MATHEMATICS Y6 SK (SEMAKAN 2017)

4 State the ratio of 12 : 18 in the simplest form. 18 units

Method 1
12 units

Group in
twos.

6 groups 9 groups

Group in 12 : 18 is simplified to 6 : 9.
threes.

2 groups 3 groups

6 : 9 is simplified to 2 : 3.

Method 2 Divide 12 and 18 Method 3
by 2. 12 : 18
12 : 18
÷2 ÷2 Divide 6 and 9 ÷6 ÷6
by 3. 2:3
6:9
÷3 ÷3 Which method would
you choose? Why?
2:3

The ratio of 12 : 18 in the simplest form is 2 : 3 .

€€Carry out a simulation by grouping objects in twos, threes, and sixes € 193
7.2.1 to simplify the ratio between two quantities.

5 Ravi bought 2 kg of chicken and 4 000 g of mutton. €
State the ratio of the mass of chicken to the total mass
of chicken and mutton bought by Ravi.

mass of chicken total mass
2 kg 2 kg + 4 000 g = 2 kg + 4 kg
= 6 kg

2:6 Convert the unit before
÷2 ÷2 finding the ratio.

:

The ratio of the mass of chicken to the total mass of chicken

and mutton is :.

6 The picture shows the price of a T-shirt and a long-sleeved shirt.

T-shirt Long-sleeved shirt

RM24 RM36

State the ratio of the total price of a T-shirt and a long-sleeved shirt to the

price of a T-shirt. total price T-shirt price 24 and 60 can be
60 : 24 divided by 12 without
total price
÷÷ any remainder.
1

RM 2 4
+ RM 3 6

RM 6 0 :

The ratio of the total price of a T-shirt and a long-sleeved shirt to the

price of a T-shirt is :.

€€Vary ratio questions involving daily life situations such as the ratio of usage € 7.2.1
194 of petrol in a day to the usage in a week.

THINK
SMART

Observe the flash cards above. Which animal group gives the ratio of 2 : 3 when
compared to the total of two animal groups?

TRY IT OUT

Pair work activity.
Build a suitable chart or a mind map to state ratio in the simplest form.

EXAMPLE

RATIO

MONEY VOLUME OF MASS LENGTH
LIQUID

State the ratio of State the ratio of € State the ratio of € State the ratio of €
RM10 to RM50. 6 to 8 000 m . 3 000 g to 9 kg. 4 m to 600 cm.

7.2.1 €€Prepare sufficient sample questions to help pupils build a chart, mind map, € 195
or mobiles for the Try It Out activity.

€€Exhibit pupils’ work or organise a contest.

LET’S DO IT

1 Jamilah prepares sandwiches, pies, and tarts for her children.

sandwiches pies tarts

State the ratio of:

a the number of sandwiches to the number of pies.

b the number of pies to the total number of tarts and pies.

c the total number of tarts and sandwiches to the number of tarts.

2 The picture shows the volume of watermelon juice in containers R and T.

600 m 400 m

RT
State the ratio of the volume of watermelon juice in container R to the

volume of watermelon juice in container T.
3 The table shows the mass of seafood ordered by Rachel’s family.

Seafood Fish Crab Squid

Mass 2 kg 1 500 g 500 g

State the ratio of:

a the mass of crab to the mass of squid.

b the mass of fish to the total mass of fish and crab.

c the total mass of squid and fish to the mass of squid.

4 State the ratio of 20 sen to RM1 in the simplest form.

5 8 000 m State the ratio of:
a the distance of EF to the
2 km
E G distance of FG.
b the distance of EF to the
F
distance of EG.
c the distance of EG to the

distance of FG.

196 7.2.1

DETERMINE THE PROPORTIONATE QUANTITY

1

We will choose 3 boys and a few
girls for the storytelling session.

The ratio of the total

number of boys to the

total number of girls that
will be chosen is 1 : 2.

How many girls will be chosen?

Method 1 3 pupils Use a model. Method 2

boys boys girls
1:2
girls
×3 ×3
1 part 3 pupils
2 parts 2 × 3 pupils = 6 pupils 3:
The number of girls
=2×3
=6

The number of girls that will be chosen is 6 .

The number of female teachers is 12. The ratio of the

number of male teachers to the number of female
teachers is 1 : 3. Calculate the number of male teachers.

€€Guide pupils to use model to represent ratio. 197
7.3.1 €€Guide pupils to find the value of a unit first. Recall the unitary method.

2 Name Zikri Wong Sudhar
Number of 12
comics read

The ratio of the number of comics read by Zikri to the
number of comics read by Wong is 3 : 2. Calculate the
number of comics read by Wong.

Method 1 12 Method 2
Zikri
Zikri Wong
Wong Find for one € 3:2
unit first.
×4 ×4
3 parts 12 comics
1 part 1 2 ÷ 3 = 4 comics 12 :
2 parts 2 × 4 comics = 8 comics
Number of comics €
read by Wong
2 × 4 comics = 8 comics

The number of comics read by Wong is 8  .

The ratio of the number of comics read by Zikri to the
number of comics read by Sudhar is 4 : 3. Calculate the

number of comics read by Sudhar.

SPORTS HOUSE SCORE

THINK The ratio of the score of blue sports BLUE 160
SMART
house to the score of green sports GREEN
house is 5 : 3. Calculate the score of

green sports house.

198 7.3.1

3 The picture shows the mass of two durians.

The ratio of the mass of the small durian
to the mass of the big durian is 1 : 3.

Find:
a the mass of the small durian.

b the mass of the big durian.

Method 1 the mass of €
the small durian
the mass of the big durian

a 4 parts 8 kg 8 kg 2 kg
1 part 8 kg ÷ 4 = 2 kg 3 × 2 kg = 6 kg
b 1 part
3 parts

Method 2 Create a table €
Durian
Part Small Big Small and big and solve.
1
Mass 34

8 kg

a 1:4 b 3:4
×2 ×2 ×2 ×2

2:8 6:8
2 kg of small durian 6 kg of big durian

The mass of the small durian is 2 kg  . The mass of the big durian is 6 kg  .

€€Vary questions which involve daily life situations such as length of an object,
7.3.1 pupils’ height, pupils’ body mass, and volume of liquid. 199

LET’S DO IT

1 Complete the following ratio in the simplest form.

a 10 : 10 b 8 : 12 c 16 : 30
÷÷
÷÷ ÷4 ÷
: 15
1 : :

2 State the ratio in the simplest form. d 18 : 81 e 32 : 28
a 4 : 14 b 5 : 20 c 8 : 24

f A B A:B g A B A:B h A B B:A

6 kg 30 kg 4 12 16 km 28 km

3 The ratio of Rusdi’s score to Anushia’s score is 2 : 7. Player Score
Rusdi’s score is 8. Calculate Anushia’s score.
Rusdi 8

Anushia

4 The table shows the number of red tokens in a box. The number of green and blue
tokens is not shown.

Token Red Green Blue
Number 60

a The ratio of the number of red tokens to the number of green tokens is 5 : 4.

Calculate the number of green tokens.
b The ratio of the number of red tokens to the number of blue tokens is 3 : 2.

Calculate the number of blue tokens.

5 The ratio of Roslinda’s savings to Sherin’s savings is 3 : 8. The total of their savings
is RM66. Calculate the savings of:

a Roslinda. b Sherin.

6 The diagram shows a right-angled triangle and a square.

8 cm 10 cm

6 cm

The ratio of the perimeter of the right-angled triangle to the perimeter of the
square is 3 : 4. Calculate the perimeter of the square.

