Outreach p6-math@

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

© 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.
i i
First Published 2010
ISBN: 978-981-4275-17-0
Published by:
Outreach Edusys Pte Ltd
(CRN: 200006571H)
Distributed by:
Outreach System Pte Ltd
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Singapore 367956
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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
ii i
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.

Contents
Semestral Assessment 1 Mock Paper 1 Paper 1
iv
Paper 2
1
8
Paper 2
17
26
Paper 2
35
43
Paper 2
52
60
Paper 2
68
76
Paper 2
83
93
Paper 2
103
112
Paper 2
121
131
Paper 2
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.
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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
1. How many ninths are there in 2
2
3
(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 5
3 cm –
10
2 mm in mm.
5
(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
( )

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
1 of the number of muffins and David received
2
( )
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
4
2 of the remainder. How many
3
muffins did Mrs Tan make if she had 9 muffins left?
(1) 108 (2) 36
(3) 18 (4) 42 ( )

12. 4 rectangles and 2 squares are used to form the solid below
Which of the following is not the net of this solid?
3
(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
( )

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
4
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: ___________________m
20. 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: _____________________

21. The cost of 3 T-shirts is $22. What is the cost of 42 T-shirts?
5
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: _____________________

4 of the students are boys. When 8 girls join the class, there are 43
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,
7
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: _____________________

28. A line of length 5 units is divided into 12 equal segments. Write a fraction to
7
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: _____________________

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
8
90
80
70
60
50
40
30
20
10
0
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

9
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: _____________________

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)
1 0
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: _____________________

8. Find the sum of ∠ a, ∠ b, ∠ c, ∠ d, ∠ e, ∠ f and ∠ g in the diagram below.
1 1
(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

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)
1 2
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. 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)
1 3
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)___________________

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)
1 4
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: _____________________

17. The patterns below start with a single square. At each stage, new squares are added
1 5
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)___________________

1 6
18.
Kate, Susan, and Xu Bin had some sweets in the ratio of 6 : 4 : 5. Kate gave
1 of her
4
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)___________________

Marks
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
3 .
3 (4) 3.94
1 7
( )
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 – 5
50
(1) 3.96 (2) 3
49
50
(3) 4
50
( )
5. What is the number in the box?
2 = 10 ×
97
50
(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
( )

1 (2)
1 (4)
5 (2)
1 (4)
18
7. What fraction of 1.5 kg is 75g?
(1)
2
1
5
(3)
20
1
50
( )
8. What fraction of the following figure is shaded area?
(1)
12
7
12
(3)
2
1
4
( )
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
( )

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
3 of her rice to cook lunch. She used
2 of a bottle’s volume. What is half of the bottle’s volume?
19
( )
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
10
3 of the remainder to cook
4
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
5
(1) 66 ml (2) 110 ml
(3) 687.5 ml (4) 1 375 ml
( )

14. The volume of the solid shown below is 4 500 cm3. What is the area of the shaded
5 kg to grams and correct to 3 decimal places.
20
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 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 13
17
Ans: _____________________

3 filled with milk. Bottle B is
21
18.
Bottle A is
5
2 filled with coffee. Bottle A is three times
3
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: _____________________

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?
22
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

3 of Ken’s height.
23
24.
David’s height is equal to
4
3 of Ken’s height is equal to
8
1 of
3
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

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?
5 of his eggs while Farmer B sold
24
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
12
5 of his eggs.
16
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: _____________________

29. How many Cube A are needed to fill the box in Figure B completely? The figures are
25
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: _____________________

1.
At a running challenge, Guo Yan covered
4 of the distance. They were 65 m apart. How far was Gu Jing from the finishing
point?
26
3 of the distance while Gu Jing covered
10
9
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: _____________________

4. PQRS is a parallelogram. PQ = PO. Find ∠ POS
27
Ans: _____________________
5. Extend the tessellation by drawing five more unit shapes in the box below.
Ans: _____________________

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)
28
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: $____________________

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)
1 of the water. Worker B, then came and filled
29
Ans: _____________________
9. A rectangular tank 20 cm long, 15 cm wide and 18 cm high was completely filled
with water. Worker A poured away
8
the tank up with another 0.5l. Find the volume of the water in the tank now.
(4 marks)
Ans: _____________________

3 of the audience are female.
30
10.
In a stadium,
5
1 of them are girls. What is the
3
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
2 of the
5
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

12. Pentagon A, rectangle B and triangle C formed the figure below. The ratio of the
1 of C is shaded, what fraction of the figure is un-shaded?
31
area of A : B : C is 6 : 5 : 3. If
4
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)___________________

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)
32
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: _____________________

