Answer :

[4 marks]

10. Use the graph paper provided to answer this question.

47

y

x

4

3

2

1

0

-1

-2

Table 10 shows the values of two variables, x and y of a function.

x -2 -1 0 1 2 3 4y 4 0 -2 -2 0 4 10

Table 10

The x-axis and the y-axis are provided on the graph paper.(a) By using the scale of 2 cm to 2 units, complete and label the y-axis.(b) Based on table 6, plot the points on the graph paper.(c) Hence, draw the graph of the function.

Answer:

[4 marks]

14.0 TRIGONOMETRY

48

y

x-2 -1 0 1 2 3 4

1. Diagram 1 shows the right-angled triangle ABC.

Find sin x°.[ 1 marks ]

2. In Diagram 2, cos xo =

Diagram 2[ 1 marks ]

3. In Diagram 3, the value of 1 + tan xo is


4. In Diagram 4, sin = . The length of PR in cm is

Diagram 4

49

P

R

Q24 cm

7 cm

8 cm

Q

A

x°

17 cm

3 cm 5 cm

P

Rx°

6 cm

x°C

Diagram 1

B

[ 2 marks ]

5. In Diagram 5, sin PQR = . The length of RS in cm is

Diagram 5

[ 2 marks ]

6. In Diagram 6, PTR and QRS are straight lines

Diagram 6Find the value of cos xo

[ 2 marks ]

7. In the Diagram 7, PQRS is a rectangle. Tan xo = and tan yo =

Diagram 7Find the length of PQ

50

RQ

P

5 cm

2 cm S

RS

Q

R

T

S

10 cm5 cm

6 cm

P

10 cm y°

x°

Q

P

x°

[ 3 marks ]

8. In the Diagram 8, PQRS is a rectangle and PT = TS. Find sin xo


9. In the Diagram 9, PSR is a straight line . Given cos xo = , find tan yo


10. In the Diagram 10, find cos xo

Diagram 10

51

=

=

P

Q

R

M

10 cm6 cm

Nx°

9 cm

P

R

S

=

Q

x°

x°

y°

T

=

S R

QP

12 cm

10 cm

15 cm

[ 2 marks ]

52

soalan topikal (pmr)

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