Maths ebook complete

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Table of Contents

1 Algebra

2 Angles

3 Solids and Nets

4 Fractions

6 Percentage

7 Speed

8 Circles

9 Pie Charts

11 Volume

5 Ratio and Fraction

10 Area and Perimeter

TOPIC 1:

Algebra

Page | 1

Section I –Writing Algebraic Expressions

1.) If 5 bags of rice cost $15k, what is the cost of 3 bags of rice?

Ans : __________

2.) Bobby weighs n kg more than Siti. If their total weight is 50 kg, how much does Siti weigh?

Ans : __________

3.) Mrs Koh paid $h for a plant after she was given a 20% discount. What was the original cost price of the plant?

Ans : __________

4.) A dress and 3 blouses cost $68. The dress costs $p more than a blouse. (a) Express the cost of a blouse in terms of p. a) Ans : __________ (b) If p= 12, how much is the cost of the dress? b) Ans : __________

5.) Mr Lee has $x. He gave $20 to his son and divided the remaining amount equally between his two daughters. How much did each daughter receive? Ans : __________

Topic 1: Algebra

Page | 2

6.) Simplify the following 12p+(3p×4p)-3p. Ans : __________

7.) A square of side 12 cm is divided into parts A, B and C.

(a) Find the total area of A and B in terms of x.

Leave your answer in the simplest form.

a) Ans : __________

(b) If x=5, find the area of B. b) Ans : __________

8.) Jacob has $15. Samuel has $3 less. Their mother gives them $k each. How much do they have altogether? Ans : __________

Topic 1: Algebra

Page | 3

Section II – Simplifying Algebraic Expressions

9.) Simplify 9d + d

10.) Simplify 6a + 2 - 4a 11.) Simplify 4c - 3 + 6c - 7

12.) Simplify 10e - 7e + 5 -2e

13.) Simplify 9 + 12 - 8p - 10 +11p

14.) Simplify 2f - 1 + 2 + 4f

Section III – Evaluating Algebraic Expressions

Find the value of each expression when k = 5

15.)

16.) 2k + 15

17.)

18.) 3k +10

19.) 9k x 2

20.) 5k + 6

Topic 1: Algebra

Page | 4

Section IV– Combined Skill Practices

Write the correct answers in the spaces provided.

21.) If w = 4, find the value of 3w + 5 – w + 12.

Ans: ____________

22.) Shu Ting is p years old now. Her father is 28 years older than her. What would their total age be ( in terms of p ) in 5 years' time?

Ans: ____________

23.) Gavin bought 6 peaches and 4 watermelons. He spent $20m altogether. If each peach cost $2m, find the cost of each watermelon.

Ans : ____________

24.) Kenny weighs c kg. His father is 3 times as heavy as he is. What is their average weight?

Ans : ____________

25.) The breadth of a rectangular field is y cm. Its length is 3 times its breadth. Express the perimeter of the field in terms of y.

Ans : ____________

Topic 1: Algebra

Page | 5

Section V – Word Problems

Solve the following problems. Calculators are allowed for use for this

section.

26.) The ratio of the number of pears to the number of oranges is 7:4. (a) If there are 8p oranges, how many more pears are there?

a) Ans: ____________ (b) What is the total number of pears and oranges together? ( Express both answers in terms of p )

b) Ans : ____________

27.) The figure below is made up of 2 rectangles and a square. Its dimensions are given in cm. (a) Find the perimeter of the figure in terms of n

a) Ans: ____________

(b) Find the area of the figure in terms of n

(c) If n = 4, what is the value of 3n+5 ?

b) Ans: ____________

c) Ans: ____________

Topic 1: Algebra

Page | 6

*28.) The table below shows the prices of pencils and sharpeners sold at a bookshop.

Item Unit Price

Pencils w cents

Sharpeners (w+20) cents

a) Express the total cost of 3 pencils and 2 sharpeners in terms of w.

a) Ans :__________

b) If Ella's mother gave her $10 to buy 5 pencils and 2 sharpeners, how much will she

have left? (State the answer in terms of $ and w)

b) Ans :__________

*29.) Find the average of following numbers in the sequence. n+1,n+2,n+3, …n+19,n+20

Ans :__________

*30.) Muthu has a packet of sweets. If he gives 5 sweets to x number of people, he has a

remainder of 3 sweets left. If he give 7 sweets to y number of people, he has a remainder of 3 sweets left also.

a) What is the smallest possible value of x and y?

a) Ans :__________

b) How many sweets does Muthu have in total? Express your answer in terms of y.

b) Ans :__________

TOPIC 2:

Angles

Page | 7

Section I – Identifying Angles

Label each angle as acute, right, obtuse, straight, or reflex. (The first

one is done for you)

1.)

Ans : straight_

2.)

Ans : _________

3.)

Ans : _________

4.)

Ans: ________

5.)

Ans: ________

6.)

Ans : ________

Topic 2: Angles

Page | 8

Section II –Finding Unknown Angles

7.) What is the total of both angles?

Ans: ________________

8.) Find angle c.

Ans : _______________

9.) In the figure, not drawn to scale, AC, AF, BD, BG and BH are straight lines. BD = BE. Find ∠f.

