primary 6 mathematics - outreach lesson publicationorlesson.com/orbook/outreach-p6-math.pdf ·...

Primary 6 Mathematics

Ace The Exams with My 24/7 Personal Tutor

Detailed Explanation of ALL Questions

by Tutor in Virtual Classroom

Consulting Editor: Dr Zhang Yong

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© Outreach Edusys Pte Ltd ALL RIGHTS RESERVED. No part of this book and the accompanying CDROM may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, CD duplication, replication, or by any information storage and retrieval system, without permission in writing from the Publisher. First Published 2010 ISBN: 978-981-4275-17-0 Published by: Outreach Edusys Pte Ltd (CRN: 200006571H) Distributed by: Outreach System Pte Ltd 20 Shaw Road, #07-03 Singapore 367956 Tel: +65 91162024 Fax: +65 35107345 Email: [email protected] Website: http://www.orlesson.org Please check URL regularly for new releases and promotions. Sample chapter and lesson for each title can be downloaded from above URL. Purchase online or call/SMS 9116-2024 today. FREE home delivery (one location within Singapore) for purchases above S$60/=.

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Preface

This book is written to assist pupils in preparing for the Primary 6 Math examinations. There are a total of 10 specially crafted examination style papers. The main features of the papers are as follows.

1. Questions are modeled after examination papers set by top well known Singapore schools.

2. Questions are crafted to highlight common misconceptions in each of

the topics. This book comes with a multimedia CDROM. The CDROM contains detailed explanation of each question in each paper by our teacher. These lessons ensure pupils understand the methods behind solving each question. Outreach Book Alive series brings the “tuition teacher” to you at zero cost. You may also want to try our online programme. These are interactive “diagnostic” modules consisting of multiple choice questions. The incorrect options to each question are carefully crafted using specific mis-conception in learners. If your child submit a wrong answer, our system will dynamically diagnose your child’s problem and bring him/her an explanation on why he/she is wrong, and what is the correct way to the solutions of such questions. Visit http://www.orlesson.org today.

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Contents Semestral Assessment 1 Mock Paper 1 Paper 1

Paper 2 1 8

Semestral Assessment 1 Mock Paper 2 Paper 1 Paper 2

17 26


35 43


52 60


68 76


83 93


103 112


121 131


139 147

Semestral Assessment 2 Mock Paper 5

Paper 1 Paper 2

155 164

Suggested Answers 174 Free Past Year School Exam Papers (from 2004 onwards) for download and print. Visit http://www.orlesson.org for links and download instructions. Subscribe to Outreach Lesson Online Access for hundreds of hours of lessons, and thousands of questions. Less than 70 cents a days for unlimited access to ALL subjects. For details, visit http://www.orlesson.org.

1

Midyear Examination: Mock Paper 1 Paper 1 (Duration: 50 mins)

Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.

1. How many ninths are there in 232

(1) 2 (2) 8 (3) 24 (4) 27 ( ) 2. The sum of length and width of a rectangle is an odd number. Which of the

following can be the perimeter of the rectangle? (1) 28 (2) 34 (3) 48 (4) 52 ( )

3. Express 5103 cm –

52 mm in mm.

(1) 52.6 mm (2) 49 mm (3) 5.26 mm (4) 4.9 mm ( ) 4. Annie has 4 boxes of sweets. She has 8, 12, 14, 6 sweets in the first box, second box,

third box and fourth box respectively. Calculate the average number of sweets in each box?

(1) 40 (2) 30 (3) 20 (4) 10 ( ) The table below shows the number of cakes which Mrs Lee, Mrs Soh, Mrs Liu and Mrs Kan made. Use the table to answer Questions 5 and 6.

Name Number of cakes Mrs Lee 10 Mrs Soh 7 Mrs Liu 13 Mrs Kan 9

5. How many cakes did Mrs Soh and Mrs Kan make? (1) 17 (2) 16 (3) 22 (4) 20 ( )

2

6. What is the difference between the number of cakes made by Mrs Lee and the number of cakes made by Mrs Kan?

(1) 4 (2) 6 (3) 1 (4) 3 ( ) 7. Express the ratio of 15 mm to 20 m in its simplest form. (1) 3 : 4 000 (2) 3 : 400 (3) 15 : 20 000 (4) 3 : 2 000 ( ) 8. Find the unit shape that forms the tessellation below.

(1)

(2)

(3)

(4)

( ) 9. The number of crayons which Betty, Chris, Linda have is in the ratio of 2 : 3 : 1.

How many crayons do Chris and Linda have if Betty has 12 crayons. (1) 18 (2) 24 (3) 30 (4) 36 ( ) 10. Two numbers A and B are the ratio of 5 : 8. If A = 20y, find the sum of A and B in

terms of y (1) 32.5y (2) 28y (3) 25.8y (4) 52y ( ) 11. Mrs Tan made some muffins and gave them to Bob and David. Bob received

41 of the number of muffins and David received

32 of the remainder. How many

muffins did Mrs Tan make if she had 9 muffins left? (1) 108 (2) 36 (3) 18 (4) 42 ( )

3

12. 4 rectangles and 2 squares are used to form the solid below Which of the following is not the net of this solid?

(1)

(2)

(3)

(4)

( ) 13. The table below shows the brands of 150 cars in the car park.

Brand Number of Cars BMW 20 Ford 35 Honda ? Huyndai 40 Toyota 15

How many Ford and Honda cars are there?

(1) 90 (2) 75 (3) 65 (4) 60 ( ) 14. Eddy has some 20-cent, 50-cent and $1 coins. The ratio of the number of the coins is

2 : 3 : 1 respectively. If Eddy has 120 coins in total, what is the value of all his 50-cent coins?

(1) $8 (2) $20 (3) $30 (4) $42 ( ) 15. Mary is 5 years older than her younger sister. If Mary will be n years old after 7

years, find their total age in term of n.

(1) (2n – 9) years old (2) (2n – 19 ) years old (3) (n – 9) years old (4) (n – 19) years old ( )

4

Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. 425 × 135 = 425 × 130 + 425 × q

Find the value of q.

Ans: _____________________17. What fraction of 7km is 55m? Express your answer in its simplest form.

Ans: _____________________18. Write 81 hundredths and 9 tenths as a decimal.

Ans: _____________________19. The distance between Ann’s school and her house is 3.6 km when it is rounded to 1

decimal place. The distance is less than 3.6 km. Write one possible value for the distance in metres.

Ans: ___________________m20. Uncle Koh put a rectangle fence around his farm. Its length and breadth is 20 m and

16 m respectively. He used posts to hold the fence. If he placed the posts 2 m apart, how many posts did he use?

Ans: _____________________

5

21. The cost of 3 T-shirts is $22. What is the cost of 42 T-shirts?

Ans: $___________________22. The table below shows the number of pencils sold last week.

No. of pencils 0 – 3 4 – 7 8 – 11 12 – 15 16 – 19 No. of customers 5 7 9 3 2

How many customers bought at least 8 pencils?

Ans: _____________________23. The average of 6 numbers is 15. The average decreases by 1 when the 7th number is

added. What is the value of the 7th number?

Ans: _____________________24. There are 80 colored papers in total. 25 of them are red papers. What percentage of

the papers is of the other colors?

Ans: _____________________

6

25. Simplify 28y – 3 – 9y + 25

Ans: _____________________ Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26. In a class,

74 of the students are boys. When 8 girls join the class, there are 43

students in total. How many boys are there in the class?

Ans: _____________________27. The normal price of a T-shirt is $15. During a sale, the price of that T-shirt is $9.

Benson bought 10 T-shirts during the sale. How many T-shirts fewer would he get had he spent the same amount of money during a non-sale period?

Ans: _____________________

7

28. A line of length 5 units is divided into 12 equal segments. Write a fraction to describe the length CD.

Ans: _____________________29. The table below shows a pattern of numbers

Column 1 Column 2 Column 3 Column 4

Row 1 2 4 6 8 Row 2 10 12 14 16 Row 3 18 20 22 24

In which column and row will the number 222 appear?

Ans: Column_______, Row____30. In order to make 6 muffins, Chris needs to use 500 g flour, 200 g butter, 100 g sugar

and 1 egg. What is the maximum number of muffins Chris can make if she has 2 kg flour, 1 kg butter, 1.5 kg sugar and 4 eggs?

Ans: _____________________

8

Midyear Examination 1: Mock Paper 1 Paper 2 (Duration: 1 hr 40 mins)

Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. The bar graph below shows the number of computers sold during the first 6 months

0102030405060708090

Jan Feb Mar Apr May Jun

Given that 65 computers were sold in March, represent this data on the graph.

2. The volume of the solid below is 336 cm3. Given that the height is 7 cm and the length is 8 cm. Find the area of the shaded face.

Ans: __________________cm2

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3.

The shape can be used to form the pattern on the right. One of the shapes does not fit into the tessellation. Shade it.

4. Given that AB is the line of symmetry, complete the figure below.

5. Ho Yuet and Hu Ting have 21 oranges in total. Ho Yuet has 5 oranges more than Hu

Ting. Find the ratio of the number of oranges Ho Yuet has to the number of oranges Hu Ting has.

Ans: _____________________

10

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. The average number of sweets, which Annie, Betty, Chris, Daisy, Emily and Linda

have, is 12. Mrs Fang gives 2 more sweets to Annie, 4 more sweets to Betty, 6 more sweets to Chris and so on, up to Linda. What is the new average number of sweets they have? (4 marks)

Ans: _____________________ 7. The table below shows the charges for printing services of shop A.

Number of pages Cost per pages

First 10 pages $0.50 Subsequent pages $0.35

Shami wants to print 3 sets of documents. Each document consists of 75 pages. How much does she need to pay? (4 marks)

Ans: _____________________

11

8. Find the sum of ∠ a, ∠ b, ∠ c, ∠ d, ∠ e, ∠ f and ∠ g in the diagram below. (4 marks)

Ans: ____________________o

9. The ratio of the height of Daniel to the height of Kelvin is 25 : 32. The ratio of the

height of Louis to the height of Kelvin is 31 : 32. If the height of Daniel is 1.25 m, what is the height of Louis? (3 marks)

Ans: ____________________m

12

10. The ratio of Matthew’s age to Jose’s age is 9 : 10. Matthew was 22 years old 5 years ago. In how many years will the ratio of Matthew’s age to Jose’s age be 14 : 15? (4 marks)

Ans: _____________________ 11. Mark, Kenvat, and Sandeep have an average mass of 63 kg. Sandeep’s mass is 6 kg

more than Mark’s mass. Kenvat’s mass is 3 kg less than Mark’s mass. Find the mass of Sandeep. (3 marks)

Ans: ___________________kg 12. Mrs Choon asked 3 carpenters to make some table tops for her coffee shop. The

dimensions of the table tops are shown below. How much wood is needed to make 25 table tops? The diagram is not drawn to scale. (4 marks)

Ans: __________________cm2

13

13. ABCD is formed by 40 small squares as shown below. Given that the area of ABCD

is 1 440 cm2, find the perimeter of each small square. (4 marks)

Ans: ___________________cm 14. In the figure below (not drawn to scale), ABCD is a rectangle, XAY is parallel to

UCV. Given that ∠BCV = 25o, find (a) ∠DCU (2 marks) (b) ∠BAY (2 marks)

Ans: (a)___________________(b)___________________

14

15. A 1.1 m square tank was 60% full of water. Water was added into the tank at the rate

of 4 litres per minute. At the same time, water began to leak from a crack at the base of the tank at the rate of 550 cm3 per minute. How long did it take to fill the tank completely? Give your answer to the nearest hours and minutes. (4 marks)

Ans: _______h________min 16. The current size of a box is 80 cm long, 60 cm wide and 40 cm high. Ann

reconstructs the box by reducing the length of the box by 40% while keeping the height the same. In order that the new box has the same volume as the current box, what are the dimensions of the new box? (4 marks)

Ans: _____________________

15

17. The patterns below start with a single square. At each stage, new squares are added

all around the outside.

Stage 1 Stage 2 Stage 3

(a) Complete the table below (1 mark) Stage 1 2 3 4 5 Number of squares 1 9 25

(b) How many squares are there in the 10th stage? (1 mark) (c) How many squares are there in the 70th stage? (2 marks)

Ans: (b)___________________

(c)___________________

16

18.

Kate, Susan, and Xu Bin had some sweets in the ratio of 6 : 4 : 5. Kate gave 41 of her

sweets to Susan and Xu Bin. After receiving Kate’s sweets, Susan had 10 sweets more than Kate while Xu Bin had 10% more sweets than before.

(a) After receiving sweets from Kate, what was the percentage increase of Susan’s sweets? (2 marks)

(b) How many sweets did Kate have at first? (2 marks)

Ans: (a)___________________

(b)___________________

17


Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. Seven million, four hundred and eighty thousand and ten in numeral is (1) 7 048 010 (2) 7 480 010 (3) 7 480 100 (4) 7 400 810 ( ) 2. Round off 9 875 567 to the nearest hundred (1) 9 875 600 (2) 9 876 000 (3) 9 875 500 (4) 9 875 570 ( ) 3. Given that A = 1.22 and D = 3.02. What is the value of B?

(1) 0.75 (2) 1.82 (3) 1.97 (4) 2.12 ( ) 4.

Find the value of Q where Q = 9 – 5503 .

(1) 3.96 (2) 3 5049

(3) 4503 (4) 3.94

( ) 5. What is the number in the box?

97502 = 10 ×

(1) 9.702 (2) 9.72 (3) 9.704 (4) 97.04 ( ) 6. The distance between Ann’s house and her school is 1.2 km further than the distance

between Venkat’s house and the school. What is the ratio of the distance between Ann’s house and the school to the distance between Venkat’s house and the school, if the distance between Ann’s house and the school is 2.8 km?

(1) 7 : 4 (2) 7 : 10 (3) 4 : 7 (4) 10 : 7 ( )

Marks

18

7. What fraction of 1.5 kg is 75g?

(1) 21 (2)

51

(3) 201 (4)

501

( ) 8. What fraction of the following figure is shaded area?

(1)

125 (2)

127

(3) 21 (4)

41

( ) 9. PQRS is a rectangle. Find ∠ x, given that y = 25o. The figure is not drawn to scale.

(1) 25o (2) 30o (3) 60o (4) 65o ( )

19

10. The cubic container below is filled with oil. The length between the oil surface and

the top face of the container is 12 cm. What is the volume of the oil in the bottle?

(1) 4 800 cm3 (2) 3 200 cm3 (3) 1 728 cm3 (4) 8 000 cm3 ( ) 11. Casper bought some stamps. His friend gave him 5 more. He then gave away 12 of

them to his brother. He put all his stamps equally into 8 envelops. How many stamps did he buy at first if each envelop has 4 stamps?

(1) 32 (2) 39 (3) 40 (4) 49 ( ) 12.

Mrs Kan used 103 of her rice to cook lunch. She used

43 of the remainder to cook

dinner. What percentage of her original rice did she have after cooking dinner? (1) 17.5 % (2) 5 % (3) 22.5 % (4) 52.5 % ( ) 13.

550 ml is 52 of a bottle’s volume. What is half of the bottle’s volume?

(1) 66 ml (2) 110 ml

(3) 687.5 ml (4) 1 375 ml ( )

20

14. The volume of the solid shown below is 4 500 cm3. What is the area of the shaded

parts?

(1) 500 cm2 (2) 360 cm2 (3) 900 cm2 (4) 430 cm2 ( ) 15. Lucy cut a 1.25-m ribbon into 25 equal pieces. How long is each piece? (1) 50 mm (2) 0.5 cm (3) 5 cm (4) 0.5 m ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Calculate the value of A, given A = 189 – 102 ÷ (25 – 8).

Ans: _____________________ 17.

Convert 13175 kg to grams and correct to 3 decimal places.

Ans: _____________________

21

18.

Bottle A is 53 filled with milk. Bottle B is

32 filled with coffee. Bottle A is three times

bigger than bottle B. What fraction of the milk is the coffee?

Ans: _____________________ 19. Express 150 l 150 ml in ml.

Ans: _____________________ 20. Express 0.7% as a decimal.

Ans: _____________________

22

21. During a sale, the price of a TV is reduced by 15%. Mr Liu bought a TV during the sale for $680. What is the normal price (not during sale) of the TV?

Ans: $____________________ 22. To bake a cake, Mrs Tan needs 300 g of sugar and 50 g of butter. Using the same

proportion, how much sugar does Mrs Tan need if she uses 200 g butter?

Ans: ____________________g 23. In the figure below AB, CD, EH, FG are straight lines. Given that ∠BOG = 25o and

∠COE = 15o, what is the sum of ∠AOC and ∠ FOH?

Ans: ____________________o

23

24. David’s height is equal to

43 of Ken’s height.

83 of Ken’s height is equal to

31 of

Terence’s height. What is the ratio of David’s height to Ken’s height to Terence’s height?

Ans: _____________________ 25. The solid below is formed by identical cubes. The area of the shaded face is 25 cm2.

What is the volume of the solid?

Ans: __________________cm3

24

Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.

Annie bought some stickers. Sticker set A is sold at $15 for every 4 stickers. Sticker set B is sold at $10 for every 3 stickers. Annie bought the same number of stickers from set A and set B. Given that she paid $85. How many stickers did she buy altogether?

Ans: _____________________ 27. Jia Wei bought 5 pencils and 7 notebooks and paid $21. A notebook costs $1.8 more

than a pencil. What is the cost of each pencil?

Ans: $____________________ 28.

At the market, Farmer A sold 125 of his eggs while Farmer B sold

165 of his eggs.

Given that they sold the same number of eggs. What is the ratio of the number of Farmer A’s eggs to the number of Farmer B’s eggs?

Ans: _____________________

25

29. How many Cube A are needed to fill the box in Figure B completely? The figures are

not drawn to scale.

Cube A

Figure B

Ans: _____________________ 30. A school library has 580 books. 25% of them are Mathematics books. Among these

Mathematics books, 20% are for P6. What fraction of the total number of books in the library is P6 Mathematics books?

Ans: _____________________

26


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1.

At a running challenge, Guo Yan covered 103 of the distance while Gu Jing covered

94 of the distance. They were 65 m apart. How far was Gu Jing from the finishing

point?

Ans: ___________________m 2. A rectangle is formed by bending a 144-cm wire. The ratio of its breadth to its length

is 5 : 7. Find the length and breadth of the rectangle.

Ans: _____________________ 3. The ratio of Suet Mei’s age to her two sisters is 11 : 14 : 15. Suet Mei is 22 years old.

What is the total age of the three sisters in 5 years’ time?

Ans: _____________________

27

4. PQRS is a parallelogram. PQ = PO. Find ∠ POS

Ans: _____________________ 5. Extend the tessellation by drawing five more unit shapes in the box below.

Ans: _____________________

28

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. (a) In the space below, draw a parallelogram in which AB = 10 cm, AD = 6 cm

and ∠BAD = 60o. The line AB is drawn for you. (2 marks)

(b) Measure the length of AC. (2 marks)

Ans: (b)___________________ 7. A muffin is $1.50 less than a cake. The total cost of a cake and a muffin is $3.10.

Mrs Lee wants to buy 10 cakes and 15 muffins for her students. How much does she need to pay? (4 marks)

Ans: $____________________

29

8. The ratio of the number of yellow pencils to the number of green pencils was 3 : 4. After adding 10 more yellow pencils, the number of green pencils is half of the number of yellow pencils. How many pencils were there before adding more pencils? (4 marks)

Ans: _____________________ 9. A rectangular tank 20 cm long, 15 cm wide and 18 cm high was completely filled

with water. Worker A poured away 81 of the water. Worker B, then came and filled

the tank up with another 0.5l. Find the volume of the water in the tank now. (4 marks)

Ans: _____________________

30

10. In a stadium,

53 of the audience are female.

31 of them are girls. What is the

percentage of women in the stadium? (4 marks)

Ans: _____________________ 11.

Andie cut a 27-cm ribbon from his long ribbon. He then cut and gave away 52 of the

remaining ribbon. If the length of the ribbon after the two cuts was 61.5 cm, what was the original length of the ribbon? (4 marks)

Ans: __________________cm

31

12. Pentagon A, rectangle B and triangle C formed the figure below. The ratio of the

area of A : B : C is 6 : 5 : 3. If 41 of C is shaded, what fraction of the figure is un-

shaded? The figure is not drawn to scale. (4 marks)

Ans: _____________________ 13. ABCD is a trapezium. AOD and BOM are straight lines. Given that ∠ABM = 15o

and ∠ADC = 65o. Find (a) ∠DOM. (1 marks) (b) Given that ∠OCD = 20o, find ∠BOC. (2 marks)

The figure is not drawn to scale.

