Set 1 mawar

DIRECTED NUMBERS

Calculate the value of

1. 90 (-15) 3

2. -9 – [ 7 (-3) ]

3. -54 9 (-2)

4. -15 – 24 8 + (-3)

5. -12 – (-7) 9

6. -9 12 (-4)

7. 3 – (-8) 9

8. -16 (-4) 2

9. -8 + (-16) (-2)

10. -9 (-3) – (-4)

INTEGER, FRACTION AND DECIMAL.

1

1. Calculate the value of and express the answer as a decimal.

2. Calculate the value of and express the answer as a decimal.

3. Calculate the value of and express the answer correct to two

decimal places.

4. Calculate the value of and express the answer as a fraction in its lowest

terms..

5. Calculate the value of

6. Calculate the value of

7. Calculate the value of and express the answer correct to two decimal

places.

8. Calculate the value of and express the answer correct to two

decimal places

SQUARE, SQUARE ROOTS, CUBE AND CUBE ROOTS

2

1. a) = b) =

2.a) = b) =

3. a) = b) =

4.a) = b) =

5. a) = b) =

6. a) = b) =

7.a) = b) =

8. a) =

b) =

9. a) = b) =

10. a) =

b) =

3

ALGEBRAIC EXPRESSIONS

1. Expand each of the following expressions:

(a) =

(b) =

(c) = (d) =

(e) = (f) =

(g) = (h) =

(i) = (j) =

(k) =

(l) =

2. Expand each of the following expressions:

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

(k) (l)

(m) (n)

4

LOCI

1. State the locus of point K such that K is always 2 cm from a fixed point T.

___________________________________________________________________________

2. Describe the locus of a point M which moves equidistant from two fixed points P

and Q.

___________________________________________________________________________

3. Point P moves such that it is always equidistant from the straight lines KL and MN.

Construct the locus of P.

5

K

L

M

N

4. A point Y moves in such a way that it is always 2cm from point O.

___________________________________________________________________________

5. A point P moves in such a way that it is always 1.5cm from the straight line KL.

__________________________________________________________________________

6. In the diagram, ABCD is a square with sides of 5 units. V and W are two moving points

which moves inside the square.

(a) construct the locus of

(i) point V which moves such that it is always 3 units from BC.

(ii) point W which moves in such a way that is always equidistant from AB

and CD.

(b) Hence, mark point P which is 3 units from BC and equidistant from AB and CD.

6

● O

K

L

AB

D C

7. (a) In the diagram, construct the locus of

(i) a moving point X which is always equidistant from point P and point Q.

(ii) a moving point Y which is always equidistant from point P and point R.

(b) Hence, mark point V which is equidistant from P, Q and R.

______________________________________________________________________________

8. The diagram shows an equilateral triangle PQR with sides 4cm each. X and Y are two

points which move inside the triangle.

(a) Construct the locus of;

(i) point X which moves such that it is always equidistant from RP and RQ.

(ii) point Y which moves such that it is always 3 cm from point P.

(b) State the number of points of intersection between the two loci.

7

R

P

Q

●●

●

P Q

R

9. The diagram shows two fixed points A and B. In the diagram, construct the locus of

(a) point X which moves so that AX = BX.

(b) point Y which moves so that BY = 3cm

Subsequently, mark the point/points of intersection of the two loci with symbol .

______________________________________________________________________________

10. The figure below shows a triangle ABC. In the figure,

(a) construct the locus of point P which moves such that its perpendicular distance

from the straight lines AB and BC is constant.

(b) construct the locus of point Q which moves such that its distance from C is 3 cm.

(c) mark the intersection point of the loci of P and Q.

8

● ●A B

CB

A

ALGEBRAIC FORMULAE

1 . Express c as the subject. 2. Express as the subject.

3. Express as the subject.

4

. Express as the subject

5

. Express as the subject.

6. Express as the subject.

7 Given, P = 5u – 3v. Find the value of v if P = 15 and u -2. 8

Given, L = h (a + b). Find the value of

L if h = 3, a = 5 and b = 1.

9Given that, q = ah. Express b as the

subject of the formula.10

Given, the 2P = Q . Express Q as the

subject of the formula.