Ans: ________________

Topic 2: Angles

Page | 9

a

b c

10.) The figure below is not drawn to scale. AB and CD are straight lines. Find ∠x.

Ans: _________________

11.) Find all 3 angles. ∠a, ∠b and ∠c.

Ans: _________________

12.) The figures below show two identical isosceles triangles. Find ∠a.

Ans: ________________

Topic 2: Angles

Page | 10

Section III –Combined-Skill Practices

Write the correct answers in spaces provided.

13.) Name a pair of complementary angles.

Ans : ________________

14.) Name a pair of adjacent angles.

Ans : ________________

15.) Name a pair of supplementary angles.

Ans : ______________

16.) Use a protractor and measure the given angle.

Ans : __________________

Topic 2: Angles

Page | 11

*17.) Complete the table below to show the values of the missing angles. State the reason for each angle being calculated.

a =

because

b =

because

c =

because

d =

because

e =

because

f =

because

h =

because

Topic 2: Angles

Page | 12

*18.) In the figure, AGED is a parallelogram. ACD and DFE are triangles. Given that

∠ FGB =70°. ∠ ACD =30° and ∠ BDA =30°, find ∠ HDB.

Ans : __________________

*19.) Use what you know about the sum of the angles in a triangle together with the properties of supplementary angles to calculate the missing angles in the figure below. Find angles a, b, c and d.

Ans : _________________

TOPIC 3:

Solids and Nets

Page | 13

Section I – Solids

Draw out the nets shape of the solid.

1.)

1.)

2.)

3.)

4.)

2.)

3.)

4.)

( This space is intentionally left blank )

Topic 3: Solids and Nets

Page | 14

Section II

Place a tick in one of boxes for the correct answer.

Solid 5 Faces 6 Faces 7 Faces 8 Faces 12 Faces 20 Faces 5.)

6.)

7.)

8.)

9.)

10.)

Topic 3: Solids and Nets

Page | 15

Section III –Nets of Solids

Circle the solid that can be formed by the net shown on the left.

11.)

A

B

12.)

A

B

13.)

A

B

14.)

A

B

15.)

A

B

TOPIC 4:

Fractions

Page | 16

Section I

i.) Multiplying A Whole Number By A Fraction

1.)

2.)

3.)

4.)

ii.) MultiplyingA Fraction By Fraction

5.)

6.)

7.)

8.)

iii.) Dividing A Whole Number By Fraction

9.)

10.)

11.)

12.)

iv.) Dividing A Fraction By A Fraction

13.)

14.)

15.)

16.)

Topic 4: Fractions

Page | 17

Section II – Combined Skill Practices


17.) How many

s are there in 10 wholes?

Ans :___________

18.) A worker takes 8 hours to paint

of a room.

How long will the worker take to paint the whole room?

Ans :___________

19.) The area of a rectangular pool is 72m2. Given that its breadth is

the length of the pool,

what is the length?

Ans :___________

20.) Mary bought

kg of flour. She packed them into bags of

kg of flour.

How many bags did she use?

Ans :___________

Topic 4: Fractions

Page | 18

Section III –Word Problems

Solve the following problems. Calculators may be used at this part.

21.)

÷

÷ … ÷

= 81

How many

s are there in total to get 81?

Ans: _______________

22.) 12 pails of water can fill

of a tank. How many pails of water can the tank hold?

Ans : ______________

*23.) In a writing competition of a class, Sara's name was in the 29th position. If her name

was just recorded behind

of the pupils, how many pupils were there in her class?

Ans : _______________

Topic 4: Fractions

Page | 19

*24.) Cindy's expenditure is an equal amount each day. After 2 days, she had

of her

money left. After another 6 days, she had $150 left.

a.) How much money did she have at first?

b.) How much did she spend each day?

a) Ans : ________________

b) Ans : ________________

*25.) Jane read a storybook in a day. When she completed reading

of the pages,

it was 11:30 am. When she had

of the pages left to read, it was 1:10 pm.

a.) How long did she take to read the whole storybook?

b.) What time would she finish reading the storybook?

a) Ans : ________________

b) Ans : ________________

Topic 4: Fractions

Page | 20

Section IV –Calculator Activities

Use the calculator to find the values.

26.) 300 ÷

Ans : ________________

27.) 180 ÷

Ans : ________________

28.)

÷

Ans : ________________

29.)

÷ =

Ans : ________________

30.)

÷ =

Ans : ________________

TOPIC 5:

Ratio and Fraction

Page | 21

Section I –Ratio And Fraction

1.) Jack had 3 times the amount of money that Steven had. (a) What ratio of money does Steven has compared to Jack? (b) If Jack had $150, how much does Steven has?

a) Ans : ___________

b) Ans : ___________

2.) 60 children attended a band concert. 18 of them were girls. (a) Find the ratio of the number of girls to the number of boys. (b) What fraction of the children were boys?

a) Ans : ____________

b) Ans : ____________

3.) Susan's savings is 1

3 of Ann's savings.

(a) Find the ratio of Susan's savings to Ann's savings to their total savings. (b) If Ann saves $120 more than Susan, how much does Ann save?

a) Ans : _____________

b) Ans : _____________

Topic 5: Ratio and Fraction

Page | 22

4.) John's height is

of his brother's height.

