Outreach p5-math@

Primary 5 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: 978-981-4275-16-3
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 5 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
15
23
Paper 2
30
38
Paper 2
45
53
Paper 2
60
67
Paper 2
74
80
Paper 2
88
94
Paper 2
101
108
Paper 2
115
122
Semestral Assessment 2 Mock Paper 5
Paper 1
Paper 2
129
137
Suggested Answers 144
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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Semestral Assessment 1: 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. Fill in the blank with an appropriate number that matches the pattern
______, 900 000, 800 000, 700 000
(1) 10 000 (2) 100 000
(3) 1 000 000 (4) 10 000 000
3 of the set below shaded, how many more squares must be
1
( )
2. How many quarters are there in 3
1 ?
2
(1) 3 (2) 5
(3) 10 (4) 14
( )
3. In order to have
5
shaded?
(1) 9 (2) 8
(3) 7 (4) 6
( )
4. Find the value of 24 + 48 ÷6 – 6
(1) 6 (2) 22
(3) 26 (4) 36
( )
5. What is the correct numeral for the following statement?
Six hundred and six thousand, six hundred and sixty six
(1) 606 606 (2) 606 666
(3) 666 606 (4) 660 660 ( )

6. How many lines of symmetry are there in this letter?
2
I
(1) 4 (2) 3
(3) 2 (4) 1
( )
7. If the product of 124 and 19 is calculated and rounded off to the nearest hundred,
what will be the final value?
(1) 2000 (2) 2300
(3) 2400 (4) 2360
( )
8. A car can travel 9 230m with 1l of fuel. 300l of fuel was consumed in a month. How
many kilometers did the car travel in that month?
(1) 2 769 (2) 27 690
(3) 276 900 (4) 2 769 000
( )
9. Mary’s weight is 27kg. She is 3
5
as heavy as David. How much does David weigh?
(1) 15 kg (2) 45 kg
(3) 54 kg (4) 84 kg
( )
10. Two numbers have a difference of 72 and a sum of 166. Find the bigger number.
(1) 138 (2) 119
(3) 94 (4) 49
( )
11. Sarimah bought 3 1
2
kg of flour. She then used 15
8
kg to bake cakes. After that, her
mother gave her another 11
4
kg of flour. How much flour did she have eventually?
(1) 3 7
8
kg (2) 31
8
kg
(3) 2 1
4
kg (4) 17
8
kg ( )
12. Caroline has 6 times as many stickers as Denise, but only half as many as Rachel
has. If Denise has 154 stickers less than Rachel, how many stickers does Caroline
have?
(1) 14 (2) 77
(3) 84 (4) 160
( )

13. Examine the pattern below carefully. How many sticks are there in the 18th pattern?
Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern 18
(1) 37 (2) 47
(3) 57 (4) 67
3
( )
14. Find the smallest value among the following expressions
(1) 0.80 (2) 17
20
(3) 3
4
(4) 0.69
( )
15. In the figure below, ∠ AOB = 93o. What is ∠BOC? Note that AOC is a straight line
and the figure is not to scale.
O
93o A
(1) 3o (2) 87o
(3) 90o (4) 273o
( )
Questions 16 to 25 carry 1mark each. Write your answers in the spaces provided. For
questions which require units, give your answers in the units stated.
16. Write 9 080 011 in words.
17. Arrange these numbers in descending order.
8 883 008, 880 300, 8 880 003, 88 380
Ans: __________, __________, __________, __________
B
C
?

4
18. What is the correct value of A?
Ans: _____________________
19. Find the total of the first 6 multiples of 7
Ans: _____________________
20. Express
49 as a mixed number
9
Ans: _____________________
21. Calculate
5 x108
9
Ans: _____________________
7 503 906
7 000 000
A
3 906
3 000
900
6

1 and simplify your answer.
5
22. Calculate 3
2 +2
5
2
Ans: _____________________
23. What is the proportion of the shaded area compared to the whole square? Write the
answer in fraction.
Ans: _____________________
24. Find the largest possible odd number between 5 000 000 and 6 000 000 using all the
digits given.
9 0 1 7 2 6 5
Ans: _____________________
25. Write the following statement as a numeral
Three million one hundred and forty-seven thousand six hundred and eighty-two
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.
Mr. Ben chose a sofa set that cost $5 250. He paid the exact amount in 90 pieces of
$100 and $50 notes. How many $50 notes did the cashier receive from Mr. Ben?
1 of these nails to his colleague and used
6
Ans: _____________________
27. 10 tables and 20 chairs cost $650.
20 tables and 10 chairs cost $850.
What is the cost of one table and one chair?
Ans: _____________________
28. Mr. Tan, a worker, had 850 long nails, 620 short nails and 930 medium nails in a
container. He gave
4
1 of these nails to
12
make tables. How many nails did he have left?
Ans: _____________________

29. An oil producer is filling two empty barrels with oil. The first barrel fills at a rate of
90l per minute. After 1 minute, he starts filling the second barrel at a rate of 105l per
minute. How many minutes will it take for the second barrel to contain the same
amount of oil as the first barrel?
7
Ans: _____________________
30. Mary and John were given the same amount of money by their mother. After
spending some of their money, Mary only has one-seventh as much money as John
had. If John spent $1 572 and Mary spent $2 892, how much did each of them have
at first?
Ans: _____________________

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. In a donation drive, team A and team B collected a total of $12 795. Team C and
team D collected a total of $17 245. Team A and team C collected the same amount
of money. Team D collected 6 times as much money as team B. How much money
did team D collect?
8
Ans: _____________________
2. A shop is selling gloves for Christmas.
3 of the pairs are red,
8
1 of the pairs are
4
white and the remaining 114 pairs are dark blue. How many pairs of gloves does the
shop have in total?
Ans: _____________________
3. 1 kg of pork cost $2 more than 1 kg of chicken. 1 kg of beef cost $3 more than 1kg
of pork. Aunt Linda spent a sum of $99.60 on 6 kg of each type of meat. How much
did she spend on the chicken and the beef?
Ans: _____________________

4. Cheese cakes are sold at $6.90 for 3. Curry puffs are sold at $5.20 for 4.
(a) If Timmy could only spend $25 on each type of food, how many more curry puffs
than cheese cakes could he buy?
(b) Bobby paid $129.60 for an equal number of cheese cakes and curry puffs. How
many cheese cakes and curry puffs did he buy altogether?
9
Ans: _____________________
5. Peter wants to send a parcel to his friend in Indonesia. At the post office, he finds the
following table which shows the postage rates:
Mass not over Postage
First 30g $1.00
Next 50g $1.70
Per additional step of 25g $0.35
How much does Peter have to pay if his parcel weighs 197g?
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. Given that AB is a line of symmetry in the figure below. Shade the squares to
1 0
complete the symmetric figure
Ans: _____________________[4]
7. The average number of Peter’s stickers and Jordan’s stickers is 924. Peter has 232
more stickers than Jordan. Albert has 172 stickers more than Peter. What fraction of
Albert’s stickers are Jordan’s stickers? Write your answer in its simplest form
Ans: _____________________[4]

8. Three years from now Dan’s father’s age will be thrice Dan’s age. How old is Dan’s
father now if he was 34 years old when Dan was born?
1 1
Ans: _____________________[4]
9. The houses along a road are numbered from 1 to 150. The house number signs are
made of steel digits. How many digits are needed altogether to number the entire
road?
Ans: _____________________[4]
10. Find the perimeter of the figure below.
Ans: _____________________[4]
5 cm
8 cm
13 cm
36 cm
9 cm
7 cm
4 cm
A
B
5 cm

11. A shop sells carpets at $15 per square meter. Uncle Tay wants to buy a carpet for his
living room, which is 10m by 7m. How much does he have to pay?
1 2
Ans: _____________________[4]
12. When 60 packs of cookies are placed in a box, the total mass is 6 790g. When the
same box contains 25 packs of cookies, the mass is 4 655g. Find the mass of the box
in kg.
Ans: _____________________[4]
13. Each tourist has to pay $1 215 for a 5-day tour to Vietnam. If there were 116 tourists
who chose that tour last month, how much did the travel agency receive?
Ans: _____________________[3]

14. Create a tessellation in the space provided by drawing 4 more unit shapes.
1 3
Ans: _____________________[4]
15. Alex, Ben and Carl collected a total of 2 151 stamps. Alex collected 224 stamps
fewer Carl. Ben’s collection was 3 times as many as Carl’s. How many stickers did
Carl have?
Ans: _____________________[4]
16. How many lines of symmetry are there in the figure below, given that all line
segments are equal
Ans: _____________________[3]

17. A water tank 90 cm long, 40 cm wide and 15 cm high needed to be filled by two taps
A and B. Tap A, which had a flow rate of 12l per minute, was turned on first. After
11 minutes, tap B, which can flow only
2
1 4
1 as fast as tap A, was turned on and both
3
tap continued to fill the tank. Since both taps were turned on, how long did it take to
fill the tank completely? Express your answer in minutes and seconds.
Ans: _____________________[4]
18. A number of trees were planted around the perimeter of a rectangular parcel of land
that was 49m long and 35m wide. There was a tree in each corner. On each side of
the land trees were planted 7m apart. How many trees were there in total?
Ans: _____________________[4]

Marks
1. 76 x 50 can also be expressed as
(1) 70 x 6 x 5 (2) 7 x 6 x 5 x 10
(3) 76 x 5 x 10 (4) 70 x 6 x 5 x 10
1 5
( )
2. Calculating 196 x 68 and rounding off to the nearest thousand, the result will be
(1) 13 000 (2) 13 300
(3) 13 400 (4) 14 000
( )
3. What is the best estimate of 635 ÷ 80?
(1) 6.35 (2) 63.5
(3) 8 (4) 7.5
( )
4. What is the value of 183 – 24 ÷ 3 x 4 + 12
(1) 139 (2) 163
(3) 224 (4) 712
( )
5. What value should be filled in the box to make the expression correct?
6.5 x 6 + x 3 = 78
(1) 13 (2) 14
(3) 39 (4) 41
6. Replace “?” with a correct number that fits the pattern below
0.7, 1.4, 0.8, 1.3, ___?___, 1.2
(1) 0.6 (2) 0.9
(3) 1.7 (4) 2.1
( )

7. MNPQ is a trapezium. Which of the following shows a parallel pair of lines?
M W T X N
Q P
(1) MQ and XY (2) WZ and XY
(3) WZ and YT (4) MQ and WZ
2 kg of meat. Aunt Irene bought
8 (2)
34 (4)
1 6
( )
8. Aunt Sophie bought
5
4 kg of meat more than aunt
7
Sophie. How many kg of meat did both of them buy?
(1)
35
22
35
(3)
35
113
35
( )
9. Find one of the letters below that does not have any line of symmetry
(1) T (2) H
(3) A
(4) Z
( )
10. Muthu had 25 kg of sugar. He packed them equally into 7 bags. There was 2kg of
sugar left over. How much sugar was there in each bag?
(1) 3.28 kg (2) 3.29 kg
(3) 3.57 kg (4) 3.58 kg
( )
Z Y

11. The graph below shows the number of customers visiting a shopping centre over a
period of 5 months.
How many customers visited the shopping centre from January to March?
1 (2)
9 (4)
1 7
4000
3500
3000
2500
2000
1500
1000
500
0
January February March April May
(1) 7 200 (2) 7 300
(3) 7 400 (4) 7 500
( )
12. A tank measures 45 cm by 30 cm by 10 cm is filled with 4.5l of water. What fraction
of the tank is not filled?
(1)
3
2
3
(3)
13
4
13
( )
13. In 147 683, which digit is in the ten thousands place?
(1) 1 (2) 4
(3) 6 (4) 3
( )
14. 4 ten thousands + 4 thousands + 4 hundreds + 4 ones =?
(1) 40 400 (2) 40 004
(3) 44 404 (4) 44 440
( )

15. Find the correct numeral for the following expression
Three hundred and three thousands, three hundred and three
(1) 303 303 (2) 330 330
(3) 330 303 (4) 333 000
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For
16. Given that MN is the line of symmetry of the figure below, shade two more squares
2 that of an adult ticket. Mrs. Lim and her
1 8
to complete the figure.
17. A child ticket to enter the zoo costs
5
daughter paid $49 for their tickets. How much does a child ticket cost?
Ans: _____________________
18. The price of a car is $180 000 when rounded off to the nearest $1 000. What could
the lowest price of the car be? Provide your answer correct to the nearest dollar.
Ans: _____________________

19. Form the biggest even number using all the digits given
3, 6, 9, 5, 1, 2
1 of his money on a shirt and
1 of the audience were children and the rest were adults. There were
1 9
Ans: _____________________
20. Tony spent
4
3 of the remaining money on a pair of
5
jeans. What fraction of his money did he spend? (Use the simplest form for your
answer).
Ans: _____________________
21. At a concert,
5
144 more adults than children. How many people were there in the audience?
Ans: _____________________
22. What is the area of the triangle below?
Ans: _____________________

7 of a cake to her 3 children to share. Each child had the same
14 32
+ + + in decimal form.
2 3 times the number of stamps that Alex has. What is the ratio of the
2 0
23. Mrs. Chan gave
9
portion. What fraction of the cake did each child get?
Ans: _____________________
24.
Express the value of
1000
5
8
10
100
Ans: _____________________
25. Fann has
5
number of Alex’s stamps to Fann’s stamps?
Ans: _____________________
Questions 26 to 30 carry 2 marks each Show your working clearly in the space below
units, give your answers in the units stated. (20 marks)
26.
In the space provided, construct a line PQ that is perpendicular to line MN
M
N

27. There are 4 teams in the Federation Cup tournament. Every team has to play one
match with each of the other teams. How many matches are there in the tournament?
2 1
Ans: _____________________
28. Selina started doing her homework at 7:45 PM. It took her 3
5 hours to complete all
12
the homework. At what time did she finish the task?
Ans: _____________________

29. The table below shows the parking rates at a shopping mall. Vanessa parked her car
from 3.40 PM to 5.25 PM. How much money did she pay more the parking?
Parking rates
1st hour $2.50
Every additional hour or part there of $1.90
2 2
Ans: _____________________
30. In the figure below, ABCD is a rectangle, ST is a straight line.
Calculate the difference between ∠x and ∠y
Ans: _____________________
A
B
C
D
S
41o T
58o
80o
x
33o
y

1. A survey at a concert showed that
1 of the audience came by car,
25
2 3
1 came by bus
4
and the rest came by train. If there were 180 people who came by car, how many
people came by train?
Ans: _____________________
2. Mrs. Ng had a rectangular parcel of land that is 9m wide. The area of the parcel is
108m2. She wanted to repaint the fence around the land.
a) Find the perimeter of the land.
b) The fence surrounds the whole perimeter of the land. She paid $126 for the
painting cost. How much did she have to pay to paint 1 meter of the fence?
Ans: _____________________
3. Harry cycles to a basketball court every day. He can take either route 1 or route 2. He
chooses route 1 from Monday to Friday and route 2 from Saturday to Sunday. If he
takes route 1, he has to cycle 4 km 300m. The total length of route 1 and route 2
together is 8 km 200 m. What is the total distance that Harry travels to the basketball
court in a week? Give your answer in km.
Ans: _____________________

4. In a training field there is a starting position and several finish lines. The first finish
line is 30m away from the starting point. Each of the finish line from the second one
is twice as far from the starting point as the previous finishing line.
Peter ran straight from the starting point to the first finish line and returned straight
back to the starting point. He then ran straight to the second finish line and returned
to the starting point again. He kept running, every time to the next finish line and
returning to the starting line.
If the last finish line is 240m away, how far did he run in total when he reached the
starting point for the last time?
2 of the visitors in July were children and there were twice as many boys
2 4
Ans: _____________________
5. The graph below shows the number of visitors who visited Science Centre in the
period from July to December.
a) What is the fraction of the number of visitors in the least visited month to the
number of visitors in the most visited month?
b) If
3
as girls, how many girls were there?
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Jul Aug Sep Oct Nov Dec
Ans: _____________________

6. Study the figures below. The figure on the left shows a rectangular strip of paper.
The figure on the right shows that strip when folded along the dotted line. It consists
of 2 squares and 1 trapezium.
a) Find the length of the paper strip.
b) Find the area of the paper strip
3 cm
7 cm
3 of his money on 18 cakes and 21 toy robots.
2 5
Ans: _____________________[4]
7. Jeffery spent
5
The cost of a toy robot is 2 times that of a cake.
How many more toy robots could he buy with the remaining money?
Ans: _____________________[3]

8. Some girls bought a packet of strawberries to share among themselves. If each girl
took 7 strawberries, there would be 4 extra strawberries. If each girl took 8
strawberries, there would be 4 strawberries short.
a) How many strawberries did they buy?
b) How many girls were there?
7 of what Jason had.
2 6
Ans: _____________________[4]
9. Freddie, Jason and Malik each had some toy cars. Jason and Malik had
11 of what
14
Freddie had, and Malik had
15
a) If Freddie had 56 toy cars, how many toy cars did Jason have?
b) How many toy cars did they have altogether?
Ans: _____________________[4]
10. Mary bought 7 similar notepads and 9 similar pens. Each notepad is $1.1 more
expensive than a pen. If the total money Mary spent was $33.3, how much did she
pay for the pens?
Ans: _____________________[3]

11. Ross paid $85 for 10 notebooks and 4 files. Each notebook cost as much as 3 files.
2 7
What is the price of a notebook?
Ans: _____________________[4]
12. Study the figure below. Note that it is not drawn to scale. Answer the following
questions:
a) What is the area of the unshaded part?
b) What fraction of the whole figure is shaded?
Ans: _____________________[4]
10 cm 18 cm
30 cm

2 of the fruits in a basket are pears. There are 30 more apples than pears. The rest of
the fruits are 90 oranges. How many more apple than oranges were there?
1 that of the body. How long is the whale skeleton?
2 8
13.
7
Ans: _____________________[4]
14. At a museum, the body of the whale skeleton on display is as long as the total length
of its head and tail. The head of the whale skeleton is 8m long. The length of the tail
is equal to that of the head plus
3
Ans: _____________________[4]
15. A train departed from Clementi station.
5 of the passengers were adults.
11
3 of the
4
children were boys. The number of adult men is
1 that of women. There were 114
4
less girls than boys. At the next station, Dover, 9 women and 5 boys boarded the
train.
a) How many passengers were there altogether when the train left Clementi
Station?
b) How many male passengers were there on the train when it departed from
Dover station?
Ans: _____________________[4]

16. Mrs. Liu bought 5 packets of sugar, A, B, C, D, and E. The mass of sugar in each
packet is 500g, 600g, 800g, 900g and 1kg, respectively. Mrs. Liu kept one packet for
herself and sold the other packets to Mrs. Chan and Mrs. Lim. Mrs. Lim bought
twice the amount of sugar that Mrs. Chan bought. Which packet did Mrs. Liu keep
for herself if she kept more than 500g?
16 her son’s age. Now her age is three times
2 9
Ans: _____________________[4]
17. Alex, Benny, Carol and Dean stand in a straight row. Alex is not standing next to
Dean and Benny does not stand at the first position, how many possible ways are
there to arrange the four pupils?
Ans: _____________________[4]
18. Seven years ago Mrs. Goh’s age was
3
her son’s age. What is Mrs. Goh’s age now?
Ans: _____________________[4]

3 of the people at a cartoon movie show are children.
1 (2)
1 (4)
3 0
1. What is the result of
5 x 63
9
(1) 14 (2) 28
(3) 35 (4) 42
( )
2.
5
4 of the children are girls.
9
What is the fraction of the number of girls to the number of people at the show?
(1)
3
7
15
(3)
2
4
15
( )
3. The ratio of the number of boys to the number of girls in a class is 3:5. If there are 32
pupils in the class, how many boys are there?
(1) 12 (2) 20
(3) 28 (4) 36
( )
4. In the figure below, which line is the base of triangle XZT if XT is its height?
(1) XY (2) ZT
(3) YZ (4) YT
( )
X
Z
Y
T