11Given that, 3x = – 2. Express y as the

subject of the formula.12

Given, T = , k = 3 and g = 10. Find the

value of L if T = 2k

13Given that, y = . Express y as the

subject of the formula.14

Given that, T = 2π . Express g as the

terms of T, π and L.

15Given that, Express y in

the terms of x.16

Given that, G = . Express H in

terms of G.

17Given that, R = . Express P in

terms of Q and R.18

. Given that, L = K – K(L + 4). Express L in terms of K.

19 Given, g = h + k. Express h in terms of

g and k.

20 Given – 7 = h. Express h in terms of k.

21

Given that, x + 6 = 3. Express y in

terms of x. 22Find the value of F. Given, F =

with a = 2.

9

LINEAR EQUATIONS

Solve each of the following equations:

1 a) k – 7 = − 13 b) 7 + 3q = 4

2 a) m + 7 = 4 b) 9 – 15b = 3b

3 a)

b) 5d = 24 + p

4 a) 3r = 15 b) 3(m - 4) = m + 6

5 a) 6s = 7s – 15 b) 8q – 5 = 17 – 3q

6 a) 6y + 5 = 7y b) 9 – 4p = − 7p + 21

7 a) 5x – 14 = 4xb)

8 a)

b) 7p + 5 = 3(5 – p)

9 a) 3m = 4m – 5 b) 3(n – 2) = 2n + 7

10 a) x + 15 = 3b)

10

LINEAR INEQUALITIES

1. a) Solve the inequality 3 + x ≤ 4

b) List all the integer values of x which satisfy both the inequalities ≤ 1 and 3 – x < 0.

2. a) Solve the inequality 7 − 4y < 6 – y.

3.List all the integer values of x which satisfy both the inequalities ≤ 1 and 1− 2x < 3.

4. List all the integer values of x which satisfy both the inequalities 6x + 4 < 5x + 7 and

5 - x ≤ 6

5. List all the integer values of m which satisfy both the inequalities 2m – 1 < 5 and − 3m ≤ 9

6. a) Solve the inequality 2m + 1 > 3

b) List all the integer values of m which satisfy both the inequalities 5 – 2m ≤ 7 and +

5 < 6.

7. Solve the following inequalities:

a) w + 3 < 2

b) 8 + 4v ≥ 20 – 2v

8. List all the integer values of w which satisfy both the inequalities 3 – 4w < 7 and 2w – 3 ≤5

9.List all the integer values of m which satisfy both the inequalities - 1 < 2 and 7 – m < 1.

10. Solve the inequality 9 – 2x < x – 6 .

INDICES

11

1.

2.

3. 4.

5. 6.

7. 8.

9, 10.

11. 12.

13.

14.

STATISTICS

1. ( a ) Find the median of the following data.

12

-4, 5, 4, -2, -5, 3, 7

( b ) Calculate the mean of the following data.

Point

Mata0 1 2 3 4

Frequency

Kekerapan3 8 9 6 4

Answer : ( a )

( b )

[3 marks/markah]

______________________________________________________________________________2. Diagram 2 shows the number of books read by 20 students in a month.

State the

( a ) mode

( b ) median

Number of books Number of students

5 2

10 7

15 4

20 8

Diagram 2 Answer : ( a )

( b )[3 marks/markah]

3. Table 1 shows the number of cars sales in three month.

13

Month Number of cars

January 80

February 60

June 50

Table 1

The information of car sales in three month shown fully in pictograph in the answer space.

Complete the pictograph to represent all the information in Table 1.

Answer:

Number of Cars

Bilangan kereta

January

Januari

February

Februari

June

Jun

Represent ……… Cars

Mewakili ………. kereta

[3 marks/markah]

4. The data in diagram 4 shows the points have been scored by 25 participants.

14

Diagram 4 Rajah 4

(a) Using the data, complete the frequency table in the answer space.

(b) State the mode.

Answer:

(a)

Marks 1 2 3 4 5 6

Frequency

(b)

[3 marks/markah]

5. The table below shows the number of members of three clubs in a school.

15

3 5 6 5 4

5 6 6 2 66 6 1 4 36 4 2 3 63 2 4 3 5

Club Number of members Angle of sector

Computer 75

Football 55 110º

Music 50

i. Complete the table above.

ii. On the circle with centre O below, draw a pie chart to represent all the information

given in the table and state the size of every angle of its sectors.