(a) Find the ratio of John’s height to his brother's height to their total height. (b) If John is 150cm tall, how tall is his brother?

a) Ans : ____________

b) Ans : ____________

5.) A bag of balloons was shared among Jack, Louis and Nick in the ratio 3:5:6. (a) Express Jack's share as a fraction of Louis' share. (b) What is Nick's share as a fraction of the total?

a) Ans : ____________

b) Ans : ____________

6.) The ratio of the sides of a triangle is 2:4:7. If the perimeter of the triangle is 66.3cm, what is the length of the longest side?

Ans :______________


Page | 23

7.) The ratio of men to women in a food court is 4:3. The ratio of women to children is 5:2. If there are 24 children, how many men are there?

Ans :______________

8.) A packet of instant coffee contains coffee powder, sugar and creamer in the ratio 1:2:4. If the packet weighs 21.7g, how much sugar is there?

Ans :______________

Section II –Combined-Skill Practices


9.) During a football match, the ratio of men to women was 3:1. The ratio of men to children was 5:1. If there were 2490 children, how many people were at the football match?

Ans :______________

10.) The area of a rectangle is 24 cm² and the perimeter is 20cm. What is the ratio of the length to the width?

Ans :______________


Page | 24

11.) The ratio of girls to boys in a class is 2:5. There are 8 girls. How many new girls must join the class so that there will be equal number of boys and girls?

Ans :______________

12.) A bundle of pens was shared among Mary, Limin and Yanyan in the ratio 4:2:3. If there were 54 pens, how many pens did Mary get?

Ans :______________

13.) The ratio of the sides of a right-angled triangle is 3:4:5. If the shortest side is 6cm, find the area of the triangle.

Ans :_____________

14.) The ratio of apples to oranges in a lorry was 5:2. There were 248 oranges. How many apples were there?

Ans : _____________


Page | 25


Calculators may be used in this section.

15.) Andrew had as much money as Jeremy. He gave $24 to Jeremy and the new ratio of Andrew's money to Jeremy's was 1:2. How much money did Andrew have at the beginning?

Ans :______________

16.) The ratio of number of Sharon's stamps to that of Ben was 3:5 at first. After Ben gave away 78 of his stamps, they had an equal number of stamps each. How many stamps did Sharon have at first?

Ans :______________

17.) There are 6 times as many pink ribbon as yellow ribbons in a box. (a) What fractions of ribbons are pink ribbons? (b) Find the ratio of the number of pink ribbons to the total number of ribbons. (c) If there are 36 pink ribbons, how many ribbons are there altogether?

a) Ans : ___________

b) Ans : ___________

c) Ans : ___________

18.) A fruit punch contained syrup, beer and water in the ratio 3:1:8. If 3 cups more of syrup than beer were added, how many cups of fruit punch were made?

Ans :______________


Page | 26

19.) Jaya's test score was 3:2 of May's test score. The ratio of Jaya's score to that of Helen was 4:5. If all 3 of them scored 175 marks altogether, how many marks did Helen score?

Ans:______________

20.) The number of boys who joined the computer club as compared to the number of girls in the computer club is 5:4. There are 16 more boys than girls. If another 36 girls joined the club, what will be the new ratio of the number of boys to the number of girls?

Ans :______________

Section IV –Thinking Questions


*21.) The ratio of Michael's money to John's was 3:4. After spending of his money, Michael had $14 less than John. Find (a) The new ratio of Michael's money to John's. (b) The amount of money Michael has left.

a) Ans :______________

b) Ans :______________


Page | 27

*22.) Ratio of volume of water in Jug A to that of Jug B was 5:2 at first. After ½ of the water was poured out from Jug A, Jug A had 280ml more water than Jug B. (a) Find the volume of water in Jug B. (b) Find the volume of water in Jug A at first.

a) Ans :______________

b) Ans :______________

*23.) At first, the ratio of Star's money to Max's money was 11:8. After each of them bought an electronic dictionary for $13.60, the ratio of Star’s money to Max's money became 3:2. How much money did Star have at first?

Ans :______________

*24.) Box A is as heavy as Box B. Box B is ¾ as heavy as Box C. (a) Find the ratio of the mass of Box A to the mass of Box C. (b) If the total mass of all 3 boxes is 4.5kg, what is the mass of Box C?

a) Ans :______________

b) Ans :______________

*25.) Andy has bought some goldfishes and guppies. The ratio of the number of goldfishes

to the number of guppies in a fish tank is 1:4. The number of goldfishes is the number of angelfishes.

(a) Find the ratio of the number of goldfishes to that or guppies to that of angelfishes. (b) If there are 15 more guppies than angelfishes, find the total number of fishes.

Ans :______________

Ans :______________

TOPIC 6:

Percentage

Page | 28

Section I

Express each of the following as a percentage in its simplest form.

1.)

Ans : ______________

2.)

Ans : ______________

3.)

Ans : ______________

4.) 0.44

Ans : ______________

5.) 2.81

Ans : ______________

6.) 4.75

Ans : ______________

7.) Express this fraction to percentage.