200 €€Surf https://bit.ly/3B8HeMQ to check the answers. 7.3.1

SOLVE THE PROBLEMS y Adnani
Kaswini
6

1 The picture shows the position 5
of Miss Norehan and her
Miss
pupils during an online class. € 4 Norehan
Miss Norehan interacts with

Kaswini during the learning 3 Amsyar
session. State the horizontal

distance and vertical distance, 2 Chi Min
in km, of Kaswini from €

Miss Norehan. 1 cm1 Azah Scale
Solution O1 1 cm represents
234 5 x 1 km
1 cm

Understand the problem

• Scale of 1 cm represents 1 km. Plan the strategy
• Find the distance of Kaswini
Mark the horizontal distance and
from Miss Norehan. vertical distance on the Cartesian
plane.
Solve

y Check
Miss Norehan’s coordinate ( 2 ,  5 )
6 3 km Kaswini’s coordinate ( 5 ,  4 )

5 Miss 1 km Horizontal distance = 5 km – 2 km
Norehan Kaswini = 3 km
4
Vertical distance = 5 km – 4 km
3 = 1 km

2 The distance of Kaswini from Miss Norehan is €
3 km horizontally and 1 km vertically.
1

O 12345 x

Horizontal distance = 3 km
Vertical distance = 1 km

Who is located 1 km horizontally
and 3 km vertically from €
Miss Norehan?

7.4.1 €€Guide pupils to solve the problems using drawing method on the € 201
Cartesian plane.

€€Get pupils to locate who is the farthest from Miss Norehan.

€€Emphasise the use of scale to determine distance.

2 There are 15 boys and 18 girls in 6 Meteor. 1 boy and 2 girls have
transferred to other schools. Calculate the ratio of the current number €
of boys to the current number of girls.

Solution

Pupils Boys Girls
Initial number 15 18
Number of pupils' transferred 1 2
Current number 14 16

The ratio of the current number of boys to the current €
number of girls is 14 : 16.

Group in 14 pupils 16 pupils
twos.

7 groups 8 groups

14 : 16 is simplified as 7 : 8.

Check 7:8 Calculate the ratio of the current
×2 ×2 number of boys to the total current

14 : 16 number of boys and girls.

The ratio of the current number of boys to the
current number of girls is 7 : 8.

€€Guide pupils using representations to express the ratio between two quantities. 7.4.1
202

3 Encik Kamarul drove from his house to town P and then from town P to

town Q. The distance from his house to town Q through town P is 45 km.

The ratio of the distance from his house to town P to the distance from €
town P to town Q is 4 : 5. What is the distance from town P to town Q?

Solution Distance from
house to town P.
45 km
9 parts 45 km Distance from
1 part 45 km ÷ 9 = 5 km town P to town Q.
5 parts 5 × 5 km = 25 km

Check

Location House to town P Town P to town Q House to town Q
Part 4 5 9

Distance 45 km

5:9
×5 ×5

25 : 45

Distance from town P to town Q is 25 km.

Calculate the ratio of the distance from Encik Kamarul’s house
to town P, to the distance from Encik Kamarul’s house €
to town Q through town P.

THINK The ratio of Mark’s money to Faizal’s money is 6 : 1. €
SMART The total of their money is RM56. Mark gave half of €

his money to Faizal. Calculate the ratio of Mark’s €
current money to Faizal’s current money.

€€Create questions similar to the question in Think Smart to enhance 203
7.4.1 pupils’ thinking skills.

LET’S DO IT

1 The Cartesian plane shows the location of four villages, A, B, C, and D.

Ny Village A 1 cm Encik Lim lives in a village which has €
1 cm an equal horizontal and vertical
6 distance from village D.

5 a C alculate the horizontal distance

4 and vertical distance, in km, of
village B from village A.

3 Village D b C alculate the horizontal distance
and vertical distance, in km, of €

2 Encik Lim’s village from village D.
State Encik Lim’s village.
Village B

1 Village C
Scale

O 1 2 3 4 5 x 0 1 2 3 4 5 km

2 There are 44 green marbles and 8 red marbles in a box. Rakesh takes out €
8 green marbles and adds another 4 red marbles into the box. Calculate €
the ratio of the current number of green marbles to the current number of €
red marbles in the box.

3 Rozi buys a purple ribbon and a yellow ribbon. The ratio of the length of the
purple ribbon to the length of the yellow ribbon is 2 : 9. The length of the yellow

ribbon is 630 cm. What is the length, in cm, of the purple ribbon?

4 There are 60 scouts and Malaysian Red Crescent members participating in

the district level anti-drug campaign. The ratio of the number of scouts to the
number of the Malaysian Red Crescent members is 7 : 5. Calculate the number

of scouts who participated in the campaign.

5 The picture shows the volume of lime juice in jug J K J

and glass K. The ratio of the volume of lime juice in
jug J to the volume of lime juice in glass K is 7 : 2. €
The volume of lime juice in jug J is 400 m more

than the volume of lime juice in glass K. Calculate
the volume, in m , of lime juice in glass K.

€€Vary questions involving measurement to enhance pupils’ understanding. 7.4.1
204

LET’S PRACTISE

1 y The Cartesian plane shows the location of three mini

6 markets owned by Encik Rosham. State, in km, the
5 E horizontal distance and vertical distance of:

4F a m ini market F from mini market G.
3 b m ini market E from mini market F.

2 c m ini market E from mini market G.

1 2 3 4 G Scale
1 cm 1 cm represents 1 km
5 6x
O1
1 cm

2 State the following ratio in the simplest form.

a 3 : 15 b 9 : 54 c 6 : 14 d 2 4 : 4 e 64 : 72

3 a T he ratio of P : Q is 3 : 7. Find the value of P if Q is 35.

b 42 cm The ratio of the length of RS to the
length of ST is 1 : 5. Calculate the

R S T length of:

4 Solve the following problems. i RS. ii S T.

a y The Cartesian plane shows two historical locations

6 on an island. Rizal is visiting historical site R. He

5 wants to visit historical site T from historical site R.
4 T State the actual horizontal distance and vertical

3R distance of historical site T from historical site R.

2
1 Scale
O 1 2 3 4 5 6 x 0 1 2 3 4 5 km

b Isaac is 13 years old, and his brother is 5 years old. State the ratio of
Isaac’s age to his brother’s age after 7 years.

c M artin has RM90. The ratio of the amount of money spent on food to €
taxi fare is 2 : 3. How much does he spend on food?

d The ratio of the number of Thai tourists to the number of Korean tourists is
4 : 9. The total number of tourists from both countries is 104. What is the

difference between the number of tourists from Thailand and Korea?

7.1.1, 7.2.1 €€Use different scale for question 1 as an additional activity. € 205
7.3.1, 7.4.1 For instance: 0 1 2 3 4 5 km

LET'S EXPLORE

Answer the following questions. Fill each of the box below with a letter which
represents the answer based on the question number to get the secret code.

1 State the ratio of 36 to 20 in the simplest form. Answer balloons

2 y The Cartesian plane shows the location 2:1 9:5
TE
5 Village W of town V and village W. The distance
4 of town V from village W is €

3 s horizontally and t vertically. Find €

2 the value of s and t. 9 RM20
YN
1 Town V 5 x Scale 3 4 5 km
O 1 234 012

3 The ratio of value A to value B is 8 : 3. The value of A is 24. € s = 3 km
Find the value of B. t = 4 km

4 Kasim and Jamil share their money to buy a shirt which L RM28
costs RM48. The ratio of Kasim’s money to Jamil’s money R
is 5 : 7. How much money does Kasim spend?