Ans: (a)___________________(b)___________________

32

14. Mr Chen wants to buy a car priced at $35 000. If he made a full payment, he can get

a discount of 5%. If he pays by installments, he needs to pay 10% of the bill and 24 monthly installments of $1 500 each. Moreover, he cannot get any discount. How much can Mr Chen save if he pays in full? (3 marks)

Ans: $___________________ 15. Betty had a total of 18 books and notebooks. The number of books was 4 more than

the number of notebooks. She gave 2 books to her younger sister and some notebooks to her cousin. The number of books is three times the number of notebooks after this. How many notebooks did Betty give to her cousin? (4 marks)

Ans: _____________________

33

16. A cubical tank of edge 30 cm is

32 filled with water. Some water is added to the tank.

After adding, the volume of water in the tank is 43 of its capacity. What is the

increase in the height of the water level in the tank? (4 marks)

Ans: ___________________cm 17. The ratio of the number of red papers to yellow papers in package A was 10 : 9. The

ratio of the number of red papers to yellow papers in package B was 5 : 6. The ratio of the number of papers in package A to the number of papers in package B was 19 : 33.

(a) Find the ratio of the number of yellow papers in package A to the number of yellow papers in package B. (2 marks)

(b) After adding 4 more red papers into package B, the ratio of the number of red papers to yellow papers in package B increased to 17 : 18. How many red papers were there in package B at first? (2 marks)

Ans: (a)___________________(b)___________________

34

18. Some beans and sticks are arranged in the pattern shown below.

Pattern 1 Pattern 2 Pattern 3 …… (a) Complete the table below to show the number of beans and sticks in Pattern 8

and 9 (2 marks) Pattern 1 2 3 8 9 Beans 2 3 4 Sticks 1 3 5

… … …

(b) How many more sticks are there in Pattern 150 than in Pattern 100? (1 marks) (c) How many sticks are there in Pattern 1000? (1 marks)

Ans: (b)___________________(c)___________________

35


Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. Round off 4 548 600 to the nearest hundred thousand. (1) 4 549 000 (2) 4 550 000 (3) 5 000 000 (4) 4 500 000 ( ) 2. Arrange 6, 6.4, 6.04 in descending order. (1) 6, 6.4, 6.04 (2) 6.4, 6.04, 6 (3) 6.04, 6.4, 6 (4) 6, 6.04, 6.4 ( )

3. 6m is the average of 3 numbers. Assumed that two of those numbers are 5m and 4. What is the value of the third number?

(1) 9m (2) m – 4 (3) 13m – 4 (4) 9 ( ) 4. Which of the following can be folded to form a cuboid?

(1)

(2)

(3)

(4)

( )

36

5. How long is a show which starts at 11.30am and ends at 2.25pm? (1) 3h 55 min (2) 2 h 55 min (3) 9h 55 min (4) 9 h and 05 min ( ) 6. The figure below is drawn with 3 semicircles. Calculate the perimeter of the figure.

(Take π = 722 )

(1) 44 cm (2) 14 cm (3) 33 cm (4) 66 cm ( ) 7. The average of 10, _________, and 7 is 19. What is the missing number? (1) 40 (2) 3 (3) 2 (4) 41 ( ) 8. Which of the following fractions is the smallest?

(1) 43 (2)

74

(3) 53 (4)

94

( ) 9. Country A has 60 000 men and 40 000 women. What percentage of the excess men

to women is there in the country? (1) 20% (2) 50% (3) 33.33% (4) 66.67% ( ) 10. Andy, Bob and Carol each had certain amount of money which are in the ratio 3 : 4 :

5 respectively. Carol had $60 more than Andy. What was the total amount of money they have?

(1) $90 (2) $720 (3) $180 (4) $360 ( )

37

11. A tank measures 19 cm by 32 cm by 40 cm. It is 60% full with water. How much

more water is needed to fill the tank completely? (1) 14 592 cm3 (2) 14680 cm3 (3) 9 728 cm3 (4) 12350 cm3 ( ) 12.

The below figure is the net of a cube. Which one of the arrows is opposite the face of the cube?

(1)

(2) (3)

(4)

( ) 13.

Bob used 54 of his money to buy books and 15% of the remainder to buy pens. What

was the ratio of the amount of money spent on pens to the amount of money spent on books?

(1) 3 : 16 (2) 3:100 (3) 3 : 80 (4) 3:50 ( ) 14. Jane usually cycles from her home to school at an average speed of 10 km/h. Her

school is 321 km away from her home. If she wants to arrive in school at 9 a.m, at

what time must she set off from her home? (1) 8.25 a.m (2) 8.39 a.m (3) 8.30 a.m (4) 8.21 a.m ( )

38

15. Mrs Tay had

25 kg of rice. She used

103 of them to cook lunch and

41 of it to cook

dinner for her family. How many kilogrammes of rice did she have left to cook for the following day?

(1) 183 (2) 1.125

(3) 1.95 (4) 167

( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Edward used 6 squares of side 4 cm to form the figure below. Calculate the perimeter

of the figure.

Ans: _____________________ 17. Find the result of this subtraction: 9.03 – 0.76

Ans: _____________________ 18. In 15 minutes, 60 pages can be printed. How many pages can be printed in 1 hour?

Ans: _____________________

39

19. The cuboid shown below is made up of 4 identical cubes of sides 7 cm. What is the

volume of the cuboid?

Ans: _______________ cm3

20. Calculate the perimeter of the figure shown below in terms of x

Ans: ___________________cm 21. A movie shown on TV lasted 1 hr and 50 min. It ended at 11.30 a.m. When did the

movie start?

Ans: _____________________

40

22.

Mrs Chen kept 87 of a cake for her four kids. She divided the cake equally among

them. What fraction of the cake did each child get?

Ans: _____________________ 23. Express 75 cents as a fraction of $1.60

Ans: _____________________ 24.

In order to have 52 of the below figure shaded, how many more squares need to be

shaded?

Ans: _____________________ 25. Mr Tan drove 30 minutes at a speed of 60 km/h and 60 minutes at a speed of 80

km/h. Find the total distance he travelled?

Ans: _________________km

41


A rectangular water tank has a base area of 9.4 m2 and a height of 2m. When the tank

is 43 full, what is the volume of water inside?

Ans: __________________m3

27. When y = 6, calculate:

17y + 5

3y - 9 – 8y

Ans: _____________________ 28. At 7.30pm, Sandeep left Singapore to drive up to Cameron Highlands which is 625

km away. His speed was 75 km/h. At what time did he reach Cameron Highlands?

Ans: _____________________

42

29. A, B, C, D in the figure shown below are the centres of 4 identical semicircles. The

radius of each semicircle is 14cm. Find the perimeter of the figure. (Take π = 722 )

Ans: _________________cm 30. Vicky went to the bookstore to buy some new pens. After buying 4 pens, she had $2

left. If she had bought 6 pens, she would need $2 more. What was the cost of the pen that Vicky bought?

Ans: $____________________

43


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Carpenter Ben wants to cut as many 5-cm cubes as possible from the rectangular

block of wood measuring 40 cm by 28 cm by 22 cm. What is the maximum number of 5-cm cubes that he can cut from the original rectangular block?

Ans: _____________________ 2. What is the average amount of money Ivan and James have if Ivan has $450 and

James has $200 more than Ivan?

Ans: $____________________ 3. 7 : 8 is the ratio of Albert’s height to that of David’s height. The ratio of David’s

height to that of Kelvin’s height is 6 : 5. Find the ratio of Albert’s height to that of Kelvin’s height.

Ans: _____________________

44

4. 60% of A is 40% of B. If B - A is 25, what is the total value of A and B?

Ans: _____________________ 5. To celebrate its 1st birthday, a shop gave a discount of 20% at each sale. With the

membership card, member could get a further 15% discount on the discounted price. The usual price of a watch was $300. How much did James need to pay for the watch with his membership card?

Ans: _____________________

45

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. The parking charges at Union Plaza’s car park is shown below.

Parking charges Monday – Saturday (before 5pm)

$1.05 for first hour $0.25 for subsequent 15 min or part thereof

Monday – Saturday (after 5pm)

$2.10 per entry

Sunday $2.50 per entry (a) Mrs Won parked her car from 2 p.m to 3.30 p.m on Tuesday and from 9 a.m

to 11 a.m on Sunday. How much did she need to pay altogether? (2 marks) (b) Mr Liu parked his car from 3 p.m to 7 p.m on Thursday. How much did he

pay for his parking slot? (2 marks)

Ans: (a)$_______________(b)$_______________

7. Salim took part in a triathlon. During the swimming event, he swam 3w m in total.

He then cycled 500m more than the distance he had swum. Finally, he ran 3 times as far as he had swum.

(a) Find the total distance Salim covered for all 3 events in term of w. (2 marks) (b) Find the total distance Salim covered for all 3 events if w = 400. (2 marks)

Ans: (a)_______________m(b)_______________m

46

8. Peter spent $40 on a textbook and

41 of the remainder on a pen. He still had

31 of his

original amount of money left. Find his original amount of money. (3 marks)

Ans: _____________________ 9. O is the centre of a square ABCD. M, N, P, Q are the mid-points of AB, BC, AD,

CD.

(a) What is the ratio of the area

of triangle MNO to the area of the square ABCD? (2 marks)

(b) If the area of ABCD is 25 cm2, what is

the total area of the 3 triangles MNO, APO and COQ? (2 marks)

Ans: (a)________________(b)________________

47

10. The line graph shows the total number of pens that a shop sold during a week.

0

5

10

15

20

25

30

35

Mon Tue Wed Thu Fri Sat Sun

(a) In which 2 days were the same number of pens sold? (1 marks) (b) Find the ratio of the number of pens sold on Wednesday to the number of

pens sold on Friday. (1 marks) (c) Find the percentage decrease in the number of pens sold from Saturday to

Sunday. (2 marks)

Ans: (a)___________________

(b)___________________(c)___________________

48

11. Lauren used 4 pieces of string to form the below shaded figure. Each string is a quarter circle of radius 5 cm.

(a) Find the perimeter of the shaded figure. (2 marks)

(b) Find the area of the shaded figure. (Take π = 722 ) (2 marks)

Ans: (a)________________cm(b)_______________cm2

12. The monthly expenditures of Ken and Daniel are the same but Ken’s monthly

income is $250 more than Daniel. Each of them spends $500 a month. After a period of time, Ken has saved $1350 while Daniel has saved $600.

(a) How long did Daniel take to save the $600? (1 marks) (b) What is Ken’s monthly income? (2 marks)

Ans: (a)_________________(b)$________________

49

13. Alice has some Singaporean and some Japanese stamps. The ratio of the number of

her Singaporean stamps to the number of Japanese stamps was 2 : 3. After giving away 30 Singaporean stamps and 30 Japanese stamps, that ratio becomes 5 : 9

(a) How many Singaporean stamps does Alice have at first? (2 marks) (b) Find the total number of Japanese stamps that she has left. (2 marks)

Ans: (a)_________________(b)_________________

14. In an event organized by 3 schools A, B and C, 30% of the participants were from

School A. The number of participants from School B was 10% more than the number of participants from School A. There were 222 participants from School C. How many students took part in this event? (4 marks)

Ans: _____________________

50

15. The admission fee to a sport game was $10. Students from School ABC have support

from their school, so they just needed to pay $5. A total of $2340 was collected. The ratio of the number of students from school ABC to the ratio of students from other schools was 4 : 7. Find the number of students from School ABC that took part in the game. (4 marks)

Ans: _____________________ 16. The patterns below are made up of stars and sticks.

Stage 1 Stage 2 Stage 3 Stage 4

(a) Complete the following table (2 marks) Stage Number of stars Number of sticks

1 1 4 2 4 12 3 9 24 4 16 40 5 6

(b) How many stars and sticks are there in Stage 100? (2 marks)

Ans: (b)__________________

51

17. Some flowers were given to Ann, Bethesda, Carol and Daisy. Ann received 180

flowers. Bethesda received 80 fewer flowers than Carol. 30% of the total number of flowers was given to Carol. Daisy received 20% of the total number of flowers. How many flowers did Bethesda receive? (4 marks)

Ans: _____________________ 18. The distance between Alice’s house and Ben’s house was 480km. At 9.30 a.m, Alice

left her house driving at a constant speed. Ben left his house at the same time and travelled towards Alice’s house. They met each other at 1.30pm. Ben drove at 20 km/h faster than Alice. What was the speed of Ben’s car? (4 marks)

Ans: _____________________

52



1. What is the value of x? 47 768 = 40 000 + 7 000 + x + 8

(1) 700 (2) 760 (3) 600 (4) 76 ( ) 2.

Express 6103 km in metres.

(1) 6 030 m (2) 6 003 m (3) 6 300 m (4) 630 m ( )

3. Dan has a bag of 20-cent coins. They add up to give a total value of $22.40. Calculate the total number of 20-cent coins Dan has.

(1) 112 (2) 224 (3) 56 (4) 448 ( ) 4. How many of the following figures can be folded to form a pyramid?

A B C D (1) 1 (2) 2 (3) 3 (4) 4 ( )

Marks

53

The graph below shows the number of pens sold by a stationery shop in 5 working

days. Use the graph to answer Questions 5 and 6

0102030405060708090100110120130140150160170180190

Monday Tuesday Wednesday Thursday Friday

5. How many pens were sold on Monday and Friday? (1) 300 (2) 295 (3) 290 (4) 285 ( ) 6. What is the average number of pens sold in the 5 days? (1) 740 (2) 148 (3) 750 (4) 285 ( ) 7. Miao Xing cycles 25 min from his house to his school every day. His school is 2 800

m away from his house. What is his speed? (1) 6.72 km/h (2) 8.4 km/h (3) 11.2 km/h (4) 70 km/h ( ) 8. During a sales promotion, a watch is sold at $240 instead of $300. Find the

percentage decrease during the promotion. (1) 20% (2) 125% (3) 80% (4) 120% ( )

54

9. Simplify 9 + 10a – 5 – 8a (1) 19a – 13 (2) 4 + 2a (3) 4 – 2a (4) 19a + 13 ( ) 10. A teacher said, “There are 25 girls and 15 boys in my class.” What percentage of the

children are girls in that class? (1) 62.5% (2) 37.5% (3) 60% (4) 25% ( ) 11. A is half of B. B is half of C. C is half of D. Which of the statement is correct?

1/. A is 41 of C

2/. D is 4 times of A 3/. D is 4 times of B

4/. A is 41 of D

(1) 1 (2) 2 and 3 (3) 4 (4) 1 and 3 ( ) 12.

Mr Liu drove 31 hour at the speed of 60km/h. He then decreased the speed to 50 km/h

and drove another 100 km at that speed. What was his average speed for the whole journey?

(1) 180 km/h (2) 55 km/h

(3) 5173 km/h (4) 52 km/h

( ) 13. In the figure below, MNO is a triangle, MOPQ is a rectangle. Which of the following

pairs of lines are not perpendicular?

(1) OP and PQ (2) MN and MO (3) MO and MQ (4) MQ and QP ( )

55

14. James bought a car which has usual price of $75 000. Because of a promotion, he got

the car at a 10% discount. A few months later, he sold the car and made a 5% gain. How much did he sell the car for?

(1) $71 300 (2) $71 250 (3) $71 000 (4) $70 875 ( ) 15. Students are required to measure their footsteps during a mathematics activity lesson.

After the lesson, Benson found that each of his footsteps was 40 centimetres on the average. To cover 1950 metres on the road, how many steps does he need to take?

(1) 4 875 (2) 780 (3) 48.75 (4) 78 000 ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Evaluate 66 – (18+22) ÷4

Ans: _____________________ 17.

The total age of Andrew and Bernoulli is 48, and Andrew is 75 of Bernoulli’s age.

How old is Andrew?

Ans: _____________________ 18.

Express 4025 as a decimal.

Ans: _____________________

56

19. For every 4 apples sold, a shop owner earns $1.25. If he sells 200 apples, how much

can he earn?

Ans: $______________________ 20. Express 5kg 5g + 25g in kg

Ans: ___________________kg 21. What is the volume of the cuboid shown below?

Ans: ___________________cm3

22.

In a secondary class, 60 students are allowed to choose a place to visit during vacation, as shown in the table. If each child is able to visit only one place, how many more students plan to visit China than Indonesia?

Place Number of student China 20 Japan 12

Thailand 10 Indonesia ?

Ans: _____________________

57

23. The table below shows the parking charges in a car park.

8am to 10pm – First hour $2 8am to 10pm – Every subsequent half an hour or part thereof $1.50

How much must Mr Tan pay if he parks his car in the car park from 1.30pm to 3.25pm.?

Ans: $____________________ 24. In a final test, Zhao Peng scored 48 marks which were 80% of the total score. What

was the total score of this test?

Ans: _____________________ 25. Mary bought some ice-creams in a shop at the price of $2.50 each. After giving the

cashier $20, she received $x change. Express the number of ice-creams that she bought in terms of x.

Ans: _____________________

58


In figure below calculate the perimeter of the largest semicircle in terms of .

Ans: _____________________ 27. Mary is given a large rectangular sheet of size 36 cm by 24 cm to cut into smaller

rectangular pieces of size 6cm by 4cm. What is the greatest number of the smaller pieces that she can make from the large sheet?

Ans: _____________________ 28. Joey initially had a certain number of candies. His mother gave him 20 more. He in

turn gave 5 to his brother. He found he now has twice his original number of candies. How many candies did Joey have initially?

Ans: _____________________

59

29. In a car park, there are 240 cars and motorbike. There are 680 wheels in total. How many cars and motorbike are there in the car park?

Ans: _____________________ 30. A square ABCD with side 6 cm is shown in the figure below.

If AB // EF // CD and AE = EB = DF = FC. Find the area of the shaded region.

Ans: ___________________cm2

60


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. The ends of the prism below are equilateral triangles. Find the area of the smallest

sheet needed to cover the prism except for the two ends.

Ans: __________________cm2

2. The chart shows the number of computers sold by a shop during the first 6 months of

a year. What is the average number of computers sold during that period?

0

10

20

30

40

50

60

70

80


Ans: _____________________

8 cm

20 cm

61

3. Six faces of a cube are shown in the following figure. Write down a possible group

of 2 faces that are opposite to each other.

Ans: _____________________ 4. If the inner angle is 120o, what is the value of angle y?

Ans: _____________________ 5. Given the sides of cube A is five times the sides of cube B, find the ratio of the

volume of cube A to the volume of cube B.

Ans: _____________________

62

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. A medium-size cake is made from 2 eggs and a big one is made from 3 eggs. How

many cakes of each size can be made with 13 eggs? There should be no leftover. (3 marks)

Ans: _____________________ 7. The table below shows the sale of chips:

Type of packet Price per packet Number of

packets sold Small $1 68

Medium $2 50 Big $3 55

How much money did the shop collect from the total sale of the chips? (3 marks)

Ans: _____________________

63

8. A garden ABCDE is shown in a grid consisting of 2-m squares. What is the area of

the garden? (4 marks)

Ans: _____________________ 9. (a) Draw a triangle ABC in the space below, with AB = 6cm, BC = 3cm, and angle

ABC = 120o. (2 marks)

(b) Measure and write down the length of AC. (2 marks)

Ans: _____________________

64

10. Harry has three electric bells. The first one will ring every 3 seconds, the second will

ring every 8 seconds and the last one needs 10 seconds to ring again. If all of them ring at 12am, when will be the earliest that they will ring together again? (4 marks)

Ans: _________________h 11.

A boy had a packet of 320 candies with 2 different flavours. 167 were orange flavour

and the rest were lemon. He gave his friend 30 orange candies and some lemon ones. As a result, the ratio of the number of orange candies to that of lemon became 11: 15. How many lemon candies did he give his friend? (4 marks)

Ans: _____________________ 12. A police car is trying to catch up with a motorbike which is 45 m ahead. In a unit of

time, the police car moves 38m while the motorbike moves 23m. How many units of time does the police car need to catch up with the motorbike? (4 marks)

Ans: _____________________

65

13. Two brothers, John and Jerry, cycle to school at speeds of 12km/h and 10km/h

respectively. John left home at 6am, and arrived in school at 6.30am. When John arrived in school, his brother was 1.5 km away from school. What time did Jerry leave home? (4 marks)

Ans: _____________________ 14. ABCD is a rectangle. Given that the ratio of ∠CNM to ∠BNM is 3 : 1, find

∠BMN. The figure is not drawn to scale. (4 marks)

Ans: _____________________

66

15.