Ans : ______________

Topic 6: Percentage

Page | 29

8.) Express this fraction to percentage.

Ans : ______________

9.) A store has 660 books in stock. If 30 percent of these books are on sale, how many books are not on sale?

Ans : ______________

10.) The enrollment at a university increased from 14,000 students to 16,000 students over a period of 5 years. What is the percent increase in enrollment?

Ans : ______________

11.) What is the percent decrease on a DVD recorder that is marked down from $400 to $350?

Ans : ______________

12.) 38% of a pole is painted red, 26% is painted yellow and the rest is painted black. If the pole is 2.6 m long, what length of the pole is painted black?

Ans : ______________

Topic 6: Percentage

Page | 30

Section II

Questions

13.) The cost of a hi-fi set was $525. It was sold for $630. Express the profit as a percentage of the cost price?

Ans : ______________

14.) Ali spent $150 to make 250 sticks of satay. He sold 80% of the satays and made a profit

of 50% on each stick of satay sold. What was Ali's total profit?

Ans : ______________

15.) Mrs Wong has 8 m of cloth. One table cloth uses 1.25 m of cloth. If she made 4 table

cloths, what percentage of cloth is she left with?

Ans : ______________

16.) 70% of a cake is flour, 20% is eggs and the remaining portion is milk. If the eggs used weigh 320 g, what is the weight of flour used?

Ans : ______________

Topic 6: Percentage

Page | 31

17.) Mr Tan's salary is 10% less than his wife's salary. His wife earns $45600 a year. What is his monthly salary?

Ans : ______________

18.) In a box there were 16% more green buttons than red buttons. If there were 84 red buttons, how many buttons were there altogether?

Ans : ______________

19.) In a test there were 80 questions. Lipin answered 92.5% of the questions and she got 75% correct on all the questions she answered. What is her score in percentage?

Ans : ______________

20.) Nigel paid $26 for a pen when it was sold at a discount of 20%. Kimberly bought the same type of pen at $26.65. What percentage discount did Kimberly get?

Ans : ______________

Topic 6: Percentage

Page | 32

Section III – Word Problems


21.) A school has 2400 students. There are 8% more girls than boys. If the principal wants to

have only 3% more girls than boys but maintain the school enrolment, how many girls must

be replaced by boys?

Ans : _______________

22.) A club has 480 members. 60% of the members are men and the rest are women. If the number of male members is increased by 25%, what is the new percentage of female members?

Ans : _______________

23.) Ali spent $600 to make 7500 sticks of satay. He sold each of the satay at $0.22. If Ali wants to increase his profit by another 25%, what price must he sell each stick of satay?

Ans : _______________

Topic 6: Percentage

Page | 33

24.) There are 60 000 people in a town. 70% of the population is made up of adults. If 2000 babies were born and 2000 adults died, what is the new percentage of adults in the town?

Ans : _______________

25.) A certain state requires that an applicant for a driver's license answer at least 80 percent of the questions on a written test correctly. If the test has 30 questions on it, at least how many of these questions must be answered correctly?

Ans : _______________

26.) A dress is selling for $100 after a 20 percent discount. What was the original selling price?

Ans : _______________

Topic 6: Percentage

Page | 34

Section IV –Thinking Questions.


*27.) A total of 60 advertisements were sold for a school yearbook. If 20 percent of the first 20 sold were in color, 40 percent of the next 30 sold were in color, and 80 percent of the last 10 sold were in color, what percent of the 60 advertisements were in color?

Ans : _______________

*28.) S is the sum of the first 100 consecutive positive even integers, and T is the sum of the first 100 consecutive positive integers. S is what percent greater than T ?

Ans : _______________

*29.) The percent increase from 8 to 14 is equal to the percent increase from 20 to what?

Ans : _______________

*30.) A store charges $28 for a certain type of sweater. This price is 40 percent more than

the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store

employees can purchase any remaining sweaters at 30 percent off the store's cost. How

much would it cost an employee to purchase a sweater of this type at this sale?

Ans : _______________

TOPIC 7:

Speed

Page | 35

Section I –Relationship between Distance, Time and Speed.

Fill in the blanks.

Distance Time Speed

1.) 200km 5hrs ____ km /hr

2.) 50m 2.5hrs ____m/hr

3.) 120 cm 60secs ____cm/sec

4.) 3600km 180mins ____ km/min

5.) 18m 1.2hr ____m/hr

6.) 10000cm 100mins ____cm/min

Section II

7.) A cheetah runs 100 metres in 3.5 seconds. A man runs the same distance in 10 seconds. During a 100 metre race, when the cheetah crossed the finishing line, how far back was the man?

Ans : _______________

8.) Lucy took 30 minutes to cycle from school to her home at an average speed of 12 km/h. If she wanted to reach home 10 minutes early, what must her average speed be?

Ans : _______________

9.) During a car speed test, a distance of 800 metres was covered in 25 seconds. What was the speed in km/h?

Ans : _______________

Topic 7: Speed

Page | 36

10.) Michael travelled of his journey at 50 km/h. The next of his journey he travelled at 40 km/h. The remaining 40 km he covered in half an hour. How much time did he take for the whole journey?

