Class:
Name:
Date:
5
3
Review 3
1
6
Section A
Choose the correct answer for each question. Write its number in the brackets
provided.
(1) What is the best estimate of 7236  68?
(1) 7000  60
(2) 7000  70
(3) 8000  70
(4) 8000  100
( 2 )
3
7
(2) Express 2 — as a decimal. Express your answer correct to 2 decimal places.
(1) 2.37
(3) 2.43
(2) 2.42
(4) 2.73
( 3 )
(3) The picture shows a wooden pole with clothes and a hand towel hanging from it.
The hand towel is 25 cm wide. Estimate the length of the pole from the picture
.
shown. It is about
(1)
(2)
(3)
(4)
1m
2m
32 cm
3.2 m
(4) Simplify 8a  7  3a  5  a.
(1) 12a  2
(3) 18a
Review 3
(2) 12
(4) 6a  12
( 2 )
( 4 )
67
(5) Which of the following is not a tessellation?
(1)
(2)
(3)
(4)
( 3 )
(6) What is the value represented by A?
10.5 cm
10.0 cm
A
(1) 10.35 cm
(3) 10.52 cm
(2) 10.4 cm
(4) 10.7 cm
( 1 )
(7) The figure below is not drawn to scale. ABDE is a trapezium and ABC is an
isosceles triangle. BCD is a straight line. Find BAC.
E
A
70°
B
(1) 40°
(3) 86°
C
94°
D
(2) 70°
(4) 110°
( 1 )
(8) Jamie has twice as many beads as Sally. Betty has half as many beads as Sally. If they
have 280 beads altogether, how many beads does Jamie have?
(1) 40
(2) 70
(3) 80
(4) 160
( 4 )
68
Review 3
(9) The length AB is 2 times the breadth. Find the volume of the solid.
7 cm
(1)
(2)
(3)
(4)
294 cm3
126 cm3
63 cm3
3 cm
42 cm3
A
B
( 2 )
(10)Find the area of the unshaded part in the figure below.
30 cm
(1)
(2)
(3)
(4)
76 cm2
12 cm
120 cm2
2
144 cm
180 cm2
24 cm
( 3 )
(11)Jimmy and Patrick have a sum of money in the ratio 5 : 6. Jimmy spent 60% of his
money on a racket which cost $18. How much did Patrick have?
(1) $12.96
(2) $25
(3) $30
(4) $36
( 4 )
(12)The charge for surfing the Internet in an Internet cafe is shown below. If Lina surfs
the Internet from 5.00 p.m. to 8.45 p.m., how much will she have to pay?
First hour of surfing
1
Every subsequent —
hour 2
or part thereof
(1) $19.50
(3) $25.50
Review 3
9.00 a.m. to 9.00 p.m.
$6.50
$2.50
(2) $21.50
(4) $26.50
( 2 )
69
(13)The graph below shows the marks Kelvin got for his tests. The total score for
each test was 100 marks. The average mark for the 4 tests was 78.
He accidentally spilled some ink on the bar graph.
What was Kelvin’s mark for the Mathematics test?
100
90
80
70
60
Marks 50
40
30
20
10
0
English
Science
Mathematics Chinese
Test
(1) 70
(3) 80
(2) 78
(4) 100
( 1 )
2
km away. His average
(14)Tim walked from his school to his house which was —
5
speed was 20 metres per minute. How long did he take to reach his home?
(1) 2 h 30 min
(2) 8 min
(3) 50 min
(4) 20 min
( 4 )
(15)A farmer harvested 200 kg of rice. He sold 20% of the rice and packed the rest
into 10 equal packets. Later he sold 5 packets to his neighbour. What percentage
of the rice did the farmer sell altogether?
(1) 20%
(2) 30%
(3) 40%
(4) 60%
( 4 )
70
Review 3
Section B
Work out each of the following questions. Write the correct answer in the space
provided.
(16)Express 215 g as a fraction of 3 kg 5 g in its simplest form.