There are 2 bookcases. The number of books on the left bookcase is equal to 37 of the

number of books on the right one. After moving 100 books from the left bookcase to

the right bookcase, the ratio changes to41 . Subsequently, 75% of books in the right

bookcase are moved out. a) What is the total number of books in both 2 bookcases initially? (2 marks) b) How many books are there in the right bookcase finally? (2 marks)

Ans: _____________________ 16. Study the number pattern below:

Position 1st 2nd 3rd 4th 5th 6th 7th 8th 9th Number 8 11 14 17 20 23 26 29 32

What is the number in 100th position? (4 marks)

Ans: _____________________

67

17. Find the area of the shaded regions. Take = 3.14. (4 marks)

Ans: ______________________ 18. Three students Annie, Betty and Chris had some books that their Mathematics

teacher gave. Annie got 31 of the number of books that Betty and Chris received.

Betty got 51 of the number of books which Annie and Chris received. If Chris

received 5 books more than Betty, how many books in total did the teacher gave the three students? (4 marks)

Ans: _____________________

68


Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. What is the missing number in the box?

100 x 7 + 77000 : = 777 :1 (1) 1 (2) 10 (3) 100 (4) 1 000 ( ) 2.

12 x115 has the same value as _______________.

(1) 12 x 111 +

115 (2) 5 x

115 + 5 x

117

(3) 5 x 115 + 5

112 (4) 5 x

1112 - 7 x

115

( ) 3. Jane was born on 17 September 1996. How old will she be on 17 January 2010? (1) 14 yr 4 mth (2) 14 yr 5 mth (3) 13 yr 4 mth (4) 13 yr 5 mth ( ) 4. Express 0.16% as a decimal (1) 0.00016 (2) 0.0016 (3) 0.016 (4) 0.16 ( ) 5. Find the ratio of 9cm to 27m (1) 1 : 3 (2) 1: 30 (3) 1 : 300 (4) 1 : 3000 ( ) 6. The ratio of P to R is 5 : 7 and Q to P is 5 : 3. What is the ratio of R to Q to P? (1) 7 : 5 : 3 (2) 21 : 25 : 15 (3) 15 : 35 : 20 (4) 5 : 7 : 3 ( ) 7. Timer A beeps every 3 minutes while timer B beeps every 5 minutes. Both timers

beeped at 9.30 a.m. When is the next time they will beep together again? (1) 9.38 a.m (2) 9.45 a.m (3) 9.35 a.m (4) 9.33 a.m ( )

69

8. Harris intends to reduce his mass by 20% to 78kg after 6 months. What is Harris’s

original mass? (1) 97.5 kg (2) 93.6 kg (3) 100 kg (4) 90 kg ( ) 9. Ken is training for his running competition. He can run round a 500-metre track 6

times in 18 minutes. How long does he take to run 1000 m? (1) 40 min (2) 6 min (3) 10 min (4) 26 min ( ) 10. Which of the following nets will form the figure below?

(1)

(2)

(3)

(4)

( ) 11. A lorry took 75 minutes to travel from Town X to Town Y at 60 km/h. It then

travelled another 50 km at a speed of 75 km/h to Town Z. What was the average speed of the lorry for the whole journey?

(1) 6721 km/h (2) 63

117 km/h

(3) 7032 km/h (4) 71

75 km/h

( )

70

12. The ratio of X to Y is 2 : 3. When X was halved and Y was increased by 15, they are

in the new ratio is 3 : 14. What is the original value of X + Y? (1) 57 (2) 25 (3) 47.85 (4) 45 ( ) 13. Given the below figure:

54 of the bigger hexagon is un-shaded while

43 of the smaller hexagon is shaded.

What is the ratio of the shaded part of the figure to the un-shaded part of the figure?

(1) 3 : 13 (2) 13 : 16 (3) 1 : 2 (4) 3 : 4 ( ) 14. The line graph below shown the number of laptops sold during the first 6 months of

the year.

0255075

100125150175200225250275300325350375400


During which 1-month period was there a 40% increase in the number of laptops sold?

(1) Jan to Feb (2) Feb to Mar (3) Mar to Apr (4) May to Jun ( )

71

15. Sarah had some green and pink T-shirts. 25% of her green T-shirts and 40% of her

pink T-shirts were made in China. Given that 53 of her T-shirts were green and the

rest were pink, what percentage of her T-shirts were made from countries other than China?

(1) 69% (2) 31% (3) 55% (4) 35% ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Simplify 7y + 25 – 6y – 8 + 19y

Ans: _____________________ 17.

Express 143 h in minutes.

Ans: __________________min 18. What is the reading indicated on the speed scale below?

Ans: _________________km/h

72

19. Coloured Korean paper is sold at 50g for $1.70 in a shop. How much would 1kg

200g of the paper cost?

Ans: $____________________ 20.

74 of A is more than 25% of A by 18. What is A?

Ans: _____________________ 21. The distance between City A and City B is 200km. A taxi started the journey at 8

a.m to travel from City A to City B at 75 km/h. At what time did the taxi reach City B?

Ans: _____________________ 22. Ann has some red and yellow origami papers. The ratio of the number of red paper to

the number of yellow paper is 2 : 3. After using 31 of the red paper and

51 of the

yellow paper, what is the new ratio of the number of red paper to the number of yellow paper?

Ans: _____________________

73

23. The net of the cube is shown below

Draw the missing symbol on the top face of this cube

Ans: _____ _________ 24. Students from Schools A, B and C participate in a Mathematics challenge. There are

20 more students from School C than School A. 25% of the total students are from School A, 40% of them are from School B and the rest are from School C. How many students are from School B?

Ans: _____________________ 25. It is 23 15 in Bangkok when it is 00 15 in Singapore. The flight from Singapore to

Bangkok took 2h 35 min. Mr Koh left Singapore at 11 30 to fly to Bangkok. Due to the bad weather, the plane landed 21 minutes late. What time was in Bangkok when the plane landed?

Ans: _____________________

74


Mrs Kan bought some small cheese cakes and blueberry muffins for her daughter’s birthday party. The ratio of the number of cheese cakes to the number of blueberry muffins is 13 : 7. The number of cheese cakes and blueberry muffins could be equal if she bought 36 more blueberry muffins. How many cheese cakes did Mrs Kan buy?

Ans: _____________________ 27. A shop had a piece of cloth with length (120 + 7k) cm. Ms Chan bought 3k cm for

her daughter and Ms Lee bought 0.8 m for a shirt. The remaining length was cut into 4 pieces as ordered by Ms Soh. What was the length of each piece in terms of k?

Ans: __________________cm 28. The distance between Seng Choon’s house and her school is 670 m. Every day, she

walks at an average speed of 75 m/min to school. On rainy days, she takes a sheltered route which is 140 m longer. How long does she take to go to school on rainy days?

Ans: _________________min

75

29. ABC is a triangle. M, N, P, Q, R are mid-points of AB, AC, BC, MN, BP

respectively. What percentage of the triangle is shaded?

Ans: __________________% 30. A T-shirt shop has a promotion. A customer receives a 20% discount for the fifth and

sixth T-shirt with every six pieces purchased. Each T-shirt costs $18. How much does a customer need to pay for 6 T-shirts?

Ans: _____________________

76


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1.

In the figure below, not drawn to scale, MA = MC, ∠ACN = 41∠ACM. Find

∠ACN.

Ans: _____________________ 2. The product of 5 numbers is 60. The first three numbers are 4, 5, and n. What is the

product of the last 2 numbers in terms of n?

Ans: _____________________ 3. A watch costs $250. A new version of the watch cost $310. By what percentage is

the price of the watch raised?

Ans: __________________%

77

4. To travel from Town A to Town B, 350km away, Mr. Lim takes 5 hours. If Mr Lim

increases his speed by 5 km/h, how long will he take to reach Town B?

Ans: ________h_______min 5. Each day, Xiao Chen saved 5 more 10-cent coins than the previous day. She started

saving with three 10-cent coins on the first day. How much money would she saved on the tenth day?

Ans: _____________________ For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. In the figure below, not drawn to scale, ABC is an equilateral triangle with a

perimeter of 18 cm. M, K, H, O are the mid-points of BC, AB, AC, AM respectively. The length of KH is 3 cm. The length of AM is 5.2 cm. AM is 4 times longer than PN. Find the area of the quadrilateral BKHP.

Ans: _____________________

78

7. Andrew, Bob and Casey participated in a 250-metre race. Andrew was the fastest.

When he finished the race, Bob and Casey were 60 m and 80 m away from the finishing line respectively. When Bob reached the finishing line, how far was Casey from the finishing line? Assuming that all the boys were travelling at a constant speed throughout the race.

Ans: _____________________ 8. Chris, Jen and May have a total height of 45y cm. The average height of Chris and

Jen is 145cm. (a) In terms of y, how tall is May? (b) Given that y = 9 cm. Find the exact height of May.

Ans: (a)_________________(b)_________________

9. Ann had some candies. She gave 25% of her candies and another 4 more to her

sister. She gave 73 of what was left to her close friend. Ann had 32 left for her

mother. How many candies did Ann have in total?

Ans: _____________________

79

10.

21 of Linda’s coloured pencils was equal to

31 of Emily’s coloured pencils. The

difference between the numbers of pencils which they have is 4. Linda and Emily paid a combined total of $40 for the pencils. Given that each colored pencil costs the same, how much did Emily pay for her pencils?

Ans: _____________________ 11. There were 1500 people in a stadium. 45% of them were men. How many more men

had to come to the stadium if the percentage of men would increase to 50%?

Ans: _____________________ 12. ABCD is a parallelogram. ∠EAB is a right angle. Given that DA = DE. Find ∠ x

Ans: _____________________

80

13. A candy shop sells 3 kinds of candies; fruit, milk and coffee candies. 43% of them

were fruit candies. The number of milk candies is 228. There were 50% fewer milk candies than coffee candies. How many percent more fruit candies than milk candies were there? Correct your answer to the nearest whole number.

Ans: _____________________ 14. The distance between Singapore and Malacca is 260 km. Mr. Smith travelled from

Singapore to Malacca. For the first 2 hours, Mr. Smith travelled at the speed of 60 km/h. Then, he decided to increase his speed. He took a total of 4 hours to reach Malacca. What was his average speed for the remaining part of the journey?

Ans: _____________________ 15. The distance between Albert’s house and David’s house was 800 km. At 10am,

Albert left his house and drove towards David’s house at 70 km/h. David left his

house 41 h later and drove towards Albert’s house at 75 km/h. What time would they

meet if they drove at the same speed without stopping? Leave the answer in 24-hour clock and correct to the nearest minute.

Ans: _____________________

81

16. Matthew has 1 rectangle and 2 circles as shown below. The breadth and length of the

rectangle are 6cm and 8cm respectively. The diameters of two circles are 4 cm and 5 cm.

He then cut each circle into half and place 4 half circles side by side with the rectangle. Find the perimeter of the new shape. Take π = 3.14.

Ans: _____________________

82

17. Motorist A was driving at 30 km/h faster than motorist B. When motorist A reached the finishing line after 3 hours, motorist B had 25% length of the race to complete.

(a) What is the total distance of the race? (b) Calculate the average speed of motorist B.

Ans: (a)_________________(b)_________________

18. A cake box contained 2 kinds of cake: strawberry and chocolate. If 2 strawberry

cakes were to be given to a kid, then the ratio of the strawberry cake and chocolate

cake was 5 : 8. If 6 chocolate cakes were to be removed, then 115 of the cakes in the

box would be chocolate cakes. If another 4 strawberry cakes were to be put into the box, what fraction of all the cakes would be strawberry cakes?

Ans: _____________________

83

Preliminary Examination: Mock Paper 1 Paper 1 (Duration: 50 mins)


1. Find the value of 75 x

118 ÷ 2

(1) 7720 (2) 2

76

(3) 72 (4)

7740

( ) 2.

Daisy spent 51 of her money on a blouse and

245 of the remainder on a skirt. How

much did the blouse cost if she had $57 left? (1) $19 (2) $28 (3) $18 (4) $31 ( )

3. Annie has y candies. Liz has 6 candies less than Annie. What is the average amount of candies each girl has?

(1) 2

6−y (2) y – 3

(3) 2y – 6 (4) 2

6 y−

( ) 4. In a competition, Dan swam 800 m, ran 11 km and cycled 30 km. What was the total

distance covered? (1) 841 m (2) 41.8 km (3) 8.41 km (4) 418 m ( ) 5. Chris needs 17 cm of ribbon to make a flower. How much ribbon does she need to

make 20 flowers? (1) 0.34 m (2) 3.4 m (3) 0.85 m (4) 850 cm ( )

84

6. Calculate the volume of the solid below. Given that the solid is formed by identical cubes of 5 cm side.

(1) 500 cm3 (2) 1 000 cm3 (3) 1 500 cm3 (4) 2 000 cm3 ( ) 7. ∠COA = 90o and ∠BOD = 90o. AOE is a straight line. Find ∠ x

(1) 15o (2) 35o (3) 50o (4) 75o ( )

85

8. How many more squares need to be shaded to have a line of symmetry?

(1) 2 (2) 3 (3) 4 (4) 5 ( ) 9. Find the value of ∠ x.

(1) 125o (2) 115o (3) 175o (4) 120o ( )

86

10. The following pie chart shows the number of people in a theatre. The number of boys

and women are half of the total number. How many more women than girls are there in this theatre?

(1) 28 (2) 10 (3) 12 (4) 2 ( ) 11. Candies were sold at 5 for $3. Ms Tan wants to buy 50 candies for her pupils who

got good marks in the mid-term test. How much does she need to spend? (1) $150 (2) $30 (3) $90 (4) $35 ( ) 12. Kate folds rectangular piece of paper along its diagonal as shown in figure 1. The

area of the paper after being folded is 85 of the area of the original piece of paper as

shown in figure 2. If the shaded area is 24cm2, calculate the area of the original rectangular paper.

Figure 1 Figure 2

(1) 64 cm2 (2) 9 cm2 (3) 15 cm2 (4) 48 cm2 ( )

Boys 25

Men 35

Girls

Women 28

87

13. Mr and Mrs Soh travelled Italia, Germany, France and Sweden during their vacation.

The pie chart below shows how they spent their time in those 4 countries. They spent the same number of days in Italia and Germany. The number of days they spent in

France is 32 the number of days they spent in Italia. How many days did Mr and Mrs

Soh spend in Sweden?

(1) 8 days (2) 9 days (3) 10 days (4) 11 days ( ) 14. For the first 6 months of the year, Jim’s average savings was $80. His average

savings would have decreased $5 if he saved $70 in June. How much did Jim actually save in June?

(1) $75 (2) $85 (3) $40 (4) $100 ( ) 15. Mrs Lee gave 30% of the cakes she made to her daughter. Her daughter then shared

55% of her cakes to her friends. What percentage of Mrs Lee’s cakes had her daughter left?

(1) 13.5% (2) 16.5% (3) 31.5% (4) 38.5% ( )

Italia

Germany 6 days

France

Sweden

88

Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. The product of three whole numbers is 30. Their sum is 10. Find those 3 numbers

Ans: _____________________ 17.

0.405 = 0.4 + What is the number in the box?

Ans: _____________________ 18. Find the product of the common factors of 12 and 32

Ans: _____________________ 19. The height and the length of a rectangular swimming pool are 22 m and 1.8 m

respectively. If that pool can store up to 633.6 m3 of water, what is its breadth?

Ans: ___________________m

89

20. Mrs Kan wants to exchange 150 5-cent coins, 101 50-cent coins and 160 20-cent

coins for $5 notes. How many notes did she get?

Ans: _____________________ 21. How many more parallelograms need to be shaded so that the area of the shaded

portion is 43 of the whole figure?

Ans: _____________________ 22. Draw a line parallel to AB passing through point C.

90

23.

Express 87 as a percentage.

Ans: ___________________% 24. Ann folds the figure below to form a cube.

She placed the cube on the table with the shape on the top face. Which shape is on the bottom face of the cube?

Ans: _____________________ 25. Kar Fai has 30% more green colored paper than red colored paper. If he has 3 more

green colored paper than red colored paper, how many papers does he has in total?

Ans: _____________________

91


Calculate the value of 250.2 – 2.3 x 6 + 14 ÷ 7

Ans: _____________________ 27. Chaoyi has 56 books needed to be packed into 6 boxes. The first book is put in the

green box, the second book is put in the black box, the third book is put in the yellow box, the forth book is put in the red box, the fifth book is put in the white box, the sixth book is put in the pink box. He repeats the process until all of his books have been places in boxes. In which box will the last book be in?

Ans: _____________________ 28. Find out the 4-digit number based on the following clues:

(1) There is a 8 in the thousands place. (2) The digit in the ones place is half of the number in thousands place. (3) The digit in the tens place is 2 less than the number in the ones place. (4) The digit in the hundreds place is 3 times the digit in the tens place.

Ans: _____________________ 29.

The area of a rectangle is 48 cm2. Its length is 34 its breadth. Assuming that its length

and breadth are whole number, what is the smallest perimeter that the rectangle can have?

Ans: _________________cm

92

30. The circle in the figure below has a diameter of 20 cm. The square is placed outside

the circle. What is the area of the shaded parts? (Take π = 3.14)

Ans: __________________cm2

93

Preliminary Examination 1: Mock Paper 1 Paper 2 (Duration: 1 hr 40 mins)

Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Find the area of the shaded region?

Ans: __________________cm2

2. How many 60-cm square tiles needed to tile the floor of the 54 m2 square classroom?

Ans: _____________________

94

3. The figure below is not drawn to scale. Given that ABC is a triangle and BD = BA. AD is parallel to CB. Find ∠ x

Ans: _____________________ 4. The rate charges for parking at a car park are shown in the table below.

1st hour $1.20 Subsequent per half hour or part thereof $0.90 After 5 p.m $2.50 per entry

Mr Cheong parked his car from 1.20 p.m to 8 p.m. How much did he pay?

Ans: $___________________ 5. Wai Hong earns a fixed monthly salary for his part-time job. Last month he saved

30% of it. This month, he saves 15% more than what he saved last month. It means that he saves $29.25 more than what he saved last month. Find Wai Hong’s monthly salary.

Ans: $____________________

95

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.

The above figure is made up of 2 equilateral triangles.

(a) Find the perimeter of the above figure in term of g cm in the simplest form. (2 marks)

(b) Find the perimeter of the figure if g = 5. (1 marks)

Ans: (a)___________________(b)___________________

96

7. The table below shows the results of a survey on 500 people.

How often do you travel by public transportation? Name of group Size of group Answer given A 22% “Always” B 35% “Very often” C 30% “Often” D 12% “Sometimes” E A small number (1%) “Hardly ever”

A pie chart is drawn to represent the results.

(a) Write the letter D in the correct part of the pie chart. (1 marks)

(b) How many people gave the answer “Always”? (2 marks)

Ans: (b)___________________

97

8. O is the center of the circle and AB // CD Find

(a) ∠ACB (2 marks) (b) ∠ACD (2 marks)

Ans: (a)___________________(b)___________________

9. Mrs Liu needed to type a 20-page report to submit to her boss. She typed at a rate of

50 words per minutes for the first 8 pages. She slowed down to a rate of 30 words per minute for the remaining pages. On average, the first 8 pages had 500 words each and the rest of the pages had 200 words each. How long did Mrs Liu take to type the entire report? Give the answer in hours and minutes. (4 marks)

Ans: _____________________

98

10. 3 kinds of candies: fruit, milk and chocolate were placed into 3 boxes. The number

of fruit candies is more than the number of chocolate candies and the number of milk candies is half of fruit candies. There are 390 candies in total. Given that the number of candies in each box is less than 200 and they are divisible by 5 and 6. How many chocolate candies were there? (4 marks)

Ans: _____________________ 11. O is the centre of the semi-circle. What is the area of the shaded part? (Take π =

3.14) (4 marks)

Ans: _____________________

99

12. To prepare for the basketball challenge, James practiced throwing the ball into the

basket. He threw 80 times in total. For the first 60 throws, the ball went through the basket 2 times out of every 5 throws. For the remaining throws, he managed to score 85% of the throws. How many times did his ball miss the basket? (4 marks)

Ans: _____________________ 13. ABCD is a rhombus. Find

(a) ∠ a (2 marks) (b) ∠ b (2 marks)

Ans: (a)__________________(b)__________________

100

14. All of Ken’s coins are 20-cent coins while his friend, Emily has a combination of 20-

cent coins and $1 coins. The ratio of Ken’s coins to Emily’s coins is 5 : 2. Emily has

45 less coins than Ken. If Ken gives 51 of his coins to Emily, she will have $14.6 in

total. How much did Emily have at the first? (4 marks)

Ans: _____________________ 15. At 6.30 a.m, a bus left town A to travel to town B at an average speed of 60 km/h. 15

minutes later, a car left town B and drove to town A. The car reached town A at 10.30 a.m while the bus reached town B at 11 a.m.