Ans : _______________

11.) A motorist travelled at 80 km/h for 120 km and at 60 km/h for another 90 km. Find his average speed for the whole journey?

Ans : _______________

12.) Joel left school at 6.30 p.m. to walk home. He walked at an average speed of 60 m/min. Along the way, he stopped at a shop for 15 minutes. He arrived home at 7:25 p.m. What is the distance between his house and the school?

Ans : _______________

13.) A car travelled at a speed of 90 km/h. It left Town Ponpon at 11.00 a.m. What time will it reach Town Dondon which is 255 km away?

Ans : _______________

Topic 7: Speed

Page | 37


Calculators may be used in this section

14.) Sunny drove from Town A to Town B at an average speed of 70 km/h. He took one and a half hour to reach Town B. From Town B to Town C he increased his speed by 50%. The distance from Town B to Town C is twice the distance from Town A to Town B. What was his average speed from Town A to Town C?

Ans : _______________

15.) The children cycled between Camp A and Camp B which are 500 m apart in 50 seconds. If they wanted to reduce the time to 40 seconds, what is the increase in speed?

Ans : _______________

16.) A woman fell from the top of a building 280 metres tall. 3 seconds later, Superman jumped off the top of the same building to save her. It took Superman 2 seconds to rescue her just before she hit the ground. What was Superman's average speed?

Ans : _______________

Topic 7: Speed

Page | 38

17.) A train departed Singapore at 10.40 a.m. and arrived in Malacca, 250 km away, at 2.00 p.m.. Along the way, it made 5 stops of 10 minutes each. Albert left Singapore in his car at the same time as the train and arrived in Malacca also at the same time but without stopping. How much faster was the train's average speed compared to that of Albert's car?

Ans : _______________

18.) Mrs Ng and Mrs Lim drove for 4 hours from Singapore to Malacca in separate cars. Mrs Ng drove at a speed of 75 km/h without stopping. Mrs Lim took a stop for 15 minutes midway along the journey, what was her average speed?

Ans : _______________

Topic 7: Speed

Page | 39



19.) Two drivers decided to compete on a circular race track to see who can go fastest.

Both drivers leave the starting point at the same, travelling in opposite directions. Driver X

travels at an average speed of 150 km/hr. He passes Driver Y exactly 2 minutes later. If

driver Y moves at an average speed of 180 km/hr, how long is the race track?

Ans : _______________

20.) In a horse race, Blackie had an average speed of 30km/hr for 6 mins and 18km/hr for

the last 4 mins before completing the race. Lucy travelled at a constant speed of 24km/hr

throughout the race. Who won the race? Show your calculations.

Ans : _______________

TOPIC 8:

Circles

Page | 40

Section I

Find the Area, Radius, Circumference and Diameter of Circle.

1.) Diameter of circle is 1.3m. Calculate the circumference of the circle.

d = 1.3 m

Ans : ___________

2.) Calculate the radius of the circle.

d = 10cm

Ans : ___________

3.) Calculate the circumference of the circle.

d = 24cm

Ans : ___________

Topic 8: Circles

Page | 41

4.) Calculate the area of the circle.

d = 5cm

Ans : ___________

5.) Calculate the circumference of the circle.

| | r = 7.9 m

Ans : ___________

6.) Calculate the radius of the circle.

| | d = 21 cm

Ans : ___________

Topic 8: Circles

Page | 42

Section II

Complete the following questions.

7.) The Frisbee used in a competition has a radius of 12cm. Find the area of the Frisbee.

Ans : ___________

8.) The diameter of a wheel is 0.1 m. For the wheel to roll over a distance of 9.42 m, how many revolutions will it make? [ π = 3.14 ]

Ans : ___________

9.) A merry-go-round has a diameter of 25m. Calculate the circumference of the merry-go-round.

Ans : ___________

10.) An hour hand on a clock has a radius of 12 cm long. From noon to 3.00 pm, what area of the clock is swept by the hour hand?

Ans : ___________

11.) The radius of a circle is 10 cm. If the radius is increased by 20%, find the percentage increase in area and circumference.

Ans : ___________

12 a.) Draw a circle of radius 8cm. b.) Find the circumference of circle.

Ans : ___________

Topic 8: Circles

Page | 43


Calculators can be used in this section.

13.) The sides of the square piece of paper is 22 cm long. If a semi-circle was cut on one side,

what is the area of the remaining piece of paper? [

]

Ans : __________

14.) ABC is a right-angle triangle. The sides have a ratio of 3:4:5 and BC is also the diameter of the circle. If the triangle has an area of 6 square cm, find the area of the circle.

Ans : __________

15.) The whole cake weighed 3.6 kg. There were 9 children and each child ate 0.3 kg of the cake. The remainder of the cake is shown as the shaded portion. If the radius of the cake was 30 cm, what is the area of the shaded portion? [ π = 3.14 ]

Ans : __________

Topic 8: Circles

Page | 44


Calculators can be used in this section.