3 kg 5 g= 3005 g
43
215
—–— = —––
3005 601
43
—––
601
(17)Find the value of 220  10  8  2  7.
220 ÷ 10 – 8 + 2 × 7
= 22 – 8 + 14
= 28
28
(18)Write the biggest number which when rounded off to the nearest hundred
gives 5700.
5749
4
8
15
(19)Find the value of —
 — . Give your answer in its simplest form.
9
4
15 5 5
4
8
— ÷ —– = — × —– = —
9
8 2 6
9
15
3
5
—
6
(20)How many ways can $1.50 be exchanged for 10¢ and 20¢?
No. of 10¢
15
13
11
9
7
5
3
1
Review 3
No. of 20¢
0
1
2
3
4
5
6
7
8
71
(21)
Mariam takes 2 years to save $2240. If she saves $112 a month, how many
months shorter will she take to save $2240? Express your answer as a fraction of
2 years in its simplest form.
Shorter time taken = 2240 ÷ 112
= 20 months
2 years = 24 months
24 – 20 = 4
1
—
6
4
1
—– = —
24
6
(22)Find the perimeter of the figure made up of two squares and two isosceles
triangles.
7+7+5+5+7+7+5+5
5 cm
5 cm
= 48 cm
7 cm
7 cm
48
cm
(23)A fruiterer sells 4 apples for 90¢. What is the greatest number of apples Meiling
can buy if she has $10?
$10 = 1000¢
1000 ÷ 90 ≈ 11
11 × 4 = 44
44 apples
(24)Some pupils were asked to choose their favourite sport. The pie chart represents
their choices. What percentage of the pupils like table tennis?
Volleyball
12%
Table tennis
72
50% – 12% = 38%
Basketball
Soccer
23%
38
%
Review 3
(25)
The figure below is made up of 2 overlapping quadrants. Find the area of the
shaded part. Give your answer correct to 2 decimal places.
12 cm
1
Area of quadrant = — × π × 12 × 12
4
≈ 113.097 cm2
1
2
Shaded area= 2 × (113.097 – (— x 12 x 12)
≈ 82.19 cm2
82.19
cm2
(26)The ages of 5 boys are shown in the table below. Find their average age.
Boy
Age
Total age= 8 years 3 months +
9 years 2 months +
Ahmad
8 years 3 months
6 years 8 months +
Ben
9 years 2 months
7 years 4 months +
Cailong
6 years 8 months
9 years
Derrick
7 years 4 months
=40 years 5 months
Fred
9 years
Average age= (40 years 5 months) ÷ 5
= 8 years 1 month
8
1
year(s)
month(s)
(27)A dotted line is drawn in each figure. Which two of the dotted lines are lines of
symmetry?
A
B
C
D
A
Review 3
and
B
73
(28)Rathi earns $15 a day on weekdays and $28 a day on weekends. She works from
Monday to Saturday every week. How much does she earn in 2 weeks?
Amount earned in 1 week= 5 × $15 + $28
= $75 + $28
= $103
Amount earned in 2 weeks= 2 × $103
= $206
$
206
(29)The total mass of 5 girls is p kg. If 2 girls have masses of 32 kg and 40 kg, what is
the total mass of the other 3 girls?
Total mass of 2 girls= 32 + 40
= 72 kg
Total mass of the other 3 girls = (p – 72) kg
(p – 72)
kg
(30)Look at the graph below. Find the average amount of flour sold by a shopkeeper
in the 4 months. Give your answer correct to 1 decimal place.
60
50
40
Amount
of flour 30
sold (kg)
20
10
0
Dec
Jan
Feb
Mar
Month
Total amount of flour= 45 + 35 + 55 + 30
= 165 kg
Average amount of flour= 165 ÷ 4
= 41.25
≈ 41.3 kg
74
41.3
kg
Review 3
(31)
Magdeline bought a bag that cost $98.02 after discount. She was given
a 42% discount. What was the usual price of the bag?
100% – 42% = 58%
58% →$98.02
100% → ($98.02 ÷ 58) × 100
= $169
$
169
(32)The figure below is made up of 2 identical squares and 4 identical rectangles.
