Olympiad Maths Trainer 2

Terry Chew B. Sc

9
–
8

years o
ld

2

THẾ GIỚI PUBLISHERS


OLYMPIAD MATHS TRAINER - 2
(8-9 years old)
ALL RIGHTS RESERVED
Vietnam edition copyright © Sivina Education Joint stock Company, 2016.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted
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ISBN: 978 - 604 - 77 - 2312 - 6
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Olympiad Maths TraineR 2

FOREWORD

I first met Terry when he approached SAP to explore the possibility of
publishing Mathematical Olympiad type questions that he had researched,
wrote and compiled. What struck me at our first meeting was not the
elaborate work that he had consolidated over the years while teaching
and training students, but his desire to make the materials accessible
to all students, including those who deem themselves “not so good” in
mathematics. Hence the title of the original series was most appropriate:
Maths Olympiad – Unleash the Maths Olympian in You!

My understanding of his objective led us to endless discussions on
how to make the book easy to understand and useful to students of various
levels. It was in these discussions that Terry demonstrated his passion and
creativity in solving non-routine questions. He was eager to share these
techniques with his students and most importantly, he had also learned
alternative methods of solving the same problems from his group of bright
students.

This follow-up series is a result of his great enthusiasm to constantly
sharpen his students’ mathematical problem-solving skills. I am sure those

who have worked through the first series, Maths Olympiad – Unleash
the Maths Olympian in You!, have experienced significant improvement
in their problem-solving skills. Terry himself is encouraged by the positive
feedback and delighted that more and more children are now able to work
through non-routine questions.
And we have something new to add to the growing interest in
Mathematical Olympiad type questions — Olympiad Maths Trainer is now
on Facebook! You can connect with Terry via this platform and share interesting
problem-solving techniques with other students, parents and teachers.
I am sure the second series will benefit not only those who are
preparing for mathematical competitions, but also all who are constantly
looking for additional resources to hone their problem-solving skills.

Michelle Yoo
Chief Publisher
SAP


Olympiad Maths TraineR 2

A  word  from
  the  author . . .
Dear students, teachers and parents,
Welcome once more to the paradise of Mathematical Olympiad
where the enthusiastic young minds are challenged by the non-routine and
exciting mathematical problems!


My purpose of writing this sequel is twofold.

The old adage that “to do is to understand” is very true of mathematical
learning. This series adopts a systematic approach to provide practice for
the various types of mathematical problems introduced in my first series
of books.

In the first two books of this new series, students are introduced to 5
different types of mathematical problems every 12 weeks. They can then
apply different thinking skills to each problem type and gradually break
certain mindsets in problem-solving. The remaining four books comprise 6
different types of mathematical problems in the same manner. In essence,
students are exposed to stimulating and interesting mathematical problems
where they can work on creatively.
Secondly, the depth of problems in the Mathematical Olympiad
cannot be underestimated. The series contains additional topics such as
the Konigsberg Bridge Problem, Maximum and Minimum Problem, and
some others which are not covered in the first series, Maths Olympiad –
Unleash the Maths Olympian in You!

Every student is unique, and so is his or her learning style. Teachers
and parents should wholly embrace the strengths and weaknesses of each
student in their learning of mathematics and constantly seek improvements.

I hope you will enjoy working on the mathematical problems in this
series just as much as I enjoyed writing them.



Terry Chew

Olympiad Maths Trainer 2

CONTENTS
Week 1 to Week 12






 Look for a Pattern
 Tell me the Time!
 Number Puzzles
 Cubes
 Solve using Models

Week 13 to Week 24






 Problems from Planting Trees
 Logic
 Make a List (1)
 Counting
 Tricks in Addition and Subtraction

Week 25

Test 1

Week 26 to Week 37






 Age Problems
 Division
 Remainder Problems
 Chicken–and–rabbit Problems
 Multiples

Week 38 to Week 49






 Queuing and Overlapping Problems
 Pigeonhole Principle
 Make a List (2)
 Number Games
 IQ Maths

Week 50

Test 2

Worked Solutions (Week 1 to Week 50)


WEEK 1

Olympiad Maths Trainer 2
Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Complete each number pattern by filling in the blanks
with correct answers.


(a) 1, 2, 4, 5, 7, 8, (

), (

(b) 3, 4, 7, 12, 19, (



(c) 2, 3, 5, 8, 12, (

), (

), …



(d) 2, 3, 5, 8, 13, (

), (

), …

), (

), …
), …

2. A lesson starts at 8.10 am. It lasts for 1 hour 10 minutes.
At what time does the lesson end?

3. Given that A and B are two different single digit numbers,
find the values of A and B in each of the following.

(a)
A

(b)

A

× A

× B

4 B

3 A



A=(

)

A=(

)



B=(

)

B=(

)

Terry Chew

WEEK 1
page 1

1


4. Find the number of cubes in the figure below.

5. The sum of two numbers is 16. The difference between
the two numbers is 2. Find the two numbers.

Olympiad Maths Trainer 2

WEEK 1
page 2

2


WEEK 2

Olympiad Maths Trainer 2
Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Complete each number pattern by filling in the blanks
with correct answers.