5 In a recipe, the ratio of the number of tablespoons of salt € 25 g 15 g
to the number of tablespoons of black pepper is 2 : 3. € UO

The mass of salt used is 10 g. What is the mass, in g, €
of the black pepper?

6 Simplify the ratio of 8 : 14.

7 State the ratio of RM25 to RM40 in the simplest form.

Question 8 until 10 is based on the diagram below. 5:8 3:2
VL

8 State the ratio of the number of to the number of . 1 : 3 s = 3 cm
9 State the ratio of the number of to the total number of A t = 4 cm

shapes. M
10 State the ratio of the total number of shapes to the number

of .

SECRET 10 5 7 1 2 3 4:7
I
CODE 4 9 8 6 5 4

7.1.1, 7.2.1,
206 7.3.1, 7.4.1

8 DATA HANDLING AND
LIKELIHOOD

COMPLETE PIE CHART AND INTERPRET DATA

1

Have a look and relate the two diagrams

with the pie chart. 1 and 45° represent
8

flower and plant stamps. Let’s try to explain.

TUESDAY STAMP COLLECTION 11 OCTOBER 2022

Insect 1 180°
20 2
90° 45°
Bird Flower 1 1 45°
10 5 4 18

Plant 8

1 has a value of 180° angle and
2

also represents 20 insect stamps.

Bird stamps are
1
represented by 4 or 90°.

State the number of flower stamps.
Give reasons.

8.1.1 €€Guide pupils to relate the fractions with angles to represent data in a pie chart.

207

Colours of the Marbles

2 Colour Number of marbles

Red 8

Blue 2 180°

Green 4 90° 45°
Yellow 2 45°

Present the data of the number of marbles in pie chart based on €

the values of angles given.

The total number Colour Number of Fractions
of marbles is 16. € Red
marbles
16 marbles
represent a circle. 8 8 = 1
16 2

Blue 2 2 = 1
16 8

Green 4 4 = 1
16 4

Yellow 2 2 = 1
16 8

Divide the circle into € Total 16 16 = 1
8 equal parts. Find the 16
number of marbles for
Colours of the Marbles
one part.

16 ÷ 8 = 2 22 Red
2 180° 2 8
180°

2 90° 45° 2 90° 45°
45° Green Blue

45° 2
4 Yellow
22 2

a The fraction of red marbles is and is represented by 180°.

b The fraction of blue marbles is and is represented by .

c The fraction of green marbles is and is represented by .

d The mode is with the highest number of marbles, which is .

208 €€Recall the meaning of mode. Encourage pupils to interpret data regarding 8.1.1
range, median, and mean based on the suitable data of the pie chart.

3 The incomplete pie chart and table show the data of 24 pupils’
favourite doughnut flavours.

Favourite Doughnut Flavours Flavour Number of doughnuts
Chocolate
45°
Strawberry Strawberry 12

90° Vanilla 6
Vanilla
Peanut

a Complete the pie chart.

24 pupils represent a circle.

The parts that Favourite Doughnut Flavours
represent chocolate
3 Peanut

45° 3 and peanut doughnuts 3 Chocolate
45° have equal values of Strawberry€45°
180° angles. 45° is half of 12 45° 3
90°or 6 doughnuts.
12 90° Half of 6 doughnuts is 180° 90°
6 Vanilla€
6
3 doughnuts.

b Complete the sentences below based on the pie chart.

i 45° represents peanut doughnuts and the number is .

ii 90° represents doughnuts and the number is .

iii Peanut and doughnuts are represented by angle

because their numbers are equal.

iv The number of most favourite doughnuts is and €

is represented by angle.

v The number of pupils who like doughnuts is half of the

number of pupils who like doughnuts.

8.1.1 €€Prepare a circle of 45°, 90° and 180° angles to carry out an activity to 209
complete pie chart and interpret data.

4 Sport Number Values of
of pupils angles

Hockey 5 45°

Football 20

Badminton 10 45°
Table Tennis 5

FAVOURITE FAVOURITE
SPORTS SPORTS

Football Alex Table Hockey Aliza
20 Tennis 5

180° 5

45° 45°

90°
Football
Table 45° 45° 20 180°
Tennis 90° Hockey
5 Badminton
5 Badminton
10
10

Who completes the pie chart correctly?
Write three information based on the correct pie chart.

THINK Mathematics Test
SMART Achievement Grades

The pie chart shows the number of pupils B 180° A
who scored grades A, B, C, and D in a 22 pupils
mathematics test. What is the total number
of pupils who sat for the test? Explain. 90°

45°
45° D

C

€€Remind pupils that the largest part of the pie chart represents the largest 8.1.1
210 value of angle and the most number of data.

TRY IT OUT PIE CHART
CARDS AND
Tools/Materials Pie chart cards and data cards. DATA CARDS
Participants 2 pupils in a group.
SCAN ME
Task
1 Each group picks a pie chart card and a data card.

Favourite Fruits Fruit Number of fruits

Apple 8
Kiwi 16
Mangosteen 8
Orange 32

2 Complete the data and values 3 Write three information based on
of angles in the pie chart card. the pie chart created.

Favourite Fruits Information based on the
pie chart
Orange 1. The most favourite
32
fruit is orange.
Apple Kiwi 2. The difference
8 16
between the number
Mangosteen of mangosteen and
8
kiwi is 8.
3. The fraction of apple

from the total number
of fruits is 81 .

4 Present your work.

8.1.1 €€Scan the QR code to print the pie chart cards and data cards to carry out 211
the Try It Out activity.

LET’S DO IT

1 Complete the pie chart by labelling the information based on the table.

Vertebrate Animals

Vertebrate animal Number of animals

Reptiles 6

45° 180° Mammals 12
90° Birds 24

45°

Fish 6

2 The Number of a Complete the number of athletes in the pie chart
Athletes from if the number of athletes from school P is €
Four Schools 3 athletes.

R b State the number of athletes from schools Q,
Q R, and S.

45° c State the value of angle represented by the
90° least number of athletes.

45° 180° d Calculate the difference between the number
P of athletes of schools S and P.

S

3 The table shows the favourite food of 64 children.

Favourite Food Number of
children
Favourite food
32
Nasi lemak

Fried noodles 8

Fried rice 16

Lontong 8

a Complete the pie chart. b Write three information based on the pie chart.

212 €€Use various questions involving different situations such as favourite cakes 8.1.1
and pupils’ ambitions.

LIKELIHOOD

1 Zakri, please read your event card. €

Can you state whether the event is
likely or unlikely to occur?

WEDNESDAY LIKELIHOOD 26 OCTOBER 2022

• possibility of an event to occur

• an event is likely to occur A sea turtle climbs
• an event is unlikely to occur a tree. This event

• there are five likelihood of an event is unlikely to
occur, teacher.
unlikely to likely to occur
occur

impossible less equally more certain
likely likely likely

Hahaha… it is impossible for a
sea turtle to climb a tree, teacher!

A sea turtle climbs a tree is an unlikely event
to occur. The likelihood for a sea turtle €
to climb a tree is impossible because €
a sea turtle is unable to climb a tree.

8.2.1 €€Explain to pupils that an event is something that will definitely occur and 213
8.2.2 likelihood is an event which is likely or unlikely to occur.

2 a Dark green colour is likely to
occur if you use more volume
I need dark €
green colour. of blue colour.

Alright, teacher. I will mix a likely Reason
more blue colour € event to
Green colour is produced
compared to yellow. occur by the mixture of blue and
yellow colour.
Event
an Reason
Dark green colour will unlikely
be produced if more event to A chick will hatch from a
blue colour is added occur chicken’s egg.
compared to yellow.

Event
b

A duckling will hatch
from a chicken’s
egg.