(a) Find the distance between 2 towns. (1 marks) (b) What was the average speed of the car? (1 marks) (c) At 9.45 a.m, how far apart were the 2 vehicles? (2 marks)

Ans: (a)__________________

(b)__________________(c)__________________

101

16. Ann, Brian, Casey had some money. The ratio of the amount of money Ann had to the amount of money Brian had was 13 : 19. Ann borrowed $4 from Casey and Brian lent $8 to Casey. In the end, Ann and Brian had the same amount of money.

(a) How much did Brian have at first? (2 marks) (b) How much did Ann and Brian have in the end? (2 marks)

Ans: (a)__________________(b)__________________

17. Tap A flows at a rate of 2 100 ml/min while Tap B flows at a rate of 2 500 ml/min.

Both taps were turned on at the same time to fill a tank with dimensions 50 cm by 40 cm by 30 cm. After 5 minutes, the plug at the bottom of the tank is removed, the two taps still running. If the water is drained at a rate of 600 ml/min, what is the water level 2 minutes after the plug is removed? (4 marks)

Ans: _____________________

102

18.

Mary bought 3 skirts by 52 of her money. She used the rest of her money to buy 2

similar skirts for her sisters and 13 T-shirts. (a) How much percentage of money did Mary buy 13 T-shirts? (2 marks) (b) If 1 T-shirt free was given for every 6 T-shirts purchased, how many T-shirts

did Mary have altogether when she spent all of her money on T-shirts? (2 marks)

Ans: (a)__________________(b)__________________

103


Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. Find the smallest number. (1) 0.112 (2) 0.211 (3) 0.21 (4) 0.121 ( ) 2. What is the value of A in the following diagram?

(1) 15.2 (2) 15.4 (3) 15.6 (4) 15.8 ( )

3.

Given that 12.75 ÷ 15 = 0.85. What is value in the box below? 12.75 ÷ = 85

(1) 15 (2) 1.5 (3) 0.15 (4) 0.015 ( ) 4. Simplify 20n – 7 – 9n + 3 (1) 11n – 4 (2) 13n – 7 (3) 17n + 4 (4) 23n – 16 ( ) 5. Calculate (22 + 13 – 27) + 2 x 3 (1) 30 (2) 29 (3) 26 (4) 14 ( ) 6. If a : b = 3 : 7 and b : c = 2 : 5. What is the ratio of a : c? (1) 6 : 35 (2) 1 : 6 (3) 7 : 2 (4) 3 : 5 ( )

Marks

104

7. ABCD is a rectangle. Find ∠ x. The figure is not drawn to scale

(1) 10o (2) 20o (3) 50o (4) 80o ( ) 8. Pipe 1 takes 3 hours to fill up the pool while pipe 2 takes 5 hours. How long does it

take to fill up the pool if pipe 1 and pipe 2 are used together? (1) 4 h (2) 8 h

(3) 187 h (4)

41 h

( ) 9. The figure below is folded to form a cube. What will be seen in the blank face?

(1) B (2) C (3) E (4) F ( ) 10.

Aeron, Ben, John drive at the constant speed. The average speed of Ben is 45 of

Aeron. The ratio of John’s average speed to Ben’s average speed is 13 : 15. If Aeron’s average speed is 60 km/h. What is John’s average speed? Give the answer to the nearest whole number.

(1) 65 km/h (2) 87 km/h (3) 55 km/h (4) 42 km/h ( )

105

11. Which of the following figure(s) has exactly 2 lines of symmetry?

1 2 3 4

(1) 2 and 3 (2) 3 and 4 (3) 4 (4) 3 ( ) 12. The following figure is formed by 1 big semi arc and 4 small arcs. Find the

perimeter of the figure assumed that the radius of the big semi arc is 10 cm. (Take π = 3.14)

(1) 188.4 cm (2) 62.8 cm (3) 282.6 cm (4) 47.1 cm ( ) 13. Each month Salma saved some money. The average saving of Salma over a couple

of months was $78. If she saved $12 more on the last month, her average saving became $82. How many months did Salma save money?

(1) 3 (2) 4 (3) 36 (4) 48 ( )

106

14. Find the percentage of the unshaded area in the below figure?

(1) 25% (2) 50% (3) 60% (4) 75% ( ) 15.

Mrs Lee was typing a report. She typed 43 h at an average speed of 50 words per

minute. Then, she increased her speed to 70 words per minute and typed for 20 minutes. How many words did she type in total? Give the answer to the nearest whole number.

(1) 1438 (2) 3650 (3) 2254 (4) 1568 ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Find the value of n.

51 +

51 +

51 +

51 +

51 +

51 +

51 +

51 = n ×

51 + 1

Ans: _____________________ 17. Calculate 25.5 ÷ 4

Ans: _____________________

107

18. When b = 3, find the value of

bb

21359

−+

Ans: _____________________ 19. The square ABCD has area 98 cm2. Find the length of AC.

Ans: _____________________ 20. 236 is the average of 5 consecutive numbers. Find the value of the smallest number.

Ans: _____________________

A B

D C

108

21. Use the following table to answer the question below:

A B C D 5 8 11 14 7 10 13 16 9 12 15 18 11 14 17 20

Which column will the number “67” display?

Ans: _____________________ 22. The figure is made up of 8 identical semi-circular arcs of diameter 28 cm. Find the

area of the figure. (Take π = 722 )

Ans: _____________________

109

23. Mr. Lee drove from his house to his friend’s house at 8.35 a.m. He drove 3 h 45 min

in total. What time did he reach his friend’s house? Give your answer in 24 hour clock.

Ans: _____________________ 24. 2 pupils can plant 2 trees in 10 minutes. How long does it take 20 pupils to grow 20

trees?

Ans: __________________min 25. A truck travels from city X to city Y at an average speed of 80 km/h while a car

travels from city Y to city X at an average speed of 60 km/h. They pass each other after 30 minutes. How far apart are the two cities?

Ans: _________________ km

110


Mrs. Kan went to grocery to buy some oranges. For every 8 oranges purchased, Mrs. Kan got 2 oranges free. How many of oranges did she buy in order to get 30 oranges in total?

Ans: _____________________ 27. 8 identical cubes are used to form the below solid. The shaded area is 36 cm2. Find

the volume of the solid?

Ans: _________________cm3

28. The pie chart below shows how Chris spent her money on her trip. How much

money did she spend for the traveling tickets?

Ans: _____________________

111

29. Jia Wei buys 2 books and 3 pencils for $ (15n + 13). If each book costs $6, what is

the price of a pencil? Leave your answer in term of n.

Ans: $___________________ 30. 32 pupils got the same amount of biscuits in a box. 8 of these pupils gave all of their

biscuits to the rest of the pupils. As the result, the rest of the pupils received 1 more biscuit each. How many biscuits were there in the box at first?

Ans: _____________________

112


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. The shaded part of the figure below is made up of 2 parallelograms. Find the area of

the unshaded part.

Ans: __________________cm2

2. Draw 3 more unit shapes on the grid provided to show tessellation.

Ans: _____________________

113

3. A Styrofoam cuboid is 50 cm long 40 cm wide and 30 cm tall. 4-cm cubes are cut

from it. What is the minimum wastage?

Ans: __________________cm3

4. The graph below shows how much money Sebastian spent over a week

$0

$1

$2

$3

$4

$5

$6

$7

$8


Sebastian had $60 at first. How much money did he have left at the end of Thursday?

Ans: $___________________

114

5. The daily car park charges for are as follows:

First hour $1.50 Each subsequent half hour or part thereof $1.00

Mr. Soh parked his car from 8.15 a.m to 6.10 p.m. How much did he pay for the car park fee?

Ans: $___________________ For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. Find the area of the shaded triangle given that 3 squares have lengths 4 cm, 5 cm,

and 3 cm respectively. (3 marks)

Ans: _____________________

115

7. ABCD is a rectangle and MN//PQ. Find ∠ n. (3 marks)

Ans: _____________________ 8. ABCD is a trapezium. Find

(a) ∠BCD (2 marks) (b) ∠ABC (2 marks)

The diagram is not drawn to scale.

Ans: (a)__________________(b)__________________

116

9.

Ann and Betty have 40 pieces of colored papers in total. 21 of Betty’s papers is 5

more than 31 of Ann’s papers. What is the total number of colored papers which

Betty has? (4 marks)

Ans: _____________________ 10. David saves $150 more than Jack. The total money which they save is $958.50. How

much does Jack save? (4 marks)

Ans: _____________________ 11. In the figure, not drawn to scale, Point O is the centre of the circle. CN and DM are

straight lines. ∠OCD = 45o, ∠OAB = 15o. Find (a) ∠NAM (2 marks) (b) ∠OBC (2 marks)

Ans: (a)___________________

(b)___________________

117

12. A pen factory signed a contract to produce a number of souvenir pens for a company.

The pen company needs to produce pens in 5 days to accomplish the contract.

On the first day, it produced 51 of the required number of pens.

On the second day, it produced another 28 pens. On the third day, it produced half of the number of pens produced on the first 2 days. On the fourth day, it produced 9 more pens more than the first day. On the fifth day, it completed the remaining 64 pens. How many pens did the factory produce in those 5 days? (4 marks)

Ans: _____________________ 13. Ben left Town A at 7.45 a.m and travelled towards Malacca at an average speed of

85 km/h. Rollend left Town A 30 minutes later and travelled to Malacca at the same route at an average speed of 80 km/h.

(a) How far apart were they at 11 a.m? (2 marks) (b) If Rollend increased his speed by15 km/h after 15 minutes, how long did he

take to overtake Ben? (2 marks)

Ans: (a)__________________(b)__________________

118

14. Annie, Chris and Lauren have some sweets. If Lauren gives 3 sweets to Annie, they

will have the same amount of sweets. If Annie gives 3 sweets to Lauren, Lauren’s number of sweets is three times Annie’s sweets. Chris has 5 sweets less than half of the total sweets which Annie and Lauren have. How many sweets do they have in total? (4 marks)

Ans: _____________________ 15. The figure below shows 8 identical semi arcs. Each arc has the radius of 5 cm.

(a) Find the total area of the shaded parts. (2 marks) (b) Find the perimeter of the shaded parts. (2 marks)

(Take π = 3.14)

Ans: (a)___________________(b)___________________

119

16. The base of a water tank is a square of side 10 cm. Uncle Tan places eight 5-cm

cubes in that tank. He then pours the water into the tank until it is 43 full. Uncle Tan

removes eight cubes and observes that the water level drops to 32 the height of the

tank. (a) Find the volume of the each cube. (2 marks) (b) Find the height of the tank. (2 marks)

Ans: (a)__________________(b)__________________

17. Benson saved one 50-cent coins on the first day. The next day, he saved four 50-cent

coins. Each day, he saved three 50-cent coins more than the previous day. (a) Complete the table below. (2 marks)

Day Number of coins saved

each day Total number of coins

1 1 1 2 4 5 3 7 12 4 5

(b) How much money did Benson have after the 10th day? (2 marks)

Ans: __________________

120

18.

In a sports competition, 6725 of the competitors were from school A. The ratio of the

number of school B’s competitors to the number of school C’s competitors is 19 : 23. School A sent 4 more competitors than school C.

(a) How many competitors were from school C? (2 marks)

(b) Some competitors from school B left the competition. As the result, 215 of the

remaining competitors were from school B. How many competitors from school B left? (2 marks)

Ans: __________________

121


Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. Find the value of 33 × 0 + 33 × 10 + 33 × 100 (1) 3 630 (2) 69 300 (3) 3 663 (4) 36 300 ( ) 2. Arrange the numbers below by ascending order

21.68, 21.608, 21.068, 21.08 (1) 21.08, 21.68, 21.068, 21.608 (2) 21.068, 21.608, 21.08, 21.68 (3) 21.068, 21.08, 21.608, 21.68 (4) 21.608, 21.08, 21.068, 21.68 ( )

3.

What is the maximum number of factors that can be placed in the shaded part of the below diagram?

(1) 4 (2) 5 (3) 6 (4) 7 ( ) 4. The lamps along the street are arranged in equal distance from one another such that

the distance between the 1st and 3rd lamp are 400 m apart. Ken is standing at the 7th lamp. What is the distance between Ken and the 12th lamp?

(1) 1.2 km (2) 800 m (3) 1 000 m (4) 400 m ( )

122

5. Find the area of the shaded part if the pattern is drawn on a 10-cm square grid. Take

π = 3.14

(1) 439.25 cm2 (2) 450.5 cm2 (3) 513.5 cm2 (4) 682.25 cm2 ( ) 6. Given that AC and BD are straight lines. Which of the two angles in the figure are

equal?

(1) ∠ a and ∠ c (2) ∠ x and ∠ y (3) ∠ b and ∠ d (4) ∠ c and ∠ e ( )

123

7. Which of the following net cannot form a cube?

1 2 3 4

(1) 1 (2) 2 (3) 3 (4) 4 ( ) 8. Jasmine went to bookstore before going to school. She took 25 minutes to reach the

bookstore and 2 times as long to go to school from the bookstore. How much time did she spend to walk to the bookstore and then walk to her school?

(1) 75 min (2) 1h 15 min (3) 1h 30 min (4) 50 min ( ) 9. A lorry drove 50 minutes at the speed of 65 km/h and 35 minutes at the speed of 70

km/h. What was the distance covered? (1) 70 km (2) 75 km (3) 85 km (4) 95 km ( ) 10. Which of the following figures completes the other symmetrical half of the figure

below?

(1)

(2)

(3)

(4)

( )

124

11.

ABCD is a square. MN = PQ = 41 AB. Find the fraction of the unshaded area.

(1)

51 (2)

41

(3) 43 (4)

81

( ) 12.

Mrs. Poh had some rice. She used 41 of the rice to cook lunch and 20% of the

remainder to cook dinner. What percentage of the rice was left? (1) 45 % (2) 60 % (3) 40 % (4) 55 % ( ) 13. The line graph shows the amount of rainfall recorded on the first 6 months of the

year.

0

50

100

150

200

250

300


How many percent more rainfalls were collected in May than in February?

(1) 86.67 % (2) 73.33 % (3) 46.43 % (4) 83.33 % ( )

125

14. Tank A is half-filled with water while tank B is empty. The length of tank B is twice

tank A and its breadth is one-third that of tank A. The heights of both tanks are the same. What fraction of tank B will be filled if all the water in tank A is poured into tank B?

(1) 61 (2)

121

(3) 65 (4)

43

( ) 15. The ratio of Kelvin’s money to Sam’s money was 5 : 3. After Kelvin spent $8 and

Sam saved $22, they had the same amount of money. How much did Kelvin have at first?

(1) $75 (2) $45 (3) $67 (4) $72 ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Express $56 879.67 to the nearest ten dollars.

Ans: $___________________ 17. Mr. Chan left his house at 11.22 a.m to drive to his friend’s house. He reached his

friend’s house at 6.23 p.m How long did he take to drive to his friend’s house?

Ans: _____h__________min

126

18. ABCDE is a regular pentagon. Find ∠ x.

Ans: _____________________ 19.

Use the shape to form a tessellation in the grid below.

The boundary of the tessellation has been drawn. Complete the tessellation by drawing the correct number of the unit shape within the boundary.

Ans: _____________________

127

20. What is the missing letter in the cube?

Ans: _____________________ 21. The bar graph below shows the number of burgers sold within a week.

0

50

100

150

200

250

300

350


The total number of burgers sold was 1 700. Complete the bar graph above.

Ans: _____________________

128

22. A restaurant prepared food to sell to 250 customers in 10 days. If the number of

customers increased to 400, how many days would the same amount of food last?

Ans: _____________________ 23.

Betty, Carol and Linda have some origami colored papers. 41 of Betty’s papers is

equal to 53 of Carol’s papers as well as

52 of Linda’s papers. Find the ratio of the

number of Betty’s colored papers to the number of Carol’s colored papers to the number of Linda’s colored papers.

Ans: _____________________ 24. Find the fraction in the box

390 ÷ 100 = 39 ×

Ans: _____________________ 25. The length of a rectangle is 7n cm. Its breadth is 3 cm less than its length. Find the

perimeter of the rectangle in terms of n.

Ans: __________________cm

129


Find the value of 79 – 5 × 7 + 56 ÷ 8 ×9

Ans: _____________________ 27. 75% of a number is 2625. What is 40% of that number?

Ans: _____________________ 28. 2 books and 3 pens cost $18.

3 books and 5 pens cost $28. Find the cost of each book.

Ans: $__________________ 29. A rectangle tank measuring 25 cm by 50 cm by 35cm is half-filled. There is a leak on

the tank which drains the water at 50 cm3 per minute. How long does it take to empty the tank?

Ans: __________________min

130

30. If the area of the square inscribed in a circle is 98 cm2, what is the area of the circle?

(Take π = 722 )

Ans: ___________________ cm2

131


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. In the space below, draw a triangle ABC with AB = 6 cm, BC = 5 cm and ∠ABC =

140o

Ans: _____________________ 2. ABCD is a parallelogram. EB = EC. Find ∠BAC.

Ans: _____________________

132

3. The pie chart below (drawn to scale) shows the number of fruit, milk, mint and

chocolate sweets in the bag.

What percentages of the sweets are chocolate?

Ans: ___________________% 4. Rossy bought some green pencils. The cost of each green pencil is $0.75. When she

bought 4 more yellow pencils at $0.85 each, it increased the average cost of green and yellow pencils to $0.79. How many pencils did Rossy buy altogether?

Ans: _____________________

Fruit

Milk

Chocolate

Mint

133

5. Emily bought some equal number of apples and bananas. The apples were sold at 5

for $3 and the bananas were sold at 4 for $5. She paid $13 more for the bananas than the apples. How much did Emily pay in total?

Ans: _____________________ For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. Mrs Smith has a schedule to have her home cleaned by 3 part-time workers. The

sweeper goes to her home once every 2 days, the gardener once every 3 days, and the cleaner once every 4 days. If the 3 workers first met on 01 Nov, when was the earliest date they would meet again? (3 marks)

Ans: _____________________

134

7. Jim saved a fixed amount of money every week. To encourage his son, Mr Koh

contributes 20% of that amount to Jim’s savings. In order to save a total of $600 after 10 weeks, how much did Jim save every week? (3 marks)

Ans: _____________________ 8. ABCD is quadrilateral and ABED is a parallelogram. The figure is not drawn to

scale.

(a) Find ∠MBE (2 marks) (b) Find the sum of ∠ADC + ∠BCD (2 marks)

Ans: _____________________

135

9. The pie chart below shows the number of men, women, boys and girls at the stadium

watching hockey match.

(a) What fraction of the spectators were adults? (2 marks) (b) The ratio of the number of men to the total number of children was 12 : 19. If

there were a total of 1 000 spectators at the match, how many men were there? (2 marks)

Ans: (a)__________________(b)__________________

10. Mrs Kan wants to print x number of name cards for her company. She has to pay a

basic fee of $40 and an additional $0.30 for each name card. (a) How much does she pay in term of x? (2 marks) (b) How much does she pay if she wants to print 500 name cards? (2 marks)

Ans: (a)__________________(b)__________________

Girls 20%

Men

Boys 18%

Women

136

11. There were a total of 100 students in 3 classes A, B and C. There were twice as many

students in class B as class A. There were fewer students in class C than class B. The number of students in class A and class B was less than 50 each. The number of students in class B was divisible by 3. How many students were there in class C? (4 marks)

Ans: _____________________ 12.

Daniel, Peter and Ivan had a collection of stamps. Peter and Ivan collected 169 of the

stamps while Daniel and Ivan collected 43 of the stamps. Peter and Daniel collected

55 stamps altogether. How many more stamps did Ivan collect than Peter? (4 marks)

Ans: _____________________ 13. The figure below is made up of thirty 5-cm cube stacked on top of each other. If the

figure is dipped into the paint, what is the total surface area of the figure that is covered in the paint? (4 marks)

Ans: _____________________

137

14. In a school, the number of boys increased by 25% to 350 and the number of girls

decreased by 20% to 300. (a) Is there an overall increase or decrease of students? (2 marks) (b) Find the overall increase or decrease in the total number of students?

