Table of Contents 1 Algebra 2 Angles 3 Solids and Nets 4 Fractions 5 Ratio and Fraction 6 Percentage 7 Speed 8 Circles 9 Pie Charts 10 Area and Perimeter 11 Volume Š 2012 A’s Tuition. All rights reserved. These materials may not be reproduced, republished, redistributed, or resold in any form without written permission from the author.
TOPIC 1: Algebra 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 : __________
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Topic 1: Algebra
6.) Simplify the following 12p+(3pĂ—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 : __________
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Topic 1: Algebra
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
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Topic 1: Algebra
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 : ____________ Page | 4
Topic 1: Algebra
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: ____________
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Topic 1: Algebra
*28.) The table below shows the prices of pencils and sharpeners sold at a bookshop. Item Pencils Sharpeners
Unit Price w cents (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 :__________
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TOPIC 2: Angles Section I – Identifying Angles Label each angle as acute, right, obtuse, straight, or reflex. (The first one is done for you) 1.)
2.)
Ans : straight_
Ans : _________
3.)
4.)
Ans : _________
Ans: ________
5.)
6.)
Ans: ________
Ans : ________
Page | 7
Topic 2: Angles
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: ________________
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Topic 2: Angles
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.
a b c
Ans: _________________
12.) The figures below show two identical isosceles triangles. Find ∠a.
Ans: ________________
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Topic 2: Angles
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 : __________________ Page | 10
Topic 2: Angles
*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
Page | 11
Topic 2: Angles
*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 : _________________
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TOPIC 3: Solids and Nets Section I – Solids Draw out the nets shape of the solid. 1.)
1.)
2.)
2.)
3.)
4.)
3.)
4.)
( This space is intentionally left blank )
Page | 13
Topic 3: Solids and Nets
Section II Place a tick in one of boxes for the correct answer. Solid
5 Faces
6 Faces
7 Faces
5.)
6.)
7.)
8.)
9.)
10.)
Page | 14
8 Faces
12 Faces
20 Faces
Topic 3: Solids and Nets
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
Page | 15
B
TOPIC 4: Fractions 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.)
Page | 16
Topic 4: Fractions
Section II – Combined Skill Practices Write the correct answers in spaces provided. 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 :___________
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Topic 4: Fractions
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 : _______________
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Topic 4: Fractions
*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 : ________________
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Topic 4: Fractions
Section IV –Calculator Activities Use the calculator to find the values. 26.) 300
÷
Ans : ________________
27.) 180
÷
Ans : ________________
28.)
÷
Ans : ________________
29.) ÷
= Ans : ________________
30.) ÷
= Ans : ________________
Page | 20
TOPIC 5: Ratio and Fraction 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.)
1
Susan's savings is of Ann's savings. 3
(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 : _____________
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Topic 5: Ratio and Fraction
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 :______________
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Topic 5: Ratio and Fraction
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 Write the correct answers in spaces provided. 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 | 23
Topic 5: Ratio and Fraction
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 : _____________
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Topic 5: Ratio and Fraction
Section III –Word Problems 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 :______________
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Topic 5: Ratio and Fraction
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 Calculators may be used in this section. *21.) The ratio of Michael's money to John's was 3:4. After spending 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.
of his money,
a) Ans :______________ b) Ans :______________
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Topic 5: Ratio and Fraction
*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 :______________ Page | 27
TOPIC 6: Percentage 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 : ______________
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Topic 6: Percentage
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 : ______________
Page | 29
Topic 6: Percentage
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 : ______________
Page | 30
Topic 6: Percentage
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 : ______________
Page | 31
Topic 6: Percentage
Section III – Word Problems Calculators may be used in this section. 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 : _______________
Page | 32
Topic 6: Percentage
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 : _______________
Page | 33
Topic 6: Percentage
Section IV –Thinking Questions. Calculators may be used in this section. *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 : _______________
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TOPIC 7: Speed Section I –Relationship between Distance, Time and Speed. Fill in the blanks. 1.) 2.) 3.) 4.) 5.) 6.)