Give another example of
events as a and b and

state the reasons.

214 €€Stimulate pupils’ thinking to determine a likely or unlikely event to occur by 8.2.1
providing a few examples of events. Ask pupils to give the reasons.

The shoot of the plant is likely to

3 grow out from one of these holes €

to get sunlight.

That’s right, Chua. The plant
is also unlikely to survive
without being watered.

Will the plant grow as tall as the box? State
whether the event is likely or unlikely to occur.

Give reasons.

4

My throw will likely
knock down both pins.

I reckon it is unlikely that both
pins will be knocked down.

8.2.1 €€Carry out 21st Century Learning activity, Think-Pair-Share to state whether an 215
event is likely or unlikely to occur and provide reasons.

CERTAIN OR IMPOSSIBLE

1

Do opposite
magnetic poles
attract each other?

Look at this, Kugan.
Opposite magnetic

poles will attract

each other.

The likelihood of opposite magnetic poles to attract each other is certain .
This is because the opposite magnetic poles will create a magnetic field

between each other.

Similar magnetic poles will attract each other as well.
What is the likelihood of this event?

2 a S eptember consists of 30 days. b O ctober comes after November.€
Likelihood of the event:€ Likelihood of the event:€
certain / impossible€ certain / impossible €

Reason: ____________________ Reason: ____________________

SEPTEMBER 2022 OCTOBER 2022 Can you justify
based on events
SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT
a and b ?
1 23 1
4 5 6 7 8 9 10 23456 78

11 12 13 14 15 16 17 9 10 11 12 13 14 15
18 19 20 21 22 23 24 16 17 18 19 20 21 22
25 26 27 28 29 30 23 24 25 26 27 28 29
30 31

216 €€Discuss with pupils regarding certain or impossible events to occur. Ask pupils to 8.2.2
provide a reasonable reason.

EQUALLY LIKELY 31 OCTOBER 2022

Spin the wheel MATHEMATICS QUIZ
to get a question

number.

12 1
11 2

10 3

94

87 5
6

What is the likelihood of the The total number of even and odd
number wheel stopping at even numbers is equal. Hence, the likelihood

numbers after being spun? of the number wheel to stop at even
numbers is equally likely.

MORE LIKELY OR LESS LIKELY

1 Based on the situation, state the likelihood of all the clothes getting
dried. What is the reason?

The weather is sunny
and windy today.

More likely that all the clothes will get dry. The sunny
and windy weather will cause evaporation to take place
and dry the clothes.

8.2.2 €€Carry out speed answer quiz by giving possible reasons individually regarding various 217
events which have the likelihood of certain, impossible, equally likely, and more likely.

2 What is the likelihood of
Alicia getting the yellow ball?

It is less likely because
there is only one yellow

ball. The number of
blue balls is more.

Event Likelihood Reason Complete €
Get yellow ball Less likely the table.
There is only one
Get blue ball yellow ball.

More likely

Get green ball

THINK Jackie throws a dice. What is the
SMART likelihood of Jackie getting a €
prime number?

TRY IT OUT GROUP ACTIVITY LIKELIHOOD
TABLES AND
EVENT CARDS

Tools/Materials Likelihood tables, event cards, scissors, SCAN ME
and glue.

Participants 2 pupils in a group.

Task

1 Cut the event cards.
2 Paste the event cards in the likelihood table.
3 Write a reasonable reason for each of the likelihood events.
4 Present the outcome in front of class.
5 Cross-check answers with other groups for improvement.
6 Display the work at the mathematics corner.

€€Scan the QR code to print the Try It Out materials. The materials can be 8.2.2
218 modified by adding the number of event cards or by giving different event

cards to each group.

LET’S DO IT

1 State whether the following events are likely or unlikely to occur and give €

a reason.

a M alaysia Day is celebrated in May . b Sarawak citizens celebrate Hari Gawai.

c A n odd number is between two € d L eap year occurs every five years.

even numbers. f T en thousands is more than hundreds

e W aterfall flows from a lower level to but less than millions.

a higher level. h A kite can fly high.

g P lants require air to breathe.

2 State the likelihood for each of the following events. Give a reasonable reason.

No. Event Likelihood Reason
a 2021 is a leap year.

b There are seven days in a week.

c A tossed coin shows a tail.

d A regular octagon consists of eight angles €
of equal size.

e A dice is rolled and the outcome of the number is
lesser than six.

f One out of 2 girls and 8 boys is chosen as a prefect
in a class.

g Heavy rain will cause flood in the area that has
drainage problem.

h A dice is rolled and the outcome is an even number.

i There are 28 days in March.

j A green marble is picked randomly from a container
that has one green marble and 5 blue marbles.

3 Write an event for each of the likelihoods. State the reason.

a c ertain b impossible c less likely

d more likely e equally likely

8.2.1 219
8.2.2

SOLVE THE PROBLEMS

1 The likelihood of Nik Syafiq The situation shows €
picking a white table tennis ball€ Nik Syafiq who is about
to pick a table tennis
is more likely. ball. Asha states that
the likelihood of €
Nik Syafiq picking the
white table tennis ball
is more likely. Is it true?€
Prove it.

Solution

Given • 10 white table tennis balls.
• 3 orange table tennis balls.
• Nik Syafiq wants to pick one table tennis ball.
• Asha states that more likely Nik Syafiq will pick a white

table tennis ball.

Asked for Prove Asha’s statement is true.

Solve Carry out simulation. Check

Colour of White Orange Colour of Colour Prediction
table tennis table tennis of table
ball picked ✔ ball tennis ball
1st trial ✔
probably
2nd trial ✔ picked
✔
3rd trial ✔ Orange and Orange or More likely a white

4th trial white white table tennis ball will

5th trial be picked because

the number of white

table tennis balls is

more.

Asha states the truth because the number of white table tennis balls is
more compared to the number of orange table tennis balls.

220 €€Carry out simulation using different objects such as blue and red pens or two 8.3.1
different colours of board game counters to enhance pupils’ understanding.

2 The pie chart shows food bought by a Food Bought at
group of pupils during recess. 12 pupils SK Seri Murni Canteen
bought nasi lemak.
a What is the value of angle that Curry noodles
represents the largest part?
b What is the total number of pupils 45° Noodles
who bought food during recess? 45° soup

Solution Fried € Nasi
rice lemak

Understand the problem

• The value of angle of curry noodles is 45°. • Find the value of angle that
• The value of angle of noodles soup is 45°. represents the largest part.
• 12 pupils bought nasi lemak.
• Calculate the total number of
Plan the strategy and Solve pupils during recess.

a The largest part is fried rice, which is half of the circle.
The value of angle for a quarter of the circle is

45° + 45° = 90°.
Two quarters of a circle is equal to half of a circle.

Therefore, the value of the angle of half a circle is
90° + 90° = 180°.

The value of angle which represents the largest part is 180°.

b 12 pupils represen t € Total number Check
a quarter of the circle. of pupils a

1 2 pupils 45° 2
1 2 pupils
12 12 1 2 pupils 180° 4 5°
pupils pupils + 1 2 pupils ×4

12 12 4 8 pupils 1 80°
pupils pupils

b 4 × 12 pupils = 48 pupils

The total number of pupils who bought food during recess is 48 pupils.

8.3.1 €€Remind pupils that the value of angle for a complete circle is 360°. 221

€€Vary questions by changing the information regarding the value of angles and

the quantities. Make sure the value of angles involve only 45°, 90°, and 180°.