2 filled with water. Some water is added to the tank.
33
16.
A cubical tank of edge 30 cm is
3
After adding, the volume of water in the tank is
3 of its capacity. What is the
4
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)___________________

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
34
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)___________________

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
35
( )
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)
( )

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
3 (2)
3 (4)
36
( )
6. The figure below is drawn with 3 semicircles. Calculate the perimeter of the figure.
(Take π =
22 )
7
(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)
4
4
7
(3)
5
4
9
( )
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
( )

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
4 of his money to buy books and 15% of the remainder to buy pens. What
1 km away from her home. If she wants to arrive in school at 9 a.m, at
37
( )
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
5
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 3
2
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
( )

3 of them to cook lunch and
3 (2) 1.125
38
15.
Mrs Tay had
5 kg of rice. She used
2
10
1 of it to cook
4
dinner for her family. How many kilogrammes of rice did she have left to cook for
the following day?
(1) 1
8
(3) 1.95 (4)
7
16
( )
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: _____________________

19. The cuboid shown below is made up of 4 identical cubes of sides 7 cm. What is the
39
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: _____________________

7 of a cake for her four kids. She divided the cake equally among
2 of the below figure shaded, how many more squares need to be
40
22.
Mrs Chen kept
8
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
5
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

26.
A rectangular water tank has a base area of 9.4 m2 and a height of 2m. When the tank
3 full, what is the volume of water inside?
41
is
4
Ans: __________________m3
27. When y = 6, calculate:
17y +
3y - 9 – 8y
5
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: _____________________

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 =
42
22 )
7
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: $____________________

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?
43
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: _____________________

4. 60% of A is 40% of B. If B - A is 25, what is the total value of A and B?
44
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: _____________________

6. The parking charges at Union Plaza’s car park is shown below.
Parking charges
45
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

1 of the remainder on a pen. He still had
46
8.
Peter spent $40 on a textbook and
4
1 of his
3
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)________________

10. The line graph shows the total number of pens that a shop sold during a week.
47
35
30
25
20
15
10
5
0
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)___________________

11. Lauren used 4 pieces of string to form the below shaded figure. Each string is a
48
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 =
22 ) (2 marks)
7
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 $600? (1 marks)
(b) What is Ken’s monthly income? (2 marks)
Ans: (a)_________________
(b)$________________

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)
49
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: _____________________

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)
50
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)__________________

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)
51
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: _____________________

Marks
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 6
3 km in metres.
10
(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
( )

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
53
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
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%
( )

1 hour at the speed of 60km/h. He then decreased the speed to 50 km/h
3 km/h (4) 52 km/h
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
1 of C
4
2/. D is 4 times of A
3/. D is 4 times of B
4/. A is
1 of D
4
(1) 1 (2) 2 and 3
(3) 4 (4) 1 and 3
( )
12.
Mr Liu drove
3
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) 51
7
( )
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
( )

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
55
( )
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
( )
16. Evaluate 66 – (18+22) ÷ 4
Ans: _____________________
17.
The total age of Andrew and Bernoulli is 48, and Andrew is
5 of Bernoulli’s age.
7
How old is Andrew?
Ans: _____________________
18.
Express
25 as a decimal.
40
Ans: _____________________

19. For every 4 apples sold, a shop owner earns $1.25. If he sells 200 apples, how much
56
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: _____________________

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.?
57
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: _____________________

26.
In figure below calculate the perimeter of the largest semicircle in terms of .
58
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: _____________________

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?
59
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

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.
60
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?
80
70
60
50
40
30
20
10
0
Ans: _____________________
8 cm
20 cm

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.
61
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: _____________________

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)
62
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: _____________________

8. A garden ABCDE is shown in a grid consisting of 2-m squares. What is the area of
63
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: _____________________

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)
64
Ans: _________________h
11.
A boy had a packet of 320 candies with 2 different flavours.
7 were orange flavour
16
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: _____________________

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)
65
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: _____________________

1 . Subsequently, 75% of books in the right
66
15.
There are 2 bookcases. The number of books on the left bookcase is equal to
7 of the
3
number of books on the right one. After moving 100 books from the left bookcase to
the right bookcase, the ratio changes to
4
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: _____________________

17. Find the area of the shaded regions. Take = 3.14. (4 marks)
1 of the number of books that Betty and Chris received.
1 of the number of books which Annie and Chris received. If Chris
67
Ans: ______________________
18. Three students Annie, Betty and Chris had some books that their Mathematics
teacher gave. Annie got
3
Betty got
5
received 5 books more than Betty, how many books in total did the teacher gave the
three students? (4 marks)
Ans: _____________________