5. In the following figure, the area of the shaded shape is 13 cm2. What is the area of
3 of David’s weight. David’s weight is
11 (2)
3 (4)
3 1
the unshaded part of the triangle?
(1) 23 cm2 (2) 30 cm2
(3) 41 cm2 (4) 60 cm2
( )
6. The Physics textbook of a university student weighs 3.9 kg. His Math textbook is
0.532 kg lighter than his Physics textbook. What is the total mass of the two books?
(1) 3.368 kg (2) 4.432 kg
(3) 7.268 kg (4) 8.332 kg
( )
7. Find the value of 60 ÷ (14 – 4) x 3
(1) 2 (2) 18
(3) 25 (4) 30
( )
8. Patrick and Albert have 72 pokemon cards. Patrick has thrice as many as Albert.
How many cards does Patrick have?
(1) 18 (2) 24
(3) 54 (4) 63
( )
9. Irene’s weight is
4
8 Peter’s weight. Express
9
Peter’s weight as a fraction of Irene’s weight.
(1)
13
59
36
(3)
2
2
3
( )
12 cm
9 cm

10. What is the area of the shaded triangle?
28 cm 11 cm
(1) 312 cm2 (2) 224 cm2
(3) 210 cm2 (4) 88 cm2
2 ?
4 (2)
4 (4)
3 2
( )
11. Which of the following is greater than
3
(1)
5
4
7
(3)
9
4
11
( )
12. What is ∠r in the figure below? XOY is a straight line.
(1) 151o (2) 119o
(3) 61o (4) 29o
( )
13. Which of the following is the best estimate for 605 x 48?
(1) 600 x 40 (2) 600 x 50
(3) 700 x 40 (4) 700 x 50
( )
29o
r
16 cm
X O Y

14. In a running competition, the total time taken by the 2 boys was 350 seconds while
the total time taken by the 3 girls was 555 seconds. Find the average time that a child
took to complete the race.
(1) 102 seconds (2) 175 seconds
(3) 181 seconds (4) 270 seconds
5 of his money. He bought a calculator with
3 3
( )
15. In 3 852 176, how many times is the value of digit 8 to the value of digit 1?
(1) 8 (2) 80
(3) 800 (4) 8 000
( )
16. Kelvin bought a pair of skates with
7
1
5
of his remainder. If he had $112 left, how much was the calculator?
Ans: _____________________
17. The figure below is made up of 8 identical squares. The total area is 32m2. Each
corner of a square at a lower row is at the midpoint of the side of the square of the
row above. What is the perimeter of the figure?
Ans: _____________________

18. While reading a book, Jerry noted that the product of the two facing pages that he
was reading is 600. What are the page numbers of the two facing pages that Jerry
was reading?
3 4
Ans: _____________________
19. Kathy bought a badminton racket for $199. She also bought 5 similar boxes of
shuttlecocks. She gave the cashier $300 and was given a change of $41. How much
was each box of shuttlecocks?
Ans: _____________________
20. Kelvin and Elizabeth shared some sweets. The ratio of Kelvin’s sweets to Elizabeth’s
is 8:5. If they have 65 sweets in total, how many sweets did Elizabeth have?
Ans: _____________________
21. Find digits X and Y from 0 to 9 so that
Ans: _____________________
X Y
Y
Y X
+

2 as many crayons as Ali. After Ali received 4 new crayons and
3 5
22. Jonathan had
3
Jonathan received 10 new crayons, they have the same number of crayons. How
many crayons did both of them have altogether before they received new ones?
Ans: _____________________
23. Miss Lisa divided 300 paper clips to her pupils. Each pupil received 15 paper clips.
The next day she divided some toy bricks to her pupils. Each pupil got 10 toy bricks.
How many toy bricks did Miss Lisa gave the class?
Ans: _____________________
24. Gupta and Davis had a total of $300. If Davis gave Gupta $18, he would have twice
as much money as Gupta. How much money did Gupta have at first?
Ans: _____________________
25. Mrs. Tan made 225 lollipops and packed them equally into some boxes, each have
15 lollipops. Each box was sold at $12.30. After selling all the boxes, how much did
she earn?
Ans: _____________________

26.
Find the area of the figure below, which consists of a square, a rectangle, and 3
1 are $5 and the rest are $10. He had saved $1 794 in total.
3 6
identical triangles.
Ans: _____________________
27. Ali counted his savings and noted that all of his money was in $2, $5 and $10 notes.
1 of the notes are $2,
3
6
What is the total value of $5 notes had he saved?
Ans: _____________________
3 cm
4 cm
7 cm

28. Darren needed to run 10km for training. He had run
3 7
4 1 km. How many more
9
kilometres did he have to run to complete the training? Express your answer correct
to 2 decimal places.
Ans: _____________________
29. Jimmy can make 30 paper birds every hour. Philip can make 50 paper birds every
hour. After Jimmy had started making paper birds for 2 hours, Philip also started.
How many hours would Philip take to make the same number of paper birds as
Jimmy?
Ans: _____________________
30. The ratio of 2 whole numbers is 2:15. The bigger number is greater than 98 but
smaller than 108. Find the smaller number.
Ans: _____________________

1. Helen cycles
7 2 km to school. Jack cycles
3 8
3
5 of that distance to school. What is the
8
difference in distance they have to cycle to school? Express your answer as a fraction
in its simplest form.
Ans: __________________km
2. Find the area of the shaded part in the figure bellow, given that ABCD is a rectangle
and CN is 3 times as long as ND.
Ans: _____________________
96 m
24 m
A B
M
N
D C

3. The ratio of the amount of petrol Mr. Quek used in January to the amount of petrol
he used in February was 4:7. He used 60l of petrol in January. How much did he
have to pay for petrol in total if the price of petrol was $2.50 per litre during those
two months?
3 9
Ans: _____________________
4. Nurbaya wanted to make 24l of strawberry drink from a 1.5l bottle of strawberry
syrup. She mixed the syrup with plain water in the ratio of 1:5.
a) How much strawberry syrup is she short of?
b) After buying more syrup and made the desired drink, she added another 2l of
syrup to make the drink sweeter. Find the new ratio of syrup to water in the new
drink.
Ans: _____________________
5. A salesman earned $10 for each unit of product A and $4 for each unit of product B
that he sold. In a month, he earned a total of $11 400. The ratio of the number of
product B units to product A units that he sold was 3:14.
a) How many units of product A did he sell?
b) What is the difference between the amount of money he collected from selling
product A and the amount of money he collected from selling product B?
Ans: _____________________

6. Nancy had some stickers.
1 of them were used to make a scrapbook. She then
2 of the remaining equally to her three friends. After making the scrapbook
4 0
3
divided
3
and sharing stickers to her friends she had 42 stickers less than what she had at the
beginning. How many stickers did each of her friends receive?
Ans: _____________________[4]
7. Suriyana and Fahan each had saved some 20-cent and 50-cent coins. Suriyana had a
total of 192 coins. The number of 20-cent coins that Suriyana had was
3 the number
5
of 50-cent coins that she had. The ratio of the number of 20-cent coins to the number
of 50-cent coins that Fahan had was 1:2. Fahan’s total number of coins is only
1
4
that of Suriyana.
a) What is the ratio of the number of 20-cent coins Suriyana had to the number
of 50-cent coins that Fahan had?
b) What is the ratio of the amount of money that Suriyana had to the amount of
money that Fahan had?
Ans: _____________________[4]

8. Find a number that gives a quotient of 189 and a remainder of 17 when divided by
5 of his working hours working with his computer. He worked for
1 of the day. How many minutes did he work with his computer?
4 1
55.
Ans: _____________________[3]
9. Mr. Ong spent
12
3
Ans: _____________________[3]
10. Tom and Jerry have some money. If Tom gives Jerry $5, he will have half what Jerry
has. If Jerry gives Tom $5, they will have the same amount.
a) How much money does Tom have?
b) How much money does Jerry have?
Ans: _____________________[4]

11. A box of 16 Pelican pens (box A) is sold at $14.70. A box of 24 Pelican pens (box B)
is sold at $22.50. Is box A or box B the cheaper buy?
4 2
Ans: _____________________[4]
12. All the people at a party shake hands with one another. How many handshakes are
there if there are
a) 3 people?
b) 5 people?
c) 10 people?
Ans: _____________________[4]
13. The ratio among 3 sides of a triangle is 4 : 2 : 5. The longest side is 300 cm. What is
the perimeter of the triangle?
Ans: _____________________[4]

4 3
14. Study the following pattern:
1
1
1
5
...
1
1
1
4
1
1
1
4 5
4
3
3 4
3
2
2 3
= −
×
= −
×
= −
×
Use the above pattern to calculate
... 1
19 20
1
4 5
1
3 4
1
2 3
×
+ +
×
+
×
+
×
Give your answer in the simplest form.
Ans: _____________________[4]
15. Mr. Green needed to go from A to B. He had travelled
3 of the distance and still
8
needed to travel another 480km. What is the distance from A to B?
Ans: _____________________[4]
16. A rectangle water tank can contain a maximum of 105m3 of water. Its base is 5m
wide and 7m long. What is the depth of the tank?
Ans: _____________________[4]

17. What is the area of the right-angled trapezium ABCD as shown below?
14 cm
4 4
Ans: _____________________[4]
18. 36 chickens and dogs have a total of 100 legs. How many chickens are there?
Ans: _____________________[4]
A B
D C
26 cm
11 cm

1. What is the area of triangle PQR?
P
Q
(1) 66 cm2 (2) 175 cm2
(3) 225 cm2 (4) 297 cm2
4 5
( )
2. Find the value of 84 ÷ (5 + 2) – 2 x 5
(1) 2 (2) 50
(3) 60 (4) 72
( )
3. COD is a straight line. Find ∠x if ∠x is 180 less than ∠y. (The figure is not drawn to
scale).
(1) 99o (2) 81o
(3) 36o (4) 9o
( )
x
y
25 cm
14 cm
R
P
S

4. What is the value of ∠a, given that AB and CD are straight lines?
a
(1) 32o (2) 48o
(3) 60o (4) 122o
4 6
( )
5. Nelson, Jordan and Joe had a number of cookies. Nelson had 2 times the number of
cookies that Jordan had. Joe had the same number of cookies as Nelson. What is the
ratio of the number of cookies that Nelson had to the total number of cookies of all
three friend?
(1) 1:5 (2) 2:5
(3) 3:5 (4) 4:5
( )
6. A triangle of height 8cm and base 6cm is cut from each corner of a square. The
perimeter of the square is 80cm. Find the area of the remaining figure?
(1) 208 cm2 (2) 250 cm2
(3) 304 cm2 (4) 352 cm2
( )
7. How many thousands are there in one and a half million?
(1) 15 (2) 150
(3) 1 500 (4) 15 000
( )
8. The difference between 430 000 and 550 000 is divided by 400. What is the final
value?
(1) 30 (2) 300
(3) 3 000 (4) 30 000
( )
9. Round off 205 621 to the nearest thousand
(1) 205 000 (2) 205 600
(3) 206 000 (4) 206 621
( )
A B
C
D
138o

2 of a Sunday practicing the piano.
4 7
10. How many sixths are there in
3 1 ?
2
(1) 0 (2) 5
(3) 15 (4) 21
( )
11. Mr. Koh’s garden is 25m long and 12m wide. The cost of mowing 1m2 of garden is
$15. How much must he pay to mow his whole garden?
(1) $20 (2) $555
(3) $1 110 (4) $4 500
( )
12. Sally spent
3
How many hours did she spend on that Sunday practicing the piano?
(1) 8 hours (2) 16 hours
(3) 20 hours (4) 36 hours
( )
13. Which of the following is not a symmetric figure?
(1) (2)
(3)
(4)
( )
14. Find the area of the shaded figure.
(1) 112 cm2 (2) 266 cm2
(3) 308 cm2 (4) 420 cm2
( )
28 cm
19 cm
8 cm

15. The graph below shows Mrs. Ong’s grocery expenses for her family from January to
May.
What is Mrs. Ong’s average grocery expense for the five months?
4 8
$200
$180
$160
$140
$120
$100
$80
$60
$40
$20
$0
Jan Feb Mar Apr May
(1) $100 (2) $125
(3) $150 (4) $175
( )
16. At a fruit stall, the ratio of apples to oranges is 2:3 and the ratio of apples to banana
is 4:9. Find the ratio of oranges to bananas.
Ans: _____________________
17. Sylvia, Alan and Ronald are making paper stars together. Ronald and Alan made 221
paper stars altogether. Alan and Sylvia made 121 paper stars altogether. If Ronald
made 5 times as many paper stars as Sylvia, how many paper stars did Alan make?
Ans: _____________________

18. Half of the pens at a stationary shop are blue.
4 9
1 of the remaining pens are red, while
8
the remaining pens are black. If there are 210 more black pens than red pens, how
many pens are there altogether?
Ans: _____________________
19. A drink stall had some cans of coke and soda water in the ratio 3:7. After selling 48
cans of soda and buying another 48 cans of coke, the shop had the same number of
cans for each drink. How many cans of coke were there at first?
Ans: _____________________
20. In triangle XYZ below, XZ = YZ = 9cm.
Calculate the area of the shaded area.
Ans: _____________________
4.5cm
2 cm
Z
X
Y

21. Danny and Fahan had $54 in total. If each boy was given another $8, the ratio of the
amount that Danny had to the amount that Fahan had became 3:4. How much money
did Fahan had at first?
5 0
Ans: _____________________
22. Arrange the following fractions in ascending orders
, 7
7
5
, 4
4
, 5
5
5
23. How many two thirds are there in 18?
Ans: _____________________
24. Betsy had an average of 56 slices of fruit a month.
How many slices of fruit did she have in
2 3 months?
4
Ans: _____________________
25. Fill in the box with an appropriate number
2
8 =
12
Ans: _____________________

Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below
26.
The number of chocolate candies in a box is between 60 and 100. If 4 or 7 children
share the box, each of them can have the same amount of candies. How many
chocolate candies are there in the box?
51
Ans: _____________________
27. Mr. Lee had a number of boxes. He packed them into 8 layers in a container. Each
layer has 7 rows. Each row has 6 boxes. How many boxes did Mr. Lee have?
Ans: _____________________
28. Find A if
2 5
12
A×5 1 =
4
Ans: _____________________

29. If a bus can carry 25 passengers, what is the minimum number of buses to carry 7
groups of passengers, each of which have 32 passengers?
52
Ans: _____________________
30. Two pumps are used to fill a swimming pool. Pump A can fill the pool completely in
3 hours. Pump B can fill the pool completely in 2 hours. How long will it take to fill
the pool completely if both taps are turned on at the same time?
Ans: __________________hours

1. Wu Wei was given a number of questions as homework. He answered
53
1 of the
2
number of questions on the first day. On the second day he answered
1 of the
10
number of questions. If he continued to answer
1 of the number of questions every
10
day from the third day, on what day will he finish all the questions?
Ans: _____________________
2. For every 5 hour of work, Daniel was paid $80. How many hours had he worked if
he was paid $1440?
Ans: _____________________

3. What is the area of the shaded part in the figure below if each square has sides of 3
54
cm?
Ans: _____________________
4. A piece of cloth is cut into two pieces. The area of the bigger piece is
7 that of the
12
original piece. If the area of the bigger piece is 138 cm2 more than that of the smaller
piece, what is the area of the bigger piece?
Ans: _____________________
5. Complete the figure below so that the dotted line is the line of symmetry
Ans: _____________________

6. In the figure below, what is the area of the square if the averaged perimeter of the
1 the volume of petrol in barrel B. 24l of petrol
55
square and the triangle is 59 cm?
Ans: _____________________[4]
7. The volume of petrol in barrel A is
4
is moved from barrel B to barrel A. The volume of petrol in barrel A is now
1 the
2
volume of petrol in barrel B. How much petrol is there in barrel B in the end?
Ans: _____________________[4]
28 cm
12 cm

8. Examine the pattern of the following figure. Find the missing number.
?
56
12
Ans: _____________________[4]
5
9. A shop is selling toy robots at $20 and dolls at $50. There are 23 more dolls than toy
robots. After selling some dolls for $900, the shop has 1.5 times as many dolls as toy
robots. How many dolls did the shop have at first?
Ans: _____________________[3]
89
115
1020
117
258
4500
205
397
4816

10. Joey, Zhong Ren and Suriya had a total of $1 326. After Joey spent
1 of his money, and Suriya spent
4 the total of cards that George and Harry had. George had twice the number of
cards Fred had.
a) If George had 104 cards, how many did Harry have?
b) What was the number of cards three of them had altogether?
1 of his brother’s money. The product of their money is $400. How much
57
2 of his money,
5
Zhong Ren spent
7
1 of her money, all of them had
3
the same amount of money. How much did they spend altogether?
Ans: _____________________[4]
11. Fred, George and Harry shared some pokemon cards. The number of cards Fred had
is
11
Ans: _____________________[4]
12. Jane had
4
money did Jane have?
Ans: _____________________[3]

13. A pair of shoes is 9 times as expensive as a pair of socks. If 3 pairs of shoes and 5
pairs of socks cost $192, how much is a pair of shoes?
1 times as heavy as a bag of powder. The average mass of the two
58
Ans: _____________________[4]
14. What is the area of the shaded part, if each small square is 4 cm x 4 cm?
Ans: _____________________[4]
15. A bag of rice is 2
2
bags is 33.25 kg. What is the mass of the bag of powder?
Ans: _____________________[4]

16. The ratio of the number of pencils to the number of pens in a stationary shop was 3:
7. The stall owner then sold 36 pens and the number of pens became equal to the
number of pencils. How many pens were there in the shop at first?
59
Ans: _____________________[4]
17. The figure below is not drawn to scale. Find the area of the shaded part.
Ans: _____________________[4]
18. Alice had 9 notepads and Ronald had 6 notepads. Alice then bought some more
notepads. After that the ratio of the number of notepads that she had to the number of
notepads Ronald had is 7: 3. How many more notepads did Alice buy?
Ans: _____________________[4]
19 cm
15 cm
15 cm
7 cm

1. Five pupils shared a 9l jug of orange juice. How many litres of orange juice did each
5 (2) l
1 4
5 (4) l
14 (2)
814 (4)
60
pupil get?
(1) l
13
8
13
(3) l
9
5
( )
2. Write 8.56 in fraction form
(1)
25
98
125
(3)
25
8 8
25
( )
3. Which of the following ratio is not equivalent to 5 : 13
(1) 15 : 39 (2) 30 : 78
(3) 35 : 91 (4) 40 : 84
( )
4. In the diagram below, ABCD is a rectangle, AB = 7cm, AD = 5cm, BO = 4 cm, AO
= 9.5 cm. What is the base and height of the shaded triangle?
(1) 4 cm and 9.5 cm (2) 4 cm and 7 cm
(3) 5 cm and 9.5 cm (4) 5 cm and 7 cm
( )
A B
O
D C
Marks

5. Each worker in a factory was given 300 short nails, 700 medium nails and 600 long
nails. Find the ratio of the number of long nails to the total number of nails
(1) 3 : 13 (2) 7 : 16
(3) 3 : 8 (4) 3 : 16
26 (2)
104 (4)
3 kg of candies. Mrs. Chua packed all the candies in the tin into 9
27 (2) kg
1 (4) kg
3 m wide has an area of 9m2. What is its perimeter?
7 1 m (2) 12m
12 3 m (4)
61
( )
6. There were 45 strawberries in basket A. Basket B had 25 more strawberries than
basket A. What was the ratio of the number of strawberries in basket B to basket A?
(1) 14 : 9 (2) 9 : 14
(3) 4 : 9 (4) 9 : 4
( )
7. What is the value of
13 × 8
?
9
4
(1)
9
21
13
(3)
9
117
32
( )
8. What is the value of 66 + 18 ÷ 3 + 4 x 5
(1) 48 (2) 92
(3) 116 (4) 160
( )
9. A tin contains
5
bags, each weighs the same. What was the mass of each candy bag?
(1) kg
5
4
5
(3) kg
15
12
5
( )
10. A rectangle
4
(1)
2
(3)
4
25 1 m
2
( )