(2 marks)

Ans: (a)__________________(b)__________________

15. Daisy saved $105 in a mixture of 10-cent, 20-cent, and 50-cent coins. There were

five times as many 50-cent coins as 10-cent coins and two times as many 20-cent coins as 10-cent coins.

(a) How many 10-cent coins did Daisy save? (2 marks) (b) Daisy wanted to exchange all of her money to 20-cent coins. How many 20-

cent coins would she have after the exchange? (2 marks)

Ans: (a)__________________(b)__________________

16. Container A and container B contain different amounts of wine at first. The total

amount of wine in 2 containers is 60 litres. The ratio of the amount of wine in container A to the amount of wine in container B is 5 : 7. Find the amount of wine in each container. (4 marks)

Ans: _______________________

138

17. Mrs Yap drives to meet her friend. If she drives at 75 km/h, she will be 25 minutes

later than she expected. If she drives 60 km/h, she will be 40 minutes late. How long will the journey take if she drives at 90 km/h? (4 marks)

Ans: _____________________ 18.

Find the area of the shaded part. (Take π = 722 ) (4 marks)

Ans: _____________________

139


Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. Which of the following number is the biggest? (1) 5.23 (2) 5.32 (3) 5.323 (4) 5.232 ( ) 2. Calculate A = 3 + 2 x 11 – 10 ÷ 5 (1) 23 (2) 9 (3) 19 (4) 11 ( )

3. A student started her exam period on 23rd November and finished all tests on 2nd December. How long did the exam period last?

(1) 9 days (2) 10 days (3) 11 days (4) 12 days ( ) 4. Alice is 2 kg heavier than her younger sister. She is 3 kg lighter than her older sister.

Given that the total mass of 3 girls is 121 kg. What is the mass of Alice, in term of kg?

(1) 43 (2) 41 (3) 40 (4) 38 ( ) 5. Find the net of the following solid

(1)

(2)

(3)

(4)

( )

140

6. Alice and Bob shared a bag of candies with the radio 3:2. If Alice was given 23 more

candies, then the number of candies of Alice would double the number of candies of Bob. How many candies were there in the bag?

(1) 46 (2) 69 (3) 115 (4) 230 ( ) 7. Currently, the age of Mary is

31 of the age of her mother. If she is p years old now,

how old will her mother be in 5 years more in terms of p? (1) 3p (2) p + 8 (3) 30 + 8 (4) 3p + 5 ( ) 8. Which of the following fractions is greater than (

51 +

201 )?

(1) 4011 (2)

122

(3) 163 (4)

245

( ) 9. Joel has $30 in 20-cent and 50-cent coins. If there are ten 20-cent coins more than

50-cent coins, how many coins in total does he have? (1) 18 (2) 24 (3) 90 (4) 120 ( ) 10. PQR is a triangle. Given that PQ = QS = SP and ∠ PRQ = 35o. Find the ∠ SPR.

(1) 15o (2) 25o (3) 35o (4) 45o ( )

141

The pie chart below (drawn to scale) shows how students go to schools. Study this chart carefully and answer questions 11 and 12.

11. How many percentages of the students go to school by MRT? (1) 35% (2) 40% (3) 25% (4) 15% ( ) 12. How many percentages of students use other kinds of transportation other than bus,

MRT, walking to go to schools? (1) 18% (2) 20% (3) 15% (4) 10% ( ) 13. Sam borrowed a book from the library. In the first day, he read

257 of the number of

pages. He read 103 of the remainder in the next day.

21 of what remained was read on

the third day. Finally, he read the rest of book, 189 pages, on the fourth day. How many pages were there in this book?

(1) 550 (2) 2100 (3) 300 (4) 1200 ( ) 14. A rectangle is formed by bending a wire of length 70 cm. Find the area of the

rectangle if the ratio of the length to the breadth of the rectangle is 4 : 3. (1) 100 cm2 (2) 200 cm2 (3) 300 cm2 (4) 400 cm2 ( )

142

15. Alice bought some note-books with the discount of 30%. Bob purchased the same

number of notebooks but he was given 20% discount only. Hence, Bob paid $480 for those notebooks. How much did Alice pay for her notebooks?

(1) $180 (2) $336 (3) $420 (4) $600 ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Evaluate 9q + 8 – 5q + 19

Ans: _____________________ 17. 25 × 25 = 25 × 10 + 25 × y

What is the value of y?

Ans: _____________________ 18. The rate of printing photographs is illustrated in the below table.

Number of photographs Cost per photograph

First 25 25 cents Second 25 20 cents Beyond 50 10 cents

Mr Liu wants to print 60 photographs. How much does he need to pay?

Ans: $_____________________

143

19. A triangular garden has 3 sides in the ratio of 4 : 3 : 3. Given that the perimeter of

garden is 80 m. What is length of the longest side of this garden?

Ans: ___________________m 20. Ming and Chen have 20 marbles altogether. Zhang has n marbles more than the

number of marbles that Ming and Chen have. What is the average number of marbles that 3 friends have, in terms of n?

Ans: _____________________ 21. Find the area of the shaded part.

Ans: __________________cm2

22. The cost of painting 3 m2 on the wall is $21. What is the cost of painting 17 m2?

Ans: $____________________

144

23. A cubic container which is full

43 is shown below. How much water has to be added

into this container in order to make it full?

Ans: __________________cm3

24. Mr. Tan drove from Town A at 4.00pm and travelled at an average speed of 75km/h.

He reached Town B at 9.30pm. How far was Town A from Town B?

Ans: _____________________ 25. Eric has

52 number of books which Jane has. Jane has

65 number of books which

Mark has. What is the ratio of the number of Eric’s books to the total number of books of Eric, Jane and Mark?

Ans: _____________________

145


For every flower sold, Beth earns $0.50. A commission of $0.30 in addition is given for every 5 flowers sold. How many flowers did she sell to earn $14?

Ans: _____________________ 27. Draw 2 more lines to form a rhombus from the 2 given lines below.

Ans: _____________________ 28. Find the shaded area of below figure. Given that the length of 3 sides of the triangle

are 5cm, 4cm, 3cm. (Take π = 3.14)

Ans: _____________________

146

29. In the figure, not drawn to scale, ABCD is a trapezium. Find ∠ y

Ans: _____________________ 30. An empty bus is picking up passengers at the following rate. At the first stop, 2

passengers come up. Then 4 others get in at the second stop. 6 people come up at the third stop. At the forth stop 8 people get in and so on. How many passengers are on this bus after it leaves 6 stops.

Ans: _____________________

147


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Shade more squares to have exactly 2 lines of symmetry in the below figure.

Ans: _____________________ 2. In the following figure, not drawn to scale, ∠ a =∠ b =∠ d. Given that ∠ c = 24o.

Find ∠ a.

Ans: _____________________

148

3. John had 115 candies. He ate 5y candies and gave the rest equally to his two

younger sisters. How many candies did each sister receive from John? Express your answer in term of y.

Ans: _____________________ 4. Ivan bought 6 books and 5 notebooks for his next semester. He spent $84 altogether.

3 notebooks have the price as much as 2 books. Find the cost of a book.

Ans: _____________________ 5. A tank has a rectangle base measuring 40 cm by 30 cm. It is filling up with water at a

rate 2 litres/minute. It takes 20 minutes to fill the tank completely. Find the height of the tank.

Ans: _____________________

149

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. There were 78 durians and 36 watermelons in the store. The storekeeper sold the

same number of durians and watermelons. The number of watermelons left is equal

to 41 the number of durians left. How many durians and watermelons are sold?

(3 marks)

Ans: _____________________ 7. ABCD is a rhombus.∠ADB = 75o and ∠BCM = 30o. The figure is not drawn to

scale.

(a) Find ∠DAB (1 marks) (b) Find ∠BMC (2 marks)

Ans: _____________________

150

8. Jan drove to visit his friend’s house, which was 500 km away. Jan spent a half of his

time to complete the first 52 of the journey and then travelled at the average speed of

60km/h on the rest of journey. a) What was the total time that he needed for the full travel? (2 marks) b) What was his average speed for the first part of his journey? (2 marks)

Ans: _____________________ 9. The ratio between the number of Robert’s beads and the number of Robin’s beads

was 1 : 4. Unfortunately Robert lost 51 of his beads. Then Robin shared 152 beads to

Robert so that they had the same amount of beads. How many beads did Robin have at first? (4 marks)

Ans: _____________________

151

10. The figure below is formed by 4 right triangles.

(a) Find the perimeter of the figure. (2 marks) (b) Find the area of the figure. (2 marks)

Ans: _____________________ 11. ABCD is a trapezium. ABK is a straight line and CM = CB. Find ∠ABD. The figure

is not drawn to scale. (4 marks)

Ans: _____________________

152

12. 6 students donated for a children protection fund.

0

10

20

30

40

50

60

70

80

90

Annie Betty Chris Daniel Emily Ken

a) What was the average amount donated by 6 students? (2 marks) b) What is the percentage of the total amount donated by Emily? (2 marks)

Ans: _____________________ 13. At 9am, motorist travelled from A to B at the constant speed. Two hours after, a car

driver started his journey on the same road and he caught the motorist at 2pm. Given that the car driver moved at the speed of 30km/h faster than motorist.

a) Find the speed of motorist. (2 marks) b) Find the distance between A and B if the car was 60km away from B at 2pm.

(2 marks)

Ans: (a)___________________(b)___________________

153

14. The ratio of the length to the breadth of a container’s rectangle base is 2 : 1.The

height was 20 cm. It was 41 full. Mr Tan added 2000 cm3 of water into the

container. As a result, the water level was up to 15 cm high. Find the breadth of the container. (4 marks)

Ans: _______________________

15. There are a cold tap and hot one filling up a bathtub. The hot tap takes 12 minutes to

full up the tub alone and the cold tap needs 8 minutes to fill up alone. Unfortunately, when turning on both taps at the same time, there is a crack at the bottom of the bathtub. The crack empties the bathtub in 24 minutes. How long will it take to fill up the tub? (4 marks)

Ans: _____________________ 16. At a book shop, the price of Mathematic book is

51 that of Literature book. Jane

decided to buy both books and was given a discount of 30%. She paid a total of $126 for them.

a) What is the price of Mathematics book before discount? (2 marks) b) What is the price of Literature book after discount? (2 marks)

Ans: _____________________

154

17. Study the following number pattern:

Stage 1 2 3 4 5 6

Number 5 8 11 14 17 20

a) What is the number in the 10th stage? (2 marks) b) What is the number in the 100th stage? (2 marks)

Ans: _____________________ 18. The figure below is formed by some semi-circles, a circle and a triangle. Given that

the lengths of the 3 sides of the rectangle are 6cm, 8cm, 10cm. Take π = 3.14

a) Find the perimeter of the figure. (2 marks) b) Find the area of the shaded part. (2 maeks)

Ans: _____________________

155



1. Find the value of x: 9 606 609 = 9 000 000 + x + 9

(1) 606 060 (2) 606 609 (3) 606 600 (4) 606 009 ( ) 2. If you add 3 tens to 3 ones and 3 thousand, what is the total number? (1) 3 033 (2) 3 330 (3) 3 003 (4) 3 030 ( ) 3. A part of figure is shaded. What fraction of the figure is this part?

(1) 32 (2)

41

(3) 43 (4)

81

( ) 4.

Fill the blank with appropriate number: ______143

201

=++

(1) 54 (2)

89

(3) 59 (4)

49

( )

156

5. At 7.30 am, Laura leaves her home to school which is 22.5 km far away from her

house by bus. The school starts at 8am. At what speed must the bus travel to reach her school on time? (km/h)

(1) 12.5 (2) 11.25 (3) 45 (4) 67.5 ( ) 6.

Find x given that x% = 253

(1) 75 (2) 3 (3) 25 (4) 12 ( ) 7. Ali has 20 coins which are equal to $5.20 in total. If there are only two types of

coins, one of which has 4 coins, what is the value of each type of coin? (1) 10 cent and 20 cent (2) 20 cent and 50 cent (3) 50 cent and 10 cent (4) None of above. ( ) 8. The figure below shows a package of sugar being weighted on a scale.

What is the mass of the package?

(1) 2 kg (2) 2.05 kg (3) 2.15 kg (4) 2150 kg ( ) 9. Among the following items, which one can be tessellated?

1 2 3 4

(1) 1 (2) 2 (3) 3 (4) 4 ( )

2kg 100g 50g

157

10. Determine the side of a square if its perimeter is 144x cm. (1) 26x cm (2) 36x cm (3) 12x cm (4) 22x cm ( ) 11. Harry bought 6m of ribbon at the price of $9. If Harry bought 9m, how much would

he pay? (1) 13.5 (2) 6 (3) 9 (4) 1.5 ( ) 12. After selling out 15 flowers in box A and 7 flowers in box B, the number of flowers

in A is equal to 31 that in B. If initially all flowers were divided equally in two

boxes, what is the number of flowers in each box initially? (1) 19 (2) 22 (3) 32 (4) 29 ( ) 13. If the ratio of the area of rectangle to the area of triangle is 3 : 2, find the breadth of

rectangle.

(1) 3 cm (2) 4 cm (3) 5 cm (4) 6 cm ( ) 14.

The number of Social Science books in the library is 41 that of Natural Science

books. The other types of books constitute 50% of the total and are 250 books. How many Natural Science books are there in the library?

(1) 10 (2) 50 (3) 200 (4) 250 ( )

158

15. The net of a cube is shown in the following figure:

If people place this dice on the table with the face facing the table’s surface. Which is the facing upward face?

(1)

(2)

(3)

(4)

( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (10 marks) 16. Fill in the boxes with appropriate operation “-“ or “x”

(0.01 0.09) 20 40 (0.08 0.03) = 0

Ans: _____________________

159

17. Arrange the following numbers in descending order:

909.9 9.909 90.99 999.0

Ans: _____________________ 18. A teacher gives 5 cakes to his students as a Christmas gift. If the cakes are divided

equally among the students in the class and each student receives 41

of a cake, how

many students are there in this class?

Ans: _____________________ 19.

Bryan is 1243 years older than his younger brother who is 2 years and 3 months old

now. What is the age of Bryan?

Ans: _____________________

160

20. Container 1 has a base of 36 cm2 and a height of 40 cm. Container 2 has a base of 80

cm2. The two containers are storing the same amount of water. The water is filled up

to 32 of container 1’s height and container 2 is fully filled. What is the height of

container 2?

Ans: _____________________ 21. Denny reads a book which has 234 pages in 5 days. The average number of pages

that she reads in the first 4 day is 46. How many pages does she read on the fifth day?

Ans: _____________________ 22. Suet Mei started her journey from Town A to Town B at 6.03 pm. It took her 2 hours

and one quarter of an hour to complete her journey. What time did she reach Town B?

Ans: _____________________

161

23. An MRT travelled at the speed of 110 m/minute on average and it took 35 minutes to

travel from City Hall to Chinese Garden. What is the distance between these two places?

Ans: _____________________ 24. Shade 2 squares of the below figure to make it symmetric.

Ans: _____________________ 25. Teddy has 500 marbles. After giving 240 marbles to his brother, he sells 40% of the

remainder to Allen. How many marbles does he have at last?

Ans: _____________________

162


Sam bought 3 shirts and 5 pairs of jeans with the cost of $220. Given that the price of a pair of jeans is $20 more than that of a shirt, finds the price of a shirt.

Ans: _____________________ 27. The number of candies that Alice has is equal to 160% the number that Max has.

Even if Alice gives up 6 candies to other friends, she also has 9 candies more than Max. Find the number of candies Max has?

Ans: _____________________ 28.

Take π =722 . Find the area of the shaded part in below figure, if O is the centre of

the circle and the square has the area of 64 cm2. Express your answer up to two decimal degrees.

Ans: _____________________

O

163

29. Tap A flows at a rate of 4 litres/minute and tap B flows at a rate of 10 litres/minute.

If both taps were turned on at the same time, how long does it take for both taps to completely fill up a tank measuring 70 cm by 50 cm by 28 cm?

Ans: _____________________ 30. In the figure below, ABCD and IJKH are rectangles. AI = JB and AI + JB = IJ. Find

the area of the shaded part.

Ans: _____________________

A B

C D

I J

K H

28 cm

16 cm

164


Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. The amount of internet data used by an office is shown in the figure below. The

horizontal axis is in a unit of data called gigabytes.

Cost of internet usage Gigabytes Price

First 40 units $10 Subsequent 5 units or part thereof $3

How much did this office pay for internet usage in March?

Ans: _____________________

165

2. A square piece of paper is folded at its corner as shown in the following figure. Find the value of ∠ k.

Ans: _____________________ 3. A plane flew from Thailand to Singapore at 6 am. One hour later, a second plane also

travelled from Thailand to Singapore at a speed of 200km/h. If Thailand is 1080 km far away from Singapore and the speed of the first plane is 160km/h, at which time did the planes pass each other?

Ans: _____________________

A I

J

K

CD

k

76°

166

4. 15% of the number of balloons that Jane has is yellow. The percentage of yellow

balloons to the total number of balloon is 31 the percentage of blue balloons to the

total number of balloons. If the rest of the balloons are all red, how many percent of the total number of balloon is red?

Ans: _____________________ 5. Study the diagram below carefully and answer the following question:

No. of lamp posts 1 2 3 No. of equal parts 2 3 4

Each equal part is 20 m long. There were 24 lamp post planted along one side of a street. How long is the street?

Ans: _____________________

167

For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks)

6. A student’s expenses over 5 days are shown in the following chart.

a) What is the daily expenditure in average of this student? (2 marks)

b) How many percent of the total expenditure did he spend on food? Provide your answer correct to 2 decimal points of the percentage. (2 marks)

Ans: _____________________

168

7. Mary is x years old now. Her mother’s age is 5 times as many as hers and her father’

age is 87 of the total age of Mary and her mother. Find the age of her father in terms

of x. (3 marks)

Ans: _____________________ 8. Sam bought 18 books and some note-books for $273. He bought 3 more books than

note-books and the price of one note-book is $6 less than that of one book. Find the price of one note-book? (3 marks)

Ans: _____________________

169

9. The below figure shows MN // PQ

Find the value of u and v. (4 marks)

Ans: _____________________ 10. In a mathematics class, the number of girls is 20% that of boys. One day, 2 more

girls joined this class and then there are 41 as many girls as boys in this class. What

is the total number of students at first? (4 marks)

Ans: _____________________

M

N

P

Q

u

v

48°

73°

170

11. In the figure below, ABC is an isosceles triangle with AB = AC, BDEF is a

trapezium with DE // BF, and EGHI is a rhombus. CEF, CAEI, BAF are straight lines. What is ∠ a? (4 marks)

Ans: _____________________ 12. In the below figure, the ratio of the area of rectangle A to the area of square B is

12:5. The ratio of the area of square B to the area of square C is 3:2. 40% of square C is shaded.

a) Find the ratio of the area of rectangle A to the area of square C? (2 marks) b) Find the ratio of the unshaded area of square B to the unshaded area of square

C? (2 marks)

Ans: _____________________

B

D

A

C

E

F

G H

I

70°

64°

a

C

A B

171

13. In a meeting room, there were 24 rows of chairs and each row has 12 chairs. The

director then decided to re-design the room, so that the chairs were re-arranged along the perimeter of a square. The number of chairs in each side of the square was identical, and there were no chairs in the corners to provide room for access. How many chairs were used to form a side? (4 marks)

Ans: _____________________ 14. Tom travelled from city A to city B, which are 250 km apart, with a speed of 45km/h

for 53

of his journey. After that, he increased the speed by 15km/h for the remainder

of his journey and reached city B at 6pm. Jerry also left city A at the same time as Tom with the speed of 50km/h for the whole journey.

a) Find the time that Tom left city A. (2 marks) b) At 5:30pm, how far apart were they? (2 marks)

Ans: _____________________

172

15. Sam has 1500 marbles and he puts them into a box with 40 holes. He put 1 marble in

the first hole, 2 marbles in the second hole, 3 marbles in the third hole, and so on until all 40 holes are filled with marbles. How many marbles are left when he has filled all the holes? (4 marks)

Ans: _____________________ 16. What is the area of the unshaded part in the figure below? The diameter of the

largest circle is 28 cm. Take . (4 marks)

Ans: _____________________

173

17. John had 60 toys in total. They were dinosaurs and robots. He then gave half of his

toy dinosaurs to his younger brother. His mother then gave him 12 more toy robots.