3 The pie chart shows four types of fruits Fruits Sold
sold. The mass of rambutan sold is 30 kg.
Complete the values of the angles and mass Mangosteen Rambutan
on the pie chart if the mass of langsat and Langsat 90°
mangosteen sold is the same.
Mango
Solution

• The mass of rambutan is 30 kg and the angle Fruits Sold
is 90°.

• The mass of langsat and mangosteen is equal.
• The mass of mangosteen is half the mass €

of rambutan.
• The mass of mango is twice the mass €

of rambutan. 15 kg

Complete the mass and angle values on the pie chart. 15 kg 45° 30 kg
45° 90°
Fruit Mass The value of 180°
angles

Rambutan 30 kg 90° 60 kg

Langsat 1 × 30 kg = 15 kg 1 × 90° = 45° Key:
2 2 Rambutan
Langsat Mangosteen
Mangosteen 15 kg 45° Mango

Mango 2 × 30 kg = 60 kg 2 × 90° = 180°

LET’S DO IT Four Types of Kuih Sold

Solve the problems. keria
a The pie chart shows four types of kuih ketayap 45° curry €

sold. 24 pieces of curry puffs are sold. 45° puff
State the number of doughnuts and €
90° 180°
keria which are sold. doughnut

b Player A has won four out of five matches against player B. What is the likelihood
of player B winning the sixth match? Give the reason.

222 8.3.1

LET’S PRACTISE

1 Identify the event which is likely or unlikely to occur. Give the reason.
October has 31 days. Malayan tiger is extinct. Sun rises in the South.

A rooster lays egg. A road has pothole. A sapling grows.
Likelihood Reason
2 Complete the table.

No. Event

a A whale feeds milk to the calf.

b The heptagon consists of nine sides.

c The weather is cloudy and it is going to
rain soon.

d Engkili or Damit will be chosen as the €
class monitor of Year 6 Galaxy.

e A red pen is picked randomly from a
container that has 1 red pen and 7 pencils.

3 Solve the problems. Mathematics e-Quiz

a T he pie chart shows the number of participants for €
a Mathematics e-Quiz. The number of participants € Labuan
from Perlis is 10. Perlis Malacca
45°
i Calculate the number of participants from Johor.
45°
ii What is the number of participants from Malacca?

iii Find the number of male participants if the 180°

number of female participants is a quarter of the Johor

total participants.

b There are 8 black buttons and 2 blue buttons in a container. €
Wafiq is requested to pick a button randomly.

i State the likelihood of Wafiq picking a blue button.

ii State the likelihood of Wafiq picking a black button.

iii What should be done to ensure that the likelihood of Wafiq
picking the blue button is equally likely?

8.1.1, 8.2.1, 223
8.2.2, 8 3.1

LET'S EXPLORE GAMES TABLE
SCAN ME
Tools/Materials Rubber bands, 15 cm stick (pushed into the
ground), drinking water bottles (fully filled),
tennis balls and games table.

Participants 2 pupils.

Rules of Game A: Stand stick Name: __________________
a Push the stick into the ground. Game A: Stand stick
b Stand 1 metre away from the stick.
Toss Likely in or out
c Toss the rubber
band to the Toss 1
targeted stick. Toss 2
Toss 3
Rules of Game B: Bottle bowling Toss 4
a Place the bottle 2 metres away Toss 5
The likelihood of your toss to land
from your position. to the targeted stick is
b Throw a tennis ball towards the bottle.

Name: __________________
Game B: Bottle bowling

How to play Throw Likely knock or not

1 Carry out the games in turns. Throw 1
2 Each pupil will play both games once and
Throw 2
toss or throw for five times.
3 Record the results of the toss and throw Throw 3

individually into the table provided for Throw 4
each game.
4 Complete the table of the game. Throw 5
5 Paste the table of the game in the The likelihood of your throw will
exercise book. knock the bottle is

224 €€Scan the QR code to get the games table. 8.2.1, 8.2.2

SELF-TEST 5.

A. Choose the correct answer.

1. 7:070:0a0.ma..m. 2:020:00p.mp..m. 50 cm A

B 30 cm

London, Friday Kuala Lumpur, Friday
25 November 2022 25 November 2022
Based on the diagrams above, the mass
Look at the local time in both cities
of block B is 45 kg. What is the mass €
above. What is the time in London when
of block A?
the time in Kuala Lumpur is 5:00 p.m.?
A. 6:00 p.m. B. 8:00 p.m. A. 50 kg B. 60 kg
C. 10:00 a.m. D. 8:00 a.m.
C. 70 kg D. 75 kg

2. 6.

Ipoh, Malaysia Tokyo, Japan
30 August 2022 31 August 2022

2345 hours 0045 hours

Compare the time in Tokyo with the € 10 cm
time in Ipoh.
1 500 m 500 m
A. 1 hour ahead of Ipoh.
B. 1 hour behind Ipoh. Based on the information given above,
C. 2 hours ahead of Ipoh.
D. 2 hours behind Ipoh. what is the height of the 1 500 m
3. Kuala Lumpur Tower,€
water bottle?
8 September 2022
6:00 p.m. A. 15 cm B. 25 cm

The time in Riyadh is 5 hours behind C. 30 cm D. 40 cm
the time shown above. State the time
in Riyadh. 7.

A. 1:00 a.m. B. 11:00 a.m. 5 kg of cooking
C. 1:00 p.m. D. 11:00 p.m.
4. Which of the regular polygon has oil is equal to
6.25 .
interior angles of 120° each?
Danish uses 3 kg of cooking oil. How much
A. B. C. D.
volume, in , of the cooking oil used?

A. 3.75 B. 3.5

C. 2.75 D. 2.5

225

j What is O and j? Questions 12 and 13 are based on the
8. Cartesian plane below.

O

The Cartesian plane shows the locations
A. O is the radius and j is the diameter. of three places.
B. O is the centre of the circle and j is €
y

the radius. 5
C. O is the centre of the circle and j is €

the diameter. 4
D. O is the diameter and j is the
Nibong Hill House

circumference of the circle. 3

9. Which of the following is a regular 2

pentagon?

A. 108° B. 96° 1 Swimming pool

108° 120° 108° 1 cm
100°
x
108° 108° O1 2 34567
116° 108° 1 cm
Scale 1 cm represents 1 km
C. 66° D.
12. What is the vertical distance, in km, of
150° 108° Nibong Hill from the swimming pool?
108° 108°
108° 108° A. 2 km B. 3 km C. 4 km D. 5 km
108° 108° 108°

10. Greenwich Mean Time (GMT) is the € 13. State the horizontal distance of Nibong

basis to determine world € Hill from the house.

time zones. A. 1 km B. 2 km C. 3 km D. 4 km

A. 12 B. 20 C. 24 D.30 14. Number of animals treated at
Permai Veterinary Clinic
11. Choose the correct meaning of €
diameter. Day Monday Tuesday Wednesday

A. A straight line which connects Number 6 12 3
the centre of the circle with the of
circumference.
animals
B. A closed curve that forms the

boundary of a circle. Based on the table above, state the

C. A point located in the middle of the ratio of the number of animals treated

circle. on Monday to the total number of

D. The straight line that connects two animals treated for the three days.

points on the circumference and A. 2 : 5 B. 1 : 3

passes through the centre of a circle. C. 2 : 7 D. 7 : 2

226

15. FLOUR 18. Online Quizzes

SUGAR 45° Key:
90°
Kahoot
Quizizz

6 kg 4 000 g 180° Google Form

State the ratio of the mass of flour to Wordwall

the mass of sugar. The pie chart shows the types of online
quizzes which have been used by
A. 3 : 2 B. 6 : 4 a group of teachers. The number of
teachers who used Kahoot were 12. €
C. 2 : 3 D. 6 : 4 000 How many teachers used Wordwall ?