16.) The radius of the smaller circle is 3.5 cm. The radius of the larger circle is twice that of

the smaller circle. Find the area of the shaded portion? [

]

Ans : __________

17.) The circumference of coin A is 66 mm. Coin B is bigger than coin A but both coins are of the same thickness and material. If coin B weighs four times as heavy as coin A, what is the

diameter of coin B. [

]

Ans : __________

18.) The right-angled triangle has a base and height of 7 cm. What is the difference in area

between the triangle and the semi-circle? [

]

Ans : __________

Topic 8: Circles

Page | 45

19.) The figure below is made up of a square of side 42 cm. One semi circle and one quadrant are drawn inside the square. Given that the total area of portion A and C is two

times the area of B, find the area of B. [

]

Ans : __________

TOPIC 9:

Pie Charts

Page | 46

Section I – Understanding Pie Charts

This pie chart shows the results of a survey that was carried out to find out how students travel to school.

1.) What is the most common method of travel?

Ans :____________

2.) What fraction of the students travel to school by car?

Ans :____________

3.) If 6 students travel by car, how many people took part in the survey?

Ans :____________

Topic 9: Pie Charts

Page | 47

The pie chart below shows the amount of money 5 men spend their income last month.

4.) If Lex spends $500, how much did Ken spend?

Ans : _________

5.) If the ratio of Mike's spendings to Lex's is 9 : 10, how much did Mike spend?

Ans : _________

6.) What was the total amount of money spent by Mike, Ian and Joe?

Ans : _________

Topic 9: Pie Charts

Page | 48

Section II –Calculations Based On Angles Of A Pie Chart

A supermarket chain sold 3600 packets of sausages last month. The pie chart shows the different flavours.

7.) How many packets of vegetarian sausages were sold?

Ans :____________

8.) What is the number of pork sausages sold?

Ans :____________

9.) How many packets of beef sausages were sold?

Ans :____________

10.) How many packages of other sausages were sold?

Ans :____________

Topic 9: Pie Charts

Page | 49

Section III –Combined Skill Practice

The pie chart below shows the types of fruits at a stall.

11.) There are 84 oranges and twice as many pears as kiwis. What fraction of the fruits are pears?

Ans :____________

12.) If each pear is sold at $0.45, how much will the fruit seller get from the sale of all the pears?

Ans :____________

13.) How many fruits are there altogether at the stall?

Ans :____________

Topic 9: Pie Charts

Page | 50

The pie chart below shows the amount of money Joseph spent on some items.

14.) How much money did he spend on the bag?

Ans : ________

15.) What is the cost of the shoes?

Ans : _________

16.) How much did Joseph spend in total?

Ans : _________

Topic 9: Pie Charts

Page | 51

The pie chart below shows how Mr Lim spends his monthly salary. He saves 12.5 % of his monthly salary.

17.) What percentage of his salary does he spend on his family?

Ans : ___________

18.) How many percent of his salary goes to his personal expenses?

Ans : ___________

Topic 9: Pie Charts

Page | 52

19.) The Prata contains 5 times as much fats than protein. What percent of it are

carbohydrates?

Ans : ___________

20.) Mee Rebus contains 18 g of fats per serving. 70 % of the food is made up of

carbohydrates. How many grams of carbohydrates are there in a serving of Mee Rebus?

Ans : ___________

21.) Prata contains 10 g of fats in a serving. Sylvia had one roti prata and a plate of mee rebus

for breakfast. How many carbohydrates did she consume in total? Give your answer in

grams.

Ans : ___________

Carbo-hydrates

Proteins

Fats

Roti Prata

Carbo-hydrates

Proteins

Fats

Mee Rebus

50⁰

30⁰

Topic 9: Pie Charts

Page | 53

The demographic breakdown of country x at a given time is shown in the pie chart.

The country has a total residential population of 4 million.

22.) What is the number of Chinese residents?

Ans : ___________

23.) The ratio of Indian to Malay residents is 2:3. The number of Indian residents is 300,000.

What is the number of Malay residents in country x?

Ans : ___________

24.) What is the ratio of Malay residents to Chinese residents in country x?

Ans : ___________

25.) Find the number of residents which belong to “Others”. Express this number as a

percentage.

Ans : ___________

Chinese

Malays

Indians

Others

TOPIC 10:

Area and Perimeter

Page | 54

Section I – Area and Perimeter of Composite Figures

1.) The perimeter of this figure is 14 cm.

Find the area.

Ans : ____________

2.) Find the area of the figure below.

Ans : ____________

3.) If the sides of the rectangle and triangle is of the same length, find the area of the whole figure.

4cm Ans : ____________ 15cm

4 cm

9 cm

8 cm

http://www.edhelper.com/perimeter.htm

Topic 10: Area and Perimeter

Page | 55

4.) The sides of the arrow measure 3cm. Find the perimeter of the figure.

Ans : ____________

5.) What is the area of the figure shown?

Ans : ____________

6.)The figure is made up of two circles of radius 7 cm and 14 cm. Find the area of the shaded

portion. (

)

Ans : ____________

6 cm

2 cm

3 cm

4 cm

3 cm


Page | 56

7.) The figure shown is made up of a square of side 4 cm and a triangle. What is its area?

Ans : ____________

8.) What is the area of the trapezium shown? Give your answer in cm2.