1. What is the missing number in the box?
100 x 7 + 77000 : = 777 :1
(1) 1 (2) 10
(3) 100 (4) 1 000
5 has the same value as _______________.
5 (2) 5 x
2 (4) 5 x
68
( )
2.
12 x
11
(1) 12 x
1 +
11
11
5 + 5 x
11
7
11
(3) 5 x
5 + 5
11
11
12 - 7 x
11
5
11
( )
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 ( )

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
1 km/h (2) 63
2 km/h (4) 71
69
( )
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) 67
2
7 km/h
11
(3) 70
3
5 km/h
7
( )

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
4 of the bigger hexagon is un-shaded while
70
( )
13. Given the below figure:
5
3 of the smaller hexagon is shaded.
4
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.
400
375
350
325
300
275
250
225
200
175
150
125
100
75
50
25
0
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
( )

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
71
3 of her T-shirts were green and the
5
rest were pink, what percentage of her T-shirts were made from countries other than
China?
(1) 69% (2) 31%
(3) 55% (4) 35%
( )
16. Simplify 7y + 25 – 6y – 8 + 19y
Ans: _____________________
17.
Express 1
3 h in minutes.
4
Ans: __________________min
18. What is the reading indicated on the speed scale below?
Ans: _________________km/h

19. Coloured Korean paper is sold at 50g for $1.70 in a shop. How much would 1kg
4 of A is more than 25% of A by 18. What is A?
72
200g of the paper cost?
Ans: $____________________
20.
7
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
1 of the red paper and
3
1 of the
5
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: _____________________

26.
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?
74
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

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?
75
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: _____________________

1.
In the figure below, not drawn to scale, MA = MC, ∠ ACN =
76
1 ∠ ACM. Find
4
∠ 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: __________________%

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?
77
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: _____________________
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: _____________________

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.
3 of what was left to her close friend. Ann had 32 left for her
78
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
7
mother. How many candies did Ann have in total?
Ans: _____________________

1 of Linda’s coloured pencils was equal to
79
10.
2
1 of Emily’s coloured pencils. The
3
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: _____________________

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.
1 h later and drove towards Albert’s house at 75 km/h. What time would they
80
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
4
meet if they drove at the same speed without stopping? Leave the answer in 24-hour
clock and correct to the nearest minute.
Ans: _____________________

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.
81
Ans: _____________________

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.
82
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
5 of the cakes in the
11
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: _____________________

Preliminary Examination: Mock Paper 1
20 (2) 2
2 (4)
1 of her money on a blouse and
y − 6 (2) y – 3
83
1. Find the value of
5 x
7
8 ÷ 2
11
(1)
77
6
7
(3)
7
40
77
( )
2.
Daisy spent
5
5 of the remainder on a skirt. How
24
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
(3) 2y – 6 (4)
6 − y
2
( )
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
( )

6. Calculate the volume of the solid below. Given that the solid is formed by identical
84
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
( )

8. How many more squares need to be shaded to have a line of symmetry?
(1) 2 (2) 3
(3) 4 (4) 5
85
( )
9. Find the value of ∠ x.
(1) 125o (2) 115o
(3) 175o (4) 120o
( )

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
5 of the area of the original piece of paper as
86
( )
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
8
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

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
2 the number of days they spent in Italia. How many days did Mr and Mrs
87
3
Soh spend in Sweden?
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

16. The product of three whole numbers is 30. Their sum is 10. Find those 3 numbers
88
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

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?
89
Ans: _____________________
21. How many more parallelograms need to be shaded so that the area of the shaded
portion is
3 of the whole figure?
4
Ans: _____________________
22. Draw a line parallel to AB passing through point C.

90
23.
Express
7 as a percentage.
8
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: _____________________

26.
Calculate the value of 250.2 – 2.3 x 6 + 14 ÷ 7
91
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
4 its breadth. Assuming that its length
3
and breadth are whole number, what is the smallest perimeter that the rectangle can
have?
Ans: _________________cm

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)
92
Ans: __________________cm2

Preliminary Examination 1: Mock Paper 1
1. Find the area of the shaded region?
93
Ans: __________________cm2
2. How many 60-cm square tiles needed to tile the floor of the 54 m2 square classroom?
Ans: _____________________

3. The figure below is not drawn to scale. Given that ABC is a triangle and BD = BA.
94
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: $____________________

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.
95
(2 marks)
(b) Find the perimeter of the figure if g = 5. (1 marks)
Ans: (a)___________________
(b)___________________

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)
96
Ans: (b)___________________

8. O is the center of the circle and AB // CD Find
97
(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: _____________________

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)
98
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: _____________________

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)
99
Ans: _____________________
13. ABCD is a rhombus. Find
(a) ∠ a (2 marks)
(b) ∠ b (2 marks)
Ans: (a)__________________
(b)__________________