11. Ding Mei’s water bottle was full and had l
1 of water. What was the fraction of the amount of water left in Ding Mei’s
19 (2)
11 (4)
Pupil’s name Test score
Joey 95
Lucy 83
Michael 77
Sam 71
62
3 and poured
3 of water. She drank l
2
10
away l
4
bottle to the full bottle?
(1)
30
19
20
(3)
20
1
20
( )
12. Miss Sally needed to use 85cm of ribbon to tie a present. If she had to make 25
similar presents to her pupils, how many meters of ribbon were used?
(1) 1.1 (2) 2.125
(3) 3.4 (4) 21.25
( )
13. Calculate the sum of 72.35 and 52.87. Round off your answer to 1 decimal place.
(1) 124.2 (2) 125.2
(3) 126.2 (4) 127.2
( )
14. Joey, Lucy, Michael and Sam attended a physics test. There scores are shown in the
table below:
Who had the score that is closest to the average score of all 4 pupils?
(1) Joey (2) Lucy
(3) Michael (4) Sam
( )
15. Fatimah needed to walk 1.8 km to school. She had walked 216m. What percentage of
the journey did she still have to walk?
(1) 12% (2) 13.64%
(3) 75% (4) 88%
( )

16. Write 8 006 500 in words.
17. What is the remainder when dividing 5603 by 7?
M K N
Q P
63
Ans: _____________________
18. What fraction of 5km is 1300 m? Provide the simplest form for your answer.
Ans: _____________________
19. Express
23 km in metres.
5
Ans: _____________________
20. In the diagram shown below, MNPQ is a rectangle; K and H are midpoints of MN
and PQ respectively. What fraction of the figure is shaded?
Ans: _____________________
H

21. Mei Mei, Jing Jing and Hui Hui were given the same homework. Mei Mei had done
1 of the homework. Hui Hui had done
64
4
1 of the homework. Jing Jing’s completed
2
portion of the homework is exactly midway between Mei Mei’s and Hui Hui’s. What
fraction of the homework had Jing Jing done?
Ans: _____________________
22. 1 carpenter can make 8 tables in a week. How many carpenters are required to make
40 tables in a week?
Ans: _____________________
23. A = 1 + 2 + 3 + … + 99 + 100.
Find the value of A.
Ans: _____________________
24. A carpenter completed a chair at 4.40 pm. It took him 2 hours 45 minutes to
complete his work. What time did he start?
Ans: _____________________

25. At first, Davis, Feng Xue and Ann had 181 stamps in total. Davis had 37 stamps.
Feng Xue and Ann had the same amount of stamps. A few weeks later, Ann
collected another 29 stamps. How many stamps did Ann have in the end?
65
Ans: _____________________
Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below
26.
Two numbers have a sum of 148.5 and a difference of 43.5. What are the two
numbers?
Ans: ______________
27. In the figure below, ABCD is a square of side 30 cm and DH =
7 HC. Find the area
3
of the shaded triangle.
Ans: _____________________
A B
D C H

28. There were 592 apples and pears in a fruit shop. After
66
4 of the apples and
9
2 of the
7
pears were sold, the number of pears and the number of apples left are the same.
How many pears were sold?
Ans: _____________________
29. At first, of a tank was filled with water. The total mass was 81.74 kg. Water was
then taken out of the tank until it was half filled. The total mass was 59.8 kg. What
was the mass of the tank? Round off your answer to 1 decimal place.
Ans: _____________________
30. Of all the adults at a concert, were women. There were 114 more children than
women. The ratio of the number of adults to the number of children was 3: 7. How
many children were there at the concert?
Ans: _____________________

1. Grapes were sold at $0.65 per 250g in a market. Mr. Khoo bought 3.25 kg of grapes.
67
How much did he have to pay?
Ans: _____________________
2. Find the area of triangle ACD in the figure below.
Ans: _____________________
A
B
C
D
8 cm 22 cm
16 cm
7 cm

3. Three packets of candies had an average mass of 903.6g. The packet of apple candies
weighed twice as much as the packet of strawberry candies. The packet of mango
candies is
4 the mass of the packet of strawberry candies. What is the mass of the
68
5
packet of apple candies? Express your answer up to 2 decimal places.
Ans: ___________________kg
4. 2 boxes of candies and 3 boxes of cookies have an average mass of 3.84 kg. 3 boxes
of candies and 2 boxes of cookies have an average mass of 3.7 kg. The candy boxes
are identical and the cookies boxes are also identical. What is the total mass of 2
boxes of candies and 1 box of cookies?
Ans: _____________________
5. There are two water taps, A and B. Tap A is used to fill in tank X and tap B is used
to fill in tank Y. In every minute, tap A can fill 8l more than tap B. However, 56.5l of
water is drawn from each tank in every minute. When tank X has 54l, tank Y has 22l.
a) How much water does tank Y receive per minute?
b) How much water is there in tank Y after 1 hour?
Ans: _____________________

6. When Tom received his salary, he gave his mother
69
1 his salary. He then used
4
1 of
7
the remaining amount plus $54 to pay his bills. After that, he spent half of the
remainder plus $27 to buy a computer. Finally, he saved the remaining $846. How
much was his salary?
Ans: _______________[4]
7. In the tables and chairs section of a warehouse, the ratio of the number of chairs to
that of tables is 5: 3. There are 64 wooden pieces of furniture and the rest are made
of plastic. The number of plastic pieces is twice the number of wooden pieces. If
there are 32 wooden chairs, what is the ratio of the number of plastic chairs to that of
wooden tables?
Ans: _______________[4]

1 m taller than she is. What is the average height
1 of a magazine on Friday and
70
8. Betsy is 1
1 m tall. Her brother is
2
6
of the two children? Round off your answer to 2 decimal places.
Ans: _______________[4]
9. Nicole read
5
1 of the remaining on Saturday. On
4
Sunday she read twice as many pages as on Friday. What fraction of the magazine
was not read?
Ans: _______________[4]
10. The ratio of the cost of an LCD monitor to that of a computer is
4 . The computer
9
costs $900. What is the average cost of the two devices?
Ans: _______________[3]

11. Ken bought 3 pairs of jeans and 2 shirts for $90. A pair of jeans was $5 more
expensive than a shirt. How much did a pair of jeans cost?
71
Ans: _______________[4]
12. The ratio of the number of Indian pupils to the number of Chinese pupils is 2: 7. The
ratio of the number of Malay pupils to the ratio of Chinese pupils is 3: 4. What is the
ratio of the number of Indian pupils to the number of Malay pupils to the number of
Chinese pupils?
Ans: _______________[4]
13. A bank paid a fixed 0.68% saving interest per year. Bill opened an account and
deposited $172 000. How much interest would he earn after a year?
Ans: __$____________[4]

14. The total amount of money that Soo Hui and Margaret had is $630. If Margaret gave
Soo Hui $52.70, Soo Hui would have eight times the amount that Margaret had.
Initially, what was the difference in the amounts that they had at first?
72
Ans: _______________[4]
15. The total volume of water in tanks A, B and C is 400l. If half of the water in tank A
is taken away and the water in tank B is doubled, and 30l is added to tank C, the ratio
of the volume of water in tank A to B to C will be 3: 2: 1. Find the amount of water
in tank B initially.
Ans: _______________[4]

16. A set of furniture costs $3290. Mr. Tay bought the set with 20% discount. However,
he had to pay 7% GST on the discounted price. How much did he have to pay for the
set of furniture?
73
Ans: _______________[4]
17. Use the following digits, each digit only once, to make the smallest even number that
is greater than 250 000.
0, 3, 7, 2, 9, 6
Ans: _______________[3]
18. In a laboratory, the mass of some bacteria doubles every 12 minutes. If the mass is
128 mg at 5 p.m, what time was it when the mass was 0.5 mg?
Ans: _______________[4]

1. The digit 9 in 5 298 637 is the _________________________ place
(1) hundreds (2) thousands
(3) ten thousands (4) hundred thousands
3 hours. For how many minutes did he study?
2 of his money and used
1 (2)
1 (4)
74
( )
2. Which of the following numbers will result in 555 000 when being rounded off to the
nearest thousand?
(1) 554 494 (2) 555 494
(3) 555 501 (4) 555 513
( )
3. 45 x 100 = ____________________-
(1) 45 x 20 x 5 (2) 40 + 5 x 100
(3) 45 x 10 + 90 (4) (45 x 20) + (45 x 5)
( )
4. Frank studied for 4
10
(1) 258 minutes (2) 300 minutes
(3) 342 minutes (4) 400 minutes
( )
5. Find the value of 650 – (27 + 123) ÷ 4
(1) 36.25 (2) 125
(3) 250 (4) 612.5
( )
6. Harry bought a pair of jeans with
3
1 of his remaining
4
money to buy some toys. What is the fraction of money left?
(1)
4
3
4
(3)
12
5
12
( )

7. Find the area of the figure below (not drawn to scale)
8 cm
(1) 30 cm2 (2) 36 cm2
(3) 42 cm2 (4) 49 cm2
1 km. What was the distance that she jogged each day?
1 km (2) 3km
3 of the participants are boys and
19 (2)
14 (4)
75
( )
8. What is the volume of a cube of side 4 cm?
(1) 16 cm3 (2) 32 cm3
(3) 64 cm3 (4) 128 cm3
( )
9. What is the maximum number of 2-cm cubes that can be fitted into a rectangular box
measuring 9 cm by 6 cm by 4 cm?
(1) 9 (2) 24
(3) 27 (4) 54 ( )
10. Annie was sitting in a concert. The chairs were arranged in rows in a rectangular
manner. There were 6 chairs on Annie’s left and 8 chairs on her right. There were 10
rows in front of her and 11 rows behind her. How many chairs were there?
(1) 294 (2) 308
(3) 315 (4) 330 ( )
11. Mei Mei jogged for the same distance every night. After a week, the total distance
covered was 17
2
(1) 2
2
(3) 5km (4) 10
1 km ( )
2
12. In a survey among pupils in a school,
5
5 of these
6
boys likes basketball. The survey also shows that
1 of the girls like basketball too.
3
What fraction of the pupils like basketball?
(1)
30
11
30
(3)
15
7 ( )
6
9

76
13. Express 21 km 3 m in km.
(1) 21. 003 km (2) 21. 03 km
(3) 21.3 km (4) 210.3 km
( )
14. What is the product of 56.31 and 60?
(1) 3.3786 (2) 33.786
(3) 333.86 (4) 3 378.6
( )
15. The average mass of two packets of rice is 4 kg. Which of the following are the
likely mass of the two packets of rice?
(1) 2.5 kg and 2.5 kg (2) 2.5 kg and 3.5 kg
(3) 2.5 kg and 4.5 kg (4) 2.5 kg and 5.5 kg
( )
16. What is the remainder when 3256 is divided by 19?
Ans: _____________________
17. Write six hundred and eighty thousand, seven hundred and ninety-five as a numeral.
Ans: _____________________
18. What is the difference between and ?
Ans: _____________________
19. Calculate
290 – 36 ÷ 4 x (27 + 5) ÷ 2 + 115
Ans: _____________________

20. How many cubic centimetres are there in 1l 25 ml?
5 l of milk in her bottle. She drank
77
Ans: _____________________
21. Pei Xin had
6
1 of the milk in the bottle. How
3
many liters of milk did she have left?
Ans: _____________________
22. Find x if × =
X 2
5
3
4
Ans: _____________________
23. Express 63.08l in terms of milliliters.
Ans: _____________________
24. The table below shows the prices of different fruits at a market.
Fruit Price (per kg)
Apple $3.65
Strawberry $4.89
Kiwi $5.99
Watermelon $4.20
Uncle Tiong bought 2 kg of apple and 3 kg of kiwi. How much did he spend?
Ans: _____________________

78
25.
Find X and Y if X : 5 : 9 = 7 : Y : 63
Ans: _____________________
26.
Mrs. Lim wants to give some pens to her pupils. If each pupil gets 7 pens, there will
be 3 pens extra. If each pupil gets 8 pens, there will be 4 pens short.
a) How many pupils are there?
b) How many pens does Mrs. Lim have?
Ans: _____________________
27. 75% of the candies in a box are chocolate flavored. 40% of the remainder is mango
flavored and the rest is strawberry flavored.
a) Express the number of strawberry flavored candies as a fraction of the total
number of candies in the box.
b) How many more chocolate flavored candies than strawberry flavored candies
are there if there are 20 mango flavored candies?
Ans: _____________________

28. The breadth of a rectangular floor is 15% of its perimeter. The length of the floor is
760 cm longer than its breadth.
a) What is the area of the floor in m2?
b) The floor is used to store identical cartons each has a base measuring 30 cm
by 30 cm. What is the maximum number of cartons that can be stored?
79
Ans: _____________________
29. The table below shows the water tariffs (charges) for monthly water consumption
Volume consumed Charges per unit (dollars)
First 40 units 1.17
Above 40 units 1.40
Mr. Choo’s family used 56 units in January. In February he paid $135 for his bill.
a) How much water did Mr. Choo’s family use in February?
b) On average, how many units of water were consumed by his family in a
month over this period?
c) On average, how much does Mr. Choo have to pay for water bill in a month?
Ans: _____________________
30. Peter has a number of books. Lixiang has
2 as many books as Peter has. Fahan has
3
half as many books as Peter has. If Lixiang has 32 books, how many books do they
have altogether?
Ans: _____________________

1. The maximum score for a physics test is 50 marks. What is the highest possible
average score for 5 pupils who took the test, if it is known that one of them scored 15
marks?
80
Ans: _____________________
2. Fred and George folded a number of paper birds. Fred folded 35% of the birds.
George folded 90 birds more than Fred. How many birds did George fold?
Ans: _____________________
3. Mary, Andy and Bob donated some money to a charity fund. Mary donated 40%
what Andy donated and 50% less than what Bob donated. If they donated $660
altogether, how much did Andy donate?
Ans: _____________________

4. In the figure below, ABCD is a rhombus. What is ∠ABE? The figure is not drawn to
81
scale.
Ans: _____________________
A
5. Kin Eu had collected some stamps. After collecting another 12 stamps, the number
of stamps in his collection increased by 30%. How many stamps did he have at first?
Ans: _____________________
116o
B
C
D
E

6. The table below shows the number of days pupils exercised in a week. What is the
fraction of the number of pupils that exercise 2 days or more to the total number of
pupils? Express your answer correct to 2 decimal places.
No. of exercised days 0 1 2 3 4
No. of pupils 5 9 7 16 5
82
Ans: _____________________[3]
7. In a festival that has 2500 participants, there are 1100 females. How many percent
more males than females are there? Round off your answer to 2 decimal places.
Ans: ____________________%[3]
8. The number of exercise questions that 3 pupils have completed is in the ratio of 2: 4:
5. If the pupil who had done the least completed 6 questions, what is the total number
of questions that they have completed?
Ans: _____________________[4]

9. There are approximately 3300 adults and 1700 children in a stadium. If both above
figures are corrected to the nearest hundred, what is the largest possible difference
between these 2 figures?
83
Ans: _____________________[4]
10. The area of the shaded part in the figure below is 54 cm2. SH =
1 PK.
4
What is the area of triangle PQR?
Ans: _____________________[4]
P
S
Q R
H K

11. The area of rectangle A is 3 times the area of square B. The unshaded area of
rectangle A is 5 times the unshaded area of square B. If the shaded area is 27 cm2,
what is the area of the square? The figure is not to scale.
84
Ans: _____________________[4]
12. Miss Chua brought some lollipops to share equally among 36 pupils at the end of a
camp. However, 9 pupils had to leave the camp early. Therefore, each of the
remaining pupils received 3 more lollipops. How many lollipops did Miss Chua
bring?
Ans: _____________________[4]
A
B

13. In the figure below, ABC is a right angled triangle at C. Its height is 9 cm and its
base is 12 cm. 4 such identical triangles are used to form the square MNPQ. Find the
side of the square MNPQ.
1 the area of triangle B. The ratio of area of triangle A to that of
85
Ans: _____________________[4]
14. In the figure below, a rectangle is divided into 4 smaller triangles A, B, C and D. The
area of triangle A is
3
triangle D is 3: 5. The width of the rectangle is 6 cm. The area of triangle D is 30
cm2. Find the perimeter of the rectangle.
Ans: _____________________[4]
A
B
C
D
Q
A
C B
M N
P

15. In a second-hand bookshop, story books are sold at $12 each and comic books are
sold at $8 each. At first, there were 50% more story books than comic books. After
some time,
2 of the story books and all the comic books were sold. The shop
1 the money that Aaron had. After that Aaron spent $45 and Lucy’s
86
3
received $6400. When all the books were sold, how much would the shop receive?
Ans: _____________________[4]
16. Lucy had
3
mother gave her $6. Aaron still had $3 more than Lucy. How much money did Lucy
have at first?
Ans: _____________________[4]

2 the number of marbles that Thomas has. Ben has
87
17.
3 of Joey’s marbles is equal to
5
7
twice the difference between Thomas and Joey’s marbles. Joey has 48 marbles less
than Ben. How many marbles do they have altogether?
Ans: _____________________[4]
18. Tank A measures 4 m by 6 m at the base and is 1 m high. Tank B has the base
dimensions of 5 m x 3 m and is twice as high as tank A. Both of them contain the
same amount of water. The height of water level in tank A is half of its height. Find
the height of water level in tank B.
Ans: _____________________[4]

1. The square below is divided into three parts, A, B and C. The ratio between the areas
A and C is 8: 3. What is the ratio of the area of B to that of C?
(1) 3 : 8 (2) 5 : 3
(3) 8 : 5 (4) 8 : 11 ( )
2. The average weight of 3 pupils is 38 kg. Andy weighs 33.5 kg. John is 3.5 kg heavier
than Bob. How heavy is John?
(1) 42 kg (2) 38 kg
(3) 33 kg (4) 30 kg
2 kg of sugar and Sarah bought 1
3 (2)
2 (4) 4
88
( )
3. Maria and Lily shared some money. Maria had of the total sum. Lily had $180
more than Maria. How much money did both of them have in total?
(1) 72 (2) 90
(3) 360 (4) 420
( )
4. Adil had 36 more stickers than Xiao Mei. Each of them then bought another 10
stickers. After that, Adil had 4 times as many stickers as Xiao Mei had. How many
stickers did Adil have initially?
(1) 38 (2) 40
(3) 58 (4) 108 ( )
5. Celine bought 2
5
5 kg of sugar. They used 2
6
1 kg
10
to bake some cakes. How many kilograms of sugar did both of them have
eventually?
(1)
10
7
15
(3) 2
15
7 ( )
30

