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)
1

INTEGER, FRACTION AND DECIMAL.
1. Calculate the value of 





×−−
5
2
10
7
9.0 and express the answer as a decimal.





+−−
10
3
2
1
2.1 and express the answer as a decimal.





−−×
10
7
11.039.5 and express the answer correct to two
decimal places.





−×
3
1
5
3
8
9
and express the answer as a fraction in its lowest
terms.
.
5. Calculate the value of
9.0
14.09 ×
6. Calculate the value of ( )12
4
1
120 −+÷
7. Calculate the value of ( )
3
4
24.08 ÷− and express the answer correct to two decimal
places.





−−×
2
1
28.026.5 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) )3(2 qk + = (b) )3(2 yxx + =
(c) )1(4 yy + =
(d) )2( yxx + =
(e) )12(3 −yx = (f) )2(3 qpq − =
(g) )3(2 nmk + = (h) ( )rpp 43 − =
(i) ( )mm 52 − =
(j) ( )xpy 36 − =
(k) ( )fef −32 = (l) ( )xyx −28 =
2. Expand each of the following expressions:
(a) ( )( ) =+− 625 xx
(b) ( )( ) =−− 532 xx
(c) ( )( ) =+− 224 pp
(d) ( )( ) =−+ 2213 xx
(e) ( )( ) =−− 234 yy
(f) ( )( ) =+− 237 mm
(g) ( )( ) =−+ yxyx 252
(h) ( )( ) =−− qpqp 323
(i) ( )( ) =+− nmnm 43
(j) ( )( ) =−− tktk 2532
(k) ( )( ) =+− qpqp 23
(l) ( )( ) =−+ srsr 3232
(m) ( )( ) =+− yxyx 2727 (n) ( )( ) =−− pfpf 222
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
A
B
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 cba 43 += . Express c as the subject. 2 3
2
14
h
g −= . Express h as the subject.
3 98
3
−
=
w
w
v . Express w as the subject.
4
222
gfe += . Express f as the subject
5
14 2
+= grp . Express r as the subject.
6 r
pq
s
2
−
= . Express q as the subject.
7
Given, P = 5u – 3v. Find the value of v if
P = 15 and u -2.
8
Given, L =
2
1
h (a + b). Find the value of
L if h = 3, a = 5 and b = 1.
9
Given that, q =
2
1
ah. Express b as the
subject of the formula.
1
0
Given, the 2P = Q 2
. Express Q as the
1
1
Given that, 3x =
3
y
– 2. Express y as the
1
2
Given, T =
2
1
, k = 3 and g = 10. Find the
value of L if T = 2k .
g
L
1
3
Given that, y =
x
xy −
. Express y as the
1
4
Given that, T = 2π
g
L
. Express g as the
terms of T, π and L.
1
5
Given that, .5
)2(3
=
−
x
y
Express y in
the terms of x.
1
6
Given that, G =
5
1 H−
. Express H in
terms of G.
1
7
Given that, R =
p
QP
6
54 −
. Express P in
terms of Q and R.
1
8
.
Given that, L = K – K(L + 4). Express L in
terms of K.
1
9
Given, g 2
= h 2
+ k. 2
Express h in
terms of g and k.
2
0
Given
k
h
– 7 = h. Express h in terms of k.
2
1
Given that, x + 6 y = 3. Express y in
terms of x. 2
2
Find the value of F. Given, F =
a
a
2
53 −
with a = 2.
LINEAR EQUATIONS
9

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) 6
12
=
c
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 = 4x
b) 63
2
3
=+t
8
a) 4
20
=
g
b) 7p + 5 = 3(5 – p)
9 a) 3m = 4m – 5 b) 3(n – 2) = 2n + 7
10 a) x + 15 = 3
b) y
y
=
−
2
56
10

LINEAR INEQUALITIES
1. a) Solve the inequality 3 + x ≤ 4
b) List all the integer values of x which satisfy both the inequalities
2
x
≤ 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
3
x
≤ 1 and 1− 2x < 3.
4. List all the integer values of x which satisfy both the inequalities 6x + 4 < 5x + 7 and
5 -
2
1
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
3
m
+ 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
3
m
- 1 < 2 and 7 – m < 1.
10. Solve the inequality 9 – 2x < x – 6 .
11

INDICES
1. ( )232
42 × 2. 55
33 −
÷
3. ( )4
2 3
53 × 4. 32
228 ×÷ −
5. ( ) 233
42 ×−
6. 23
5
2
9273 ÷×−
7.
( )32
43
3
39 −
×
8.
2
3
2
18 







−
9, ( )332
2 ba
10. 3
75
−
mn
nm
11.
rp
pr
2
2
49
7 12. ( ) ( ) 944232
3 nmnmn ÷×
13. 5
23
p
pp −
×
14. 5
3
−
×
p
pp
STATISTICS
12

1. ( a ) Find the median of the following data.
-4, 5, 4, -2, -5, 3, 7
( b ) Calculate the mean of the following data.
Point
Mata
0 1 2 3 4
Frequency
Kekerapan
3 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 6
6 6 1 4 3
6 4 2 3 6
3 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 paper
Hence, draw the graph on the function.
0 1 2 3 4-1-2
y

18
x
Question 2
x-3-2-10123y-32-11-2141334
0 1 2 3-3 -1-2
y

19
x
Question 3
x-3-2-1-0.511.52y07101040-5
0 1 2-3 -1-2
y

20
x
Question 4
x0123456y53-3-13-27-45-67
0 1 2 3 64 5
y

21
x
Question 5
x-3-2-10123y-19-31-1-3117
0 1 2 3-3 -1-2
y

22
x
Question 6
x-3-2-10123y-37-18-11-10-13-20-30
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 :
2
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 :
2
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 :
2
1
Answer :
PYTHOGORAS THEOREM
33
I II
2cm
3cm6cm
x cm

1.
In the diagram above, PQST is a trapezium.
Calculate the area of the shaded region, in cm 2
.
Answer:
2.
15 cm
G H
14 cm
Given that
5
4
=
EH
EF
, 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 2
,
Find the area of PWUV in cm 2
.
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 =
4
1
. Find the value of cos x.
36
13 cm
6 cm
x
E
8 cm
A B
D
C
8 cm
6 cm
3 cm
x
C
B
E
D
A

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
A
y
B
C
x
D

Answer:
TRANSFORMATION
38
15 cm
C
d cm
B
x°
A

1. In diagram, triangle P is the image of triangle Q under translation





−
−
3
4 . On a square grid
in the answer space, draw triangle Q.
P
39

2. In diagram, P’ is the image of P under transformation M.
Describe in full transformation M
40

3. H’ is the image of H under transformation L. Describe in full transformation L
H’
H
_____________________________________________________________________________
4. Diagram below shows two polygons, H and H’ was drawn on a grid of equal squares with
sides of one unit.
H’
H
41

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
Complete the image of quadrilateral PQRS
42
M
N
P Q
R
S
S’
R’

6. In Diagram, P is enlarged by scale factor of 3, with O as a centre of enlargement.
Draw the image of P.
43
P

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
44

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