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
1 of his coins to Emily, she will have $14.6 in
5
total. How much did Emily have at the first? (4 marks)
10 0
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)__________________

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)
10 1
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: _____________________

2 of her money. She used the rest of her money to buy 2
10 2
18.
Mary bought 3 skirts by
5
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)__________________

Marks
1. Find the smallest number.
(1) 0.112 (2) 0.211
(3) 0.21 (4) 0.121
10 3
( )
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
( )

7. ABCD is a rectangle. Find ∠ x. The figure is not drawn to scale
(1) 10o (2) 20o
(3) 50o (4) 80o
7 h (4)
10 4
( )
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) 1
8
1 h
4
( )
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
5 of
4
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
( )

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
10 5
( )
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
( )

14. Find the percentage of the unshaded area in the below figure?
(1) 25% (2) 50%
(3) 60% (4) 75%
1 + 1
10 6
( )
15.
Mrs Lee was typing a report. She typed
3 h at an average speed of 50 words per
4
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
( )
16. Find the value of n.
1 +
5
1 +
5
1 +
5
1 +
5
1 +
5
1 +
5
1 +
5
1 = n ×
5
5
Ans: _____________________
17. Calculate 25.5 ÷ 4
Ans: _____________________

10 7
18. When b = 3, find the value of
b
13 2
9 5
−
b
+
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

21. Use the following table to answer the question below:
10 8
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 =
22 )
7
Ans: _____________________

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.
10 9
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

26.
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?
11 0
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: _____________________

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.
11 1
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: _____________________

1. The shaded part of the figure below is made up of 2 parallelograms. Find the area of
11 2
the unshaded part.
Ans: __________________cm2
2. Draw 3 more unit shapes on the grid provided to show tessellation.
Ans: _____________________

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?
11 3
Ans: __________________cm3
4. The graph below shows how much money Sebastian spent over a week
$8
$7
$6
$5
$4
$3
$2
$1
$0
Sebastian had $60 at first.
How much money did he have left at the end of Thursday?
Ans: $___________________

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?
11 4
Ans: $___________________
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: _____________________

7. ABCD is a rectangle and MN//PQ. Find ∠ n. (3 marks)
11 5
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)__________________

1 of Ann’s papers. What is the total number of colored papers which
11 6
9.
Ann and Betty have 40 pieces of colored papers in total.
1 of Betty’s papers is 5
2
more than
3
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)___________________

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
1 of the required number of pens.
11 7
5
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)__________________

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)
11 8
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)___________________

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
11 9
3 full. Uncle Tan
4
removes eight cubes and observes that the water level drops to
2 the height of the
3
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: __________________

25 of the competitors were from school A. The ratio of the
12 0
18.
In a sports competition,
67
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,
5 of the
21
remaining competitors were from school B. How many competitors from
school B left? (2 marks)
Ans: __________________

1. Find the value of 33 × 0 + 33 × 10 + 33 × 100
(1) 3 630 (2) 69 300
(3) 3 663 (4) 36 300
12 1
( )
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
( )

5. Find the area of the shaded part if the pattern is drawn on a 10-cm square grid. Take
12 2
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
( )

7. Which of the following net cannot form a cube?
1 2 3 4
(1) 1 (2) 2
(3) 3 (4) 4
12 3
( )
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)
( )

1 AB. Find the fraction of the unshaded area.
1 (2)
3 (4)
1 of the rice to cook lunch and 20% of the
12 4
11.
ABCD is a square. MN = PQ =
4
(1)
5
1
4
(3)
4
1
8
( )
12.
Mrs. Poh had some rice. She used
4
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.
300
250
200
150
100
50
0
How many percent more rainfalls were collected in May than in February?
(1) 86.67 % (2) 73.33 %
(3) 46.43 % (4) 83.33 %
( )

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 (1)
(2)
5 (4)
12 5
6
1
12
(3)
6
3
4
( )
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
( )
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

18. ABCDE is a regular pentagon. Find ∠ x.
12 6
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: _____________________

20. What is the missing letter in the cube?
12 7
Ans: _____________________
21. The bar graph below shows the number of burgers sold within a week.
350
300
250
200
150
100
50
0
The total number of burgers sold was 1 700. Complete the bar graph above.
Ans: _____________________

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?
3 of Carol’s papers as well as
2 of Linda’s papers. Find the ratio of the
12 8
Ans: _____________________
23.
Betty, Carol and Linda have some origami colored papers.
1 of Betty’s papers is
4
equal to
5
5
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