7 kg of charcoal for a BBQ but only used
7 (2) 1
3 (4) 1
89
6. Ivy bought
4
3 of them. How many
5
kilograms of charcoal were left over?
(1)
10
1
20
(3) 1
20
7
20
( )
7. There are 32 students in a class. There are 24 students wearing spectacles. What is
the ratio of the number of students who wear spectacles to the number of students
who do not?
(1) 1 : 3 (2) 3 : 1
(3) 3 : 4 (4) 4 : 3 ( )
8. Ali is living in Singapore and he has collected stamps from Singapore, China and
India. The ratio of the number of Singapore stamps to the number of China stamps to
the number of India stamps that he collected is 1: 1: 2. Ali collected 108 foreign
stamps in total. How many local stamps were there?
(1) 27 (2) 36
(3) 81 (4) 144
( )
9. A container having a capacity of 33.5l is filled with lime juice drink. This container
is dispersed into 100 similar glasses for guests. How many liters of juice drink is
there in each glass?
(1) 0.0335 l (2) 0.335 l
(3) 3.35l (4) 3 350 l
( )
10. Find the difference between 125.22 and 38.19. Express your answer as correct up to
1 decimal place.
(1) 87.0 (2) 87.1
(3) 87.9 (4) 88.0 ( )
11. A box containing 24 identical cans weighs 8.36 kg. What is the mass of the box (in
kg) if each can weighs 340g?
(1) 0.2 kg (2) 0.418 kg
(3) 0.5 kg (4) 2 kg
( )
12. The distance from Hassan’s house in Serangoon to Patrick’s house in Paya Lebar is 5
515 m. Write that distance rounded off to the nearest kilometer.
(1) 5 km (2) 6 km
(3) 5 500 km (4) 60 km
( )

13. What is the value of digit 3 in 238 962
(1) 30 (2) 300
(3) 3 000 (4) 30 000
90
( )
14. Last month, a shop collected $65 098 from selling goods.
Express this amount to the nearest hundred
(1) 65 000 (2) 65 100
(3) 66 000 (4) 66 100
( )
15. Express 3
1 as a percentage
4
(1) 0.325% (2) 3.25%
(3) 32.5% (4) 325%
( )
16. In an orchard there are apple trees and pear trees. The ratio of the number of apple
trees to the number of pear trees is 5: 9. What is the ratio of the number of pear trees
to the total number of trees in the orchard?
Ans: _____________________
17. A caterer mixed 2070 ml of orange syrup to 12.42 l of water to make orange juice
drink. What is the volume of juice drink made? Express your answer in liters.
Ans: _____________________

18. How many percent of the figure below is shaded?
5 Kg of flour is divided equally into 10 bags. What is the mass of flour in each bag?
Give your answer in its simplest fraction form.
2 that of his brother. He is 15 years old now. How
91
Ans: _____________________
19. Express
8 in decimal form.
125
Ans: _____________________
20.
6
Ans: _____________________
21. 3 years ago, Mohammed’s age is
3
old is his brother now?
Ans: _____________________

22. What percentage of the number of days in 2009 is the number of days in September?
105 , 0.051, 0.501, 100
92
Ans: _____________________
23. Arrange these number in an ascending order
1000
51
Ans: _____________________
24. 56 x 28 = 29 x 28 + 1 x 28 + ______ x 28
Ans: _____________________
25. Write 64% as a simplest fraction.
Ans: _____________________
26.
The price before tax of a plasma TV is $2100. A GST of 7% is charged on the price.
How much does a buyer have to pay for the TV?
Ans: _____________________

27. The first carton has 1.25 l of lime juice. The second carton has 2
5 as much as Joshua saved. The two pupils saved $1053. How much
93
1 l of lime juice.
8
The third carton had 786 ml of lime juice. How many liters of lime juice are there in
total? Round off your answer to 2 decimal places.
Ans: _____________________
28. Kavitha saved
8
is Kavitha’s savings?
Ans: _____________________
29. A small swimming pool of dimension 20 m x 10 m x 1.5 m is half filled with water.
4 pumps, each is running at a rate of 375 l per minute, is used to pump the pool. How
long will it take to fill the pool completely?
Ans: _________________mins
30. A movie ticket for an adult is $8.50 and that for a child is $5. During a certain
period, 126 more adults than children visited the cinema. The cinema collected
$2907. How many adults visited the cinema in that period?
Ans: _____________________

1. Two boys and eight girls have saved an average of $604. The two boys have saved
an average of $592. What is the average of the savings of the girls?
1 of the balloons. The number of balloons he sold on the second day is
94
Ans: _____________________
2. There are 1200 pupils in a school. 20% of them are Indian. 65% of the remaining
pupils are Chinese and the rest are Malay.
a) How many Chinese pupils are there?
b) What percentage of pupils is Malay?
Ans: _____________________
3. Mr. Chan sold a number of balloons in a 3-day carnival. On the first day he sold
5
2 of what he
3
sold on the last day. 92 more balloons were sold on the last day than on the second
day. Balloons are sold at $1.20 each. How much did Mr. Chan earn?
Ans: _____________________

4. Mr. Feng had 225 more tulips than roses in his garden to sell. After selling
1 of the roses, he had 858 flowers remaining. How many flowers did he
F E
95
3 of the
5
tulips and
3
have at first?
Ans: _____________________
5. The following figure is not drawn to scale. ABCD is a square. AEDF is a rhombus.
Triangle DFG is isosceles. C, G, D are on the same line. F is the midpoint of AG.
Find
a) ∠ AFD
b) ∠ EDC
c) ∠ DAE
A B
D C
Ans: _____________________
G
40o

6. What is the total mass of a bag that weighs
4 of the previous height for every bounce. Find the total
96
3 of 4500g and a box that weighs 48%
8
of 18 kg? Express your answer in kg correct to 2 decimal places.
Ans: ___________________kg[3]
7. There are 15 trees planted in a line. The distance between any two adjacent trees is
the same. The seventh tree is 7920 cm away from the third tree. How far from the
first tree is the last tree? Express your answer in meters.
Ans: _____________________[4]
8. When dropping a tennis ball from a height of 15m to the ground, Johannes realized
that the ball went up to
5
distance that the ball had travelled when it hit the ground the second time.
Ans: _____________________[4]

9. Mr. Lee has 4 children. His age is 3 times that of his youngest child. Each child was
born 3 years before the next one. The total age of the 4 children and the father is 193
years. Find the age of Mr. Lee’s first child.
97
Ans: _____________________[4]
10. Each small truck has 10 wheels. Each large truck has 14 wheels. A truck
manufacturer ordered 408 wheels for their 32 trucks. How many large trucks are
there?
Ans: _____________________[4]
11. Francis gave half of his salary plus $100 to his mother. He spent 25% of the
remaining plus $49 on furniture. He bought some books for $61. He gave
3 of his
5
remaining sum plus $53 to his sister. He saved the final $443. How much is Francis’s
salary?
Ans: _____________________[4]

12. An elephant is 5.5 times as heavy as a zebra. The total mass of 2 elephants and 3
zebras is 1260 kg. What is the mass of 1 elephant and 4 zebras?
98
Ans: _____________________[4]
13. From January to August, Phoebe earned an average of $2340 per month. From
September to December, she earned some more money and the average earning over
the entire year is $3290. What was the average amount of money that Phoebe earned
a month in the period from September to December?
Ans: _____________________[4]
14. In a charity event, 3 scouts Benny, Ray and Kathy raised $1459 altogether. Ray
raised $296 less than Benny while Katy raised an amount
1 as much as Benny. How
4
much money did Kathy raise?
Ans: _____________________[4]

15. The ratio of the number of roses to the number of lilies to the number of tulips is
3:5:9. If there are 954 more tulips than roses, how many more lilies than roses are
there?
99
Ans: _____________________[3]
16. There are 20 more pages in a mathematics book than in a physics book. There are 70
more pages in a chemistry book than in a mathematics book. The total number of
pages in 20 books of each type is 10 000. How many pages are there in a physics
book?
Ans: _____________________[4]

17. In the figure below, the rectangle on the left is made by bending a wire. Another wire
with the same length is bent to make the two identical isosceles triangles on the right.
What is the area of one isosceles triangle?
1 on stationeries. He also bought two pairs of shoes
10 0
Ans: _____________________[4]
18. The ratio of the amount of money Josh had to that Derek had was 3: 5. Derek spent
25% of his money on toys and
5
for $150. He saved the remaining $246. How much money did Josh have?
Ans: _____________________[4]
33 cm
75 cm
36 cm

1 hours to 56 minutes?
10 1
1. What is the ratio of
3
(1) 5 : 14 (2) 14 : 5
(3) 3 : 5 (4) 5 : 3
( )
2. What percentage of 4 m is 25 cm?
(1) 6.25% (2) 62.5%
(3) 0.16% (4) 16%
( )
3.
In a factory, soya drink is poured from a 5.2l tank to fill some identical cans, each of
which has a capacity of 330ml. What is the maximum number of cans that can be
filled using one tank?
(1) 14 (2) 15
(3) 16 (4) 17
( )
4. Jane spent an average amount of $127 a month over 5 months. Find the total amount
that Jane spent over 5 months.
(1) $600 (2) $635
(3) $660 (4) $700
( )
5. John had some money. He used 25% of his money to buy furniture and used of the
remainder to buy clothes. If the spent $300 on clothes, how much did he spend on
furniture?
(1) $240 (2) $500
(3) $1200 (4) $1500
( )
6. Jane bought some pieces of clothes for an average cost of $24. After that, she bought
another piece that costs $96 and the average cost became $36. How many pieces of
clothes did Jane buy altogether?
(1) 5 (2) 6
(3) 8 (4) 4
( )

7. In the figure below, 1, 2, 3 and 4 together make a square. 2 and 3 are also squares
and they contribute 50% of the area of the figure. Which of the following pair will
form
8 (2)
23 (4)
7 (2)
7 (4)
10 2
5 of the figure?
8
1
2
3
(1) 1 and 2 (2) 3 and 4
(3) 1 and 4 (4) 2 and 3
( )
8. Harry and Jack each had some Pokémon cards.
2 of what Harry had is equal to
5
3
4
of what Jack had. What fraction of the total number of cards are Jack’s cards?
(1)
23
15
23
(3)
8
23
15
( )
9. Find the value of 7 x (2 + 16 ÷ 2) – 1
(1) 14 (2) 21
(3) 62 (4) 69
( )
10. Find the largest fraction of the following
(1)
9
7
10
(3)
11
7
12
( )
11. The distance from A to B is eight times the distance from B to C. What is the ratio of
the distance from A to B to the total distance?
(1) 1 : 8 (2) 1 : 9
(3) 8 : 9 (4) 9 : 8
( )
4

12. The volume of a tank is 56l when rounded off to the nearest litre. Which of the
following is likely to be the actual volume of the tank in liter?
(1) 55.05 (2) 55.49
(3) 56.45 (4) 56.51
10 3
( )
13. David had $32 left after spending $48. What percentage of his money did he spend?
(1) 40% (2) 60%
(3) 67% (4) 80%
( )
14. What is the ratio of the shaded part to the whole figure below?
(1) 1 : 4 (2) 4 : 5
(3) 4 : 9 (4) 5 : 9
( )
15. What is ∠ h in the figure below? FG is a straight line. The figure is not to scale.
(1) 35o (2) 45o
(3) 55o (4) 65o
( )
F h 35o G

16. Write
10 4
12 in percentage form.
25
Ans: _____________________
17. A card board is 30 cm in length and 16 cm in breadth. What is the area of the card
board?
Ans: _____________________
18. Four cans of iced tea costs $6. How much is two dozen cans?
Ans: _____________________
19. Find ∠x given that ∠x = ∠y
x
y
Ans: _____________________
162o

20. In the figure below, ABCD is a rectangle, AI = ID, BJ = JC.
What percentage of the whole area is the shaded area?
A B
I J
D C
10 5
Ans: _____________________
21. A pencil case can contain 12 pencils. If there are 390 pencils, how many pencil cases
are needed?
Ans: _____________________
22. Angela has some short sleeved and long sleeved shirts.
7 of the shirts are long
15
sleeved. What is the ratio of the short sleeved shirts to the long sleeved shirts?
Ans: _____________________
23. Brian has 50% more $2 notes than $5 notes. He has 45 notes in total. How much
money does he have?
Ans: _____________________

24. What are the common factors of 18 and 45?
10 6
Ans: _____________________
25. Kiara walked 55m in every minute. It took her 18 minutes to walk from home to
school. How far is her school from her home?
Ans: _____________________
26.
In 2009, Raphael is 9 years old. His father is 38 years older than he is. In how many
years will his father’s age become three times his age?
Ans: _____________________
27. Find the volume of a bottle if 36% of it can fill a 72ml cup completely.
Ans: _____________________

28. Find the maximum number of 40 cm cubic boxes that can be stored in a storeroom
that is 5m wide, 6m long and 3m high.
2 km. He had walked some distance and still had to walk
3 km. How far had he walked? Give your answer in meters.
10 7
Ans: _____________________
29. Yvonne weighs 42.5 kg. Her bag weighs 4750g. If Yvonne wears her bag and stands
on an electronic scale, what value will the scale indicate? The scale expresses mass
in kg.
Ans: _____________________
30. Antoine needed to walk 1
5
for another
4
Ans: _____________________

1. A water tank has dimensions 60 cm x 25 cm x 30 cm. Uncle Tiong is using a 3l pail
to fill the tank. How many times does he use the pail?
10 8
Ans: _____________________
2. Study the figure below carefully.
ABCD is a square piece of paper. If I fold the piece along the line IK and then cut
away along the lines IJ and JK, what is the area of the remaining piece?
Ans: _____________________
18 cm
A B
I
K
J
D C
A I
J
K
D C
25 cm
2 cm

3. Mrs. Ong bought 2 kg of grapes at a price of $3.20 per 100g.
Mrs. Choo bought the same kind of grapes with a discount of $0.70 per 100g. She
paid the same amount of money as Mrs. Ong did. How many more kilograms of
grapes did Mrs. Choo buy compared to Mrs. Ong?
10 9
Ans: _____________________
4. Fill in the blank with an appropriate number to complete the pattern.
1 , 4 , 9 , ________ , 25
Ans: _____________________
5. The average distance that Mei Mei jumped over 5 attempts is 145 cm. The average
distance of the first 3 attempts is 155 cm. What is the average distance of the last 2
attempts?
Ans: _____________________

6. The figure below is not drawn to scale. ∠MNQ is 29o. MNPQ is a rhombus.
Q O
1 of the carton of milk on the first day. Over the next two days he
11 0
a) Find ∠ NMQ.
b) If MN = NO, find ∠ NOP.
Ans: _____________________[4]
7. Guo Qi drank
5
drank 75% of the remaining milk. There was still 750ml of milk left.
What is the volume of the carton of milk? Express your answer in liters.
Ans: _____________________[4]
M
N
P

8. An apple drink is made by mixing apple syrup and plain water in the ratio 2: 5. How
many milliliters of apple syrup is needed to make 1.4 l of apple drink?
11 1
Ans: _____________________[3]
9. Study the pattern below. The shapes are made by using toothpicks.
a) How many toothpicks are needed to make 5 shapes?
b) How many shapes can be made using 258 toothpicks?
Ans: _____________________[4]
10. The number of stickers that Pamela had is 40% of the number of stickers that Zoe
had. If the two children had 952 stickers altogether, how many stickers did Zoe
have?
Ans: _____________________[3]
1 shape 2 shapes 3 shapes

5 that of Chek Khoon and Chek Khoon is 4kg more than Darren. If
11 2
11. Bala’s weight is
6
the average mass of the three boys is 44 kg, what is the mass of Chek Khoon?
Ans: _____________________[4]
12. A restaurant had sold 3 times more honey roasted chicken than black pepper chicken.
If 90 less honey roasted chicken had been sold, the number of black pepper chicken
would have been twice the number of honey roasted chicken.
a) How many honey roasted chickens were sold?
b) How many black pepper chickens were sold?
Ans: _____________________[4]
13. If Andy buys 3 story books and 5 comic books, he will have $24 left. If he buys 5
story books and 3 comic books, he will need $16 more. Given that a comic book is
sold at $18, how much does Andy have?
Ans: _____________________[4]

14. In the figure below, 1, 2, 3, 4 and 5 are all squares. What is the ratio of the total area
of 1 and 2 to the total area of all the squares?
2 3 4 5
1 of the pupils like basketball,
11 3
Ans: _____________________[4]
15. Plastic tables were sold at $75 each and wooden tables were sold at $80 each. There
were 150 plastic tables in a shop at first. After selling all the tables, the shop received
$12850. How many wooden tables were sold?
Ans: _____________________[4]
16. In a class,
3
1 of the remainder like chess, the rest like
4
swimming. There are 10 pupils who like chess. Each pupil only likes one sport. What
is the number of pupils who like either chess or basketball?
Ans: _____________________[4]
1

17. Mr. Wong hired a transport company to deliver some glass products for him. For
every safely transported product, the company charges $16.5. For every product that
was broken on the way, the company compensates $66. Mr. Wong was charged
$15,015 for the delivery. 90% of the products were delivered safely. How many
products were broken on the way?
11 4
Ans: _____________________[4]
18. Mindy and Ryan had an equal amount of cookies. Each day, Mindy ate 23 cookies
and Ryan ate 8 more cookies than Mindy.
a) How many days had passed when Mindy had 149 cookies left and Ryan had 53
cookies left?
b) How many cookies did each of them have at first?
Ans: _____________________[4]

1. An equilateral triangle and a right-angled triangle are placed next to each other as in
the figure below (not to scale). HAE is a straight line. Find ∠ EHB
(1) 30o (2) 60o
(3) 120o (4) 150o ( )
2. Which of the following has the largest value?
(1) 25% (2)
1 (2)
4 (4)
11 5
1
5
(3) 0.26 (4)
24 ( )
1000
3. The average mass of a bag of rice and 3 bags of flour is 14 kg. If the bag of rice
weighs 17 kg, what is the average mass of the three bags of flour?
(1) 6 kg (2) 8 kg
(3) 10 kg (4) 13 kg
( )
4. Amanda had 6 m of ribbon. She used 60% of the ribbon on the first day and of the
remainder on the second day. How many centimeters of ribbon did she have left?
(1) 60 cm (2) 90 cm
(3) 180 cm (4) 240 cm ( )
5. Sarimah bought two similar pizzas. She saved
2 of a pizza for her mother and
3
shared the rest among herself and 5 friends. What fraction of a pizza did each child
get?
(1)
3
2
9
(3)
15
2 ( )
15
A
B
C
H E

6. The table below shows the number of maximum marked papers scored by pupils in a
11 6
class from August to November
Month Number of maximum marked papers
August 33
September 49
October ?
November 52
The class scored an average of 46 maximum marked papers a month. How many
maximum marked papers were there in October?
(1) 48 (2) 50
(3) 134 (4) 184
( )
7. Knowing that 483 x 7 = 3381, find the value of 483 x 0.07
(1) 3381 (2) 338.1
(3) 33.81 (4) 3.381
( )
8. Sally bought an LCD with a 30% discount and 7% GST for $749. What is the
original price of the LCD?
(1) $700 (2) $1000
(3) $1042 (4) $1200
( )
9. Below is the parking charges at the car park of a shopping centre
First 2 hours $2.50
Subsequent 30 minutes or part thereof $1.50
Kelvin entered the car park at 3.45 pm. He paid $9.50 for parking charges when
leaving the car park. What is the latest time possible that he left the car park?
(1) 7.15 pm (2) 7.45 pm
(3) 6.15 pm (4) 6.45 pm
( )
10. Josh wrote down two numbers on a piece of paper. 40% of the larger number is 84.
The difference between the two numbers is 78. What is the smaller number?
(1) 288 (2) 34
(3) 132 (4) 210 ( )
11. How many eighths are there in ?
(1) 13 (2) 16
(3) 24 (4) 26 ( )