[4 marks/markah] Answer/ Jawapan:

4. ( a ) Find the median of the following data.

-4, 5, 4, -2, -5, 3, 7

16

•O

( b ) Calculate the mean of the following data.

Point 0 1 2 3 4

Frequency 3 8 9 6 4

Answer : ( a ) ( b )

[3 marks/markah]

GRAPH OF FUNCTIONS

17

x

Question 1

Table shows the value of two variable, x and y of a function.x-2-101234y321882028

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

By using the scale of 2 cm to 4 units, complete and label the y-axis.Based on table, plot the points on the graph paperHence, draw the graph on the function.

0 1 2 3 4-1-2

y

18

x

Question 2 Table shows the value of two variable, x and y of a function.

x-3-2-10123y-32-11-2141334The x–axis and the y-axis are provided on the graph paper .

By using the scale of 2 cm to 10 units, complete and label the y-axis.Based on table, plot the points on the graph paperHence, draw the graph on the function.

0 1 2 3-3 -1-2

y

19

x

Question 3 Table shows the value of two variable, x and y of a function.

x-3-2-1-0.511.52y07101040-5The x–axis and the y-axis are provided on the graph paper .

By using the scale of 2 cm to 2 units, complete and label the y-axis.Based on table, plot the points on the graph paperHence, draw the graph on the function.

0 1 2-3 -1-2

y

20

x

Question 4Table shows the value of two variable, x and y of a function.

x0123456y53-3-13-27-45-67The x–axis and the y-axis are provided on the graph paper .

By using the scale of 2 cm to 10 units, complete and label the y-axis.Based on table, plot the points on the graph paperHence, draw the graph on the function.

0 1 2 3 64 5

y

21

x

Question 5 Table shows the value of two variable, x and y of a function.

x-3-2-10123y-19-31-1-3117The x–axis and the y-axis are provided on the graph paper .

By using the scale of 2 cm to 5 units, complete and label the y-axis.Based on table, plot the points on the graph paperHence, draw the graph on the function.

0 1 2 3-3 -1-2

y

22

x

Question 6 Table shows the value of two variable, x and y of a function.

x-3-2-10123y-37-18-11-10-13-20-30The x–axis and the y-axis are provided on the graph paper .

By using the scale of 2 cm to 5 units, complete and label the y-axis.Based on table, plot the points on the graph paperHence, draw the graph on the function.

0 1 2 3-3 -1-2

y

GEOMETRICAL CONSTRUCTIONS

1. Set square and protractors are not allowed for this question

23

Diagram in the answer space below shows a straight line AB.

(a) Using only a ruler and a pair of compasses

( i ) construct a triangle ABC beginning from the straight line AB such that

BC = 6 cm and AC = 5 cm.

( ii ) hence, construct the perpendicular line to the straight line AB which

passes through the point C.

(b) Based on the diagram constructed in (a), measure the perpendicular distance

between point C and the straight line AB.

( 5 marks )

2. Set squares and protractor are not allowed for these questions.

(a) Beginning from the straight line BC, construct a triangle ABC with

24

AB=4cm and ABC = 120°.

(b) Construct a parallelogram PQRS beginning from the straight line PQ

such that PS = 3.5 cm and QPS=60°.

3. Diagram below in the answer space shows a straight line AC.

(a) Using only a ruler and a pair of compasses

25

(i) construct a triangle ABC beginning from the straight line AC such

that AB = 5 cm and BC = 4 cm.

(ii) hence, construct the perpendicular bisectors of the straight lines

AB and BC in the triangle ABC.

(iii) mark the point where these two perpendicular bisectors meet T.

(b) Based on the diagram constructed in (a) measure the distance of BT.

4. Diagram below shows triangle DEF.

26

(a) Using only a ruler and a pair of compasses, construct the diagram above

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 D and the point F.

Answer :

5. Diagram in the answer space shows a straight line PQ.

27

(a) By using a ruler and pair of compasses,

(i) construct a triangle, PQR, such that PQ = 6 cm, PR = RQ = 7 cm.

(ii) construct a parallelogram PQSR,

(iii) construct TPQ = 30° such that T is on the line SQ.