26.
Find the value of
12 9
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

30. If the area of the square inscribed in a circle is 98 cm2, what is the area of the circle?
13 0
(Take π =
22 )
7
Ans: ___________________ cm2

1. In the space below, draw a triangle ABC with AB = 6 cm, BC = 5 cm and ∠ ABC =
13 1
140o
Ans: _____________________
2. ABCD is a parallelogram. EB = EC. Find ∠ BAC.
Ans: _____________________

3. The pie chart below (drawn to scale) shows the number of fruit, milk, mint and
13 2
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

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?
13 3
Ans: _____________________
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: _____________________

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)
13 4
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: _____________________

9. The pie chart below shows the number of men, women, boys and girls at the stadium
13 5
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

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)
3 of the stamps. Peter and Daniel collected
13 6
Ans: _____________________
12.
Daniel, Peter and Ivan had a collection of stamps. Peter and Ivan collected
9 of the
16
stamps while Daniel and Ivan collected
4
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: _____________________

14. In a school, the number of boys increased by 25% to 350 and the number of girls
13 7
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: _______________________

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)
13 8
Ans: _____________________
18.
Find the area of the shaded part. (Take π =
22 ) (4 marks)
7
Ans: _____________________

1. Which of the following number is the biggest?
(1) 5.23 (2) 5.32
(3) 5.323 (4) 5.232
13 9
( )
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)
( )

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
1 of the age of her mother. If she is p years old now,
11 (2)
3 (4)
14 0
( )
7. Currently, the age of Mary is
3
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 (
1 +
5
1 )?
20
(1)
40
2
12
(3)
16
5
24
( )
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
( )

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%
3 of the remainder in the next day.
14 1
( )
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
7 of the number of
25
pages. He read
10
1 of what remained was read on
2
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
( )

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
14 2
( )
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: $_____________________

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?
14 3
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: $____________________

3 is shown below. How much water has to be added
2 number of books which Jane has. Jane has
14 4
23. A cubic container which is full
4
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
5
5 number of books which
6
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: _____________________

26.
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?
14 5
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: _____________________

29. In the figure, not drawn to scale, ABCD is a trapezium. Find ∠ y
14 6
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: _____________________

1. Shade more squares to have exactly 2 lines of symmetry in the below figure.
14 7
Ans: _____________________
2. In the following figure, not drawn to scale, ∠ a = ∠ b = ∠ d. Given that ∠ c = 24o.
Find ∠ a.
Ans: _____________________

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.
14 8
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: _____________________

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
4
1 the number of durians left. How many durians and watermelons are sold?
(3 marks)
14 9
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: _____________________

8. Jan drove to visit his friend’s house, which was 500 km away. Jan spent a half of his
2 of the journey and then travelled at the average speed of
1 of his beads. Then Robin shared 152 beads to
15 0
time to complete the first
5
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
5
Robert so that they had the same amount of beads. How many beads did Robin have
at first? (4 marks)
Ans: _____________________

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)
15 1
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: _____________________

12. 6 students donated for a children protection fund.
15 2
90
80
70
60
50
40
30
20
10
0
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)___________________

14. The ratio of the length to the breadth of a container’s rectangle base is 2 : 1.The
1 full. Mr Tan added 2000 cm3 of water into the
15 3
height was 20 cm. It was
4
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
1 that of Literature book. Jane
5
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: _____________________

15 4
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: _____________________

2 (2)
3 (4)
4 (2)
9 (4)
15 5
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)
3
1
4
(3)
4
1
8
( )
4.
1 + 3
+ =
Fill the blank with appropriate number: 1 ______
4
20
(1)
5
9
8
(3)
5
9
4
( )

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
15 6
( )
6.
Find x given that x% =
3
25
(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
( )
50g 2kg 100g

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
1 that in B. If initially all flowers were divided equally in two
15 7
( )
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
3
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
1 that of Natural Science
4
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
( )

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?
15 8
(1)
(2)
(3)
(4)
( )
16. Fill in the boxes with appropriate operation “-“ or “x”
(0.01 0.09) 20 40 (0.08 0.03) = 0
Ans: _____________________

17. Arrange the following numbers in descending order:
909.9 9.909 90.99 999.0
3 years older than his younger brother who is 2 years and 3 months old
15 9
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
1
of a cake, how
4
many students are there in this class?
Ans: _____________________
19.
Bryan is 12
4
now. What is the age of Bryan?
Ans: _____________________

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
3
2 of container 1’s height and container 2 is fully filled. What is the height of
container 2?
16 0
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: _____________________

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?
16 1
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: _____________________

26.
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.
22 . Find the area of the shaded part in below figure, if O is the centre of
16 2
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 =
7
the circle and the square has the area of 64 cm2. Express your answer up to two
decimal degrees.
Ans: _____________________
O