Ans : ____________

9.) The figure shown is made up of 12 equal sides of length 3 cm each. (a) Find the total area of the figure. (b) What is its perimeter?

a) Ans : ____________

b) Ans : ____________

6 cm

5 cm 7 cm

4 cm

6 cm


Page | 57

10.) The figure below has a perimeter of 38 cm. Find its area. (

)

Ans : ____________

8 cm

8 cm


Page | 58

Section II – Combined Skill Practices

11.) Calculate the area of the diagrams shown

a) Ans : ____________ b) Ans : ____________ c) Ans : ____________

12.) What is the perimeter of the figure shown? (

)

Ans : ____________


Page | 59

13.) Find the area and perimeter of whole figure.

Ans : ____________

14.) The diagram shows the plan view of a small pool. What is the perimeter of the pool?

Ans : ____________

15.)If the perimeter of the figure shown is 62 cm, what is its area?

Ans : ____________


Page | 60


16.) Find the area and perimeter for the given diagram.(

)

Ans : _____________

17.) The diagram shows a figure made up of 2 quadrants of radius 0.6 cm and 1 cm and 2 rectangles of similar length of 2.4 cm. Calculate it’s a) area and b) perimeter.

(

)

a) Ans : ____________

b) Ans : ____________


Page | 61

18.) Calculate the area of the figure shown.

Ans : ___________

19.) What is the perimeter of the given diagram? (

)

Ans : ____________

20.) Find the area of the shape as shown. Give your answer in cm2. (

)

Ans : ____________

TOPIC 11:

Volume

Page | 62

Section I – Finding an unknown side.

Fill in the blanks.

Length Width Height Volume

1.) _____ cm 3 cm 4 cm 48 cm3

2.) 5 cm _____ cm 1 cm 10 cm3

3.) 8 cm 6 cm _____ cm 96 cm3

4.) 9 cm 5 cm 8 cm _____ cm3

5.) 12 cm 7 cm 2 cm _____ cm3

Section II – Find the unknown area.

6.) Find the volume and area of whole cuboid.

Ans : ___________

7.) Find the area of the shaded part where l = 8 m, w = 5 m and h = 4 m. Give your answer in square metres.

Ans : ___________

Topic 11: Volume

Page | 63

8.) Find the area of the shaded portion where l = 4 cm, w = 3 cm and h = 2 cm. Give your answer in square centimetres.

Ans : ___________

9.) Find the surface area of this cuboid.

Ans : ___________

10.) Find the total surface area for the figure shown. Give your answer in square centimetres.

Ans : ___________

4 cm

2 cm

8 cm

Topic 11: Volume

Page | 64

Section III – Combined Skill Practices

11.) A rectangular box measuring 12 cm by 8 cm by 6 cm is filled with 2-cm cubes. How many cubes can fit inside?

Ans : ___________

12.) Find the volume of this cuboid.

Ans : ___________

13.) Find the volume of the cuboid shown. Express your answer in cubic metres.

Ans : ___________

4 m

1 m

2 m

Topic 11: Volume

Page | 65

14.) Find the volume of this square prism.

Ans : ___________

15.) The volume of the cuboid is 252 cm3. Find the length of AB.

Ans :__________

16.) A fish tank is filled with water to a height of 40 cm. Find the volume of water in the tank where L = 80 cm, W = 50 cm, H = 70 cm.

Ans :__________

Topic 11: Volume

Page | 66

Section IV – Word Problems

17.) A wooden block measuring 10 cm by 4 cm by 6 cm is cut into 3 smaller blocks of equal size.

Calculate the volume of each block.

Ans : ___________

18.) The tank below has a base of 5 cm and a width of 2 cm. The water-level was 4 cm at first.

After some water was poured into the tank, the height increased to 7 cm. Find the volume of

the water poured into the tank.

Ans : __________ 19.) Six cubes, each of length 3 cm, are joined to form a rectangular block of base area 54 cm2. Find the volume of the rectangular block.

Ans : ___________

20.) What is the volume of a cube of edge length 4 cm? Ans : ___________

Answer Sheet

Topic 1 : Algebra

1. 15k

2.

kg

3.

4. a) –

b) $26

5.

– 10

6. 3p(3 + 4p)

7. a) (12–x)(12+x) cm2

b) 49 cm2

8. $ (27 + 2k)

9. 10d

10. 2(a + 1)

11. 10(c – 1)

12. e + 5

13. 11 + 3p

14. 6f + 1

15. 2

16. 25

17. 8

18. 25

19. 90

20. 31

Answer Sheet

21. 25

22. p + 38

23. $2m

24. 2c

25. 8y cm

26. a) 6p

b) 14p

27. a) 4n + 13

b) n(n + 11)

c) 17

28. a) (5w + 40) cents

b) $ (9.6 – 7w)

29. n + 10.5

30. a) x = 7, y =5

b) 7y + 3n + 10.5

Answer Sheet

Topic 2 : Angles

1. straight

2. acute

3. acute

4. obtuse

5. right angle

6. reflex

7. 79⁰

8. 85⁰

9. 161⁰

10. 68⁰

11. a = c = 154⁰, b = 26⁰

12. 38⁰

13. ∠ LMY, ∠ PML

14. ∠ JXQ, ∠ UXJ

15. ∠ GPH, ∠ CPG

16. 158⁰

Answer Sheet

17. a = 105⁰ , a = e (corresponding ∠s)

b = 75⁰, b = 180⁰ – a (supplementary ∠s)

c = 105⁰, a = c (opposite ∠s)

d = 75⁰, d = b (opposite ∠s)

e = 105⁰, e = 105⁰ (opposite ∠s)

f = 75⁰, f = 180⁰ – e (supplementary ∠s)

h = 75⁰ because h = 180⁰ - 105⁰ (supplementary ∠s)

18. 50⁰

19. a = 35⁰, b = 50⁰,

c = 85⁰, d = 30⁰

Answer Sheet

Topic 3 : Solids and Nets

1.