12. ABCD is a parallelogram. ∠ABD = 47o. ∠ BCD = 105o. What is ∠ BDA?
A B
(1) 28o (2) 38 o
(3) 152 o (4) 208 o
5 (2)
5 (4)
11 7
( )
13. 3 sticks have a total length of 192 cm. What is the average length?
(1) 32 cm (2) 64 cm
(3) 96 cm (4) 576 cm
( )
14. There are 184 red, white and green marbles altogether. The number of green and
white marbles is 54. There are 150 red and white marbles altogether. What fraction
of the total number of marbles is the number of white marbles?
(1)
36
5
46
(3)
51
5
97
( )
15. Mrs. Liu made 4.82 l of lemon tea in a container. She poured them into 8 cups, each
of which had a capacity of 352 ml. What was the volume of lemon tea remaining in
the container?
(1) 2.004l (2) 2.04l
(3) 2.24l (4) 2.4l
( )
16. In an aquarium, the ratio of the number of goldfish to that of clownfish is 2: 7. The
ratio of the number of clownfish to that of angelfish is 5: 2. What is the ratio of the
number of goldfish to that of angelfish?
Ans: _____________________
D C

17 × . Remember to simplify your answer.
5 l left. How much milk was there in the fridge at first?
11 8
17. Calculate
3
34
9
Ans: _____________________
18. Uncle Tan kept some milk in the fridge. After his children drank 1
1 l of milk, there
2
was 1
6
Ans: _____________________
19. If a pen costs $1.20 and I have $11, how many pens can I buy at most?
Ans: _____________________
20. The following diagram is not drawn to scale. Find ∠ i, given that WSX and YSZ are
straight lines.
Ans: _____________________
W Z
154o
i 87o
X
Y
S

21. The average of the two numbers A and B is 80. The average of those two numbers
and a third number C is 85. What is the value of C?
11 9
Ans: _____________________
22. 9 x 5.6 = 5.6 + 5.6 + 5.6 + 5.6 x A
Find the value of A.
Ans: _____________________
23. Benjamin received 72 marks for Mathematics, 83 marks for Physics and 67 marks
for Chemistry. What is his average score for the three subjects?
Ans: _____________________
24. What are the common factors of 24 and 36?
Ans: _____________________

25. A convenience store collects an average of $5839 a day. How much does the store
12 0
collect in a week?
Ans: _____________________
26.
The sum of the area of all the faces of a solid cube is 54 cm2. What is the volume of
the cube?
Ans: _____________________
27. A journey 12.8 km long was divided into 9 parts. Of these 9 parts, there were 5 parts
that were 0.91 km long each and 3 parts that were 1.32 km each in length. What was
the length of the remaining part?
Ans: _____________________

28. There are 10 200 people in a village. 30% of the villagers are children and the rest
are adults. 40% of the adults are working outside the village. How many adults are
working outside the village?
93o D
37o 43o
12 1
Ans: _____________________
29. Calculate ∠ ABD in the figure below. Note that it was not drawn to scale.
Ans: _____________________
30. Lucy bought 6 similar skirts and 4 similar shirts for $162. The price of 2 shirts is
equal to the price of 3 skirts. How much is a shirt?
Ans: _____________________
A
B C

1. Stanley withdrew some money from the bank to purchase some goods. He spent
1 of the remainder on a game console. He still had
12 2
$1144 to buy a new laptop and
4
half of what he withdrew from the bank. How much did Stanley withdraw from the
bank?
Ans: _____________________
2. 5 similar bags of potatoes have a total mass of 86.25 kg. A porter can carry a
maximum of 60 kg. How many porters are needed to carry 20 of such bags?
Ans: _____________________
3. The distance from Mary’s house to her grandmother’s house is 14 km. Mary had
cycled 3.115 km from her home to her grandmother’s. What percentage of the
journey had she covered?
Ans: _____________________

4. In the figure below, there are two adjacent squares and the shaded shape overlaps
both. The larger square has a side of 36 cm and the smaller square has a side of 20
cm. What is the area of the shaded shape?
12 3
Ans: _____________________
5. The ratio of Charles’ stamps to Mark’s stamps to Shawn’s stamps is 3: 7: 9. Mark
has 168 stamps.
a) How many stamps do the boys have altogether?
b) After Mark gives some stamps to Charles, the two boys have the same
number of stamps. How many stamps did Mark give Charles?
Ans: _____________________

6. There are some flowers in a garden. 0.2 of the flowers are daisies and the remaining
5 of the roses are red and the rest are white. There are 24 more red
12 4
flowers are roses.
7
roses than white roses.
a) How many white roses are there?
b) How many daisies are there?
Ans: _____________________[4]
7. In the figure below, AB = BC = CA. FCD, BCE and ACG are straight lines. The
figure is not to scale. Find
a) ∠ CED
b) ∠ ACF
Ans: _____________________[4]
A
F
C
E
G
B
D
42o
31o

8. Mrs. Foo bought 3.3 kg of fish at $1.59 per 100g, 2.8 kg of beef at $4.89 per 500 g,
and 7 packages of vegetable at $0.86 per package. How much did she pay for all the
goods?
12 5
Ans: _____________________[4]
9. The ratio of the number of curry puffs to the number of cakes in a shop is 1: 4. A
curry puff costs $2. Each cake is sold at $5. The total amount that the shop will
receive from selling all the cakes and curry puffs is $1892. How many cakes are
there?
Ans: _____________________[4]
10. A shop had 280 pens. 70% of the pens were blue. A week later, a number of blue
pens were sold and 60% of the remaining pens were blue. How many pens altogether
were there in the shop a week later?
Ans: _____________________[4]

11. A textbook and a bag cost $30. A textbook and a comic book cost $22.5. David
bought 4 textbooks, 2 bags and 1 comic book for $100. What is the cost of a comic
book?
12 6
Ans: _____________________[3]
12. Marion and Nina had some beads in the ratio 5: 7. If Marion gave Nina 24 beads,
Nina would have three times as many beads as Marion had. How many beads did
Marion have at first?
Ans: _____________________[4]
13. What fraction of 4l is 350ml? Express your answer in the simplest form.
Ans: _____________________[3]

14. 40% of the fruits in an orchard are apples, 80% of the remainder is oranges and the
rest are mangoes. There are 648 more oranges than apples. After some apples have
been sold, 10% of the remaining fruits in the basket are apples. How many apples
have been sold?
12 7
Ans: _____________________[4]
15. A salesman’s salary is $1575 a month. Apart from the salary, he earns a commission
of $1.20 for every $5 of sales he makes. In 8 months, the total sales he makes is
$72000. What is his average earning a month over these 8 months?
Ans: _____________________[4]
16. A rectangular tank measures 60 cm by 43 cm by 24 cm is filled with water up to
1
3
its height. At 1.p.m, water from a tap started to flow into the tank at a rate of 1.8 l per
minute. How much water is in the tank at 1.20 pm?
Ans: _____________________[4]

17. Three identical squares, each is made up of 9 identical squares, are overlapped as in
the figure below. Find the ratio of the shaded portion to the total area of the figure.
12 8
Ans: _____________________[4]
18. Joanne thinks of a number. The difference between thrice that number and of that
same number is 36 more than that number. What is the number that Joanne thinks of?
Ans: _____________________[4]

1. The figure below is made up of 2-cm cubes. How many more cubes are needed to
make it into a larger cube with sides 6 cm?
(1) 10 (2) 12
(3) 17 (4) 20
12 9
( )
2. Johan has some coins. 12.5% of them are 20 cent coins.
3 of them are 10 cent coins.
8
The remainders are 50 cent coins. All the 10 cent coins together are worth $2 more
than all the 20 cent coins together.
How many 50 cent coins does Johan have?
(1) 40 (2) 80
(3) 120 (4) 160
( )
3. The ratio of the number of orangees to the number of mangoes in a basket is 4: 5. If
there are 5 more mangoes than oranges, how many oranges are there in the basket?
(1) 20 (2) 25
(3) 45 (4) 5
( )
4. Which of the following statements is true?
(1)
If one of the angles in an
isosceles triangle is 60o, the
triangle is equilateral.
(2) A rhombus has all the properties of
a square.
(3) No angle can be 60o in a right-angled
triangle. (4) The sum of all the angles in a four-sided
figure is always different.
( )

5. Three pupils shared a number of books. Katrina contributed 0.5 of the number of
3 and Patrick contributed the rest. What percentage of
14 (2)
29 (4)
13 0
books, Melisa contributed
10
the number of books is Patrick’s contribution?
(1) 20% (2) 35%
(3) 53% (4) 80% ( )
6. Sally read 40% of her book and had 120 pages left. How many pages were there in
the book?
(1) 200 (2) 280
(3) 300 (4) 520 ( )
The following graph shows the number of students in different grades in a secondary
school. Study the graph carefully and answer the questions below.
7. What is the difference between the number of Sec 3 and the number of Sec 1
students?
(1) 30 (2) 40
(3) 70 (4) 80
( )
8. What fraction of the total number of students is the number of Sec 1 students?
(1)
57
16
57
(3)
114
25
114
( )

9. Sabrina planned to complete her drawing in
1 h (2)
11 h (4)
1 of a pizza equally. What fraction of a whole pizza did each boy
5 (2)
1 (4)
5 ?
15 (2)
25 (4)
13 1
4 hours. However, she only used
5
3 of
4
the time intended. How much time did she save?
(1)
20
1 h
5
(3)
20
3 h
5
( )
10. 3 boys shared 1
4
get?
(1)
12
12
5
(3)
12
15
4
( )
11. Find the missing value
8.507 = ________ x 1000 ÷ 100
(1) 0.8507 (2) 8.507
(3) 85.07 (4) 850.7
( )
12. Which of the following is not equal to
9
(1)
27
45
81
(3)
36
35
63
( )
13. The average of 3 numbers is 27. Two of the numbers are 19 and 25. What is the third
number?
(1) 17 (2) 37
(3) 59 (4) 81
( )
14. Find a number between 40 and 50 that has a remainder of 2 when divided by either 4
or 5.
(1) 42 (2) 46
(3) 47 (4) 49
( )

15. Study the figure below. ABC is an isosceles triangle at A, CDE is an isosceles
triangle at D. Find the value of ∠x. The figure is not to scale.
(1) 25o (2) 36o
(3) 55 o (4) 70 o
13 2
( )
16. Alice bought some chocolates. She saved
1 of the chocolates for her brother. She
3
divided the rest of the chocolates equally among herself and her 5 friends. What
fraction of the total number of chocolates did each of Alice’s friends get?
Ans: _____________________
17. Mr. Smith had dinner at a restaurant. The cost of the food was $150. If he had to pay
7% GST and 10% service charge on the cost of the food, how much more did he
have to pay?
Ans: _____________________
A
B C
D
E
144o x

18. Calculate the sum of the first 7 multiples of 9 that are larger than 90.
13 3
Ans: _____________________
19. Express 20.08l in litres and millilitres.
Ans: ________l________ml
20. A container measures 20 cm by 15 cm by 10 cm. Another container measures 15 cm
by 7 cm by 5 cm. What is the total volume of the two containers?
Ans: _____________________
21. Draw the corresponding height to base BC for the triangle ABC below.
22. Calculate 199 – 53 x 2 + 14 ÷ 7
Ans: _____________________
A
C
B

23. What is the smallest positive common multiple of 36 and 48?
1 hours?
13 4
Ans: _____________________
24. Calculate 2215 ÷ 9, corrected up to 2 decimal places.
Ans: _____________________
25. How many seconds are there in 1
3
Ans: _____________________
26.
Find the missing numbers.
_____ : 18 : 22 = 28 : ______ : 77
Ans: _____________________

27. The table below shows the prices of air ticket to country X
AIR TICKET TO COUNTRY X
2 of that number by 33. What is the number?
13 5
Ticket class
Adult
(price per person)
Child (below 12 years old)
(price per person)
Economy $900 $450
Business $1200 $600
First class $1600 $800
Mr. Mohammed, his wife, 9-year-old daughter and 15-year-old son travelled to
country X. How much did they pay altogether if they chose Business class?
Ans: _____________________
28. 10% of a number is less than
5
Ans: _____________________

29. Refer to the figure below. Three identical squares are arranged in a row. If the area of
each square is 144 cm2, what is the perimeter of the rectangle that is made by the
three squares?
13 6
Ans: _____________________
30. The time on the clock is exactly 9 a.m. When the minute hand turns 450o clockwise,
what time will it be?
Ans: _____________________

1. Swee Swee had a saving account of $30 000 in a bank. The interest rate is 3.75% per
year. How much interest will Swee Swee receive after a year?
13 7
Ans: _____________________
2. Construct a line that goes through M and is perpendicular to AB.
3. Below is the menu at a restaurant:
Appetizer Main course Dessert
Tom Yam soup Grilled fish Banana split
Spring roll Beef stew Ice cream
Mango salad Roasted chicken Cheese cake
How many different combinations could a person choose if he wanted to have an
appetizer, a main course and a dessert?
Ans: _____________________
M .
A
B

4. What is the average of the first 8 multiples of 9?
4 kg of meat and cooked
13 8
Ans: _____________________
5. Nicolas bought
5
7 kg for dinner. What is the quantity of
10
meat that has not been cooked? Give your answer in decimals.
Ans: _____________________
6. Mrs. Khoo mixed 6l grape syrup with 9l of water. After that, she used some
rectangular containers to store the drink. Each container measures 12 cm by 7 cm by
5 cm. Each container is filled completely.
a) How many containers could be filled?
b) What is the volume of the drink that was left over?
Ans: _____________________[4]

7. Find ∠ x in the figure below. AOB, COD, EOF are straight lines.
78o 33o
A B
13 9
Ans: _____________________[4]
8. In the figure below, the breadth of the rectangle is
3 its length. What is the area of
4
the shaded portion? The figure is not drawn to scale.
Ans: _____________________[4]
6.5 cm
17.5 cm
O
C
D
E
F
x

9. Michael participated in a swimming competition. On average, he completed a lap in
3.2 minutes. He needed to swim 8 laps to complete the race. What was the total time
he took to complete the race? Give your answer in minutes and seconds.
14 0
Ans: _____________________[3]
10. A farmer planted 400 flowers in his garden.
5 of them were roses. The farmer then
8
sold some roses. The remaining number of roses was then
3 of the total number of
8
flowers remained in the garden. How many roses were sold?
Ans: _____________________[3]
11. The figure below is made up of two adjacent squares and a shaded triangle. The
smaller square has an area of 16 cm2. The larger square has an area of 49 cm2. What
is the area of the shaded triangle?
Ans: _____________________[4]

12. Find ∠z in the following figure. AOB and COD are straight lines. ∠y = ∠z. ∠x =
D
y z
1 hours on Monday. On Tuesday he spent some time to
14 1
12o. The figure is not to scale.
Ans: _____________________[4]
O
142o
x
13. Peter studied Physics for 2
2
continue his Physics study. On Wednesday, he spent twice as many hours as on
Tuesday to finish his Physics lesson. Over those 3 days, Peter spent an average of
138 minutes a day studying Physics. In how many hours did Peter study Physics on
Wednesday?
Ans: _____________________[4]
A
C B

14. Jordan is a basketball player. On the first match of the 2009 league he scored 7 goals.
In every later match he scored 2 more goals than the previous match. He played 7
matches altogether in the league.
a) How many goals did he score in total?
b) What is his average number of goals per match?
15. Nelson’s height is 152 cm. Nelson’s sister is 0.2 m shorter than he is. What fraction
of Nelson’s height is his sister’s height? Express your answer in the simplest form.
14 2
Ans: _____________________[4]
16. In a volleyball tournament, there are 10 school teams. Each team has to play one
match against each of the other teams. How many matches will be played between
the teams?
Ans: _____________________[4]

17. Mr. Teo bought a table and two chairs for $300. The two chairs were sold at the
same price. The table’s price is twice as much as a chair’s. What is the price of the
table?
14 3
Ans: _____________________[4]
18. Peter wrote all the number from 1 to 100 continuously
1234567891011121314……979899100
How many digits did he write?
Ans: _____________________[4]

Answers to Semestral Assessment 1: Mock Paper 1
Paper 1
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15
3 4 4 3 2 3 3 1 2 2 2 3 1 4 2
16 Nine million eighty thousand and eleven 17 8 883 008, 8 880 003, 880 300, 88 380
18 3 906 = 3 000 + 900 + 6
5 4 21 60
14 4
7 503 906 = 7 000 000 + 500 000 + 3 906
The value of A is 500 000
19 The first 6 multiples of 7 are 0, 7, 14, 21, 28 and 35.
0 + 7 + 14 + 21 + 28 + 35 = 105
The sum of the first 6 multiples of 7 is 105
20
9
22
5 9
10
24 5 976 201
25 3 147 682
26 If 90 pieces were in $100 notes, the money would be
90 x 100 = 9000
The number of $50 notes
(9000 – 5250) ÷ 50 = 75
The cashier received 75 notes of $50 from Mr. Ben.
27 10 tables and 20 chairs cost $650
Thus 20 tables and 40 chairs cost $1300
20 tables and 10 chairs cost $850
Therefore 30 chairs cost $450
The cost of a chair is 450 ÷ 30 = 15
The cost of 1 table is (650 – 20 x 15) ÷ 10= 35
The cost of 1 table and 1 chair is 35 + 15 = 50
The cost of one table and one chair is $50
23
Equal
areas
Equal
areas
The two shaded triangles at the bottom are equal to
the two unshaded triangle at the top. So they and the
shaded trapezium add up to a rectangle that is
1
1
of the big square. The shaded area is
of the
3
3
total area.
28 850 + 620 + 930 = 2400
2400x
1 =600, 2400 x
4
1 =200
12
2400 – 600 – 200 = 1600
He had 1600 nails left.
29 90 x 1 ÷ (105 – 90) = 6
It takes 6 minutes.
30
One equal part is (2892 – 1572) ÷ 6 = 3112
Each of them had $3112 at first
Paper 2
1
Value of 1 equal crossed part
(17245 – 12 795) ÷ 5 = 890
Team B collected $890
890 x 6 = 5340
Team D collected $5340
3
The total price of 1 kg of each type
99.60 ÷ 6 = 16.60
The price of 1 kg of chicken
(16.60 – 5 – 2) ÷ 3 = 3.20
The price of 1 kg of beef
3.20 + 5 = 8.20
(3.20 + 8.20) x 6 = 68.40
She spent $68.40 on the beef and the chicken.
2
1− 3 − 1
= 3
,
8
4
8
114 ÷ 3 =
304 8
The shop has 304 pairs of gloves in total.
4 One cheese cake: 6.90 ÷ 3 = 2.30
One curry puff: 5.20 ÷ 4 = 1.30
25 ÷ 2.30 = 10.87 => 10 cheese cakes
25 ÷ 1.30 = 19.23 => 19 curry puffs
19 – 10 = 9
(a) Timmy could buy 9 more curry puffs than cheese
cakes.
(b) number of cheese cakes and curry puffs altogether
is =129.6 /(2.3+1.3) x 2 = 72