Find the area of the figure.
Area of figure= (2 × 20 × 20) + (4 × 10 × 20)
= 800 + 800
= 1600 cm2
10 cm
20 cm
1600
cm2
(33)Natalie has some cookies. The number of cookies she has is more than 30 but
less than 50. She has enough cookies to put them equally into either 6 red boxes
or 8 blue containers. What is the least number of cookies she has?
Multiples of 6 more than 30 but less than 50: 36, 42, 48
Multiples of 8 more than 30 but less than 50: 32, 40, 48
48 cookies
(34)The ratio of the number of pears to the number of lychees is 2 : 3. The ratio of
the number of lychees to the number of rambutans is 4 : 3. Find the ratio of the
number of pears to the number of lychees to the number of rambutans.
Number of pears:Number of lychees:Number of rambutans
2
:
3
4
:
3
=
8
:
12
:
9
Review 3
8 : 12 : 9
75
(35)The figure below is not drawn to scale. BCDE is a parallelogram. DFG is an
equilateral triangle. ABC, FGH and BEH are straight lines. Find ABE.
H
FDG = 60°
G
E
D
F
A
CBE = FDG
= 60°
ABE= 180° – 60°
= 120°
120
C
B
°
Section C
For each of the following questions, show your working clearly and write your
answer in the space provided.
(36)Look at the rectangle shown below. If the length and the breadth of the rectangle
were doubled, what would be the increase in the area of the rectangle?
3 cm
Before :
Area of rectangle = 3 × 2 = 6 cm2
2 cm
After :
Area of rectangle = 6 × 4 = 24 cm2
Increase in the area = 24 – 6 = 18 cm2
The increase in the area of the rectangle would be 18 cm2.
(37)In the figure on the right, shade four small squares
so that the pattern will have the dotted line shown
as the line of symmetry. Accept any correct answer.
76
Review 3
(38)The figure below is made up of 4 identical rectangles. The length of each rectangle
is twice its breadth. If the total area of the figure is 200 cm2, what is the length of
the rectangle?
rea of 1 rectangle = 200 ÷ 4
A
= 50 cm2
Area of 1 rectangle= Length × Breadth
50= Length × Breadth
= 10 × 5
The length of the rectangle is 10 cm.
(39)The figure below is not drawn to scale. It is made up of a parallelogram ACEF
and a rhombus ABCD. Find BCE.
A
B
110°
D
80°
180° – 80°
2
100°
= —––
2
ACB= ————–
F
= 50°
ACE= AFE
= 110°
C
BCE= 110° + 50°
= 160°
E
(40)Pei Xin was given a sum of money. She spent the same amount of money each day.
2
of her money in 6 days. After another 5 days, she had $20 left. How
She spent —
7
much money did she have at first?
1
2
2
1
— ÷ 6 = — × — = —–
21
7
7
6
11
1
—– × 11 = —–
21
21
11
10
21
1 – —–
= —–
21
Review 3
10
—– of her money = $20
21
1
—– of her money = $2
21
21
—– of her money= 21 × $2
21
She had $42 at first.
= $42
77
(41) The pie chart shows the population of different animals in a pond habitat. There
are 50 pond skaters and the number of water snails is the same as the number of
tadpoles.
(a) How many animals are there?
(b) How many water scorpions are there?
Kingfisher
Water snail
(a)4 × 50 = 200
There are 200 animals.
10%
15
100
(b) —— × 200 = 30
Backswimmer
Pond skater
There are 30 water scorpions.
Water
scorpion Tadpole
15%
(42)(a) Line AB, 6 cm long, is given below. Draw a triangle ABC in which
CAB = 75° and CA = 8 cm.
C
8 cm
75°
A
78
6 cm
B
Review 3
(b) Extend the tessellation by adding four more unit shapes.
Review 3
79
(43)A shop sells a CD for $2.80 but gives a discount of $2.20 for every 4 CDs bought.
(a) Find the cost of buying 4 CDs, with the discount.