2.

3.

4.

5. Solid for 5 faces






11. B

12. A

13. B

14. A

15. A

Answer Sheet

Topic 4 : Fractions

1.

2. 9

3. 21

4. 6

5.

6.

7.

8.

9. 24

10. 36

11. 10

12. 36

13.

14. 6

15.

16. 2

17. 16

18. 20 hrs

19. 12 m

20. 8

21. 4

22. 21

Answer Sheet

23. 36

24. a) $ 250

b) $12.50

25. a) 4 hrs

b) 3:30 pm

26. 600

27. 225

28. 1.67

29.

30.

Answer Sheet

Topic 5 : Ratio and Fraction

1. a) 1 : 3

b) $ 50

2. a) 3 : 7

b)

3. a) 1 : 3 : 4

b) $ 180

4. a) 3 : 4 : 7

b) 200 cm

5. a)

b)

6. 35.7 cm

7. 80 men

8. 6.2 g

9. 19090

10. 3 : 2

11. 12 girls

12. 36 pens

13. 24 cm2

14. 620 apples

15. $ 96

16. 234 stamps

Answer Sheet

17. a)

b) 6 : 7

c) 42 ribbons

18. 18 cups

19. 75

20. 4 : 5

21. a) 9 : 16

b) $ 18

22. a) 1120 ml

b) 2800 ml

23. $ 74.80

24. a) 1 : 2

b) 2 kg

25. a) 2 : 8 : 3

b) 39 fishes

Answer Sheet

Topic 6 : Percentage

1. 65 %

2. 44 %

3. 45 %

4. 44 %

5. 281 %

6. 475 %

7. 85 %

8. 58.3 %

9. 462 books

10. 14.3 %

11. 12.5 %

12. 0.936 m

13. 20 %

14. $ 30

15. 37.5 %

16. 160 g

17. $ 3420

18. 200

Answer Sheet

Topic 7 : Speed

1. 40

2. 20

3. 2

4. 20

5. 15

6. 100

7. 65 m

8. 18 km/h

9. 115.2 km/h

10. 1.8 hrs

11. 70 km/h

12. 2.4 km

13. 1.50 pm

14. 90 km/h

15. 2.5 m/s

16. 140 m/s

17. 25 km/h

18. 80 km/h

19. 11 km

20. Blackie

Answer Sheet

Topic 8 : Circles

1. 4.08 m

2. 5 cm

3. 75.4 cm

4. 19.6 cm2

5. 49.6 m

6. 10.5 cm

7. 452 cm2

8. 30 rev

9. 78.5 m

10. 113 cm2

11. Area : 44 %

Circumference : 20 %

12. b) 50.2 cm

13. 294 cm2

14. 19.6 cm2

15. 706.5 cm2

16. 115.5 cm2

17. 42 mm

18. 5.25

19. 787.5 cm2

Answer Sheet

Topic 9 : Pie Charts

1. Bus

2.

3. 24 students

4. $ 400

5. $ 450

6. $ 650

7. 900 packets

8. 400

9. 1500 packets

10. 800 packets

11.

12. $ 18.90

13. 336 fruits

14. $ 25

15. $ 125

16. $ 500

17. 62.5 %

18. 25 %

19. 70 %

20. 105 g

21. 133 g

22. 3 million

Answer Sheet

23. 450,000 residents

24. 3 : 20

25. 6.25 %

Answer Sheet

Topic 10 : Area and Perimeter

1. 14 cm2

2. 52 cm2

3. 74 cm2

4. 22 cm

5. 32 cm2

6. 462 cm2

7. 20 cm2

8. 36 cm2

9. a) 45 cm2

b) 36 cm

10. 109 cm2

11. a) 4 cm2

b) 34 cm2

c) 12 cm2

12. 61.7 m

13. Area : 20 cm2,

Perimeter : 16 cm

14. 48 cm

15. 137 cm2

16. Area : 637

Perimeter : 115

Answer Sheet

17. a) 9.25 cm2

b) 21.7 cm

18. 44

19. 26.6

20. 301 cm2

Answer Sheet

Topic 11 : Volume

1. 4

2. 2

3. 2

4. 360

5. 172

6. Volume : 200

Area : 220

7. 20 m2

8. 12 cm2

9. 174

10. 112 cm2

11. 72 cubes

12. 360

13. 8 m3

14. 396

15. 7

16. 160, 000 cm3

17. 80 cm3

18. 30 cm3

19. 324 cm2

20. 64 cm3

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Maths ebook complete