5 197g > 30g => $1.00 for the first 30g, left 197g – 30g
= 167g.
167g > 50g => $1.70 for the next 50g, left 167g – 50g
= 117g.
117 ÷ 25 = 4.68 => pay for 5 steps of 25g.
$0.35 x 5 = $1.75
$1.00 + $1.70 + $1.75 = $4.45
Peter has to pay $4.45
7 Total of Peter’s and Jordan’s stickers: 924 x 2 = 1848
14 5
Peter’s stickers: (1848 + 232) ÷ 2 = 1040
Jordan’s stickers: 1040 – 232 = 808
Albert’s stickers: 172 + 1040 = 1212
808 =
Jordan’s stickers are 3 2
3 2
1212
of Albert’s.
6
8 Three years later:
Dan’s age: 34 ÷ (3 – 1) = 17
Dan’s father’s age: 17 x 3 = 51
Now:
Dan’s father’s age: 51 – 3 = 48
Dan’s father is 48 years old now.
9 From 1 to 9: 9 x 1 = 9
From 10 to 99: 90 x 2 = 180
From 100 to 150: 51 x 3 = 153
9 + 180 + 153 = 342
342 steel digits are necessary.
10
5 cm
5 cm
8 cm
B
13 cm
36 cm
9 cm
7 cm
4 cm
A
A = 36 – 13 – 8 – 5 = 10 cm
B = 7 + 9 – 4 – 5 = 7 cm
7 + 10 + 9 + 5 + 5 + 8 + 7 + 13 + 4 + 36 = 104 cm
The perimeter is 104 cm
14
11 10 x 7 = 70 m2
70 x 15 = $1050
12 The difference in the number of bags
60 – 25 = 35 bags
The mass of one bag
(6790 – 4655) ÷ 35 = 61 g
The mass of the box is
6790 – 60 x 61 = 3130g = 3.13 kg
The box weights 3.13 kg.
13 $1 215 x 116 = $140 940
The agency received $140 940
15
If Alex had 224 more stamps, there would be five
equal parts.
Value of one equal part
(2151 + 224) ÷ 5 = 475
Carl had 475 stamps.
16 The figure has 5 lines of symmetry
17 Tank’s volume: 90 x 40 x 15 = 54000 cm3 = 54l
× 1 = l
12 1 18 2
54 – 18 = 36l
Rate of tap B 12 4l 3
× 1 = in a minutes
Total rate 12 + 4 = 16l in a minute
Time taken: 36 ÷16 = 2.25 minutes = 2 minutes 15
seconds.
18 4 trees in the corners. Along the length: 49 ÷ 7 – 1 = 6 trees. Along the breadth: 35 ÷ 7 – 1 = 4 trees.
Total: 6 x 2 + 4 x 2 + 4 = 24 trees. There were 24 trees in total

Paper 1
3 1 3 2 1 2 2 4 4 2 3 2 2 3 1
17
14 6
Cost of a child ticket
49 ÷ (2 + 5) x 2 = 14
A child ticket costs $14
18 $179 501
19 965312
20
7
10
1 − 3
(1− 1
) =
4
5
4
He spent 10
7 of his money
16
21 Number of children: 144 ÷ 3 = 48
Total: 48 x 5 = 240
There were 240 people in the audience
22
12 x 9 ÷ 2 = 54 cm2
The area is 54 cm2
24 0.14 + 0.8 + 5 + 0.032 = 5.972
23
7 ÷ 3 =
7
9
27
Each child got 27
7 of the cake
25 1: 2 3 = 1: 13
=
5 :13 5
5
27 The first team will play 3 matches with the 3
remaining teams.
The second team already played 1 match with the first
team, so it will play only 2 matches with 2 remaining
teams.
Similarly, the third team will play 1 match with the
last team.
The last team already played 3 matches with the 3
teams.
3 + 2 + 1 = 6, There are 6 matches in total.
26
28
3 5 12
hours = 3 hours 25 minutes
7:45 + 3:25 = 11:10
Selina finished the task at 11:10 PM
30 x = 180o – 90o – 58o = 32o
y = 180o – 33o – 80o = 67o
y –　 x = 67o – 32o = 35o , The difference is 35o
M
29 5:25 – 3:40 = 1:45
Vanessa parked her car for 1 hour 45 minutes. So she
will pay $2.50 for the first hour and $1.90 for the
second hour.
$2.50 + $1.90 = $4.40
Vanessa paid $4.40
Paper 2
1 Total audience: 180 ÷ 1 =
4500 25
People came by train:
4500 × (1 − 1 − 1
) =
3195 25
4
There were 3195 people who came by train
2 108 ÷ 9 = 12
(12 + 9) x 2 = 42
The perimeter is 42m
126 ÷ 42 = 3
She paid $3 for each meter of the fence.
4 First finish line: 30m, Second line: 60m
Third line: 120m, Fourth line: 240m
Peter ran (30 + 60 + 120 + 240) x 2 = 900 m in total.
3 From Mon to Fri (5 days), Harry travelled on route 1.
Total distance on route 1: 4.3 x 5 = 21.5 km
Length of route 2: 8.2 – 4.3 = 3.9 km.
Total distance travelled on route 2: 3.9 x 2 = 7.8 km
Total distance: 21.5 + 7.8 = 29.3 km
Harry travels 29.3 km to the basketball court in a
week.
6 a) Length: 7 + (7 + 3 + 7) + 7 = 31 cm
b) Breadth: 7 cm
Area: 31 x 7 = 217 cm2
5 a) Least visited month: Sep, 1200 visitors. Most visited month: Dec, 1900 visitors. Fraction 1200 =
12
1900
19
b) Children visitors in July: 1800 1200 3 2
× = . Number of girls: 1200 ÷ 3 = 400
N

14 7
7 Cost of a toy robot is 2 times that of a cake.
5 Cost of 3
18 cakes is 18 ÷ 2 = 9 times that of a toy
robot.
Therefore, with the amount spent, Jeffery could have
bought 21 + 9 = 30 toy robots.
With of his money, he could by 30 toy robots
2 of his money, the number of toy robots he
With 5
could buy is 30 ÷ 5 3
2 = 20
x 5
Jeffery could buy 20 more toy robots with the
remaining money.
8 If each girl had 7 strawberries, there would be 4
strawberries extra.
To give each girl one more strawberry so that each
would have 8 strawberries, the 4 extra strawberries
would be given to 4 girls first. There were 4
strawberries short so there were 4 girls left.
Therefore, there were 8 girls.
Number of strawberries
7 x 8 + 4 = 60
a) There were 60 strawberries
b) There were 8 girls
9 Total number of toy cars that Jason and Malik had
11 = 44
56 x 14
Number of toy cars that Jason had
44 ÷ (7 + 15) x 15 = 30
Number of toy cars that Malik had 44 – 30 = 14
Total number of toy cars 30 + 14 + 56 = 100
a) Jason had 30 toy cars
b) They have 100 toy cars altogether
10 Each notepad is $1.1 more than a pen.
So 7 notepads is $7.7 more than 7 pens
Cost of a pen
(33.3 – 7.7) ÷ (7 + 9) = 1.6
9 x 1.6 = 14.4
Mary paid $14.40 for the pens.
11 1 notebooks = 3 files
10 notebooks = 30 files
Cost of a file 85 ÷ (30 + 4) = 2.5
Cost of a notebook 2.5 x 3 = 7.5
The price of a notebook is $7.50
12 a) Area of the shaded part: 30 x 10 ÷ 2 = 150 cm2
Total area: 30 x (10 + 18) ÷ 2 = 420 cm2
Area of the shaded part:
420 – 150 = 270 cm2
b) 14
10 = 5
+ of the whole figure is shaded.
10 18
13
Value of one equal part (90 + 30) ÷ 3 = 40
Number of apples 40 x 2 + 30 = 110
110 – 90 = 20,
There were 20 more apples than oranges.
14
Body = Head + Tail, 3B = 8 + B + 8 = B + 16
B = 8
Body = 8 x 3 = 24, Tail = 8 + 8 = 16
8 + 16 + 24 = 48m
The whale skeleton is 48m long
16 Total amount of sugar:
500 + 600 + 800 + 900 + 1000 = 3800g
The total mass of sugar in the sold packages must be a
multiple of 3.
Mrs. Liu did not keep packet A since she kept more
than 500.
So she must have kept packet C.
15
At Clementi:
Number of girls
114 ÷ 2 = 57
Number of boys
57 x 3 = 171
Number of children 171 + 57 = 228
Number of adults 228 ÷ 6 x 5 = 190
Number of men 190 ÷ 5 = 38
Number of women 38 x 4 = 152
Total number of passengers 228 + 190 = 418
At Dover:
The number of male passengers. 171 +5 + 38 = 204
a) There were 418 passengers altogether when the
train left Clementi Station
b) There were 204 male passengers when the train left
Dover station.
18
From the diagram
7 = 13u ÷ 2 – 3u, u = 2
Mrs. Goh’s age 7 years ago
2 x 16 = 32, 32 + 7 = 39
Mrs. Goh is 39 years old now.
17 There are 3 ways to arrange the first pupil: Alex, Carol and Dean (Benny does not stand at the first position).
If Alex is at the first position, there are 2ways to arrange the second position (Benny and Carol) since Alex is not
standing next to Dean.
For each of the case, there are 2 ways to arrange the remaining 2 pupils.
If Carol is at the first position, Benny cannot be at the second position since Alex and Dean have to be next to each

other then. Therefore, there are only two ways to arrange the second position (Alex and Dean).
For each of the case, there are only one way to arrange the third and last position, since the third position must be
Benny.
If Dean is at the first position, there are two ways to arrange the second position (Benny or Carol).
For each of the case, there are two ways to arrange the remaining pupils.
The number of possible ways is 1 x 2 x 2 + 1 x 2 x 1 + 1 x 2 x 2 = 10
There are 10 ways to arrange these pupils.
Paper 1
3 4 1 2 3 3 2 3 3 2 1 3 2 3 4
16
14 8
1− 5 = 2
7
7
, 35
1− 2 − =
1 × 2
= 2
5
7
, 2
8
7
35
35
112 490 35
÷ 8 = , 490 × 2 =
28 35
The calculator cost $28
17 Area of one square: 32 ÷ 8 = 4m2
Side of each square is 2m.
Perimeter 32m
18 600 = 2 x 2 x 2 x 3 x 5 x 5
The two page numbers are two continuous factors of
600.
2 x 2 x 2 x 3 = 24, 5 x 5 = 25
The two pages are 24 and 25
19 Total cost 300 – 41 = 259
Cost of 5 boxes of shuttlecocks 259 – 199 = 60
Cost of 1 box, 60 ÷ 5 = 12. Each box is $12.
20 8 + 5 = 13
65 ÷ 13 x 5 = 25
Elizabeth had 25 sweets.
21 X + 1 = Y, Y + Y = 10 + X
X + 1 + X + 1 = 10 + X
X = 8, Y = 9, 89 + 9 = 98
22
Total number of crayons at first (10 – 4) x 5 = 30
They had 30 crayons altogether at first.
23 300 ÷ 15 = 20
There were 20 pupils.
10 x 20 = 200
Miss Lisa gave the class 200 toy bricks.
24 After David gave Gupta, the amount that Gupta had
was 300 ÷ (2 + 1) = 100
The amount Gupta had at first was 100 – 18 = 82
Gupta had $82 at first.
25 225 ÷ 15 = 15
15 x 12.30 = 184.5
Mrs. Tan earned $184.50
26 Area of one triangle: 3 x 4 ÷ 2 = 6 cm2+
Area of 3 triangles:3x6=18 cm2
Area of the square: 4 x 4 = 16 cm2
Area of the rectangle: 4 x 7 = 28 cm2
Total area: 18+ 16 + 28 = 62 cm2
27 Fraction of $10 notes 1− 1 − 1
=
1
3
6
2
Ratio of $2 notes to $5 notes to $10 notes 2 : 1 : 3
Ratio of total amount $2 to that of $5 to that of $10
4 : 5 : 30
Amount of $5 notes 1794 ÷ 39 x 5 = 230
The total value of $5 notes Ali saved is $230
28 10 4 5 5.89 9 8
− = ≈
9 1
Darren had to run 5.89 km more.
29 After 2 hours, Jimmy already made
30 x 2 = 60 paper birds
So the time that Philip would take is
60 ÷ (50 – 30) = 3 hours
30 108 ÷ 15 = 7.2, 98 ÷ 15 = 6.53, Therefore the bigger number is 15 x 7 = 105.
The smaller number is 105 ÷15 x 2 = 14
Paper 2
1
8 7 × 5
= 4 19
8
24
7
, 24
3 2
7 − 4 19
= 2
3 2
The difference in their distances is 2 8 7
km
2 CN = 96 ÷ 4 x 3 = 72 cm
Area of triangle MNC is
72 x 24 ÷ 2 = 864 cm2
3 60 ÷ 4 x 7 = 105l
(105 + 60) x 2.50 = 412.50
Mr. Quek paid $412.50
4 Volume of strawberry syrup needed 24 ÷ 6 = 4l
Volume of strawberry syrup short: 4 – 1.5 = 2.5l
Original volume of water 24 – 4 = 20l
New ratio (4 + 2) : 20 = 6 : 20 = 3 : 10

9
= 1 − + − + − ...+ − = − =
14 9
5 Ratio of number of units of product A to that of
product B 14 : 3
Ratio of total amount received from product A to that
of product B 14 x 10 : 3 x 4 = 35 : 3
Total amount from selling product A
11400 ÷ (35 + 3) x 35 = 10500
Total amount from selling product B
10500 ÷ 35 x 3 = 900
Number of product A
10500 ÷ 10 = 1050
10500 – 900 =9600
a) He sold 1050 units of product A
b) The difference between the amount of money
collected from product A and B is $9600
6 Fraction of stickers left after making scrapbooks
1− 1 =
Fraction of stickers given to friends 9
3 2
3
4
3 2
3 2
× =
4
4 ÷3 =
Fraction of stickers each friend received 9
27
2
1− 1 − 4
=
Fraction of stickers left 3
9
9
Number of stickers at first 42 ÷ (9 – 2) x 9 = 54
Each friend received 54 × 4 = 8 27
stickers
8 189 x 55 + 17 = 10 412
The number is 10 412
9
24× 1 × 5
= 3
1
3
12
3
3 hrs 20 mins
Mr. Ong worked with his computer for 3 hours 20
minutes
7 Number of 20-cent coins that Suriyana had
192 ÷ (3 + 5) x 3 = 72
Number of 50-cent coins that Suriyana had
192 – 72 = 120
Suriyana had 72 twenty-cent coins and 120 fifty-cent
coins.
Fahan’s total number of coins:
192 × 1 = 48 4
coins
Number of 20-cent coins Fahan had 48 ÷ 3 = 16 coins
Number of 50-cent coins Fahan had 16 x 2 = 32 coins
a) Ratio of the number of 20-cent coins Suriyana had
to the number of 50-cent coins that Fahan had
72 ÷ 32 = 9:4
b) Ratio of the amount of money that Suriyana had to
the amount of money that Fahan had
(72 x 20 + 120 x 50) : (16 x 20 + 32 x 50) = 31 : 8
10
1 equal part = 5 x 4 = 20
Tom: 20 + 5 = 25
Jerry: 20 x 2 – 5 = 35
a) Tom had $25
b) Jerry had $35
11 Cost of a pen in box A: 14.70 ÷ 16 ≈0.92
Cost of a pen in box B: 22.50 ÷ 24 ≈ 0.94
Box A is the cheaper buy
13 The length of the shortest side: 300 ÷ 5 x 2 = 120 cm
The length of the last side: 300 ÷ 5 x 4 = 240 cm
Perimeter 120 + 240 + 300 = 660 cm
14
1 ... × × × × + + + +
1
19 20
1
4 5
1
3 4
2 3
20
1
20
1
2
1
20
1
19
1
5
1
4
1
4
1
3
1
3
2
12 a) The first person shakes hand with the other 2
people. There are 2 handshakes.
The second person already shook hand with the first,
so there is one more handshake.
The last person already shook hand with the other two
people.
The number of handshakes is 2 + 1 = 2
b) Similarly, the number of handshakes when there
are 5 people is 4 + 3 + 2 + 1 = 10
c) N umber of handshakes when there are 10 people
is 9 + 8 + 7 + 6 + 5 + 4+ 3 +2 + 1 = 45
15
1− 3 = 5
, 480 ÷ 5 =
768 8
8
8
The total distance from A to B is 768 km
16 Base area: 5 x 7 = 35 m2
Depth: 105 ÷ 35 = 3 m
The tank’s depth is 3 m.
17 (14 + 26) x 11 ÷ 2 = 220 cm2
18 If all the animals were dogs, the number of legs would
have been 4 x 36 = 144
Number of chickens (144 – 100) ÷ 2 = 22
There are 22 chickens.

Paper 1
2 1 2 2 2 3 3 2 3 4 4 2 3 4 2
16 Apples : oranges = 2 : 3 = 4 : 6
21 If each boy was given $8, the total of their money 5 , , ,
15 0
Apples : bananas = 4 : 9
Oranges : bananas = 6 : 9 = 2 : 3
17
Sylvia made (221 – 121) ÷ 4 = 25 stars
Alan made 121 – 25 = 96 stars
18 Fraction of red pens 1
1
2
16
8 1
(1− ) =
7
1− 1 − 1
=
Fraction of black pens 2
16
16
Ratio of blue pens to red pens to black pens 8 : 1 : 7
Number of red pens 210 ÷ (7 – 1) = 35
Number of black pens 35 x 7 = 245
Number of blue pens 35 x 8 = 280
Total number of pens 35 + 245 + 280 = 560
19 The difference in the number of cans of coke and soda
at first was 48 + 48 = 96 cans
Number of cans of coke 96 ÷ (7 – 3) x 3 = 72
There were 72 cans of coke at first.
20 Area of the triangle XYZ 9 x 9 ÷ 2 = 40.5 cm2
Area of the unshaded part
(9 – 4.5) x (9 – 2) ÷ 2 = 15.75 cm2
Area of the shaded part 40.5 – 15.75 = 24.75 cm2
22
7
5
5
4
4
5
7
would be 54 + 8 + 8 = 70
Amount that Fahan had at the end
70 ÷ (3 + 4) x 4 = 40
Amount Fahan had at first 40 – 8 = 32
Fahand had $32 at first.
23 18 27 3 2
÷ =
There are 27 two-thirds in 18.
24 54 2 154 4 3
× =
2 months.
Betsy had 154 slices of fruit in 4 3
25
8 =
The value of the box is 3.
3 2
12
27 6 x 7 x 8 = 336， Mr. Lee had 336 boxes.
28 A= 2 5 ÷5 1
=
29
12
4
63
26 The number of candies in the box is a common
multiple of 4 and 7.
The smallest multiple of 4 and 7 is 4 x 7 = 28
We have 28 x 2 = 56 < 60
28 x 3 = 84 and 60 < 84 < 100
28 x 4 = 112 > 10
So the number of candies in the box is 84.
29 32 x 7 = 224
224 ÷ 25 = 8.96
9 buses are needed.
30 In one hour pump A can fill 3
1 the pool and pump B can fill 2
1 the pool.
The time taken for both pump to fill the pool completely is 1 / (1/2 + 1/3)= 1.2 hours。
Paper 2
2 1440 ÷ 80 x 5 = 90
Daniel had worked for 90 hours.
1 The fraction of the number of questions remained
after the second day
1− 1 − =
Number of days to answer these questions:
5 2
1
10
2
2 ÷ 1
= 4
days
5
10
So on the sixth day he finishes all the questions.
3 The shaded area can be divided into two parts: a
triangle at the top and a rectangle at the bottom.
The area of the shaded part is
3 x 3 ÷ 2 + 3 x 1 = 7.5 squares
The area of each square is 3 x 3 = 9 cm2
So the area of the shaded part is 9 x 7.5 = 67.5 cm2
4 Fraction of the area of the smaller piece is
1− 7 =
5
12
12
Area of the bigger piece
138 ÷ (7 - 5) x 7 = 483
The area of the bigger piece is 483 cm2
6 Total perimeter 59 x 2 = 118 cm
Perimeter of the triangle 30 + 12 + 28 = 70 cm
Perimeter of the square 118 – 70 = 48 cm
Side of the square 48 ÷ 4 = 12 cm
Area of the square 12 x 12 = 144 cm2
5