(b) Based on the diagram constructed in (a), measure the length of QT.

Answer ;

28

SCALE DRAWING

1.

On the square grids in diagram 1, redraw figure P according to a scale of 1 : .

Answer :

29

6 units

4 units

Figure P

2.

Diagram 2

Diagram 2 shows a trapezium. On the grid in the answer space, draw the diagram using

scale of 1 : 200. The grid has equal squares of 1 cm each.

Answer:

30

3. In the figure, Q is the scale drawing of P with a scale of 1 : 5.

20 cm

15cm

Find the perimeter of Q, in cm.

Answer :

_____________________________________________________________________________

4. The figure shows a trapezium. Redraw the trapezium according to a scale of 1 :

Answer :

5. In the diagram, figure S is the scale drawing of figure R.

31

P Q

Find the scale used.

Answer :

______________________________________________________________________________

6.

Answer :

_____________________________________________________________________________

7. If a distance of 25km is represented by 50cm on a map, what is the scale used?

Answer :

______________________________________________________________________________

8. The scale of a map is 1cm : 4km. The distance between two towns is 16km. What is the

distance between these two towns on the map.

Answer:

9. In diagram, figure II is the scale drawing of figure 1. Find the value of x.

32

Q

P

B

A

1.5cm

6cm

In the diagram, AB is the scale drawing of PQ. Calculate

the scale used.

5cm

R S

20cm

Answer :

______________________________________________________________________________

10. Draw the figure of T in the answer space according to a scale of 1 :

Answer :

PYTHOGORAS THEOREM

33

I II2cm

3cm6cm

x cm

1.

In the diagram above, PQST is a trapezium.

Calculate the area of the shaded region, in cm .

Answer:

2.

15 cm

G H 14 cm

Given that , find the length of EF in cm.

Answer:

3.

34

E

F H

V

T S

5 cm P

Given that PTUV is a rhombus and QRST is a square. UTQ and PQR are straight lines.

Calculate the perimeter of the whole diagram, in cm.

Answer:

4.

In the diagram above, PWUV and RSTW are squares. If the area of RSTW is 36 cm ,Find the area of PWUV in cm .

Answer:

TRIGONOMETRY

35

12 cm Q

U

R

1.

In the diagram above, BEC is a straight line. Find tan x.

Answer:

2. In the diagram below, AEB is a straight line and AE = EB. Find the value of sin x.

Answer:

3. In the diagram below, BCD is a straight line and sin y = . Find the value of cos x.

36

13 cm

6 cm

xE

8 cm

A B

D

C

8 cm

6 cm

3 cm

x

CB

E

DA

Answer:

4. The diagram below shows two triangles JKL and KMN. KL = LM. Find the value of p + r in cm.

Answer:

p

10 cm

M 9 cm N

L

r

K8 cmJ

5. In the diagram below, ABC is a right-angled triangle.

Given sin x = 0.6, calculate the value of d.

37

20 cm

26 cm

Ay

B

C

x

D

Answer:

TRANSFORMATION

38

15 cm

C

d cm

Bx

A

1. In diagram, triangle P is the image of triangle Q under translation . On a

square grid in the answer space, draw triangle Q.

P

2. In diagram, P’ is the image of P under transformation M.

Describe in full transformation M

39

3. H’ is the image of H under transformation L. Describe in full transformation L

40

H’

H

_____________________________________________________________________________

4. Diagram below shows two polygons, H and H’ was drawn on a grid of equal squares with sides of one unit.

41

H’

H

H’ is the image of H under transformation M. Describe in full transformation M.

5. Diagram in the answer space shows quadrilateral PQRS, R’S’ is the image of RS under a

reflection at a straight line MN

42

M

N

P Q

R

S

S’

R’

Complete the image of quadrilateral PQRS

6. In Diagram, P is enlarged by scale factor of 3, with O as a centre of enlargement.

43

P

Draw the image of P.

44

7. Diagram in the answer space shows two quadrilaterals, JKLM and J’K’L’M’ drawn on

grid of equal squares. J’K’L’M’ is the image of JKLM under an enlargement.

On the diagram in the answer space, mark P, as a centre of enlargement

45

46

47

48

49

50