Distance 200km 50m 120 cm 3600km 18m 10000cm
Time 5hrs 2.5hrs 60secs 180mins 1.2hr 100mins
Speed ____ km /hr ____m/hr ____cm/sec ____ km/min ____m/hr ____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 : _______________
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Topic 7: Speed
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 : _______________
Page | 36
Topic 7: Speed
Section III –Word Problems 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 : _______________
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Topic 7: Speed
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 : _______________
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Topic 7: Speed
Section IV –Thinking Questions Calculators may be used in this section. 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 : _______________
Page | 39
TOPIC 8: Circles 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 : ___________
Page | 40
Topic 8: Circles
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 : ___________
Page | 41
Topic 8: Circles
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 : ___________
Page | 42
Topic 8: Circles
Section III – Word Problems 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 : __________
Page | 43
Topic 8: Circles
Section IV –Thinking Questions 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 : __________ Page | 44
Topic 8: Circles
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 : __________
Page | 45
TOPIC 9: Pie Charts 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 :____________
Page | 46
Topic 9: Pie Charts
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 : _________
Page | 47
Topic 9: Pie Charts
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 :____________
Page | 48
Topic 9: Pie Charts
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 :____________
Page | 49
Topic 9: Pie Charts
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 : _________
Page | 50
Topic 9: Pie Charts
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 : ___________
Page | 51
Topic 9: Pie Charts
Roti Prata
Mee Rebus Fats
Fats
30â °
Proteins
Proteins
Carbohydrates
Carbohydrates
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? 50â °
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 : ___________
Page | 52
Topic 9: Pie Charts
Chinese Malays Indians Others
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 : ___________
Page | 53
TOPIC 10: Area and Perimeter 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.
4 cm
8 cm
9 cm
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 Page | 54
Topic 10: Area and Perimeter
4.) The sides of the arrow measure 3cm. Find the perimeter of the figure. 6 cm
3 cm
2 cm
4 cm 3 cm
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 : ____________ Page | 55
Topic 10: Area and Perimeter
7.) The figure shown is made up of a square of side 4 cm and a triangle. What is its area? 4 cm
6 cm
Ans : ____________ 8.) What is the area of the trapezium shown? Give your answer in cm2.
7 cm
5 cm
6 cm
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 : ____________ Page | 56
Topic 10: Area and Perimeter
10.) The figure below has a perimeter of 38 cm. Find its area. (
)
8 cm
8 cm
Ans : ____________
Page | 57
Topic 10: Area and Perimeter
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 | 58
Topic 10: Area and Perimeter
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 | 59
Topic 10: Area and Perimeter
Section III – Word Problems 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 | 60
Topic 10: Area and Perimeter
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 : ____________
Page | 61
TOPIC 11: Volume Section I – Finding an unknown side. Fill in the blanks. 1.) 2.) 3.) 4.) 5.)
Length _____ cm 5 cm 8 cm 9 cm 12 cm
Width 3 cm _____ cm 6 cm 5 cm 7 cm
Height 4 cm 1 cm _____ cm 8 cm 2 cm
Volume 48 cm3 10 cm3 96 cm3 _____ cm3 _____ 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 : ___________ Page | 62
Topic 11: Volume
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. 8 cm
4 cm
2 cm
Ans : ___________
Page | 63
Topic 11: Volume
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.
2m
1m 4m
Ans : ___________
Page | 64
Topic 11: Volume
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 :__________
Page | 65
Topic 11: Volume
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 : ___________
Page | 66
Answer Sheet
Topic 1 : Algebra
1.
15k
10.
2(a + 1)
11.
10(c – 1)
12.
e+5
13.
11 + 3p
b) $26
14.
6f + 1
– 10
15.
2
2.
kg
3.
4.
5.
–
a)
6.
3p(3 + 4p)
16.
25
7.
a) (12–x)(12+x) cm2
17.
8
b) 49 cm2
18.
25
8.
$ (27 + 2k)
19.
90
9.
10d
20.
31
Answer Sheet
21.
25
22.
p + 38
23.
$2m
29.
n + 10.5
24.
2c
30.
a) x = 7, y =5
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)
b) 7y + 3n + 10.5
Answer Sheet
Topic 2 : Angles
1.
straight
10.
68⁰
2.
acute
11.
a = c = 154⁰, b = 26⁰
3.
acute
12.