(b) If Ali paid $92.80 for some CDs, how many CDs did he buy?
(a) $2.80 × 4 = $11.20
$11.20 – $2.20 = $9.00
It cost $9 to buy 4 CDs.
(b) $92.80 ÷ 9 ≈ 10
10 × $9 = $90
$92.80 – $90 = $2.80
(10 × 4) + 1 = 41
He bought 41 CDs.
(44)Mr Tan sold 40% of the stationery in his shop. Peter had some stationery items
at first. He then bought 40% of the number of stationery items that Mr Tan sold.
Now Mr Tan and Peter each has 270 stationery items.
(a) How many stationery items did Mr Tan sell?
(b) How many stationery items did Peter have at first?
(a) 60%→ 270
1%→ 4.5
40%→ 180
Mr Tan sold 180 stationery items.
40
100
(b) —— × 180 = 72
270 – 72= 198
Peter had 198 stationery items at first.
80
Review 3
(45)Look at the solids shown below.
(a) From Solid 3, how many more blocks are needed to build Solid 5?
(b) How many blocks are needed altogether to build Solid 20?
Solid 2
Solid 1
Total number
Solid
of blocks
needed
Solid 1
1 (12)
(a) 25 – 9 = 16
16 more blocks are needed to build Solid 5.
Solid 2
4 (22)
(b) 202= 20 × 20
= 400
Solid 3
9 (32)
Solid 4
16 (4 )
Solid 5
25 (52)
Review 3
Solid 3
400 blocks are needed to build Solid 20.
2
81
(46)
4 circles each of radius 4 cm were cut out from a big circular cardboard as
shown below.
(a) Find the area of the cardboard that was cut out.
(b) Find the area of the cardboard left.
(Take π = 3.14)
20 cm
(a) Area cut out= 4 × π × Radius × Radius
= 4 × 3.14 × 4 × 4
= 200.96 cm2
The area of the cardboard that was cut was 200.96 cm2.
(b) Area of big circular cardboard
= π × Radius × Radius
= 3.14 × 10 × 10
= 314 cm2
314 – 200.96 = 113.04
The area of the cardboard left was 113.04 cm2.
82
Review 3
*(47)Town A and Town B were 360 km apart. A car left Town A for Town B at
10.30 p.m., at an average speed of 70 km/h. At the same time, a van left Town B
for Town A, travelling along the same road, at an average speed of 50 km/h. At what time did the car and van pass each other?
Car
50 km/h
Van
? km/h
Town A
Town B
360 km
Time Distance Distance
taken travelled travelled
by car
by van
1 h
70 km
50 km
Total
distance
travelled
120 km ✗
2 h
140 km
100 km
240 km ✗
3 h
210 km
150 km
360 km 3
3h
10.30 p.m.
11.30 p.m.
12.30 a.m.
1.30 a.m.
The car and van passed each other at 1.30 a.m. the next morning.
Review 3
83
*(48)The Robotics Club had twice as many pupils as the Science Club. The ratio of
the number of girls to the number of boys in the Robotics Club was 4 : 1. The
ratio of the number of girls to the number of boys in the Science Club was 2 : 3.
(a) Find the ratio of the number of girls in the Robotics Club to the number of
girls in the Science Club.
(b) After 38 girls left the Robotics Club to join the Science Club, the ratio of
the number of girls to the number of boys in the Science Club became 9 : 4.
How many girls were in the Science Club in the end?
(a)
boys
girls
Robotics
Club
Science
Club
boys
girls
Number of girls in the Robotics Club : Number of girls in the Science Club
=8:2
=4:1
The ratio of the number of girls in the Robotics Club to the number of girls in the Science Club was 4 : 1.
(b) Before:
Science
Club
boys
girls
After:
Science
Club
38
boys
girls
The number of boys in the Science Club remained the same.
27 units – 8 units = 19 units
19 units→38 pupils
1 unit→38 ÷ 19
= 2 pupils
27 units→27 × 2
= 54 girls
84
There were 54 girls in the Science Club in the end.
Review 3