16. The total body mass of Selena and

Patricia is 85 kg. The ratio of Selena’s A. 12 teachers B. 24 teachers

body mass to Patricia’s body mass is € C. 36 teachers D. 48 teachers
2 : 3. Find Selena’s body mass.
19. A dice is tossed once. What is the
A. 17 kg B. 21 kg likelihood of getting a number that €
is more than 3?
C. 34 kg D. 51 kg

17. y A. Equally likely

5 House A B. Certain

4 C. More likely
House D
House C D. Less likely
3
20. Choose an event that has a certain
likelihood.

2 House B A. J ames can lift a 700 kg weight.
B. R izal can jump 500 m in a long jump
1
event.
SchoolSEKOLAH C. K umari celebrates her birthday on €

xO 1 2 3 4 5 6 29 February 2024.
D. S yira is 10 years old and she is €
Scale
1 2 3 4 5 km a Year 6 pupil.

The horizontal distance of Aliff’s house 21. Which of the following regular polygon
from the school is 6 km and the vertical
distance is 4 km. Which one is Aliff’s can be produced by the combination of
house?
six equilateral triangles?
A. House A B. House B
A. Pentagon B. Hexagon
C. House C D. House D
C. Heptagon D. Octagon

227

B. Solve the following questions. b A fan from Riyadh, Saudi Arabia
watches the match. The time
1. Puan Hamimah Rafiq Dina in Riyadh is 5 hours behind
Malaysia. State the time in Riyadh.
Muar, Johor Cairo, € Jakarta,
1515 hours Egypt Indonesia€ c C alculate the time difference
between Amsterdam and Riyadh.
0915 hours
4. 1.5 kg

The pictures and information above 60 cm
show three family members who are
living in different countries. The picture above shows the length
and mass of a piece of wood. The
a W hat is the time difference wood is cut into two parts. The length
between Muar and Cairo? of one part of the wood is 40 cm. Is
the mass of the 40 cm wood 1 000 g?
b T he time in Jakarta is 1 hour Prove it.
behind Muar. State the time in
Jakarta at that moment.

2. Town A and town B are in different 5. 50 cm
time zones. The time in town A is € 25 cm 40
5 hours ahead of town B.
The picture shows two cylindrical-shaped
a S tate the time in town B when the grape juice containers of the same size.
time in town A is 1235 hours.
a S tate the ratio of the level of grape juice
b T he clock tower in town B shows in container A to the level of grape juice
the time as 10:45 in the evening, in container B.
Friday, 12 August 2022. Find the
local time in town A. b C alculate the volume of grape juice in
container A.
3. A few players from several countries
take part in an online sports c F ind the percentage of the volume of
competition. The Malaysian player grape juice in container A.
is scheduled to face a player from
Amsterdam, Netherlands in the first
round on 5 March 2022. The time
in Malaysia is 7 hours ahead of
Amsterdam. The game starts at 8:10 in
the evening in Kuala Lumpur.

a W hat is the time in Amsterdam at
that moment?

228

6. The mass of brown sugar is 823 g and 11. The Cartesian plane shows the

becomes 1 000 m of brown sugar locations of a few buildings in a town.

syrup after being melted. y

a M um melts 411.5 g of brown sugar. 5
Calculate the volume of the brown

sugar syrup that will be produced. Stall

b M um needs 2 500 m of brown 4 Shopping
mall
sugar syrup. What is the mass of 3
the brown sugar, in g, needed? 2 Bus
terminal
7. A polygon consists of 6 sides of

equal length and 6 interior angles 1 cm 1 Museum Theme park x
of equal size. Complete the picture O 12 345
of the regular polygon below and
measure the interior angles.

1 cm
Scale 1 : 100 000

8. Using a protractor, draw and name a W hat is the vertical distance of the
the following angles. museum from the stall?

a 2 0° b 1 45° c 9 0° b S tate the horizontal distance of the
theme park from the museum.
9. Draw a circle based on the information
given. Label all the characteristics of c C alculate the horizontal and
the circle. vertical distances of the theme
park from the stall.
a 4 cm of radius.
d W hich building is located 4 km
b 5 .5 cm of radius. horizontally and 3 km vertically €
from the museum?
10. Sardi draws three circles. The radius of
circle A is 2 cm more than the radius e N ame two buildings that have
of circle B. The radius of circle C is 1 cm an equal horizontal and vertical
more than the radius of circle A. Which distances from the bus terminal.
circle is the largest?
12. The ratio of the number of books read
by Shanti to the number of books read
by Chua in a week is 3 : 4. €
The total number of books read €
by both of them is 21. Calculate the
number of books read by:

a S hanti. b C hua.

229

13. 15. Leisure Activities

Reading

45° Sports
Gardening

Fried noodles Chicken rice 180°
RM4 RM6 Fishing

The pictures show the price for two

types of food. State the ratios in the

simplest form: The number of residents who like
a t he price of fried noodles to the price fishing is 32 people.

of chicken rice. a H ow many residents like to do
b t he price of chicken rice to the price
gardening, reading, and sports?
of fried noodles.
c t he price of fried noodles to the total b S tate the value of angle that

price of fried noodles and chicken represents sports activity.

rice. c C alculate the difference between

d t he price of chicken rice to the total the number of residents who

price of fried noodles and chicken like fishing and the number of

rice. residents who like reading.

14. The pie chart shows the islands in 16.
Malaysia which are preferred to be

visited by 120 pupils. Emilia has 12 pieces

Preferred Islands to be Visited of chocolate cookies
and 3 pieces of
butter cookies in the

Langkawi Island container as shown
in the picture.

Tioman 45°
Island
45° Mabul Island

Redang Island a W hat is the likelihood of Emilia

a S tate the values of angles of € choosing a piece of butter cookies?

Why?
Langkawi Island and Tioman Island. b W hat is the likelihood of Emilia
b H ow many pupils prefer to visit €
choosing a piece of chocolate
Mabul Island?
cookies? Give your reason.
c F ind the difference between the c W hat is the likelihood of Emilia
number of pupils who prefer to visit
choosing a piece of peanut
Tioman Island and Redang Island.
cookies? State the reason.

230

GLOSSARY Arrangement of numbers from the smallest to the largest value.
Mathematical operations, which are addition, subtraction, multiplication,
Ascending order and division.
Basic operations A pair of number that determine the point over the x-axis and the y-axis.
The people (buyer or user) who does transaction with sellers or service providers.
Coordinates The position of a digit after the decimal point.
Customer A point that separates whole number and decimal fraction.
Decimal place Numbers that represent fractions with denominators of 10, 100, 1 000, and so on.
Decimal point Arrangement of numbers from the largest to the smallest value.
Decimal Differences in quantity or value between two groups of objects or values.
Descending order The difference is obtained by subtracting two numbers.
Difference Percentage of profit given on money invested for business or shares.
A number that divides another number.
Dividend rate One of the four directions of the wind. Opposite of the west. The Sun rises in
Divisor the east.
East A triangle that has three sides of equal length and all angles are of equal size.