38⁰
4.
obtuse
13.
∠ LMY, ∠ PML
5.
right angle
14.
∠ JXQ, ∠ UXJ
6.
reflex
15.
∠ GPH, ∠ CPG
7.
79⁰
16.
158⁰
8.
85⁰
9.
161⁰
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
8.
Solid for 8 faces
9.
Solid for 6 faces
10.
Solid for 20 faces
11.
B
12.
A
13.
B
14.
A
15.
A
1.
2.
3.
4.
5.
Solid for 5 faces
6.
Solid for 6 faces
7.
Solid for 12 faces
Answer Sheet
Topic 4 : Fractions
1.
12.
2.
9
13.
3.
21
14.
4.
6
5.
6.
7.
8.
36
6
15.
16.
2
17.
16
18.
20 hrs
19.
12 m
9.
24
20.
8
10.
36
21.
4
11.
10
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.
2.
a) 1 : 3
7.
80 men
b) $ 50
8.
6.2 g
a) 3 : 7
9.
19090
10.
3:2
a) 1 : 3 : 4
11.
12 girls
b) $ 180
12.
36 pens
a) 3 : 4 : 7
13.
24 cm2
b) 200 cm
14.
620 apples
15.
$ 96
16.
234 stamps
b)
3.
4.
5.
a)
b)
6.
35.7 cm
Answer Sheet
17.
a)
24.
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
a) 1 : 2
b) 2 kg
25.
a) 2 : 8 : 3
b) 39 fishes
Answer Sheet
Topic 6 : Percentage
1.
65 %
11.
12.5 %
2.
44 %
12.
0.936 m
3.
45 %
13.
20 %
4.
44 %
14.
$ 30
5.
281 %
15.
37.5 %
6.
475 %
16.
160 g
7.
85 %
17.
$ 3420
8.
58.3 %
18.
200
9.
462 books
10.
14.3 %
Answer Sheet
Topic 7 : Speed
1.
40
12.
2.4 km
2.
20
13.
1.50 pm
3.
2
14.
90 km/h
4.
20
15.
2.5 m/s
5.
15
16.
140 m/s
6.
100
17.
25 km/h
7.
65 m
18.
80 km/h
8.
18 km/h
19.
11 km
9.
115.2 km/h
20.
Blackie
10.
1.8 hrs
11.
70 km/h
Answer Sheet
Topic 8 : Circles
1.
4.08 m
11.
Area : 44 %
2.
5 cm
3.
75.4 cm
12.
b) 50.2 cm
4.
19.6 cm2
13.
294 cm2
5.
49.6 m
14.
19.6 cm2
6.
10.5 cm
15.
706.5 cm2
7.
452 cm2
16.
115.5 cm2
8.
30 rev
17.
42 mm
9.
78.5 m
18.
5.25
10.
113 cm2
19.
787.5 cm2
Circumference : 20 %
Answer Sheet
Topic 9 : Pie Charts
1.
Bus
2.
12.
$ 18.90
13.
336 fruits
3.
24 students
14.
$ 25
4.
$ 400
15.
$ 125
5.
$ 450
16.
$ 500
6.
$ 650
17.
62.5 %
7.
900 packets
18.
25 %
8.
400
19.
70 %
9.
1500 packets
20.
105 g
10.
800 packets
21.
133 g
22.
3 million
11.
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
b) 34 cm2
3.
74 cm2
c) 12 cm2
4.
22 cm
12.
61.7 m
5.
32 cm2
13.
Area : 20 cm2,
6.
462 cm2
7.
20 cm2
14.
48 cm
8.
36 cm2
15.
137 cm2
9.
a) 45 cm2
16.
Area : 637
b) 36 cm
10.
109 cm2
11.
a) 4 cm2
Perimeter : 16 cm
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
11.
72 cubes
2.
2
12.
360
3.
2
13.
8 m3
4.
360
14.
396
5.
172
15.
7
6.
Volume : 200
16.
160, 000 cm3
Area : 220
17.
80 cm3
7.
20 m2
18.
30 cm3
8.
12 cm2
19.
324 cm2
9.
174
20.
64 cm3
10.
112 cm2