After that, the number of robots he had was equal to 32 of the remaining number of

dinosaurs. How many dinosaurs and how many robots did he have initially? (4 marks)

Ans: _____________________ 18. In a stationary store, there are 3 kinds of pencil: 2B, 3B and 4B. 40% of the pencils

are 2B, 90% of the remainder are 3B, and the rest are 4B. There are 28 more 3B pencils than 2B pencils. The store owner sells some 2B pencils and 20% of the remaining pencils are 2B pencils. How many 2B pencils were there in the store in the end? (4 marks)

Ans: _____________________

174

Answers to Midyear Examination: Mock Paper 1-Paper 1

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 3 2 1 4 2 3 1 1 2 4 2 1 2 3 2

16 q = 5 17

kmm

755

=700055

=1400

11

18

10081

+109

=1.71 19 3550 m

20 (20 + 16) x 2 = 72; The perimeter of the farm is 72 m. 72 ÷ 2 = 36; The number of posts needed is 36.

21 (42 ÷ 3) x $22 = $308; The cost of 42 T-shirts is $308. 22 9 + 3 + 2 = 14; There are 14 customers who bought at least 8 pencils. 23 15 x 6 = 90，Sum of 1st 6 numbers is 90.

15 – 1 = 14, Average is 14 after adding 7th number. 14 x 7 = 98， Sum of 7 numbers is 98. 98 – 90 = 8， The 7th number is 8.

24 80 – 25 = 55; 55 papers have other colors than red.

8055

x100% = 68.75%; The percentage of papers having other colors is 68.75%.

25 19y + 22 26

43 – 8 = 35; There are 35 students in the class. 35 x 74

= 20 ; There are 20 boys in the class.

27 10 x $9 = $90 ; Benson spent $90 for 10 T-shirts. $90 ÷ 15 = 6 ; He can buy 6 T-shirts at normal price with the same amount of money. 10 – 6 = 4 ; He can buy 4 T-shirts fewer with the same amount of money during a non-sale period.

28 Each segment equals

125

unit ; 5 x 125

= 1225

units

29 Divide each number by 2, and then divide each number by 4. The column is the reminder of the division and the row is the result of the division after adding 1 (eg: 18 ÷ 2 = 9; 9 ÷ 4 = 2 with remainder = 1. Hence, 18 is in column 1, row 2 + 1 = 3) Hence, 222 is in column 3, row 28

30 As Chris’s recipe: + 2kg flour can be used to make (2kg ÷ 500g) x 6 = 24 + 1 kg butter can be used to make (1kg ÷ 200g) x 6 = 30 + 1.5 kg sugar can be used to make (1.5kg ÷ 100g) x 6 = 90 + 4 eggs can be used to make (4 ÷ 1) x 6 = 24. Chris can make at most 24 muffins.

Midyear Mock Paper 1-Paper 2 1

2 336 ÷ 7 ÷ 8 = 6 Width is 6 cm. 7 x 6 = 42 Area of the shaded face is 42 cm2.

3

4

5 21 – 5 = 16 ; 16 ÷ 2 = 8; Hu Ting has 8 oranges. 8 + 5 = 13; Ho Yuet has 13 oranges.

The ratio is 13 : 8 6 12 x 6 = 72; They have 72 sweets at first.

72 + 2 + 4 + 6 + 8 + 10 + 12 = 114 ; They have 114 sweets after receiving more sweets. 114 ÷ 6 = 19; The new average number is 19.

7 75 x 3 = 225 ; Total number of pages is 225. 10 x $0.5 + (225 – 10) x $0.35 = $80.25 ; She needs to pay $80.25.

175

9

(1.25×32)÷25 = 1.6; Kelvin’s height is 1.6 m. (1.6×31)÷32 = 1.55; Louis’s height is 1.55 m.

10 22 + 5 = 27; Matthew is 27 years old now. (27 x 10) ÷ 9 = 30; Jose is 30 years old now.

After x (years) xx

++

3027

=1514

=> x = 15

The ratio of their ages will be 14 : 15 after 15 years.

8

The diagram consists of 5 triangles. 180o x 5 = 900o ; The sum of 7 angles is 900o.

11 63 × 3 = 189; The total mass is 189 kg. (189 – 6 – 3 – 3) ÷ 3 = 59 Kenvat’s mass is 59 kg. 59 + 3 = 62; Mark’s mass is 62 kg 62 + 6 = 68; Sandeep’s mass is 68 kg.

12

24555x

= 1237.5 cm2

The area of 1 table is 1237.5 cm2 1237.5 x 25 = 30 937.5 cm2 30 937.5 cm2 of wood is needed to make 25 tables.

13 1440 ÷ 40 = 36 The area of each square is 36 cm2. Each side of the square is 6 cm. 6 x 4 = 24 The perimeter of each square is 24 cm.

14 (c) ∠DCU = 90o – 25o = 65o ∠XAU =∠AUV = ∠ BCV = 25o ; ∠ BAY = 90o – ∠XAU = 65o

15 110 x 110 x 110 x 40% = 532 400 cm3 = 532.4l 4 – 0.55 = 3.45l ; 3.45l of water filled in the tank per minute. 532.4 ÷ 3.45 = 154 ; It takes 154 minutes = 2h 34 min to fill the tank completely.

16 80 x 60 x 40 = 192 000 cm3 ; The current volume is 192 000 cm3. 80 x 60 % = 48 cm ; The new length is 48 cm. 192 000 ÷ 48 ÷ 40 = 100 ; The new width is 100 cm. The new size of the box is 100cm x 48cm x 40 cm

17 Stage n: a square, with (2n-1)-small-square side, consist of (2n-1)×(2n-1) small squares. (a) (2 × 4 – 1) × (2 × 4 – 1) = 49 ; (2 × 5 – 1) × (2 × 5 – 1) = 81 (b) (2 × 10 – 1) × (2 × 10 – 1) = 361

18 (a) K : S : X = 6 : 4 : 5 = 60 : 40 : 50 ; Kate gave away: 60 ×

41

= 15

Xu Bin’s sweets increased: 50 × 10% = 5 ; Susan’s sweets increased: 15 – 5 = 10

4010

× 100% = 25% ; The percentage increase of Susan’s sweets was 25%

(b) (40 + 10) – (60 – 15) = 5n = 10 => n = 2 ; 60 × 2 = 120 ; Kate had 120 sweets at first.

Answers to Midyear Examination: Mock Paper 2- Paper 1


16 A = 183 17 13294.118g 18

Coffee : Milk = 3

2B÷

53A

and BA

= 3 ; Coffee : Milk = 2710

19 150 l50 ml 20 0.007 21 $680 ÷ (100% – 15%) = $800 ; The normal price of the TV is $800 22 (200 × 300) ÷ 50 = 1 200

Mrs Tan uses 1 200g sugar 23 ∠AOC +∠ FOH = ∠ AOC +∠ GOE = 180o –

∠ BOG – ∠ COE = 140o

176

24 Let d, k, t be heights of David, Ken and Terence.

d = 4

3k;

83k

=3t

=> t = 8

9k; Hence, d : k : t =

43k

: k :8

9k= 6 : 8 : 9

25 Length of each side is 5 cm. 5 × 5 × 5 = 125 cm3; The volume of each cube is 125 cm3. There are 8 cubes formed the solid. 125 × 8 = 1 000 ; The volume of whole solid is 1 000 cm3.

26 The number of stickers bought from set A and set B is divisible by 12.

412

×15 + 3

12× 10 = 85 ; The number of stickers

bought from set A and set B is 12. 12 + 12 = 24 ; Annie bought 24 stickers in total.

27 21 – 1.8 = 19.2 Jia Wei paid $19.2 if he bought 6 pencils and 6 notebooks. 19.2 ÷ 6 = 3.2 The cost of 1 pencil and 1 notebook was $3.2 (3.2 – 1.8) ÷ 2 = 0.7 Each pencil costs $0.7

28 a : b =

165

÷125

= 43

29 2 × 2 × 2 = 8 ; Volume of cube A is 8 cm3

28 × 56 × 80 = 125 440 Volume of Figure B is 125 440 cm3 125 440 ÷ 8 = 15 680 ; There are 15 680 cubes needed to fill in Figure B completely.

30 580 × 25% = 145; There are 145 Mathematics books. 145 × 20% = 29; The number of P6 Mathematics books is 29.

58029

=201

; 201

of books in library are P6 Mathematics books

Midyear Mock Paper 2- Paper 2 1

Guo Yan was 107

of the distance from the finishing point. Gu Jing was 95

of the distance from the finishing

point.

65 ÷ ⎟⎠⎞

⎜⎝⎛ −

95

107

= 450 ; The length of the running distance is 450 m. 450 ×95

= 250 ;

Gu Jing was 250 m from the finishing point. 2 144 ÷ 2 = 72; The sum of breadth and length is 72 cm.

72 ÷ (5 + 7) = 6 ; 6 × 5 = 30 ; 6 × 7 = 42 ; The size of the rectangle is 42cm × 30cm. 3 22 × 14 ÷ 11 = 28; 22 × 15 ÷ 11 = 30 ; (22 + 5) + (28 + 5) + (30 + 5) = 95

The total age of them is 95 after 5 years. 4 ∠ PSR = 180o – 35o = 145o

∠ QSR = 145o – 85o = 60o ∠ POS =∠ PQS =∠ QSR = 60o

6 (b) 14 cm 7 (3.1 – 1.5) ÷ 2 = 0.8 ; Each muffin costs $0.8

0.8 + 1.5 = 2.3 ; Each cake costs $2.3 10 × 2.3 + 15 × 0.8 = 35 Mrs Lee needs to pay $35.

5

8 3 : 4, 2 : 1 = 8 : 4

8 – 3 = 5, 10 ÷ 5 = 2, 2 × 3 = 6 There were 6 yellow pencils. 2 × 4 = 8 There were 8 green pencils. 6 + 8 = 14 There were 14 pencils before adding more pencils.

9 20 × 15 × 18 = 5 400 The volume of the tank is 5 400 cm3.

5 400 × 87

= 4 725 cm3 = 4.725l

4.725 + 0.5 = 5.225l The volume of the water in the tank now is 5.225l

10 1 –

31

= 32

; 32

of female are women. 53

×32

× 100% = 40% ; 40% of the audience is women.

11 61.5 – 27 = 34.5 ; The length of the 2nd cut was 34.5 cm.

177

34.5 ÷ 52

= 86.25 have not change working. The length of the ribbon after the 1st cut was 86.25 cm.

86.25 + 27 = 129.5cm. The original length is 113.25 cm 12

41

÷ 36

= 81

; 81

of A is shaded. 1 – 81

=87

; 87

of the figure is un-shaded.

13 (a) ∠ DMO =∠ ABM = 15o ; ∠ DOM =∠ ADC – ∠ DMO = 65o – 15o = 50o (b) ∠ BOC =∠ DMO +∠ OCD = 15o + 20o = 35o

14 35 000 × 95% = 33 250 ; Mr Chen pays $33 250 if he wants to make a full payment. 35 000 × 10% = 3 500 ; 1 500 × 24 = 36 000 3 500 + 36 000 = 39 500 ; Mr Chen pays $39 500 if he wants to pay by installments. 39 500 – 33 250 = 6 250 ; He saves $6 250 if he pays in full.

15 (18 – 4) ÷ 2 = 7 ; 7 + 4 = 11 ; There were 11 books and 7 notebooks. 11 – 2 = 9 ; Betty had 9 books after giving 2 books to her sister. 9 ÷ 3 = 3 ; Betty had 3 notebooks after giving some notebooks to her cousin. 7 – 3 = 4 ; Betty gave 4 notebooks to her cousin.

16 30 × 30 × 30 = 27 000 ; The volume of the tank is 27 000 cm3.

27 000 × 32

= 18 000; The tank has 18 000 cm3 at first.

27 000 × 43

= 20 250 ; The tank has 20 250 cm3 after adding water.

20 250 – 18 000 = 2 250; 2 250 cm3 is added to the tank.

30302250×

= 2.5 ;The increase in the height of water level in the tank is 2.5 cm

17 Let a, b be the number of red and yellow papers in package A; c, d be the number of red and yellow papers in package B.

(a) ba

=9

10 => a =

910b

; dc

=65

=> c = 6

5d;

dcba

++

=3319

=> dd

bb

+

+

659

10

=3319

=> db

=21

The ratio of the number of yellow papers in package A to the number of yellow papers in package B was 1:2. (b) 5 : 6 = 15 : 18, 17 : 18 ; 17 – 15 = 2, 4 ÷ 2 = 2 ; 2 × 15 = 30 There were 30 red papers in package B at first.

18 (a) Pattern 1 2 3 8 9 Beans 2 3 4 9 10 Sticks 1 3 5

… … … 15 17

(b) In pattern n, the number of sticks = 2 × n – 1; 2 × 100 – 1 = 199; There are 199 sticks in pattern 100 2 × 150 – 1 = 299 ;There are 299 sticks in pattern 150 299 – 199 = 100; There are 100 more sticks in pattern 150 than in pattern 100 (c) 2 × 1000 – 1 = 1999; There are 1999 sticks in pattern 1000



16 6 × (10+5) = 75

The perimeter of the figure is 75 cm 17 8.27

178

18

156060×

= 240

There are 240 pages printed in 1 hour = 60 minutes

19 4 × (7 × 7 × 7) = 1 372 The volume of the cuboid is 1 372 cm3.

20 (2x + 5) × 4 + (3x + 1) × 4 = 20x + 24 The perimeter of the figure is (20x + 24) cm.

21 11h30min – 1h50min = 9.40 a.m

22

87

÷ 4 = 327

; Each kid got 327

of the cake. 23

3215

24 10 ×

52

– 1 = 3 ; 3 more squares need to be shaded. 25 (0.5 × 60) + (1 × 80) = 110

Mr Tan travelled 110km in total.

26 9.4 × 2 = 18.8; The volume of the tank is 18.8 m3.

18.8 × 43

= 14.1; The volume of the water inside is 14.1 m3.

27 y = 48.6 28

625 ÷ 75 = 325

h = 8h20min; Time needed to travel is 8h20min.

19h30min + 8h20min = 27h50min = 3.50 am next day; Sandeep reached Cameron Highlands at 3.50 am next day.

29 14 × 2 ×

722

÷ 2 = 44; The perimeter of each semicircle is 44 cm.

44 × 4 = 176; The perimeter of 4 semicircles is 176 cm. 14 × 4 = 56; The length of 4 straight lines is 56 cm. 176 + 56 = 232 cm. The perimeter of the figure is 232 cm.

30 6 – 4 = 2 ;2 + 2 = 4 ;4 ÷ 2 = 2 ;Each book costs $2 Midyear Mock Paper 3- Paper 2

1 40 ÷ 5 = 8 ; Ben can cut at most 8 cubes by the side of 40 cm. 28 ÷ 5 = 5.6 ; Ben can cut at most 5 cubes by the side of 28 cm. 22 ÷ 5 = 4.4 ; Ben can cut at most 4 cubes by the side of 22 cm. 8 × 5 × 4 = 160 ; Ben can cut at most 160 5-cm cubes.

2 450 + 200 = 650 James has $650. (450 + 650) ÷ 2 = 550 The average is $550.

3

87

×56

=2021

The ratio of Albert’s height to that of Kelvin’s height is 21 : 20.

4

BA

=%60%40

=32

; 25 ÷ (3 – 2) = 25

A = 25 × 2 = 50 ; B = 25 × 3 = 75 50 + 75 = 125 ; The total value of A and B is 125.

5 300 × 80% = 240 After 20% discount, the price was $240. 240 × 85% = 204 James needed to pay $204 after 15% discount on the discounted price with his membership card.

6 (a) ($1.05 + $0.25×2) +$ 2.50 = $4.05 Mrs Won needed to pay $4.05 altogether. (b) 3pm to 5pm: $1.05 + $0.25 × 4 = $2.05 5pm to 7pm: $2.10 $2.05 + $2.10 = $4.15 Mr Liu needed to pay $4.15 for his parking slot.

7 (a) Salim cycled: 3w + 500 (m) Salim ran: 3 × 3w = 9w (m) (3w) + (3w + 500) + (9w) = 15w + 500 Salim covered 15w + 500 (m) on total. (b) 15 × 400 + 500 = 6 500 Salim covered 6 500 m if w = 400.

8 6u – 1u = 5u = $40 u = $8 9 × 8 = $72 His original amount of money is $72.

9 (a) 1 : 8; (b) 25 ×

83

= 9.375 cm2.

The total area of 3 triangles MNO, APO and COQ is 9.375 cm2.

10 (a) Thursday and Saturday; Monday and Friday. (b) 3 : 2 (c)

251025 −

× 100% = 60%

179

11 (a) (5 × 2 ×

722

) ÷ 4 = 755

; The perimeter of each quarter circle is 755

cm.

755

× 4 = 3173

; The perimeter of the shaded figure is 3173

cm.

(b) 5 × 5 × 2 = 50; The area of the shaded figure is 50 cm2. 12 (a) 1350 – 600 = 750

750 ÷ 250 = 3 Daniel took 3 months to save. (b) 1350 ÷ 3 = 450 450 + 500 = 950 Ken’s monthly income is $950.

13 (a) 3u = 120; 2u =

3120

×12

= 80

Alice has 80 Singaporean stamps. (b) 120 – 30 = 90 She has 90 Japanese stamps left.

14 10% × 30 = 3; 30 + 3 = 33; 33 + 30 = 66; 100 – 63 = 37; 37% of the participants were from school C. 222 ÷ 37% = 600; There were 600 participants in total.

15 $10 × 7 = $70; $5 × 4 = $20; $70 + $20 = $90 $2340 ÷ $90 = 26; 26 × 4 = 104; There were 104 students from school ABC.

16 In stage n has n×n stars, 2×(n+1)×n sticks (a)Stage 5: 5×5=25 stars, 2×6×5=60 sticks; Stage 6: 6×6=36 stars, 2×7×6=84 sticks (b) Stage 100: 100×100=10 000 stars, 2×101×100=20 200 sticks

17 180 – 80 = 100; 2u = 100 => 3u = (100 ÷ 2) × 3 = 150; 150 – 80 = 70 Bethesda received 70 flowers.

18 20 × 4 = 80; 480 – 80 = 400; 400 ÷ 2 = 200; 200 ÷ 4 = 50; 50 + 20 = 70 The speed of Ben’s car was 70 km/h



16 56 17 48 ÷ (5 + 7) = 4; 4 × 5 = 20

Andrew’s age is 20. 18 0.625 19 (200 ÷ 4) × 1.25 = 62.5; He can earn $62.5 20 5.005 + 0.025 = 5.03 kg 21 25 × 15 × 7 = 2 625 cm3.

The volume of the cuboid is 2 625 cm3. 22 60 – 20 – 12 – 10 = 18

18 students choose Indonesia. 20 – 18 = 2 2 more students plan to visit China than Indonesia.

23 1.30pm – 2.30pm: $2 2.30pm – 3.25pm: $1.5 working to change $2 + $1.5 = $3.5 Mr Tan pays $3.5

24 48 ÷ 80% = 60 The total score of the test is 60.

25

5.220 x−

26 8 + 4 + 5 = 17 The diameter of the largest semicircle is 17 cm. The perimeter of the largest semicircle is

217π

(cm)

27 36 × 24 = 864; Area of the sheet is 864 cm2. 6 × 4 = 24; Area of each piece is 24 cm2. 864 ÷ 24 = 36 She can make 36 pieces from the sheet.

28 20 – 5 = 15; Joey has 15 candies at first. 29 Car and motorbike have 4 and 2 wheels respectively.

240 × 4 = 960; If all are cars, there are 960 wheels. (960 – 680) ÷ 2 = 140; 240 – 140 = 100; There are 100 cars and 140 motorbikes in the car park.

30 AEFD and BEFC are trapeziums with equal sizes. (change question paper, AB is perpendicular to EF) 6 ÷ 2 = 3; The height of the trapezium is 3 cm.

180

23)64( ×+

= 15; The area of each trapezium is 15 cm2.

15 × 2 = 30; The shaded area is 30 cm2. Midyear Mock Paper 4- Paper 2

1 (20 × 8) × 3 = 480; The smallest area is 480 cm2. 2 (40+70+60+55+45+50) ÷ 6 = 53 1/3 3 C and E 4 240o 5 5 × 5 × 5 = 125; The ratio of the volume of cube A to the volume of cube B is 125 : 1 6 3 big-size cakes and 2 medium-size cakes. 7 ($1 × 68) + ($2 × 50) + ($3 × 55) = $333

The shop collected $333 from the sale. 9 (b) 7.9 cm 10 LCM of 3, 8, 10 is 120.