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?
A B
D C
16 3
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: _____________________
I J
H K
28 cm
16 cm

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?
16 4
Ans: _____________________

2. A square piece of paper is folded at its corner as shown in the following figure. Find
76°
k
16 5
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
D C

4. 15% of the number of balloons that Jane has is yellow. The percentage of yellow
balloons to the total number of balloon is
16 6
1 the percentage of blue balloons to the
3
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: _____________________

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)
16 7
Ans: _____________________

7. Mary is x years old now. Her mother’s age is 5 times as many as hers and her father’
7 of the total age of Mary and her mother. Find the age of her father in terms
16 8
age is
8
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: _____________________

16 9
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
1 as many girls as boys in this class. What
4
is the total number of students at first? (4 marks)
Ans: _____________________
M
N
P
Q
u
v
48°
73°

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)
17 0
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
B A

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)
3
of his journey. After that, he increased the speed by 15km/h for the remainder
17 1
Ans: _____________________
14. Tom travelled from city A to city B, which are 250 km apart, with a speed of 45km/h
for
5
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: _____________________

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)
17 2
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: _____________________

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
17 3
2 of the remaining number of
3
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: _____________________

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
81
17 4
m
7
55
km
55
=
7000
11
=
1400
18
100
9
=1.71
+
10
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.
55
80
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
4
= 20 ; There are 20 boys in the class.
7
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
5
unit ; 5 x
12
5
12
25
=
12
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.

A
= 3 ; Coffee : Milk =
17 5
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)
x
+
x
27
+
30
14
=
15
=> 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
55x45
2
= 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 ×
1
= 15
4
Xu Bin’s sweets increased: 50 × 10% = 5 ; Susan’s sweets increased: 15 – 5 = 10
10
× 100% = 25% ; The percentage increase of Susan’s sweets was 25%
40
(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
2 1 3 4 3 1 3 2 4 2 2 1 3 4 3
16 A = 183 17 13294.118g
18
Coffee : Milk =
2B
3
3A
÷
5
and
B
10
27
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

3k
1
of books in library are P6 Mathematics books
7
of the distance from the finishing point. Gu Jing was
2
× 100% = 40% ; 40% of the audience is women.
17 6
24 Let d, k, t be heights of David, Ken and Terence.
d =
3k
4
3k
;
8
t
=> t =
=
3
9k
8
; Hence, d : k : t =
4
: k :
9k
8
= 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.
12
12
×15 +
4
3
× 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 =
5
÷
16
5
12
3
=
4
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.
29
1
=
;
580
20
20
Midyear Mock Paper 2- Paper 2
1
Guo Yan was
10
5
of the distance from the finishing
9
point.
⎛ 7
65 ÷ ⎟⎠
−
⎞
⎜⎝
5
9
10
= 450 ; The length of the running distance is 450 m. 450 ×
5
= 250 ;
9
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 ×
7
= 4 725 cm3 = 4.725l
8
4.725 + 0.5 = 5.225l
The volume of the water in the tank now is 5.225l
10
1 –
1
=
3
2
;
3
2
of female are women.
3
3
×
5
3
11 61.5 – 27 = 34.5 ; The length of the 2nd cut was 34.5 cm.

2
= 86.25 have not change working. The length of the ribbon after the 1st cut was 86.25 cm.
7
of the figure is un-shaded.
2
= 18 000; The tank has 18 000 cm3 at first.
3
= 20 250 ; The tank has 20 250 cm3 after adding water.
a +
b
+
17 7
34.5 ÷
5
86.25 + 27 = 129.5cm. The original length is 113.25 cm
12
1
÷
4
6
=
3
1
;
8
1
of A is shaded. 1 –
8
1
=
8
7
;
8
8
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 ×
3
27 000 ×
4
20 250 – 18 000 = 2 250; 2 250 cm3 is added to the tank.
2250
30 ×
30
= 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)
a
=
b
10
9
=> a =
10b
9
c
=
;
d
5
=> c =
6
5d
6
;
c d
19
=
33
=>
b +
b
10
9
d +
d
5
6
19
=
33
=>
b
=
d
1
2
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)
…
…
… 15 17
Pattern 1 2 3 8 9
Beans 2 3 4 9 10
Sticks 1 3 5
(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
4 2 3 1 2 1 1 4 2 4 3 3 3 2 2
16 6 × (10+5) = 75
The perimeter of the figure is 75 cm
17 8.27