8 (89 + 115) x 5 = 1020
1300 = 19
15 1
(117 + 258) x 12 = 4500
So (205 + 397) x ? = 4816
? = 4816 ÷ 602 = 8, The missing value is 8.
7
Volume of barrel A at first
24 x 3 ÷ 2 = 36
Volume of barrel B in the end
36 x 2 + 24 x 2 = 120
There is 120l of petrol in barrel B in the end.
9 Number of dolls sold: 900 ÷ 50 = 18
Number of dolls more than toy robots at the end
23 – 18 = 5
Number of dolls in the end 5 ÷ (1.5 – 1) x 1.5 = 15
Number of dolls at first 15 + 18 = 33
There were 33 dolls at first
11 The number of cards Fred had: 104 ÷ 2 = 52
Total number of cards that George and Harry had
52 ÷ 4 11
= 143
Number of cards Harry had 143 – 104 = 39
The total number of cards three of them had:
104 + 52 + 39 = 195 cards
12 400 = 2 x 2 x 2 x 2 x 5 x 5
We have 2 x 5 = 10
2 x 2 x 2 x 5 = 40
Therefore Jane had $10 and her brother had $40
10
From the figure we can see that 1 equal part in
Joey’s money is 2 equal parts in Zhong Ren’s
money (2 squares) and 1 equal part in Suriya’s
money is equal to 3 equal parts in Zhong Ren’s
money.
Total number of squares 2 x 5 + 7 + 3 x 3 = 26
Value of one square 1326 ÷ 26 = 51
Joey spent 51 x 2 x 2 = 204
Zhong Ren spent 51 x 1 = 51
Suriya spent 51 x 1 x 3 = 153
Total amount spent 204 + 51 + 153 = 408
They spent $408 altogether.
13 Ratio of the cost of 1 pair of shoes and 1 pair of socks
is 9 : 1
Ratio of the cost of 3 pairs of shoes and 5 pairs of
socks is 27 : 5
Cost of 3 pairs of shoes 192 ÷ (27 + 5) x 27 = 162
Cost of 1 pair of shoes 162 ÷ 3 = 54
A pair of shoes costs $54.
14 Area of the shaded parts
2 x 4 ÷ 2 + 3 x 4 ÷ 2 = 10 squares
Area of each square 4 x 4 = 16 cm2
Area of the shaded part 16 x 10 = 160 cm2
15 Total mass of the two bags
33.25 x 2 = 66.5 kg
The mass of the powder bag
66.25 (2 1) 19 2
÷ 1 + = kg
16 Number of pens 36 ÷ (7 – 3) x 7 = 63
There were 63 pens at first.
17 Area of the rectangle 15 x 19 = 285 cm2
Area of the triangle 19 x (15 – 7) ÷ 2 = 76 cm2
Area of the shaded part 285 – 76 = 209 cm2
18 6 ÷ 3 x 7 = 14, 14 – 9 = 5, Alice bought 5 more notepads.
Paper 1
4 3 4 4 3 1 1 2 3 4 1 4 2 2 4
16 Eight million six thousand five hundred. 17 3
18
13
50
5000
23 = 4 3
It is 4600metres.
5
5
20 Area MQH = area KNP = 4
1 area MNPQ
1 area MNPQ
=> Area MKPH = 2
1 area MKPH = 4
Shaded area = 2
1 area MNPQ.
21
(1 + 1
) ÷ 2 =
3
2
4
8
Jing Jing had done 8
3 of the homework.
22 40 ÷ 8 = 5
5 carpenters are required.
23 A = (100+1)×100 =
5050 2
24 4 hours 40 minutes – 2 hours 45minutes = 1 hour 55
minutes. The carpenter started at 1.55 pm.
25 Feng Xue and Ann each had (181 – 37) ÷ 2 = 72
stamps. Ann later had 72 + 29 = 101 stamps
Ann had 101 stamps in the end.

15 2
26 (148.5 + 43.5) ÷ 2 = 96
(148.5 – 43.5) ÷ 2 = 52.5
The two numbers are 96 and 52.5
27 DH = 30 ÷ (7 + 3) x 7 = 21 cm
Area BDH = 21 x 30 ÷ 2 = 315 cm2
28
5 of the apples is equal to 7
9
5 of the pears
Ratio of apples to pears is 9 : 7
Number of pears at first 592 ÷ (9 + 7) x 7 = 259
Number of pears sold 259 × 2 =
74 7
74 pears were sold.
30 Women : adults = 3 : 4 = 9 : 12
Adults : children = 3 : 7 = 12 : 28
Women : children = 9 : 28
Number of children
114 ÷ (28 – 9) x 28 = 168
There were 168 children at the concert.
29 Fraction of the full water volume taken from the tank
5 − 1
=
1
6
2
3
Mass of the water taken out
81.74 – 59.8 = 21.94 kg
Mass of the full water
volume 21.94 ÷ 1 =
65.82kg 3
Mass of half of the water volume
65.82 × 1 =
32.91kg 2
Mass of the tank 59.8 – 32.91 = 26.89 kg
Paper 2
1 3.25 kg = 3250 g
3250 ÷ 250 x 0.65 = 8.45
Mr. Khoo paid $8.45
2 Area ABC = 22 x 16 ÷ 2 = 176 cm2
Area BCD = 22 x 7 ÷ 2 = 77 cm2
Area ACD = 176 – 77 = 99 cm2
3 Total mass of 3 packets 903.6 x 3 = 2710.8 g
4 = 10 : 5 : 4
Apple : strawberry : mango = 2 : 1 : 5
Mass of the packet of apple candies
2710.8 ÷ (10 + 5 + 4) x 10 ÷ 1000 = 1.43 kg
5 In every minute, tank X receives 8l more than tank Y
54 – 22 = 32
Time taken so that tank X is 32l more than tank Y
32 ÷ 8 = 4 minutes
Rate of water flowing in tank Y 22 ÷ 4 + 56.5 = 62
After 1 hour, the volume of water in tank Y is
(62 – 56.5) x 60 = 330l
4 2 boxes of candies and 3 boxes of cookies is 5 x 3.84
= 19.2 kg
Therefore 4 boxes of candies and 6 boxes of cookies
is 19.2 x 2 = 38.4 kg
3 boxes of candies and 2 boxes of cookies is 5 x 3.7 =
18.5 kg
Therefore 9 boxes of candies and 6 boxes of cookies
is 18.5 x 3 = 55.5 kg
So 5 boxes of candies is 55.5 – 38.4 = 17.1 kg
1 boxes of candies is 17.1 ÷ 5 = 3.42 kg
1 boxes of cookies is (19.2 – 2 x 3.42) ÷ 3 = 4.12 kg
The total mass of 2 boxes of candies and 1 box of
cookies is 2 x 3.42 + 4.12 = 10.96 kg
6 The remainder before Tom bought the computer:
(846 + 27) x 2 = 1746
The remainder before Tom paid his bills:
(1746 + 54) ÷ 6 7
= 2100
Tom’s salary is 2100 ÷ 4 3
= 2800
Tom’s salary is $2800
7 Number of plastic pieces 64 x 2 = 128
Number of chairs (128 + 64) ÷ 8 x 5 = 120
Number of tables 120 ÷ 5 x 3 = 72
Number of plastic chairs 120 – 32 = 88
Number of plastic tables 128 – 88 = 40
Number of wooden tables 72 – 40 = 32
Ratio of the number of plastic chairs to that of
wooden tables 88 : 32 = 11 : 4
8
1 1
1
1
+ ÷ = ≈
(1 1 ) 2 1 7
1.58m
12
3 2
1
2
3 2
6
2
+ =
The average height of the two children is 1.58m.
9 Fraction of the magazine:
1 )x 4
read on Saturday (1- 5
1
1 = 5
1 x2= 5
read on Sunday 5
2
Fraction of the magazine that was not read
1- 1 - 1 - 2 1
5
5
5
= 5
10 Cost of the LCD 900 ÷ (9/4) = 400
Average cost (400 + 900) ÷ 2 = 650
The average cost of the two devices is $650.
11 A pair of jeans cost $5 more than a pair of shirts.
Therefore, if Ken bought 2 pairs of jeans instead of 2
shirts, he would have to pay 5 x 2 = 10 more
The cost of 1 pairs of jeans (90 + 10) ÷ 5 = 20
A pair of jeans costs $20.
12 Indian : Chinese = 2 : 7 = 8 : 28
Malay : Chinese = 3 : 4 = 21 : 28
Indian : Malay : Chinese = 8 : 21 : 28
13 172000 x 0.68% = 1169.6
Interest that Bill would earn after a year is $1169.60

15 3
14 After giving money, the total would not change.
Amount that Margaret had in the end
630 ÷ (8 + 1) = 70
Amount that Margaret had at first
70 + 52.70 = 122.70
Amount that Soo Hui had at first
630 – 122.70 = 507.30
507.30 – 122.70 = 384.60
The difference is $384.60
16 3290 x 80% = 2632
2632 x 107% = 2816.24
Mr. Tay paid $2816.24 for the furniture.
17 263790
15
Value of one equal part
(400 + 30) ÷ 8 = 53.75l
The initial volume of water in tank B was 53.75l
18 128 ÷ 2 = 64, 64 ÷ 2 = 32, 32 ÷ 2 = 16, 16 ÷ 2 = 8, 8 ÷ 2 = 4, 4 ÷ 2 = 2, 2 ÷ 2 = 1, 1 ÷ 2 = 0.5
It took 8 times 12 minutes for the bacteria to reach 128 mg. Time taken is 12 x 8 = 96 minutes.
So the starting time was 5 hours – 96 minutes = 3 hours 24 minutes.
The starting time was 3:24 pm.
Paper 1
3 2 1 1 4 1 2 3 2 4 1 1 1 4 4
16 3256 = 19 x 191 + 7
The remainder is 7
17 680 795
18 23
19 261
30
3 1 − 2
= 2
5
6
20 1l 25 ml = 1025 cm3
22 5 4 30 3 2
21 x = ÷ × =
×(1− ) =
The volume of milk left in the bottle is l 9 5
9 5
1
3
6 5
23 63.08l = 63 080 ml
24 2 x 3.65 + 3 x 5.99 = 25.27
Uncle Tiong spent $25.27
25 5 : 9 = 35 : 63 => Y = 35
7 : 35 = 1 : 5 => X = 1
26 If each pupil gets 7 pens, there will be 3 pens extra.
To give each pupil 8 pens, the 3 extra pens can be
given to 3 pupils. There are 4 pens short.
So the number of pupil is 4 + 3 = 7
Number of pens 7 x 7 + 3 = 52
a) There are 7 pupils
b) There are 52 pens.
27 100% - 75% = 25% , 25% x 40% = 10%
3
100% - 75% - 10% = 15% , 15%= 20
Total number of candies 20 ÷ 10% = 200
Number of chocolate candies: 200 x 75% = 150
Number of strawberry candies: 200 x 15% = 30
a) The number of strawberry flavored candies is 3
20
of the total.
b) 150 – 30 = 120 There are 120 more chocolate
candies than strawberry candies.
28 Percentage of the breadth to half-perimeter
15% x 2 = 30%
Percentage of the length to half-perimeter
100% - 30% = 70%
Ratio of breadth to length is 3 : 7
The breadth is 760 ÷ (7 – 3) x 3 = 570 cm = 5.7m
The length is 760 + 570 = 1330 cm = 13.3m
Area = 5.70 x 13.30 = 75.81 m2
570 ÷ 30 = 19
1330 ÷ 30 =44.33
The maximum number of cartons that can be stored is
19 x 44 = 836 cartons
30 Number of Peter’s books: 32 48 3 2
÷ =
Number of Fahan’s books: 48 ÷ 2 = 24
Total number of books: 48 + 24 + 32 = 104.
29 In January
Charges for first 40 units: 1.17 x 40 = 46.80
Charges for the remaining units
1.40 x (56 – 40) = 22.40
Total bill: 46.80 + 22.40 = 69.20
In February
Charges for the units above the first 40 units:
135 – 46.80 = 88.20
Number of units above the first 40 units:
88.20 ÷ 1.40 = 63
Total consumption in February 40 + 63 = 103
Average consumption: (56 + 40 + 63) ÷ 2 = 79.5
Average bill (69.20 + 135) ÷ 2 = 102.1
a) 103 units
b) 79.5 units
c) $102.10

Paper 2
1 Four other pupils each can have a maximum score of
2 that of Thomas.
15 4
50 marks.
Highest possible average is
(50 + 50 + 50 + 50 + 15) ÷ 5 = 43 marks.
2 George folded 100% - 35% = 65% of the birds.
The difference between them is 65% -35% = 30% of
the birds. Total number of birds: 90 ÷ 30% = 300.
George folded 300 x 65% = 195 birds.
3 Mary : Andy = 0.4 : 1 , Mary : Bob = 1 : 2
Mary : Andy : Bob = 2 : 5 : 4
660 ÷ (2 + 5 + 4) x 5 = 300, Andy donated $300.
4 　ABD = (180° - 116°) ÷ 2 = 32°
　ABE = 180° - 32° = 148°
5 12 ÷ 30% = 40
He had 40 stamps at first.
6 7 + 16 + 5 = 28 , 5 + 9 + 28 = 42
28 ÷ 42 x100% = 66.67%
7 Number of males: 2500 – 1100 = 1400
1400 ÷ 1100 x 100% = 127.27%
There are 27.27% more males than females.
8 2 : 4 : 5 = 6 : 12 : 15
Total number of questions done is
6 + 12 + 15 = 33
9 The largest possible difference is when the number of
adults is largest and the number of children is
smallest.
The largest possible number of adults is 3349.
The smallest possible number of children is 1651.
The largest difference is
3349 – 1651 = 1698
10 Triangle SQR and triangle PQR have the same base
QR and their heights are in the ratio of 1 : 4.
Therefore there areas are also in the ratio of 1 : 4.
Therefore the ratio of the shaded area to that of
triangle PQR is 3 : 4
Area of triangle PQR is 54 ÷ 3 x 4 = 72 cm2
12 Number of students remained 36 – 9 = 27
Number of extra lollipops 27 x 3 = 81
Ratio of the number of student left to the total number
of students 9 : 36 = 1 : 4
Number of lollipops 81 x 4 = 324
Miss Chua bought 324 lollipops.
11
From the figure, the unshaded area of Square B is
27 x 2 ÷ (5 – 3) = 27 cm2+
Area of the square is 27 + 27 = 54 cm2
The area of the square is 54 cm2
13 AC = 9 cm
BC = 12 cm
Side of the small square inside: 12 – 9 = 3 cm
Area of triangle ABC 9 x 12 ÷ 2 = 54 cm2
Area of the small square 3 x 3 = 9 cm2
Area of the square MNPQ 54 x 4 + 9 = 225 cm2
14 Height of triangle D is the width of the rectangle, so it
is 6 cm.
The base of triangle D is 30 x 2 ÷ 6 = 10 cm
Triangles A and D have the same height. Therefore
the base of triangle A is 10 x 3 ÷ 5 = 6 cm
Triangles A and B also have the same height.
So the base of triangle B is 6 x 3 = 18 cm
The length of the rectangle is 18 + 10 = 28 cm
The perimeter of the rectangle is (28 + 6) x 2 = 68 cm
16
(45 + 6 + 3) ÷ 2 = 27
Lucy had $27 at first.
15 Ratio of story books to comic books is 1.5 : 1 = 3 : 2
Ratio of story books sold to comic books sold
(3 x ) : (2 x 1) = 2 : 2 = 1 : 1
3 2
Ratio of money received from selling story books to
comic books (1 x 12) : (1 x 8) = 12 : 8 = 3 : 2
Money received from selling story books
6400 ÷ (3 + 2) x 3 = 3840
Money the shop would received from selling the
remaining 1 3
of the story books
3840 ÷ 2 = 1920
Money the shop would receive at the end
6400 + 1920 = 8320
When all the books were sold, the shop would receive
$8320.
17 From the figure, 5 3
of Joey’s marbles is 7
Ratio between Joey’s marbles and Thomas’s marbles is 10 : 21
Ratio between Joey’s marbles to the difference between them is 10 : 11
Ratio between Joey’s marbles to Ben’s marbles is 10 : 22 = 5 : 11
Joey’s marbles is 48 ÷ (11 – 5) x 5 = 40
Thomas’s marbles is 40 / 10 x 21 = 84
Ben’s marbles is 40 ÷ 5 x 11 = 88 , 84 + 40 + 88 = 212. They have 212 marbles altogether.
18 Volume of tank A 4 x 6 x 1 = 24 m3 , Volume of tank B 5 x 3 x 2 = 30 m3
The volume of water in each tank is 4 x 6 x 0.5 = 12 m3. The height of water in tank B is 12 ÷ (5 x 3) = 0.8 m

Paper 1
2 1 4 1 3 1 2 2 2 1 1 2 4 2 4
16 9 : (5 + 9) = 9 : 14
15 5
The ratio is 9 : 14
17 12.42 + 2.07 = 14.49
The volume of juice drink is 14.49 l
19 0.064
20
1
12
18 Number of squares: 3 x 3 = 9
1 of a square, so each triangle is
Each triangle is 2
1 × = 1
18
of the figure
So the fraction shaded is 9
9 1
2
1 ×4 = 2
of the figure.
18
i.e. 22.22% of the figure is shaded
21 3 years ago Mohammed was 15 – 3 = 12 years old.
His brother’s age was 12 18 3 2
÷ =
His brother’s age now is 18 + 3 = 21 years old.
22 2009 is a normal year so there are 365 days.
There are 30 days in September.
30 ÷ 365 x 100% = 8.22%
23
51
100
0.051, 105 ,0.501,
1000
24 26
25
16
25
26 2100 x 107% = 2247
The price is $2247
27 1.25 + 2.125 + 0.786 = 4.161 ≈ 4.16
The total volume is 4.16
28 1053 ÷ (5 + 8) x 5 = 405
Kavitha’s saving is $405
29 Volume of the pool 20 x 10 x 1.5 = 300 m2
Volume of water to be filled 300 ÷ 2 = 150 m2
Total volume of water that can be filled in a minute
0.375 x 4 = 1.5 m3
Total time required 150 ÷ 1.5 = 100 minutes
30 8.5 – 5 = 3.5 An adult ticket cost 3.5 more than a child ticket.
126 ÷ 2 = 63 If there were 126 more child tickets sold, the cinema would received
2907 + 126 x 5 = 3537
By then there would be an equal amount of adult and child ticket. Ratio of the money received from selling adult
tickets to child tickets would be 8.5 : 5
Amount received from selling adult tickets 3537 ÷ (8.5 + 5) x 8.5 = 2227
Number of adult tickets 2227 ÷ 8.5 = 262. There were 262 adults.
Paper 2
1 Total money saved by all children: 604 x 10 = 6040
Total money saved by the boys 592 x 2 = 1184
Total money saved by the girls 6040 – 1184 = 4856
Average of savings of the girls 4856 ÷ 8 = 607
On average, each girl saved $607.
2 Number of Indian pupils 1200 x 20% = 240
Percentage of Chinese pupils (100% - 20%) x 65% =
52%
Number of Chinese pupils 1200 x 52% = 624
Percentage of Malay pupils 100% - 20% - 52% = 28%
a) 624 Chinese pupils
b) 28% of the pupils are Malay.
3 Fraction of the balloons sold on the last two days:
1− 1 =
4
5
5
Fraction of the balloons sold on the last day
4 ÷5×3 =
12
5
25
Fraction of the balloons sold on the second day
4 ÷5×2 =
8
5
25
Ratio of the number of balloons sold on the first day
to the second day to the last day 5 : 8 : 12
Number of balloons sold on the last day
92 ÷ (12 – 8) x 12 = 276
Number of balloons sold on the second day
276 – 92 = 184
Number of balloons sold on the first day
184 ÷ 8 x 5 = 115
Total number of balloons 115 + 184 + 276 = 575
Money received 575 x 1.2 = 690
Mr Chan earned $690 in total.
4
2u + 2v = 858 => 6u + 6v = 2574
5v – 3u = 225 => 10v – 6u = 450
=> 16v = 3024
=> v = 189
Number of tulips
189 x 5 = 945
Number of roses
945 – 225 = 720
945 + 720 = 1665
There were 1665 flowers at first.