Equilateral triangle An event or something that happens.
Event Part of one thing, a group, or a number.
Fraction A set of things.
Group The length between two dots or objects that are parallel to the x-axis.
Horizontal distance A coverage agreement that has conditions for compensation in the event of theft,
Insurance damage, injury, or death.
The profit rate in percentages fixed against a particular savings or loan for
Interest rate a specified period.
The angle formed by the latitude of two lines, and is located between the two lines.
Interior angle Money used for certain businesses that will provide future profits.
Investment The person who makes fixed contribution to a fund or company.
Investor Distance or measurement between two points or from end to end.
Length A probability that something is likely or unlikely to occur.
Likelihood Financing for a purpose received from a financial institution and is charged with
Loan interest. Also known as debt.
Real time for local area.
Local time The quantity of matter of an object that is not affected by gravitational pull.
Mass Imaginary lines drawn on Earth from the South Pole to the North Pole. This line
Meridian from south to north is called a longitude line or longitude only.
A number represented by a whole number and a proper fraction.
Mixed numbers Combination of two or more mathematical operations.
Mixed operations The value that has the highest frequency in a set of data.
Mode Specific pattern in the order of number.
Number pattern

231

Percentage The way to specify a number as a fraction of 100 with the % symbol.
Perpendicular line
Pie chart A straight line that intersect or cross another straight line at a right angle.

Proportion Diagrams that show division or breakdown of data or information in circles.
Each value is represented by one sector of the circle.
Protractor
Provider A mathematical statement that shows the relationship between two quantities
Quantity or values in the same ratio.
Regular heptagon
Regular hexagon A tool for measuring angles.
Regular octagon
Regular pentagon The person who provides or supplies goods or services.
Regular polygon
Remainder Total or number of things.
Sales discount
Scale A two-dimensional closed shape with 7 straight sides of equal length.
Simplest form
Square A two-dimensional closed shape with 6 straight sides of equal length.

Straight line A two-dimensional closed shape with 8 straight sides of equal length.

Takaful A two-dimensional closed shape with 5 straight sides of equal length.

Time zone A two-dimensional closed shape with all straight sides of equal length.

Time Surplus after two numbers is subtracted or by a division that has a balance.

Traders Discount given to wholesaler for goods bought in cash and in large numbers.
Unknown
Vertical distance The ratio of the size of the drawing to the size of the actual object.
Volume of liquid
West Smallest form where numerators and denominators are in prime numbers except 1.

Whole number A quadrangular that has four sides, four upright corners, and each side
of equal length.

A line that is not crooked, has no width and is either horizontal, vertical,
or inclined.

Islamic insurance concept that adhere to the ethics and transparency of Syariah
guidelines that prohibit uncertainty (Gharar), gambling (Maisir), and interest (Riba).

An area of 18 longitudes wide which throughout its parts have the same time and
starts from the Greenwich meridian.

The past period to the present period until the future that can be measured using
clocks or other time calculation tools.

The person who provides goods for sale (the seller).

Unknown value or quantity and written as a symbol or letter.

The length between two dots or objects that are parallel to the y-axis.
The amount of liquid that can fill a container.

One of the four directions of the wind. Opposite of the east. The Sun sets in
the west.

Number that starts from zero and so on, and does not have fraction or decimal.

232

ANSWERS UNIT 3: MONEY ........................................................................................................................

UNIT 1: WHOLE NUMBERS AND OPERATIONS ............................................................... THINK SMART (pg. 109)

THINK SMART (pg. 3) 25%, RM15
3 647 915 , 3 791 465 , 3 915 764 , 3 157 946 Accept any reasonable answers.
LET’S PRACTISE (pg. 133 – 135)

THINK SMART (pg. 8) THINK SMART (pg. 12) 1. a. Loss, RM22 b. Profit, RM145 c. Loss, RM20 d. Profit, RM60
1 234 321 = 1 111 × 1 111 P = 2 375 000 , Q = 2 875 000
e. Loss, RM5.50

THINK SMART (pg. 26) 2. a. RM450 b. RM790 c. RM750

3. a. RM280 b. RM3 600 c. RM4 079 d. RM392 000

4. A4 Papers = RM400, Files = RM120, Pocket dictionaries = RM1 200

6.23 million ÷ 7 = 0.89 million Total = RM1 720, Deduct sale discount 10% = RM172, Total payment = RM1 548

5. a. Total: RM500, Service tax 6%: RM30, Total payment = RM530

THINK SMART (pg. 35) THINK SMART (pg. 36) b. Voucher value: RM50
1.74 million 0.3 million or 300 000
6. a. RM950 b. RM120

7. Total value of asset: RM150 500, Total value of liability: RM63 460

THINK SMART (pg. 38) 8. i. to accommodate medical treatment expenses
1.715 million or 1 715 000
ii. receive financial compensation due to house destruction

LET’S PRACTISE (pg. 58) iii. claim insurance to repair car due to accident

1. a. three million five hundred eighteen thousand and fourty-two 9. a. i. RM1 302 ii. RM9 548

b. one million ninety thousand two hundred and fifty-six b. Ain: RM87 844, Maryanti: RM87 499, Puan Ain manages her financial better.

c. four million seven thousand nine hundred and eighty c. RM3 570 d. RM135

d. five million fourty thousand and nineteen e 17000 × RM2.50 = RM1.75

e. 8 709 181 f. 9 253 000 g. 2 050 806 17000 × RM4.50 = RM3.15

2. a. The number pattern increases by twelves. b. x = 8 007 092

y = 8 007 104 17000 × RM8 = RM5.60
Total = RM10.50 (insufficient)
3. Prime Composite 4. a. one and three-fourths of a million,
number number
one and three-quarters of a million. f. RM40 and RM40, RM50 and RM30, and accept any reasonable answers.
11 8
29 24 b. 1 million SELF-TEST (pg. 137 – 140)
41 35 8
67 80 A. Choose the correct answer.
c. 5 170 million
1. C 2. C 3. B 4. D 5. B
9. D 10. C
6. A 7. B 8. B 14. B 15. C
19. B 20. D
11. D 12. D 13. A 24. A 25. B
29. B
5. a. 200 000 b. 1 095 000 c. 200 000 d. 4 375 000 e. 6 900 000 16. A 17. D 18. D

6. 600 000 750 000 2 800 000 3 500 000 9 625 000 21. D 22. B 23. C

26. A 27. A 28. D

0.6 million 0.75 million 2.8 million 3.5 million 9.625 million B. Solve the following questions.
2 45 million 3 21 million 9 85 million
3 million 3 million 1. a. 7, 13, 43 b. 9, 35, 81 2.a. R b. 100 000
5 4
3. a. 1 130 b. 6 52 4. a. 2 b. 25.35 c. 87%
7. a. 9 290 680 b. 2.692 million or 2 692 000 c. 1.26 million or 1 260 000 5. RM260, RM350 6. a. 250% b. q = 2.25, 1.5

d. 6.44 million or 6 440 000 9. a. 503 000 b. 1 million 7. 12
8. a. 7.7 million b. 3.075 million 4
10. a. 1.76 million b. 4 190 million c. 8.25 million or 8 250 000 or 8 41 million 8. 284 000 9. a. 2 475 000 b. R = 625 000
d. 4.44 million or 4 440 000
S = 2.5 × 250 000

e. 3.95 million or 3 950 00 = 625 000 (true)
10. a. RM72 b. RM1 272 11. 12.6 km
f. 0.285 million or 285 000 1 b. 4.75 m
2 13. a. 2.16
11. a. 270 000 or 0.27 million b. 4 000 or 0.004 million c. 2.95 million or 2 950 000 12. a. 0.5 m/ m b. RM1 485 000 b. 150%

d. 0.642 million or 642 000 e. 4 000 or 0.004 million f. 1.775 million or 1 775 000 14. a. RM15 000 15. RM27.90

12. a. 3.142 million or 3 142 000 b. 1.241 million or 1 241 000 16. 100 000 17. RM6 100
(25
c. 5.425 million or 5 425 000 d. million – 0.04 million) ÷ 100 = 3600 18. RM480
e. 2.775 million or 2 775 000
19. Assets: RM50 000 + RM35 000 = RM85 000

UNIT 2: FRACTIONS, DECIMALS, AND PERCENTAGES ........................................................ Liabilities: RM1 460 + RM15 000 = RM16 460

THINK SMART (pg. 66) THINK SMART (pg. 69) Yes. The value of assets exceeds the value of liabilities.