120 seconds = 2 minutes. 12am + 2 minutes = 12h 02 min They will ring together again at 12h 02 min.

8

Area of triangle XAE = (2 × 6) ÷ 2 = 6 Area of triangle YBC = (8 × 6) ÷ 2 = 24 Area of triangle ZCD = (2 × 4) ÷ 2 = 4 Area of triangle TED = (4 × 8) ÷ 2 = 16 Area of XYZT = 12 × 10 = 120 Area of the garden = 120 – 6 – 24 – 4 – 16 = 70 m2.

11 320 ×

167

= 140; 320 – 140 = 180

He had 140 orange and 180 lemon candies at first. 140 – 30 = 110 ;He had 110 orange candies after giving to some his friend.

110 ÷ 1511

= 150;180 – 150 = 30

He gave 30 lemon candies to his friend. 12 38 – 23 = 15; 45 ÷ 15 = 3; The police car catches up with the motor after 3 time units. 13 6.30 am – 6 am = 30 min; 12 ÷ 2 = 6km, 6 – 1.5 = 4.5km; 60 min ÷ 10 = 6 min with 1 km

6 min ÷ 2 = 3 min with 0.5 km; 6 + 3 = 9 min; 4 × 6 = 24 min; 24 + 3 = 27 min; 6.30 am + 9 min = 6.39 am 27 + 9 = 36 min; 6.39 am – 36 min = 6.03 am.; Jerry left home at 6.03 am.

14

∠ BNM = 180o ÷ (3 + 1) = 45o. ∠ BMN = 90o – 45o = 45o.

16 Position i: 3i + 5 3 × 100 + 5 = 305

17 5 × 5 × 3.14 ÷ 4 = 19.625 The area of each quarter circle is 19.625 cm2.

19.625 ×32

+ 19.625 ×31

= 19.625 cm2.

The shaded areas are 19.625 cm2.

15 a) At first Later L : R L : R 7 : 3 = 10u 1 : 4 = 5u 2 : 8 = 10u 5u = 100 => u = 20, 10u = 10 x 20 = 200 The total number of books is 200 at first. b) 20 × 7 = 140, 20 × 3 = 60, The left and right bookcase has 140 and 60 books at first. 60 + 100 = 160, The right bookcase has 160 after adding more books. 160 × 25% = 40, The right bookcase has 40 books after all.

18 9 – 2 = 7; Difference between Chris and Betty = 7 – 2 = 5u = 5 => u = 1 12 × 1 = 12; The teacher gave 12 books to his 3 students.

Answers Midyear Examination: Mock Paper 5- Paper 1


16 20 y + 17 18 73 km/h

17 1

43

×60 = 105 min

19 1200 × 1.7 ÷ 50 = $40.8 1kg 200g of that paper costs $40.8

20 18 ÷ (

74

- 25%) = 56; A is 56.

181

21 200 ÷ 75 =

38

h = 160 min = 2h 40min; The taxi took 2h 40min to reach B.

8am + 2h 40 min = 10.40 am; The taxi reached B at 10.40 am 22

Before using: YR

=32

. After using, Ann has 3

2Rand

54Y

; The new ratio =

543

2

Y

R

= 32

×45

×YR

= 5 : 9

23

24 100 – 25 – 40 = 35 35% of the students are from school C. 20 ÷ (35% - 25%) = 200 The total number of students is 200. 200 × 40% = 80; 80 students are from school B.

25 11 30 + 2h35min + 21min – 1h = 13 26 The time in Bangkok was 13 26.

26 36 ÷ (13 – 7) = 6; 6 × 13 = 78 Mrs Kan bought 78 cheese cakes.

27 120 + 7k – 3k – 80 = 4k + 40; The total length after cutting was (4k+40)cm. (4k + 40) ÷ 4 = k + 10; The length of each piece was (k + 10) cm.

28 (670 + 140) ÷ 75 = 10.8 She takes 10.8 min to go to school on rainy days.

29 25%

30 5th and 6th T-shirt: $18 x 80% = $14.4; Total: $18 x 4 + $14.4 x 2 = $100.8 Midyear Mock Paper 5- Paper 2

1 ∠ AMB = 180 – 75 – 35 = 70o. ∠ ACM = 70o ÷ 2 = 35o. ∠ ACN =

41

× 35o = 8.75o

2 60 ÷ ( 4 × 5 × n) =

n3

; The product of the last 2 numbers is n3

.

3

250250310−

x 100% = 24%; The watch will be raised 24%.

4 350 ÷ 5 = 70; His current speed is 70 km/h 70 + 5 = 75; After increasing, his speed is 75km/h 350 ÷ 75 = 4h40min; He takes 4h 40min to reach town B.

5 3 ; 8 ; 13 ; 18 ; 23 ; 28 ; 33 ; 38 ; 43 ; 48 48 coins of 10 cents = $4.8; She saved $4.8 on the 10th day.

6 OM = AM ÷ 2 = 5.2 ÷ 2 = 2.6 cm Area of the trapezium KHCB =

26.2)63( ×+

=11.7 cm2.

PN = AM ÷ 4 = 5.2 ÷ 4 = 1.3 cm.

Area of triangle BPC = 2

3.16×= 3.9 cm2.

Area of the quadrilateral BKHP = 11.7 – 3.9 = 7.8 cm2.

7 250 – 60 = 190, 250 – 80 = 170 The ratio of the speed of Bob to that of Casey is 19 : 17

250 × 17 ÷ 19 = 2231913

; 250 – 2231913

= 26196

Casey was 26196

m away from the finishing point

when Bob reached.

8 (a) 145 × 2 = 290 The sum of the height of Chris and Jen is 290 cm. May’s height is (45y – 290) cm (b) 115 cm

9 32 ÷

74

= 56; 56 + 4 = 60; 60 ÷ 75% = 80

Ann had 80 candies at first. 10 3 – 2 = 1, 4 × 2 = 8, 4 × 3 = 12

Linda had 8 pencils. Emily had 12 pencils. 40 ÷ (12 + 8) = 2 Each pencil costs $2. 12 × $2 = $24 Emily paid $24.

11 1500 x 45% = 675 The current number of men is 675. 1500 x 50% = 750 750 – 675 = 75 75 more man needed to come to increase the percentage.

12 ∠ EAD = (180 – 130) ÷ 2 = 25o. ∠ DAB = 90 – 25 = 65o.

182

∠ ADC = 180 – 65 = 115o. ∠ x = 360 – 115 – 130 = 115o. 13 228 × 2 = 456; There are 456 coffee candies.

(456 + 228) ÷ 57% = 1200; There are 1200 candies in total. 1200 × 43% = 516; There are 516 fruit candies. (516 – 228) ÷ 228 × 100% = 126%; There are 126% more fruit candies than milk candies.

14 260 – (60 × 2) = 140; The length of remaining part was 140 km. 4 – 2 = 2; Time taken for that part was 2h. 140 ÷ 2 = 70; The average speed for the remaining part of the journey was 70 km/h.

15 Distance between Albert and his house when David started: 70 x ¼ = 17.5 km After x(h), they meet: 70x + 75x = 800-17.5 => x = 5.4(h); They meet at: 10 15 + 5.4h = 15 39

16 2 × 2 × 3.14 ÷ 2 = 6.28 2.5 × 2 × 3.14 ÷ 2 = 7.85 The length of each half circle is 6.28 cm and 7.85 cm. 7.85 + (8-5) + (6-4) + 6.28 + 7.85 + (8-5) + (6-4) + 6.28 = 38.26cm The perimeter of the new shape is 38.26 cm.

17 (a) When A finished the race, B finished 75% length of the race. So, the ratio of B’s speed to A’s speed 75% = 3 : 4; 4 – 3 = 1 30 × 4 = 120; A’s speed was 120 km/h 120 × 3 = 360; The total distance of the race was 360 km. (b) 30 × 3 = 90; B’s speed was 90 km/h

18 Let s, c be the number of strawberry and chocolate cakes.

After 1st case: strawberry : chocolate = 5 : 8 => s = 85c

+ 2

After 2nd case: strawberry : chocolate = 6 :5 => c = 65s

+ 6 = 4825c

+ 323

c = 16; The number of chocolate cakes was 16. 8165×

+ 2 = 12. The number of strawberry cakes was 12.

16 – 6 = 10, 12 + 4 = 16, 1016

16+

= 138

; 138

of the cakes would be strawberry cakes after the last move.

Answers to Preliminary Examination: Mock Paper 1- Paper 1


16 2, 3, 5 17 0.005 18 12’s factors: 1, 2, 3, 4, 6, 12; 32’s factors: 1, 2, 4, 8, 16, 32

Their common factors: 1, 2, 4; 1 × 2 × 4 = 8; Their product is 8. 19 633.6 ÷ (22 × 1.8) = 16; The breadth is 16 m. 20 (150 × 0.05 + 101 × 0.5 + 160 × 0.2) ÷ 5 = 18; Mrs Kan got 18 notes. 21

16 × 43

- 4 = 8; 8 more parallelograms need to be shaded.

23 87.5% 24

25 G:R = 13:10; 13-10 = 3; 3u = 3; 1u = 1

13u + 10u = 23u = 23x1 = 23

22

26 238.4

27 56 ÷ 6 has remainder 2; The box is black. 28 8624 29 The smallest length and breadth of the rectangle are 8cm and 6cm.

(8 + 6) × 2 = 28; The smallest perimeter is 28 cm. 30 20 ÷ 2 = 10; The radius of the circle is 10 cm.

10 × 10 × 3.14 = 314; 314 ÷ 4 = 78.5; The area of each quarter circle is 78.5 cm2. 78.5 + 10 × 10 = 178.5 ; The area of the shaded parts is 178.5 cm2.

183

Preliminary Examination: Mock Paper 1- Paper 2 1 10 × 10 ÷ 2 = 50; 15 × 15 ÷ 2 = 112.5; 5 × 25 ÷ 2 = 62.5; 50 + 112.5 + 62.5 = 225

The area of unshaded region is 225 cm2. 25 × 15 = 375; The area of the rectangle is 375 cm2. 375 – 225 = 150; The area of shaded triangle is 150 cm2.

2 0.6 × 0.6 = 0.36; The area off each tile is 0.36 m2. 54 ÷ 0.36 = 150; 150 tiles are needed.

3 85 + x = 150 x = 150 – 85 = 65o.

4 1.20pm -> 2.20pm: $1.2; 2.20pm -> 4.20pm: $0.9 x 4 = $3.6; 4.20pm -> 5pm: $0.9 x 2 = $1.8 5pm -> 8pm: $2.5; 1.2 + 5.4 + 2.5 = 9.1 Mr Cheong paid $9.1.

5 $29.25 ÷ 15% = $195; Last month saving was $195. $195 ÷ 30% = $650;Wai Hong’s monthly salary is $650. 6

(a) 6g + 6g + 3g + 3g + 3g = 21g The perimeter of the figure is 21g cm. (b) 21 × 5 = 105 The perimeter of the figure is 105 cm.

8 (a) ∠ ACB = 90o. (b) ∠ ACD = 90o + 25o = 115o.

7

(a) (b) 500 × 22% = 110 110 people gave the answer “Always”.

9 150 × 12 ÷ 50 = 36; She took 36 min to type the first 12 pages. 100 × (40-12) ÷ 40 = 70; She took 70 min to type the first remaining pages. 36 + 70 = 106 min = 1h 46 min; She took 70 min to type the whole report.

10 6 × 5 = 30; 390 ÷ 30 = 13 There were: 6 × 30 = 180 fruit candies; 3 × 30 = 90 milk candies; 4 × 30= 120 chocolate candies

11 8 × 8 × 3.14 ÷ 2 = 100.48; The area of the semi-circle is 100.48 cm2. 2 × (8 × 2) ÷ 2 = 16; The area of the triangle MAB is 16 cm2. 100.48 – 16 = 84.48; The area of the shaded part is 84.48 cm2.

12 The first 60 throws missed: 60 × 2/5 = 24 The last 20 throws missed: (80-60) × (1-85%) = 3 24 + 3 = 27 He missed 27 times.

13 (a) ∠ AMD = ∠MAC +∠ ACD 80 = ∠MAC + 65; ∠MAC = 15o. ∠ a = ∠ DAC -∠MAC = 65 – 15 = 50o. (b) ∠ b = 180 – 65 – 65 = 50o.

14 5 – 2 = 3; 45 ÷ 3 = 15; 15 × 5 = 75; Ken has 75 coins. 15 × 2 = 30; Emily has 30 coins.

75 × 51

= 15; Ken gives Emily 15 coins, costs 15 × 0.2 = $3; 14.6 – 3 = 11.6; Emily has $11.6 at first.

15 (a) 11am – 6.30am = 4h 30min = 4.5 h. The bus took 4.5h to travel. 60 × 4.5 = 270; The distance between 2 towns was 270 km. (b) The car departed at 6.45 am; 10.30am – 6.45am = 3h 45 min = 3.75 h.; The car took 3.75h to travel. 270 ÷ 3.75 = 72; Its speed was 72 km/h. (c) 9.45am – 6.30 am = 3.25h; 60 × 3.25 = 195; The bus covered 195 km at 9.45am 9.45am – 6.45am = 3h; 72 × 3 = 216; The car covered 216 km at 9.45am 216 – 195 = 21; They were 21 km apart.

16 (a) 8 + 4 = 12; Brian had $12 more than Ann. 19 – 13 = 6; 12 ÷ 6 = 2; 2 × 19 = 38; Brian had $38 at first. (b) 2 × 13 = 26; Ann had $26 at first. 26 + 4 = 30; Ann had $30 after borrowing $4 from Casey. Ann and Brian had $30 in the end.

17 1 min = 2100ml + 2500ml = 4600ml; 4600ml water was added in 1 min.; 4600 × 5 = 23 000ml 23 000ml water was added in 5 mins. 4600ml – 600ml = 4 000ml; 4 000ml × 2 = 8 000ml; 2300ml + 8 000ml = 3100ml; 3100 ÷ (50 × 40) = 15.5 The water level is 15.5cm after the plug is removed.

18 (a)

52

÷ 3 = 152

; 1 skirt costs 152

of her money. 52

+ 2 × 152

= 32

; She spent 32

of her money on skirts.

1 – 32

= 31

= 33.33%; She spent 33.33% of her money on T-shirts.

(b) 13 ÷ 33.33% = 39; All of her money can buy 39 T-shirts. 39 ÷ 6 = 6 with remainder 3; 36 + 6 = 42; 42 + 3 = 45; She got 45 T-shirts in total.

184

Answers to Preliminary Examination: Mock Paper 2- Paper 1


16 n = 3 17 6.375 18

474

19 The length of each side is 98 cm

AC = 98 × 2 = 14 cm 20 234 21 In row i, column j, the number is 2i + 3j; 2i + 3j = 67; i = 11, j = 15; The number “67” is in column 15. 22 28 ÷ 2 = 14; The radius of each arc is 14 cm.

14 × 14 × 722

= 616; The area of each circle of radius 14 cm is 616 cm2.

616 ÷ 4 = 154; The area of each quarter circle is 154 cm2. 14 × 14 = 196; The area of the square of side 14 cm is 196 cm2. 196 – 154 = 42; (154 × 3 + 42) × 2 = 1008; The area of the figure is 1 008 cm2.

23 8.35 am + 3h45min = 12h 20min; He reached his friend’s house at 12 20 24 1 pupil plants 1 tree in 10 mins. 20 pupils plant 20 trees in 10 mins. 25 30 min = 0.5h; 80 × 0.5 = 40; The truck covers 40 km after 30 minutes.

60 × 0.5 = 30; The truck covers 30 km after 30 minutes. 40 + 30 = 70; 2 cities are 70km apart.

26 30 ÷ 8 = 3 with remainder 6; She got 3x2 = 6 free oranges. 8 × 3 = 24; She bought 24 oranges in order to have 30 oranges.

27 36 ÷ 4 = 9; Each square side has area of 9 cm2. Each square has side of 3 cm. 3 × 3 × 3 = 27; The volume of each cube is 27 cm3. 27 × 8 = 216 cm3. The volume of the solid is 216 cm3.

28 100 – 30 – 40 – 10 = 20; She spent 20% of her money on tickets. 29 6 × 2 = 12; Jia Wei spends $12 on books.

(15n + 13 – 12) ÷ 3 = 5n + 31

; The price of each pencil is $ (5n + 31

)

30 32 – 8 = 24; 8 pupils received 24 biscuits. 24 ÷ 8 = 3; Each student received 3 biscuits. 3 × 32 = 96; There were 96 biscuits in the box at first.

Preliminary Mock Paper 2- Paper 2 1 (1+1)×4÷2 = 4; 6 – 4 = 2; (1+1)×2÷2 = 2

4 + 2 = 6; The area of the shaded area is 6 cm2. 6 × 10 = 60; The area of the rectangle is 60 cm2. 60 – 6 =54 The area of the unshaded area is 54 cm2.

2

3 50 ÷ 4 = 12.5; The length of the Styrofoam cuboid can be cut to form 12 4-cm cubes.

40 ÷ 4 = 10; The length of the Styrofoam cuboid can be cut to form 10 4-cm cubes. 30 ÷ 4 = 7.5; The length of the Styrofoam cuboid can be cut to form 7 4-cm cubes. 50 × 40 × 30 = 60000; The volume of the cuboid is 60 000 cm3. (12×4)×(10×4)×(7×4)=53760; 60000 – 53760 = 6240; The minimum wastage is 6 240 cm3.

4 60 – 6 – 4.5 – 7 – 5.5 = 37; She had $37 left. 5 6.15pm – 8.15 am = 10; He parked 10 hours. 1.5 + 1 × (10×2 – 2) = 19.5; He paid $19.5 for parking.

6 4 + 5 + 3 = 12; The length of the triangle’s base is 12 cm. The height of the triangle is 4 cm. 12 × 4 ÷ 2 = 24; The area of the shaded triangle is 24 cm2.

7 ∠ BMN = ∠ DQP = 20o. 8 (a) ∠ BCD = 55 + 20 = 75o.

185

∠ n = ∠ ABC – ∠ BMN = 90 – 20 = 70o. (b) ∠ ABC = 180 – 75 = 105o. 9 40 + 5 × 3 = 55; 2 + 3 = 5; 55 ÷ 5 = 11

11 × 2 = 22; Betty has 22 papers. 10 958.5 – 150 = 808.5

808.5 ÷ 2 = 404.25; Jack saves $404.25 11 (a) ∠ DAC = 90 - ∠ OCD = 90 – 45 = 45o. ∠ NAM = ∠ DAC = 45o.

(b) ∠ COB = 2 × ∠ OAB = 2 × 15 = 30o. ∠ OBC = (180 – 30) ÷ 2 = 75o. 12 Let y be the number of pens.

1st day: 0.2y; 2nd day: 28; 3rd day: (0.2y+28)÷2=0.1y + 14; 4th day: 0.2y + 9; 5th day: 64 y = 0.2y + 28 + (0.1y + 14) + (0.2y + 9) + 64; y = 230 The factory produced 230 pens in those 5 days.

13 (a) 11am – 7.45 am = 3.25h; 85 × 3.25 = 276.25; Ben covered 276.25 km at 11am 7.45 am + 30min = 8.15 am; Rollend departed at 8.15am 11am – 8.15 am = 2.75h; 80 × 2.75 = 220; Rollend covered 220 km at 11am 276.25 – 220 = 56.25; They were 56.25 km apart at 11am (b) 80 × 0.25 = 20; At 8.30am, Rollend covered 20 km and started increasing speed to 80+15 = 95 km/h 8.30 am – 7.45 am = 0.75h; 85 × 0.75 = 63.75; At 8.30 am, Ben covered 63.75 km. 63.75 – 20 = 43.75; They were 43.75 km apart at that time. 43.75 ÷ (95 – 85) = 4.375 = 4h 22min30s Rollend took 4h22min30s to overtake Ben.

14 Lauren has 3 × 2 = 6 sweets more than Annie => 3 times of Lauren’s sweets are 6 × 3 = 18 sweets more than 3 times of Annie’s. 3 times of Annie’s sweets are 3 × ( 3 + 1) = 12 sweets more than Lauren’s. 12 + 18 = 30; 3 – 1 = 2; 30 ÷ 2 = 15; Lauren has 15 sweets. 15 – 6 = 9; Annie has 9 sweets. (15 + 9) ÷ 2 = 12; 12 – 5 = 7; Chris has 7 sweets. 15 + 9 + 7 = 31; They have 31 sweets in total.