2
– 1 = 3 ; 3 more squares need to be shaded.
3
= 14.1; The volume of the water inside is 14.1 m3.
17 8
18
60 × 60
15
= 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
7
÷ 4 =
8
7
; Each kid got
32
7
of the cake.
32
23
15
32
24
10 ×
5
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 ×
4
27 y = 48.6
28
625 ÷ 75 =
25
3
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 ×
22
7
÷ 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
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
7
×
8
6
=
5
21
20
The ratio of Albert’s height to that of Kelvin’s
height is 21 : 20.
4
A
=
B
40%
60%
2
; 25 ÷ (3 – 2) = 25
=
3
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 ×
3
= 9.375 cm2.
8
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)
25 −10
25
× 100% = 60%

3
; The perimeter of the shaded figure is 31
17 9
11
(a) (5 × 2 ×
22
7
) ÷ 4 =
55
7
; The perimeter of each quarter circle is
55
7
cm.
55
7
× 4 = 31
7
3
cm.
7
(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 =
120
3
2
= 80
×
1
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
2 3 1 4 2 2 1 1 2 1 4 3 2 4 1
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
20 − x
2.5
26 8 + 4 + 5 = 17
The diameter of the largest semicircle is 17 cm.
The perimeter of the largest semicircle is
17π
(cm)
2
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.

18 0
(4 + 6) × 3
2
= 15; The area of each trapezium is 15 cm2.
15 × 2 = 30; The shaded area is 30 cm2.
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 ×
7
16
= 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.
11
110 ÷
15
= 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.
2
19.625 ×
+ 19.625 ×
3
1
= 19.625 cm2.
3
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
3 2 3 2 3 2 2 1 2 2 2 4 1 3 1
16 20 y + 17
17
3
18 73 km/h
×60 = 105 min
1
4
19 1200 × 1.7 ÷ 50 = $40.8
1kg 200g of that paper costs $40.8
20
18 ÷ (
4
- 25%) = 56; A is 56.
7

8
h = 160 min = 2h 40min; The taxi took 2h 40min to reach B.
3
; The product of the last 2 numbers is
18 1
21
200 ÷ 75 =
3
8am + 2h 40 min = 10.40 am; The taxi reached B at 10.40 am
22
Before using:
R
=
Y
2
. After using, Ann has
3
2R
3
and
4Y
5
; The new ratio =
R
2
3
4
Y
5
2
×
=
3
5
×
4
R
= 5 : 9
Y
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
1
∠ AMB = 180 – 75 – 35 = 70o. ∠ ACM = 70o ÷ 2 = 35o. ∠ ACN =
1
× 35o = 8.75o
4
2
60 ÷ ( 4 × 5 × n) =
n
3
.
n
3
310 − 250
250
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 =
(3 + 6) × 2.6
2
=11.7 cm2.
PN = AM ÷ 4 = 5.2 ÷ 4 = 1.3 cm.
6 ×1.3
Area of triangle BPC =
2
= 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
13
250 × 17 ÷ 19 = 223
19
; 250 – 223
13
19
= 26
6
19
Casey was 26
6
m away from the finishing point
19
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 ÷
4
= 56; 56 + 4 = 60; 60 ÷ 75% = 80
7
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.

∠ ADC = 180 – 65 = 115o. ∠ x = 360 – 115 – 130 = 115o.
5c
5s
5 ×16
8
of the cakes would be strawberry cakes after the last move.
3
- 4 = 8; 8 more parallelograms need to be shaded.
18 2
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 =
8
+ 2
After 2nd case: strawberry : chocolate = 6 :5 => c =
6
+ 6 =
25c
48
23
+
3
c = 16; The number of chocolate cakes was 16.
8
+ 2 = 12. The number of strawberry cakes was 12.
16 – 6 = 10, 12 + 4 = 16,
16
+
16 10
8
;
=
13
13
Answers to Preliminary Examination: Mock Paper 1- Paper 1
1 3 2 2 2 3 4 3 4 2 2 1 1 4 2
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 ×
4
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.

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.
1
= 15; Ken gives Emily 15 coins, costs 15 × 0.2 = $3; 14.6 – 3 = 11.6; Emily has $11.6 at first.
2
+ 2 ×
1
= 33.33%; She spent 33.33% of her money on T-shirts.
18 3
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 ×
5
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)
2
÷ 3 =
5
2
; 1 skirt costs
15
2
of her money.
15
5
2
15
2
; She spent
=
3
2
of her money on skirts.
3
1 –
2
=
3
3
(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.

Answers to Preliminary Examination: Mock Paper 2- Paper 1
1 4 3 1 4 1 3 3 2 1 4 2 1 2 2
16 n = 3 17 6.375
18
1
; The price of each pencil is $ (5n +
18 4
4
4
7
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 ×
22
7
= 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 +
3
1
)
3
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.