= 1 = 2 = 3 3.1 x 2.6 or 2.6 x 3.1 UNIT 4: TIME ............................................................................................................................

THINK SMART (pg. 77) THINK SMART (pg. 85) THINK SMART (pg. 146)
City P 1710 hours, City Q 1210 hours, 5 hours
400% 0.75
LET’S PRACTISE (pg. 153)
THINK SMART (pg. 89) THINK SMART (pg. 91) 1. 24 time zones
a=5 2. T he time difference between Rio de Janeiro and Greenwich: 3 hours
1 or 0.2 The time difference between Madrid and Labuan: 7 hours
5 The time difference between Labuan and Gold Coast: 2 hours
The time difference between Greenwich and Mecca: 3 hours
LET’S PRACTISE (pg. 99 – 100) The time difference between Mecca and Gold Coast: 7 hours
3. 5 hours
1. a. 81 b. 61 c. 25 d. 115 e. 32 f. 2 1121 g. 2 281 h. 6 i. 18 25 4. 0754 hours or 7:54 a.m.
2. a. 2 45 c. 21 d. 1 21 d. 4.8 e. 9.9 f. 0.225 g. 3.65 5. a. 2300 hours
3. a. 1.08 b. 12 b. i. 1835 hours or 6:35 p.m.
ii. 1200 hours or 12:00 noon.
b. 4.757 c. 60.354 c. i. 0430 hours or 4:30 a.m.
ii. 0310 hours or 3:10 a.m.
h. 9.64 i. 20.631 j. 1.5 k. 30.6 l. 84.28

4. a. 165%, 3.3, 660% b. 1.6, 2.72

5. a. i. 65% ii. 25% b. i. 301% ii. 12%

6. a. 10.5 m b. 22.05 hours c. 7.992 kg d. 89.44

e. 3.16

× 9 . 2 UNIT 5: MEASUREMENT .........................................................................................................

632 LET’S PRACTISE (pg. 163)
a. 1 000 g
+ 2 8 4 4 0 b. i. 7.65 kg
ii. 2.55 kg
2 9.0 7 2 c. 52.5 cm
d. i. 576 m of water and 160 g of anchovies
7. a. 300% b. 140% ii. 500 g of wheat flour and 360 m of water

8. a. 255% b. 190%

9. 10.5 × 100% = 1 050 %
2.5 2.5

= 1025.500%

= 420% (true) UNIT 6: SPACE ........................................................................................................................

10. a. 6.5 minutes b. 0.02 c. 4.07 km d. 63.6 kg e. 1.44 f. 0.315 g. 41 21 THINK SMART (pg. 177)
Raymond might draw an equilateral triangle and a square.
h. 1.5 i. 16.35 j. 62.3 Charles might draw a hexagon and an octagon.
b. i. 34 m ii. 6 c. 0.55
11. a. 465.125 cm2 d. 1.68 hours
e. i. 150% ii. 1.6

233

THINK SMART (pg. 182) 2. a. 1 : 5 b. 1 : 6 c. 3 : 7 d. 6 : 1 e. 8 : 9

circumference 3. a. 15 b. i. 7 cm ii. 35 cm
of the circle
diameter 4. a. 5 km horizontal distance and 2 km vertical distance

O radius b. 5 : 3 c. RM36 d .40
4 cm
centre of UNIT 8: DATA HANDLING AND LIKELIHOOD ....................................................................
the circle
THINK SMART (pg. 210) THINK SMART (pg. 218)
LET’S PRACTISE (pg. 185 – 186) 88 pupils equally likely

1. a. b. LET’S PRACTISE (pg. 223)

5 cm 1. October has 31 days is likely to occur as there are 31 days in October.

60° 3 cm Malayan tiger extinct is likely to occur because their number is decreasing in the
135° habitat.

Sun rises in the south is unlikely to occur as the sun rises in the east.

c. 2. A rooster lays egg is unlikely to occur as hen lays egg.
6.5 cm 108° 5.3 cm
90° A road has pothole is likely to occur as the result of the weather and traffic passing
over every day.

A sapling growth is likely to occur as the sapling can survive and grow with
sufficient amount of light, water, and air.

*accept any other reasonable answers and reasons from the above.

3. a. b. 2. a. Certain because whale is a mammal and it feeds milk to the calf.
b. Impossible because heptagon consists of 7 sides.
40° 65° c. More likely because cloudy weather is a sign that it will rain.
c. d. d. E qually likely because only one out of two pupils will be chosen as the class

125° monitor.
f. e. L ess likely because the number of red pens is less than pencils.

173° 3. a. i. 40 persons ii. 20 persons iii. 60 persons
iii. T ake out 6 black buttons
b. i. less likely ii. more likely from the box.
Put more 6 blue buttons
89° into the box.
160°




e. SELF-TEST (pg. 225 – 230)

A. Choose the correct answer.

1. C 2. A 3. C 4. D 5. D
9. D 10. C
6. C 7. A 8. B 14. C 15. C
19. A 20. C
11. D 12. B 13. D

4. A circle has a centre of a circle, radius, diameter, and circumference of a circle. 16. C 17. C 18. D

5. a. b. 21. B
4 cm O
O B. Solve the following questions.
4.7 cm
1. a. 6 hours b. 1415 hours 2. a. 0735 hours b. 3:45 in the
morning,
Saturday,
13 August 2022
c. 2 hours

c.

3. a. 1:10 p.m. b. 3:10 p.m.

5.2 cm 4. Yes. 40 × 1.5 kg = 6 kg
O 60 6
= 1 kg

= 1 000 g

6. a. 5 cm 5 cm 5. a. 1 : 2 b. 20 c. 50%

6. a. 500 m b. 2 057.5 g

7.

5 cm 5 cm 120°

5 cm

b. i. ii. 1m A ccept any
1m 3m 1m other
3m reasonable
answers.
8. a. acute angle. b. obtuse angle. c. right angle


1m

c. The size of cake board should be 20° 145° 90°
bigger than the cake size.
28 cm long and 28 cm wide. 9. a. b.
Accept any other reasonable O
answers. 28 cm 4 cm
O 5.5 cm

28 cm 10. circle C c. 3 km horizontal distance and 3 km vertical distance
11. a. 3 km b. 3 km e. theme park and stalls
UNIT 7: COORDINATES, RATIO, AND PROPORTION .......................................................... d. shopping mall

THINK SMART (pg. 188) THINK SMART (pg. 195) 12. a. 9 books b. 12 books
7 cm The number of cats to the total
number of cats and tortoises. 13. a. 2 : 3 b. 3 : 2 c. 2 : 5 d. 3 : 5

14. a. Langkawi Island 180°, Tioman Island 90° b. 15 pupils c. 15 pupils

THINK SMART (pg. 198) THINK SMART (pg. 203) 15. a. Gardening = 8 b. 90° c. 24 residents

96 3:4 Reading = 8

LET’S PRACTISE (pg. 205) Sports = 16

1. a. 4 km horizontal distance and 3 km vertical distance 16. a. Less likely because there is less number of butter cookies.

b. 3 km horizontal distance and 2 km vertical distance b. More likely because there is more number of chocolate cookies.

c. 1 km horizontal distance and 5 km vertical distance c. Impossible because there are no peanut cookies in the container.

234

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