(a) 2, 4, 7, 9, 12, (

), (



(b) 3, 6, 12, 24, 48, ( ), ( ), …



(c) 1, 1, 2, 3, 5, (



(d) 1, 2, 3, 6, 7, ( ), ( ), …

), (

), …

), …

2. The movie started at 2.10 pm. It finished at 3.50 pm.
How long was the movie?

3. Given that A and B are two different single digit numbers,
find the values of A and B in each of the following.


(a)
A

(b) A

× B

× 8

2 B

B

0

A=(

)

A=(

)



B=(

)

B=(

)

Terry Chew

WEEK 2
page 1

3


4. Find the number of cubes in the figure below.

5. Sarah has 80 more marbles than Polly. They have 400

marbles altogether. How many marbles does each of
them have?

Olympiad Maths Trainer 2

WEEK 2
page 2

4


WEEK 3

Olympiad Maths Trainer 2

Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Find the missing numbers.

3

7

4

8

5

5

6

6

7

9

2. What is the sum of all the numbers on the clock?

3. Given that A and B are two different single digit numbers,
find the values of A and B in each of the following.


B
(a)
A B 0
7 2

(b)

B
A 4 0
3 B



B
A=(

)

B
A=(

)



B=(

)

B=(

)

Terry Chew

WEEK 3
page 1

5


4. Find the number of cubes in the figure below.

5. Molly scores a total of 194 marks in two tests. The score
for the second test is 4 marks more than that of the first
test. How many marks does she score in each test?

Olympiad Maths Trainer 2

WEEK 3
page 2

6


WEEK 4

Olympiad Maths Trainer 2
Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Find the missing numbers.

9

6

15

9

3

5

6

4

4

9

9

5

7

3

2. Divide the clock below into halves by drawing a straight
line so that the sum of all the numbers for each part is
equal.

3. A, B, C and D represent 5, 6, 7 and 8, but not in that order.

If A × B = CD, find the values of A, B, C and D.


A=(

)

B=(

)



C=(

)

D=(

)

Terry Chew

WEEK 4
page 1

7


4. Find the number of cubes in the figure below.

5. Penny has 14 pencils. When she gives Jane 2 pencils,
both of them have the same number of pencils. How many
pencils does Jane have at first?

Olympiad Maths Trainer 2

WEEK 4
page 2

8


WEEK 5

Olympiad Maths Trainer 2

Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Complete each number pattern.


(a) 6, 3, 8, 5, 10, 7, ( ), ( ), …



(b) 1, 3, 9, 27, (



(c) 4, 5, 7, 11, 19, (



(d) 1, 4, 9, 16, 25, ( ), ( ), …

), (

), (

), (

), …
), …

2. Draw the minute and hour hands on the last clock.

3. Given that 2 × A = 8, A + B = 14


and B + B + C = 25, find the values of A, B and C.



A=(

Terry Chew

)

B=(

WEEK 5
page 1

)

C=(

)

9


4. Many small cubes are used to make a big cube as shown
below. The center of the big cube is hollow. Find the
total number of small cubes.

5. Jeffrey saves $300. His brother, James, saves $220.
How much money must Jeffrey give to his brother so
that both of them will have the same amount of money?

Olympiad Maths Trainer 2

WEEK 5
page 2

10


WEEK 6

Olympiad Maths Trainer 2
Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Find the missing numbers in the following Triangular
Number Pattern.
1
2

4

3
4
5
6

(

(
)

6
(
)
(

)
(
)

9
12
)

16
20

24

(

(
)

)
(

)

2. Draw the hour and minute hands on the third clock. Then
fill in each blank with the correct answer by finding the
difference in time.




( ) 2 h 45 min ( )

3. If a × b = 24,

b × c = 30,



c × d = 35,



find a + b + c + d.

Terry Chew

WEEK 6
page 1

11


4. Find the number of cubes in the figure below.

5. A strawberry and a peach weigh 120 g. The weight of
the peach is thrice that of the strawberry. How much
does each fruit weigh?

Olympiad Maths Trainer 2

WEEK 6
page 2

12


WEEK 7

Olympiad Maths Trainer 2

Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Find the missing numbers.
1

6

31

51

76

141

2. Sam can tell the time on each clock from the mirror. Can
you do so?

pm

am

3. A × B = 63


B × C = 42



A×B×C=(

Terry Chew

)

WEEK 7
page 1

13


4. Find the number of cubes in the figure below.

5. Two different cups weigh 320 g. The weight of the big cup
is thrice that of the smaller cup. How heavy is each cup?

Olympiad Maths Trainer 2

WEEK 7
page 2

14


WEEK 8

Olympiad Maths Trainer 2
Name:

Date:

Class:

Marks:

/20

Solve these questions. Show your working clearly. Each question
carries 4 marks.
1. Find the missing numbers.

4

3

13

9
6

5

10

18

7

2

2. By drawing two straight lines, divide the clock into three
parts so that the sum of all the numbers on each part is
the same.

3. Find the value of each letter.


A
(a)



A

(b)



A

B

A

B

+

A

+



6

1C A

9

A=(

)

A=(

)



B=(

)

C=(

)

WEEK 8


Terry
Chew
page 1

15


4. Find the number of cubes in the figure below.

5. Mrs Howard bought 24 oranges, apples and peaches
altogether. She bought 2 more apples than oranges.
There were 7 more peaches than oranges. How many

oranges, apples and peaches of each did she buy?

Olympiad Maths Trainer 2

WEEK 8
page 2

16