∠ n = ∠ ABC – ∠ BMN = 90 – 20 = 70o. (b) ∠ ABC = 180 – 75 = 105o.
18 5
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
2
full.
3
3
–
4
2
=
3
1
12
1000 ÷
1
12
= 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
25
67
of the competitors minus 4; School B sent 1 -
25
67
25
-
67
17
=
67
of the competitors plus 4
School B and C sent
42
67
of the competitors; 19 + 23 = 42
School B sent
19
67
of the competitors and school C sent
23
67
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.

5
(134 – y) => y = 8; 8 competitors from school B left the competition.
8
L
22
18 6
38 – y =
21
Answers to Preliminary Mock Paper 3- Paper 1
1 3 2 3 4 2 3 1 4 3 3 2 4 4 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
1
=
4
5
;
20
3
=
5
12
20
2
=
;
5
8
20
5
B =
;
20
12
20
C =
20
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 ×
7
= 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.

(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.
5
of the stamps. Peter and Daniel collected
5
h = 50 min. It takes 50 min.
18 7
12
Daniel collected 1 –
9
=
16
7
16
of the stamps. Peter collected 1 –
3
=
4
1
of the stamps.
4
Ivan collected 1 -
7
16
1
=
-
4
16
7
+
16
1
=
4
11
16
of the stamps.
The collection had 55 ÷
11
16
= 80 stamps. Ivan had (80 ×
5
) – (80 ×
16
1
) = 5 more stamps than Peter.
4
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 =
7
h ; 75 × (
12
7
+
12
25min
60
) = 75
The distance is 75 km. 75 ÷ 90 =
6
18 The area of the shaded part is equal to the area of 8 squares of 7-cm side.
7 × 7 × 8 = 392 cm2.
3 1 2 3 1 3 4 1 3 2 1 4 2 3 3
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.
n + 40
The average is
3
.
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.

22 17 × 21 ÷ 3 = 119; It costs $119.
23 20 × 20 × 20 = 8000; The volume of the container is 8 000 cm3.
1
= 2000; 2000 cm3 water has to be added to make the container full.
2
= 200; Jan drove 200km when spending half of his time.
18 8
8000 ×
4
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
2
13
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.
2 360 – 90 – 24 = 246o.
∠ a = 246 ÷ 3 = 82o.
1
3 John had (115 – 5y) candies after eating 5.
Each sister received
115 − 5y
2
4 9 notebooks had the same price with 6 books.
9 + 5 = 14; 14 notebooks cost $84
84 ÷ 14 = 6; Each notebook cost $6
84 − 5 × 6
6
= 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
1
40000 ÷ (40 × 30) = 33
cm.
3
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 ×
5
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.

∠ 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.
1
the container. 2000 ÷
18 9
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
15
20
3
full ;
=
4
3
–
4
1
=
4
1
2
2000 cm3 of water can fill
2
1
= 4000; The volume of the container is 4000 cm3.
2
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
1
12
1
-
+
8
1
=
24
1
; 1÷
6
1 = 6
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.
3 1 2 3 3 4 2 2 2 2 1 1 1 3 1
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 ÷
1
= 20
4
There were 20 students.
19
3 months =
1
years; 12
4
3
+ 2
4
1
= 15
4
Bryan is 15 years of age.
20
36 x 40 x
2
= 960
3
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

3
22 the area of the circle. × 2 × =
150.86
2 ÷ 1 = ; There are 40 boys in this class.
19 0
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
4
8 3
4
7
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
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
( 5 ) 21
8
Mary is x years old. Her mother’s age is 5x; Her father’s age is x x x
4
7 + =
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
1 − = 1
; 40
20
1
5
4
20
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
11
1− 4 =
15
11 B C = =
5 B : C = 3 : 2 ; : 3
33
: 33 :18 15
5
6
15
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.

150 ÷ 45 = 3 1 ; 250-150=100; 45+15=60;
60×11 + = 1 ; 50× 4 =
225
22 2 × = ; Area of a small shaded circle is 38.5 cm2
22 2 × = ; Area of the big circle is 616 cm2
616 – 38.5 x 4 = 462; Area of the unshaded part is 462 cm2
19 1
14
250× 3 = ;
150
5
3
3 1 + =
1 2
100 ÷ 60 = 1 2 ; 5
3
3
3
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 =
4 1 hours >
2
3 1 hours
3
4 1 -
2
3 1 =
3
11 ; 150 220
6
6
2
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
(40 + 1) ×
40 =
1+2+3+ …+ 38+39+40 ; = 820
2
1500-820=680; Sam had 680 marbles left.
16 28 ÷ 4 = 7; Diameter of a small shaded circle is 7 cm
38.5 4
7
7
616 4
28
7
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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