15 6
5 　AFD = 　　FGD = 80°
　ADE = (180° - 　AFD) ÷ 2 = 50°
　EDC = 90° - 50° = 40°
　DAE = 　ADE = 50°
6
3 8
x4500g=1687.5g=1.6875 kg
48%x18 kg=8.64 kg
Total mass
1.6875 + 8.64 = 10.3275 ≈10.33 kg
7 There are 4 spaces between the third tree and the
seventh tree.
Distance between any two trees
7920 ÷ 4 = 1980 cm = 19.8 m
Distance from the 15th tree to the first tree:
19.8 x 14 = 277.2 m
8 Distance travelled when the ball hit the ground the
first time: 15m
Distance bounced up 15x 5 4
=12 m
Distance travelled to hit the ground the second time:
12 m
Total distance: 15 + 12 + 12 = 39 m
10 If all trucks were small trucks, the number of wheels
would be 10 x 32 = 320
Number of wheels extra 408 – 320 = 88
Number of large trucks 88 ÷ (14 – 10) = 22
There are 22 large trucks.
9
Age of the last child (193 – 3 – 3 x 2 – 3 x 3) ÷ 7 = 25
Age of the first child 25 + 9 = 34
The first child is 34 years old.
11 Francis’s money before he gave to his sister
÷ 2 =1240
(443+53) 5
Francis’s money before he bought the book
1240 + 61 = 1301
Francis’s money before he bought the furniture
(1301 + 49) ÷ 75% = 1800
Francis’s salary (1800 + 100) x 2 = 3800
Francis’s salary is $3800.
12 The ratio of the mass of an elephant to that of a zebra
is 5.5 : 1
The ratio of the mass of 2 elephants to that of 3 zebras
is 5.5 x 2 : 1 x 3 = 11 : 3
Mass of 2 elephants 1260 ÷ (11 + 3) x 11 = 990
Mass of an elephant 990 ÷ 2 = 495
Mass of a zebra 495 ÷ 5.5 = 90
Mass of an elephant and 4 zebras
495 + 4 x 90 = 855
The total mass of one elephant and 4 zebras is 855 kg.
13 Total money earned from January to August
2 340 x 8 = 18 720
Total money earned for the year
3 290 x 12 = 39 480
Total money earned from September to December
39 480 – 18 720 = 20 760
Average earning during that period
20 760 ÷ 4 = 5 190
15 Number of roses
954 ÷ (9 – 3) x 3 = 477
Number of lilies
477 ÷ 3 x 5 = 795
795 – 477 = 318
There were 318 more lilies than roses.
14
(1459 + 296) ÷ (4 + 4 + 1) = 195
Kathy raised $195
16 The total number of pages in 1 book of each type
10 000 ÷ 20 = 500 pages
The number of pages in a Physics book
(500 – 20 – (20 + 70)) ÷ 3 = 130
There are 130 pages in a Physics book
17 Perimeter of the rectangle
(75 + 33) x 2 = 216 cm
That is also the total perimeter of the two triangles.
The base of each triangle is
(216 – 39 x 4) ÷ 2 = 30 cm
The area of one triangle is
36 x 30 ÷ 2 = 540 cm2
18 Derek’s money after buying stationeries
150 + 246 = 396
Fraction of Derek’s money that he spent on toys on
stationary
The amount of money that Derek had:
The amount of money that Josh had
720 ÷ 5 x 3 = 432. Josh had $432.

Paper 1
1 1 2 2 2 2 1 1 4 1 3 3 2 1 3
16 48% 17480 cm2
18 6 ÷ 4 x 24 = 36
15 7
Two dozen cans cost $36
19 x = 162° ÷ 2 = 81°
21 390 ÷ 12 = 32.5
33 pencil cases are needed.
22
1− 7 = 8
, 8 : 7
=
8: 7 15
15
15
15
The ratio is 8 : 7
23 Number of $5 notes 45 ÷ (1 + 1.5) = 18
Number of $2 notes 18 x 1.5 = 27
Total amount of money 27 x 2 + 18 x 5 = 144
Brian has $144
24 18 = 2 x 3 x 3
45 = 3 x 3 x 5
The common factors are 3, 9
25 55 x 18 = 990
Kiara’s school is 990m from her home.
20
M
A B
1 MBJH =
I
H
The shaded area on the right = 2
1 4
MBCN
The shaded area on the left = 2
1 IHND = 4
J
1 AMND
Ratio of the total shaded area to the area of ABCD is
1
4
26 At some times later, the difference in ages will still
remain the same
Raphael’s age then 38 ÷ (3 – 1) = 19
The number of years is 19 – 10 = 9
After 10 years, Raphael’s father‘s age will be three
times his age.
27 72 ÷ 36% = 200 ml
The bottle is 200 ml
29 4750 g = 4.75 kg
42.5 + 4.75 = 47.25
The scale indicates 47.25 kg
28 500 ÷ 40 = 12.5
600 ÷ 40 = 15
300 ÷ 40 = 7.5
The maximum number of boxes that can be stored is
12 x 15 x 7 = 1260 boxes
30 1 5
2 km = 1.4 km = 1400 m, 4 3
km = 0.75 km = 750 m, 1400 – 750 = 650, Antoine had walked 650 m
Paper 2
1 60 x 25 x 30 = 45000, 45000 cm3 = 45 l
45 ÷ 3 = 15, Uncle Tiong has to fill 15 times.
2 Area IBK = (25 – 18) x (25 – 2) ÷ 2 = 80.5 cm2
Remaining area = 25 x 25 – 2 x 80.5 = 464 cm2
3 Price at which Mrs. Choo bought the grapes
3.20 – 0.70 = 2.50 per 100 g
Amount that Mrs. Ong paid 2000 ÷ 100 x 3.20 = 64
Amount of grapes that Mrs. Choo bought
64 x 100 ÷ 2.50 ÷ 1000 = 2.56, 2.56 – 2 = 0.56
Mrs. Choo bought 0.56 kg more than Mrs. Ong.
4 1 = 1 x 1
4 = 2 x 2
9 = 3 x 3
25 = 5 x 5
So the missing value is 16, since 16 = 4 x 4
5 Total distance of the first 3 attempts
155 x 3 = 465 cm
Total distance of all attempts 145 x 5 = 725 cm
Total distance of the last 2 attempts
725 – 465 = 260 cm
Average distance of the last 2 attempts = 130 cm
6 　NMQ = 180° - 29° x 2 = 122°
　QNP = 　MNQ = 29°
　ONP = 180° - 29° = 151°
　NOP = (180° - 151°) ÷ 2 = 14.5°
8 1.4 ÷ (2 + 5) x 2 = 0.4 l = 400 ml
The volume of syrup needed is 400 ml
7 Fraction of the milk that Guo Qi drank on the next 2
days
(1- 5
1 )x75%= 5 3
5 3
Fraction of the remaining milk
1- 1 - = 1
5
5
Volume of the carton
750 ÷ 1 = 3750ml =
3.75l 5
9 Number of toothpicks needed to make n shapes is 6 +
4(n – 1)
To make 5 shapes, the number of toothpicks needed is
6 + 4(5 – 1) = 22
Using 258 toothpicks 6 + 4 (n – 1) = 258
n = 64
64 shapes can be made.
D C
N

15 8
10 952 ÷ (0.4 + 1) = 680
The number of stickers that Zoe had is 680
11 Total mass 44 x 3 = 132 kg
Chek Khoon’s mass is
(132 + 4) ÷ (5 + 6 + 6) x 6 = 48 kg
12
Number of black pepper chickens 90 ÷ 5 x 2 = 36
Number of honey roasted chickens 36 x 3 = 108
a) 108 honey roasted chickens were sold.
b) 36 black pepper chickens were sold.
13 If Andy only bought 3 comic books and 3 story
books, he would save 18 x 2 = 36
Amount left after buying 3 comic books and 3 story
books 36 + 24 = 60
With this $60, if he buys 2 more story books, he will
need $16 more. Therefore, cost of a comic book is
(60 – 16) ÷ 2 = 38
Amount of money that Andy had
3 x 38 + 5 x 18 + 24 = 228
Andy has $228
14 Area of 2, 3, 4 and 5 is 1 unit
Area of 1 is 4 x 4 = 16 units
Area of 1 and 2 is 16 + 1 = 17 units
The ratio is 17 : (16 + 4) = 17 : 20
15 Amount received from selling plastic tables
75 x 150 = 11250
Number of wooden tables (12850 – 11250) ÷ 80 = 20
20 wooden tables were sold.
16 Fraction of the pupils who like chess
1 )x 4
(1- 3
1 = 1
6
Total number of pupils 10 ÷ 1 =
60 6
1 =20
Number of pupils who like basketball 60x 3
Number of pupils who like either chess or basketball
20 + 10 = 30 pupils
17 Ratio of the amount paid for safe delivery to amount
received for broken products
9 x 16.5 : 1 x 66 = 9 : 4
Amount received for broken products
15015 ÷ (9 – 4) x 4 = 12012
Number of broken products
12012 ÷ 66 = 182
There were 182 products broken on the way.
18 149 – 53 = 96
Each day Ryan ate 8 more cookies than Mindy. Number of days taken to eat 96 more cookies: 96 ÷ 8 = 12
Number of cookies each of them had at first 149 + 23 x 12 = 425
a) 12 days b) 425 cookies.
Paper 1
4 3 4 3 2 2 3 2 1 3 2 1 2 2 1
16 Goldfish : clownfish = 2 : 7 = 10 : 35
Clownfish : angelfish = 5 : 2 = 35 : 14
Goldfish : angelfish = 10 : 14 = 5 : 7
17
1
6
18
1
3
11 +1 = 3
There was 3 3
6 5
2
1 l of milk in the fridge at first
19 11 ÷ 1.20 = 9.17
At most, 9 pens can be bought
20 i = 154° - 87° = 67°
22 A = 9 – 1 – 1 – 1 = 6
21 A + B = 80 x 2 = 160 , A + B + C = 85 x 3 = 255
C = 255 – 160 = 35
23 (72 + 83 + 67) ÷ 3 = 74
Benjamin’s average mark is 7
24 24 = 2 x 2 x 2 x 3, 36 = 2 x 2 x 3 x 3
The common factors are 2, 4, 6, 12
25 5 839 x 7 = 40 873
27 12.8 – 0.91 x 5 – 1.32 x 3 = 4.29 km
26 Area of one face 54 ÷ 6 = 9 cm2
Since 9 = 3 x 3, the sides of the cube are 3 cm.
Volume of the cube 3 x 3 x 3 = 27 cm3
28 Percentage of adults 100% - 30% = 70%
Number of adults 10 200 x 70% = 7140
Number of adults working outside
7140 x 40% = 2856
There are 2856 adults working outside the village.
29 ABC = 180° - 93° - 43° = 44°
ABD = 44° - 37° = 7°
30 The price of 2 shirts is equal to the price of 3 skirts. Therefore the price of 4 shirts is equal to the price of 6 shirts.
The price of 4 shirts 162 ÷ 2 = 81. The price of a shirt 81 ÷ 4 = 20.25. A shirt costs $20.25

15 9
Paper 2
2 5 bags weigh 86.25 Kg.
1 bag weighs 17.25 Kg.
Each porter can lift Maximum of 60/17.25 =3.47 that
is 3 bags.
For lifting 20 bags we need 20/3=6.666
That is 7 porters.
1
Amount left after spending 1144 ÷ 2 x 3 = 1716
Amount withdrawn 1716 x 2 = 3432
3 3.115 ÷ 14 x 100% = 22.25%
4 Area of unshaded triangle at the bottom left
20 x (20 + 36) ÷ 2 = 560 cm2
Area of the unshaded triangle at the top right
36 x 36 ÷ 2 = 648 cm2
Total area 20 x 20 + 36 x 36 = 1696 cm2
Area of the shaded part 1696 – 560 – 648 = 488 cm2
5 Total number of stamps
168 ÷ 7 x (3 + 7 + 9) = 456
Number of Charlie’s stamp
168 ÷ 7 x 3 = 72
Number of stamps that Mark gave Charlie
(168 – 72) ÷ 2 = 48
6 Number of red roses 24 ÷ 3 x 5 = 40
Number of white roses 24 ÷ 3 x 2 = 16
Total number of flowers (40 + 16) ÷ (1 – 0.2) = 70
Number of daisies 70 x 0.2 = 14
7 CED = 42° - 31° = 11°
FCB = 180° - 42°= 138°
ACF = 138° - 60° = 78°
8 Cost of the fish 3300 ÷ 100 x 1.59 = 52.47
Cost of the beef 2800 ÷ 500 x 4.89 = 27.38
Cost of the vegetable 0.86 x 7 = 6.02
Total cost 52.47 + 27.38 + 6.02 = 85.87
Mrs. Foo paid $85.87
9 Ratio of the amount the shop received from selling
curry puffs to that from selling cakes
1 x 2 : 4 x 5 = 1 : 10
Amount from selling cakes
1892 ÷ (10 + 1) x 10 = 1720
Number of cakes 1720 ÷ 5 = 344
There are 344 cakes.
10 The number of pens at first was 280 x 70% = 196
Number of other pens 280 – 196 = 84
After selling some blue pens, the number of other
pens was 40% total.
Total number of pens in the end 84 ÷ 40% = 210
Number of blue pens sold 280 – 210 = 70
11 A textbook and a bag cost $30.
A textbook and a comic book cost $22.5.
2 textbooks and a bag and a comic book cost 30 +
22.5 = 52.5
4 textbooks, 2 bags and 1 comic book for $100
2 textbooks and 1 bag cost 100 – 52.5 = 47.5
Cost of 1 text book 47.5 – 30 = 17.5
Cost of 1 comic book 22.5 – 17.5 = 5
A comic book cost $5
12
24 ÷ 12 x 5 = 60
Marion had 60 beads at first.
13 350 ÷ 4000 x 100% = 8.75%
15 Earning from sales 72 000 ÷ 5 x 1.2 = 17280
Average earning from sale a month
17 280 ÷ 8 = 2160
Average earning a month 2160 + 1575 = 3735
16 Initial water volume
1 = 20 640 cm3 = 20.64 l
60 x 43 x 24 x 3
After 20 minutes, volume of water flowed into the
tank is 1.8 x 20 = 36 l
Total volume of water in the tank
20.64 + 36 = 56.64 l
17 Total area: 21 squares
Shaded area: 6 squares
Ratio: 6 : 21 = 2 : 7
18 3N - 3 2
N = N + 36
N = 27
The number is 27.
14 Fraction of apples: 2/5
2 )x 25
Fraction of oranges: (1- 5
12
5 4
=
Fraction of mangoes:
1− − 12
=
3
25
25
Ratio of the number of apples to that of oranges to
that of mangoes
10 : 12 : 3
Total number of fruits
648 ÷ (12 – 10) x (10 + 12 + 3) = 8100
Number of apples
8100 x 5
5 2
2 = 3240
3 = 972
8100 x 25
Total of oranges and mangoes
8100 – 3240 = 4860
After some apples have been sold, the total of oranges
and mangoes is 90% of the total fruits.
Number of fruits at the end
4860 ÷ 90% = 5400
Number of apples sold
8100 – 5400 = 2700
2700 apples have been sold.

Paper 1
3 2 1 1 1 1 3 4 2 1 1 3 2 1 2
17 150 x (1 + 0.07 + 0.1) = 175.5
16 0
Mr. Smith had to pay $175.50
18 99 + 108 + 117 + 126 + 135 + 144 + 153 = 882
16 1- 3
1 = 3 2
1
3 2
÷ 6 =
, 9
1 of the chocolates.
Each friend got 9
19 20.08 l = 20 l 80 ml
20 Volume of container 1: 20 x 15 x 10 = 3000 cm3
Volume of container 2: 15 x 7 x 5 = 525 cm3
Total volume 3000 + 525 = 3525 cm3
22 95
23 36 = 2 x 2 x 3 x 3, 48 = 2 x 2 x 2 x 2 x 3
The smallest common factor is 2 x 2 x 2 x 2 x 3 x 3 =
144
24 246.11
25 1 3
1 x 60 x 60 = 4800
There are 4800 seconds.
21
26 18 : 22 = 63 : 77
28 : 63 = 8 : 18
Therefore 8 : 18 : 22 = 28 : 63 : 77
A
C
27 Ticket price for the 9-year-old daughter: $600.
Ticket price for each of other family members: $1200
Total ticket cost 600 + 1200 x 3 = 4200
The family paid $4200 altogether.
28 0.1N = 5
2 N– 33
N = 110
The number is 110
29 144 = 12 x 12
The side of each square is 12 cm
The perimeter of the large rectangle is
(12 x 3 + 12) x 2 = 96 cm
30 450° = 360° + 90° Therefore 1 hour and 15 minutes have passed. The time then will be 10.15 am.
Paper 2
1 30 000 x 3.75% = 1125
Swee Swee will receive $1125 of interest after a year
3 There are 3 options for the appetizer, 3 options for
main course, and 3 options for dessert.
Total number of options is 3 x 3 x 3 = 27
4
31.5
( 9 7 8
) 2
9 0 9 1 ... 9 6 9 7 = =
8
8
× ×
× + × + + × + ×
5
− 7
=
1
10
10
0.1 kg of meat has not been cooked.
5 4
2
M .
A
6 Total volume: 6 + 9 = 15 l 7 x = 180° - 78° - 33° = 69°
Volume of a container
12 x 7 x 5 = 420 cm3 = 0.42 l
15 ÷ 0.42 = 35.71
35 containers could be filled completely.
Volume of drink left over: 15 – 35 x 0.42 = 0.3 l
8 Length of the rectangle 6.5 + 17.5 = 24 cm
Breadth of the rectangle 24 x 4 3
= 18 cm
Area of the shaded part (17.5 x 18) ÷ 2 = 157.5 cm2
9 Total time
3.2 x 8 = 25.6 minutes = 25 minutes 36 seconds.
10 Number of roses 400 x 8
5 = 250
Number of other flowers 400 – 250 = 150
Total number of flowers after selling
150 ÷ (1 − 3 ) =
375 5
Number of roses sold 400 – 375 = 25
25 roses were sold
11 16 = 4 x 4, 49 = 7 x 7
B
The side of the smaller square is 4 cm and that of the
larger square is 7 cm.
Total area 16 + 49 = 65 cm2
Area of the large triangle at the bottom
(4 + 7) x 7 ÷ 2 = 38.5 cm2
Area of the triangle on top of the smaller square
4 x 4 ÷ 2 = 8 cm2
Area of the triangle on top of the larger square
(7 – 4) x 7 ÷ 2 = 10.5 cm2
Area of the shaded part 65 – 38.5 – 8 – 10.5 = 8 cm2

16 1
12 x + 　y + 　z = 142°
z = (142° - 12°) ÷ 2 = 65°
14 a) Number of goals scored on the last match
7 + 2 x 6 = 19
Total number of goals
7 + 9 + … + 17 + 19 = 2
(19+7) x7 = 91
b) Average number of goals per match 91 ÷ 7 = 13
13 Total time spent
6 9 hours
138 x 3 = 414 minutes = 10
Total time spent on Tuesday and Wednesday
6 9 − 2 1
= 4 2
10
2
5
hours
Time spent on Wednesday 15
4 2 ÷ 3× 2 = 2 14
hours
5
15 Nelson’s sister’s height 1.52 – 0.2 = 1.32 m
33
1.32 ÷ 1.52 = 38
17 The price of the table
300 ÷ 4 x 2 = 150
The price of the table is $150
16 The first team has to play 9 matches again 9 other
teams.
The second team already played one match with the
first team, so it has to play 8 matches more with 8
remaining teams.
Similar reasoning can be applied for the other teams.
Total number of matches :
9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 +1 =45
There are 45 matches altogether.
18 Number of digits to write from 1 to 9: 9 x 1 = 9
Number of digits to write from 10 to 99: 90 x 2 = 180
Number of digits to write 100: 3
Total number of digits: 9 + 180 + 3 = 192
Peter wrote 192 digits.

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