15 (a) 5 × 5 × 3.14 = 78.5; 78.5 ÷ 2 = 39.25; Each arc has the area of 39.25 cm2. 39.25 × 8 = 314; The total area of the shaded part is 314 cm2. (b) 5 × 2 × 3.14 = 31.4; 31.4 ÷ 2 = 15.7; Each arc has the perimeter of 15.7 cm. 15.7 × 8 = 125.6; 10 × 8 = 80; 125.6 + 80 = 205.6 The total perimeter of the shaded part is 205.6 cm.

16 (a) 5 × 5 × 5 = 125; The volume of each cube is 125 cm3. (b) 125 × 8 = 1000; The volume of eight cubes is 1000 cm3.

After removing the cubes, the tank is 32

full.

43

–32

= 121

1000 ÷ 121

= 12000; The volume of the tank is 12000 cm3.

12000 ÷ (10 × 10) = 120 cm. The height of the tank is 120 cm. 17 (a) 10, 22; 13, 35

(b) 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 = 151 He had 151 coins after the 10th day. 151 × 0.5 = 75.50 He had $75.50 after the 10th day.

18 (a) School C sent

6725

of the competitors minus 4; School B sent 1 -6725

- 6725

= 6717

of the competitors plus 4

School B and C sent 6742

of the competitors; 19 + 23 = 42

School B sent 6719

of the competitors and school C sent 6723

of the competitors.

Ratio A : B : C = 25 : 19 : 23; 25 – 23 = 2; 4 ÷ 2 = 2; 23 × 2 = 46; There were 46 competitors from school C. (b) 19 × 2 = 38; 38 competitors were from school B. 25 × 2 = 50; 50 competitors were from school A. 50 + 38 + 46 = 134; There were 134 competitors in total. Let y be the number of school B’s competitors leaving.

186

38 – y = 215

(134 – y) => y = 8; 8 competitors from school B left the competition.

Answers to Preliminary Mock Paper 3- Paper 1


16 $56 880 17 18.23pm – 11.22am = 7h 1min

He took 7h 1min to drive. 18

∠ DEC =∠ BEA = (180 – 108) ÷ 2 = 36o. ∠ × = 108 – 36 – 36 = 36o.

20 E 21 1700 – 200 – 250 – 175 – 275 – 300 – 225 = 225

The number of burgers sold on Sunday is 225. 22 (400 × 10) ÷ 250 = 16

The same amount of food would last 16 days.

19

23

41

=205

; 53

=2012

;52

=208

; 205

B = 2012

C = 208

L

B:C = 12:5, C:L=8:12, establishing common terms gives B:C:L= 96:40:60 = 24:10:15 24 1/10 25 The length of the breadth is 7n – 3; (7n + 7n – 3) × 2 = 28n – 6

The perimeter of the rectangle is (28n – 6) cm 26 107 27 2625 ÷ 75% = 3500; The number is 3500. 3500 × 40% = 1400. 28 2 books and 3 pens cost $18 => 10 books and 15 pens cost $90

3 books and 5 pens cost $28 => 9 books and 15 pens cost $84; 90 – 84 = 6; Each book costs $6. 29 25 × 50 × 35 = 43750; The volume of the tank is 43 750 cm3.

43750 ÷ 2 = 21875; The tank contains 21 875 cm3 water. 21875 ÷ 50 = 437.5; It takes 437.5 min to empty the tank.

30 98 × 2 = 14; The diameter of the circle is 14 cm.

14 ÷ 2 = 7; The radius of the circle is 7 cm. 7 × 7 × 722

= 154; The area of the circle is 154 cm2.

Preliminary Paper 3- Paper 2 2 ∠ ABC = (180 – 140) ÷ 2 = 20o.

∠ BAC = 180 – 140 – 20 = 20 3 25%

1

4 4 × 0.85 = $3.4; Let y be the number of green pencils. 0.75y + 3.4 = 0.79 × (y + 4) y = 6; She bought 6 green pencils. 6 + 4 = 10; She bought 10 pencils altogether.

5 3 ÷ 5 = 0.6; Each apple costs $0.6; 5 ÷ 4 = 1.25; Each banana costs $1.25 The number of apples bought is divisible by 5 and the number of bananas bought is divisible by 4. The numbers were the same, so, it must be divisible by 20. Try 20: 1.25 × 20 – 0.6 × 20 = $13 Emily bought 20 apples and 20 bananas. 1.25 × 20 + 0.6 × 20 = 37; She paid $37.

6 The smallest common factor of 2, 3, 4 is 12. They would meet again after 12 days. It was 13 Nov.

7 600 ÷ 10 = 60 60 ÷ (100% + 20%) = 50 He saved $50 every week.

8 (a) ∠ ADE = 180 – 135 = 45o. ∠MBE = 90 – 45 = 45o. (b) ∠ ADC + ∠ BCD = 360 – 135 – 45 – 45 = 135o.

9 (a) 100 – 20 – 18 = 62%; 62% of the spectators were adults.

187

(b) 20 + 18 = 38; 38% of the spectators were children. 12 : 19 = 24 : 38; 24% of the spectators were men. 1000 × 24% = 240; 240 men were in the stadium.

10 (a) $(40 + 0.3x); (b) 40 + 0.3 × 500 = $190 11 There were twice as many students in class B as class A => B is divisible by 2.

B is divisible by 3 => B is divisible by 6; B = 2A < 50 => A < 25; A + B + C = 100 Possible answers:

A 24 18 12 6 B 48 36 24 12 C 28 46 64 82

Since C < B, A = 24, B = 48, C = 28; There were 28 students in class C. 12

Daniel collected 1 – 169

=167

of the stamps. Peter collected 1 – 43

=41

of the stamps.

Ivan collected 1 - 167

- 41

= 165

of the stamps. Peter and Daniel collected 167

+41

=1611

of the stamps.

The collection had 55 ÷ 1611

= 80 stamps. Ivan had (80 × 165

) – (80 × 41

) = 5 more stamps than Peter.

13 5 × 5 = 25; The area of each side is 25 cm2. Level 1 has 5 faces to be covered by paint.

Level 2 has 20 faces to be covered by paint. Level 3 has 61 faces to be covered by paint. 25 × (5 + 20 + 61) = 2150; The total surface area that is covered by paint is 2 150 cm2.

14 350 ÷ 125% = 280; There were 280 boys at first. 300 ÷ 80% = 375; There were 375 girls at first. 280 + 375 = 655; 350 + 300 = 650 (a) There is an overall decrease of students. (b) 655 – 650 = 5; The overall decrease is 120.

15 (a) 5 + 1 + 2 = 8 parts; y coins in each part. 5y × 0.5 + y × 0.1 + 2y × 0.2 = $105 y = 35; Daisy saved 35 10-cent coins. (b) 105 ÷ 0.2 = 525 She would have 525 20-cent coins after the exchange.

16 7 + 5 = 12 parts. 60 ÷ 12 = 5; 5 × 5 = 25; 5 × 7 = 35 There are 25 l of wine in container A and 35 l of wine in container B.

17 Let y be the expected time.

The same distance = 75 × (y + 25min) = 60 × (y + 40min) => y = 127

h ; 75 × (127

+60min25

) = 75

The distance is 75 km. 75 ÷ 90 = 65

h = 50 min. It takes 50 min.

18 The area of the shaded part is equal to the area of 8 squares of 7-cm side. 7 × 7 × 8 = 392 cm2.



16 4q + 27 17 15 18 25 × 0.25 + 25 × 0.2 + 10 × 0.1 = $12.25

Mr Liu needs to pay $12.25 19 4 + 3 + 3 = 10 equal parts

80 ÷ 10 = 8; 8 × 4 = 32; The longest side is 32 m. 20 Zhang has (n + 20) marbles.

20 + (n + 20) = n + 40 Ming, Chen, Zhang have n + 40 marbles in total.

The average is 3

40+n.

21 In the shaded part, there are 24 whole squares and 20 half squares. 2 × 2 = 4; Each square has area of 4 cm2. 4 × 24 + 4 × 20 ÷ 2 = 136 The area of the shaded part is 136 cm2.

188

22 17 × 21 ÷ 3 = 119; It costs $119. 23 20 × 20 × 20 = 8000; The volume of the container is 8 000 cm3.

8000 × 41

= 2000; 2000 cm3 water has to be added to make the container full.

24 9.30pm – 4pm = 5.5h. He took 5.5h to reach town B. 75 × 5.5 = 412.5 Town A and town B was 412.5 km apart.

25 E : J = 2 : 5; J : M = 5 : 6; E : J : M = 2 : 5 : 6 2 + 5 + 6 = 13 equal parts.

The ratio of the number of Eric’s books to the total number of books of Eric, Jane and Mark is 132

26 0.5 × 5 + 0.3 = 2.8 For every 5 flowers, Beth earns $2.8 14 ÷ 2.8 = 5 5 × 5 = 25 She sold 25 flowers in order to earn $14.

27

28 4 × 3 ÷ 2 = 6; The area of the triangle is 6 cm2. 5 ÷ 2 = 2.5; The radius of the circle is 2.5 cm. 2.5 × 2.5 × 3.14 = 19.625; The area of the circle is 19.625 cm2. 19.625 ÷ 2 = 9.8125; 9.9125 – 6 = 3.8125; The area of the shade part is 3.8125 cm2.

29 ∠ACD = 180 – 75 – 40 = 65o. ∠CAB =∠ACD = 65o. ∠ y = 180 – 110 – 65 = 5o.

30 2 + 4 + 6 + 8 + 10 + 12 = 42 There are 42 passengers on the bus after it leaves the 6th stop.

Preliminary Mock Paper 4- Paper 2 2 360 – 90 – 24 = 246o.

∠ a = 246 ÷ 3 = 82o. 1

3 John had (115 – 5y) candies after eating 5.

Each sister received 2

5115 y−

4 9 notebooks had the same price with 6 books. 9 + 5 = 14; 14 notebooks cost $84 84 ÷ 14 = 6; Each notebook cost $6

66584 ×−

= 9; Each book cost $9

5 2 × 20 = 40 The volume of the tank is 40 l = 40 000 cm3. The height of the tank is

40000 ÷ (40 × 30) = 3331

cm.

6 4 – 1 = 3 equal parts. 78 – 36 = 42; 42 ÷ 3 = 14; There were 14 watermelons left. 14 × 4 = 56; There were 56 durians left. 78 + 36 – 14 – 56 = 44; 44 durians and watermelons were sold.

7 (a) ∠DAB = 180 – 75 × 2 = 30o. (b) ∠DCM = 30 + 30 = 60o. ∠BMC = 180 – 60 – 75 = 45o.

8 (a) 500 ×

52

= 200; Jan drove 200km when spending half of his time.

500 – 200 = 300; 300 ÷ 60 = 5; He spent 5 hours on each half. 5 × 2 = 10; He needed 10 hours to travel. (b) 200 ÷ 5 = 40; His average speed for the first part of his journey is 40 km/h.

9 Robin shared 152 to Robert and they had the same amount of beads. The number of beads that Robert had is 5 equal parts. Robin had 4 times what Robert had so he had 20 equal parts. Therefore, the difference before sharing is 152 x 2 = 304 304 ÷ (5 x 3 + 1) = 19; 19 x 20 = 380; Robin had 380 beads at first.

10 (a) (3 + 4) × 4 = 28; The perimeter of the figure is 28 cm. (b) (3 + 4) × (3 + 4) = 49; The area of the figure is 49

11 ∠BCD = ∠CBK = 75o. ∠BCM = 180 – 55 × 2 = 70o. ∠MCD = 75 – 70 = 5o.

189

∠BDC = 55 – 5 = 50o. ∠ABD = ∠BDC = 50o. 12 (a) (60 + 70 + 50 + 65 + 80 + 75) ÷ 6 = $66.67; The average amount donated by 6 students was $66.67

(b) 80 ÷ 400 × 100% = 20%; Emily donated 20% of the donation. 13 (a) 2pm – 11am = 3h. 3 × 30 = 90

They were 90 km apart when the car driver departed. It means the motorist covered 90 km in 2 hours. 90 ÷ 2 = 45; His speed is 45 km/h. (b) 45 + 30 = 75; The speed of the car driver is 75 km/h. 3 × 75 = 225; The car covered 225 km before meeting the motor. 225 + 60 = 285; The distance was 285 km.

14 The water level was 15 cm high => the container was

2015

= 43

full ; 43

–41

=21

2000 cm3 of water can fill21

the container. 2000 ÷ 21

= 4000; The volume of the container is 4000 cm3.

4000 ÷ 20 = 200 is the area of the base. => breadth = 10 cm as the ratio of the length to the breadth of a container’s rectangle base is 2 : 1

15

121

+ 81

- 241

=61

; 1÷

61 = 6

It takes 6 min to fill up the tub.

16 (a) 126 ÷ 70% = 180; The price without discount was $180; 1 + 5 = 6 equal parts; 180 ÷ 6 = 30 The price of a Mathematics book was $30 (b) 30 × 5 × 70% = 105; The price of Literature book after discount was $245.

17 Stage i: number = 3i + 2 (a) 3 × 10 + 2 = 32 (b) 3 × 100 + 2 = 302

18 (a) 6 ÷ 2 = 3; 3 × 2 × 3.14 ÷ 2 = 9.42; 8 ÷ 2 = 4; 4 × 2 × 3.14 ÷ 2 = 12.56; 10 ÷ 2 = 5; 5 × 2 × 3.14 ÷ 2 = 15.7 The perimeter of each semi-arc is 9.42, 12.56, 15.7 cm. 9.42 + 12.56 + 15.7 = 37.68; The perimeter is 37.68 cm. (b) 3 × 3 × 3.14 ÷ 2 = 14.13; 4 × 4 × 3.14 ÷ 2 = 25.12; 5 × 5 × 3.14 ÷ 2 = 39.25 The areas of 3 semi arcs are 14.13, 25.12 and 39.25 cm2. 6 × 8 ÷ 2 = 24; The area of the triangle is 24 cm2. 14.13 + 25.12 + 24 – 39.25 = 24 cm2. The area of the shaded part is 24 cm2.



16 (0.01 + 0.09) x 20 – 40 x (0.08 – 0.03) = 0 17 999.0, 909.9, 90.99, 9.909 18

5 ÷ 41

= 20

There were 20 students.

19 3 months =

41

years; 1243

+ 241

= 15

Bryan is 15 years of age. 20

36 x 40 x 32

= 960

Each container is keeping 960 cm3 of water. 960 ÷ 80 = 12; The height of container 2 is 12 cm.

21 Total number of pages read in the first 4 days 46 x 4 = 184 Number of pages read on the fifth day 234 – 184 = 50

22 1 quarter hour = 15 minutes 6 hours 3 minutes + 2 hours 15 minutes = 8 hours 18 minutes. Suet Mei reached town B at 8.18 pm

23 110 x 35 = 3850 m The distance is 3850 m

190

25 500 – 240 = 260; Teddy had 260 marbles left after giving to his brother. 260 x 40% = 104; Teddy sold 104 marbles to Allan. 260 – 104 = 156; Teddy had 156 marbles at last.

26 A pair of jeans is $20 more than a pair of T-shirt If Sam bought 3 more pairs of jeans instead of 3 shirts, the amount he would have to pay more is 3 x 20 = 60 Cost of a pair of jeans: (220 + 60) ÷ 8 = 35 Cost of a shirt: 35 – 20 = 15; A shirt costs $15.

24

27 (9 + 6) ÷ (1.6 – 1) = 25; Max has $25 28 64 = 8 x 8; The side of the square is 8 cm therefore the radius of the circle is 8 cm

Area of the shaded part is 43

the area of the circle. 86.150438

722 2 =××

Area of the shaded part is 150.86 cm2 29 70 x 50 x 28 = 98 000 cm3 = 98l ; Volume of the tank is 98l

98 ÷ (4 + 10) = 7; It takes 7 minutes to fill up the tank completely. 30 AI = 28 ÷ (1 + 1 + 2) = 7 cm; IJ = 7 x 2 = 14 cm

Area IJKH = 14 x 16 = 224 cm2 ; Shaded area = 224 ÷ 2 = 112 cm2 Preliminary Mock Paper 5- Paper 2

1 In March, the office used 60 units of internet data. For the first 40 units, it paid $10. For the remaining 20 units; 20 ÷ 5 = 4; 3 x 4 = 12 In total: 10 + 12 = 22; The office paid $22 for internet usage in March.

2 JKI = 90° - 76° = 14° ; k = 90° - 14° - 14° = 62° 3 160 x 1 = 160; After 1 hour, the first plane had travelled 160 km.

160 ÷ (200 – 160) = 4; After 4 hour since the second plane started, the two planes would pass each other. That time would be 6 + 1 + 4 = 11am

4 15% x 3 = 45% ; The number of blue balloons is 45% of the total. 100% - 15% - 45% = 40%; The number of red balloons is $40 of the total.

5 24 + 1 = 25; There were 25 equal parts 25 x 20 = 500; The street is 500 m long.

6 4 + 5 + 6 + 3 = 18; 18 ÷ 5 = 3.6; The daily expenditure is $3.60 4 ÷ 18 x 100% = 22.22%; The food expense is 22.22% of the total expenses.

7 Mary is x years old. Her mother’s age is 5x; Her father’s age is xxx

421)5(

87

=+

8 18 – 3 = 15; Sam bought 15 note-books. If he bought 18 note-books instead of books, he would save 6 x 18 = 108 Price of one note-book (273 – 108) ÷ (15 + 18) = 5; The price of one note-book is $5

9 u = 73°; v = 180° - 48° = 132° 10

201

51

41

=− ; 402012 =÷ ; There are 40 boys in this class.

40 ÷ 5 = 8; There were 8 girls at first 8 + 40 = 48; There were 48 students at first.

11 GHI = 180° - 70° x 2 = 40°; GEI = GHI = 40°; AEF = 40°; AED = 180° - 64° - 40° = 76° BAC = EAD = AED = 76°　　 ; a = (180° - 76°) ÷ 2 = 52°

12 A : B = 12 : 5 = 36 : 15 ; B : C = 3 : 2 = 15 : 10 ; A : C = 36 : 10 = 18 : 5 ; C : B = 2 : 3 0.4 x C : B = 0.4 x 2 : 3 = 4 : 15 Therefore the ratio of the unshaded are to the total area of square B is 15

111541 =−

B : C = 3 : 2 ; 18:33:: 56

1533

53

1511 ==CB

The ratio of the unshaded area of square B to the unshaded area of square C is 33 : 18 13 24 x 12 = 288; There were 288 chairs

288 ÷ 4 = 72; There were 72 chairs on each side.

191

14 150

53250 =× ;

31345150 =÷ ; 250-150=100; 45+15=60;

32160100 =÷ ; 5

321

313 =+

It took Tom 5 hours to travel from city A to city B. 6 – 5 = 1 ; Tom left city A at 1pm.

5:30 – 1 = 4:30 =214 hours >

313 hours

214 -

313 =

611 ; 220150

61160 =+× ; 225

21450 =×

At 5.30 pm, Tom was 220 km away from city A and Jerry was 225 km away from city A. 225 – 220 = 5; They were 5 km apart.

15 1+2+3+ …+ 38+39+40 ; = 820

240)140(

=×+

1500-820=680; Sam had 680 marbles left. 16 28 ÷ 4 = 7; Diameter of a small shaded circle is 7 cm

5.3847

722 2 =× ; Area of a small shaded circle is 38.5 cm2

616428

722 2 =× ; Area of the big circle is 616 cm2

616 – 38.5 x 4 = 462; Area of the unshaded part is 462 cm2 17 (60 + 12) ÷ (2 + 3 + 3) x 2 =18; John had 18 robots in the end

18 – 12 = 6; John had 6 robots at first 18 ÷ 3

2 x 2 = 54; John had 54 dinosaurs at first. 18 Percentage of 3B pencils (100% - 40%) x 90% = 54%

Percentage of 4B pencils 100% - 40% - 54% = 6% Ratio of 2B to 3B to 4B pencils 40 : 54 : 6 = 20 : 27 : 3 Total number of pencils at first 28 ÷ (27 – 20) x (20 + 27 + 3) = 200 Number of 2B pencils 200 x 40% = 80 Number of the other pencils 200 – 80 = 120 Total number of pencils in the end 120 ÷ (100% - 20%) = 150 Number of 2B pencils in the end 150 x 20% = 30

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