Terry Chew B. Sc
8
–
7
years o
ld
1
THẾ GIỚI PUBLISHERS
OLYMPIAD MATHS TRAINER - 1
(7-8 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 - 2311 - 9
Printed in Viet Nam
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Olympiad Maths TraineR 1
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 1
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 1
CONTENTS
Week 1 to Week 12
 Addition
 Number Patterns
 Tell me the Time!
 Age Problems
 Intervals
Week 13 to Week 24
 Solve by Comparison
 Make a List
 Number Puzzles (1)
 Logic
 Counting
Week 25
Test 1
Week 26 to Week 37
 Counting Money
 Queuing Problems
 Number Puzzles (2)
 Odd and Even Numbers
 Remainder Problems
Week 38 to Week 49
 Multiples and Halves
 Length
 IQ Maths 1
 Number Games
 IQ Maths 2
Week 50
Test 2
Worked Solutions (Week 1 to Week 50)
WEEK 1
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question carries
4 marks.
1.
2.
Find the sum of each series by pairing the first number with
the last one, the second number with the second last one and
so on.
(a)
1 + 2 + 3 + 4 + 5
(b)
2 + 4 + 6 + 8 + 10 + 12
(c)
1 + 3 + 5 + 7 + 9 + 11
(d)
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
Complete each number pattern below.
(a)
1, 3, 5, 7, (
), (
(b)
1, 4, (
), 10, 13, (
(c)
3, 6, (
), (
(d)
1, 2, 4, 8, (
), ...
), ...
), 15, 18, ...
), 32, ...
WEEK 1
Olympiad Maths Trainer - 1
page 2
hew
3.
Write the correct time for each clock.
(a)
(b)
(c)
4.
Chloe is 4 years old. Her brother is 12 years old. How many
years older is her brother than Chloe in 10 years’ time?
5.
Five trees are planted from end to end along a road. The
distance between every two trees is 3 m. How long is the
road?
3m
WEEK 1
page 1
2
WEEK 2
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
The
clock
chimes
once
at
1
o’clock,
twice
at
2
o’clock,
thrice
at
3
o’clock
and so on. How many times does the clock chime
altogether in the first six hours?
2.
Complete each number pattern.
3.
(a)
2, 3, 5, 8, 13, (
), ...
(b)
1, 2, 4, 7, (
(c)
1, 6, 7, 12, 13, (
(d)
1, 1, 2, 3, 5, (
), (
), ...
), (
), (
), ...
), ...
Write the correct time for each clock.
(a)
(b)
(c)
WEEK 2
Olympiad Maths Trainer - 1
page 2
Terry Ch
hew
4.
Matthew’s mother is 34 years old. Matthew is 7 years
old. How many years older is his mother than Matthew?
5.
Jeffrey’s house is on the 3rd floor of an apartment. The
staircase between every floor has a flight of 12 steps. How
many steps must Jeffrey climb in order to reach home?
WEEK 2
page 1
4
WEEK 3
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
2.
Find the sum of each series by pairing two numbers that
make up a sum of tens.
(a)
2 + 3 + 4 + 5 + 6 + 7 + 8
(b)
2 + 3 + 4 + 5 + 15 + 16 + 17 + 18
(c)
1 + 3 + 5 + 7 + 13 + 15 + 17 + 19 + 20
(d)
12 + 14 + 16 + 24 + 26 + 28
Find the missing numbers.
15
5
10
11
7
4
9
18
4
6
WEEK 3
Olympiad Maths Trainer - 1
page 2
Terry Ch
hew
3.
Given the time, draw the hour and minute hands on
each clock.
(a)
(b)
6.00
3.00
(c)
8.00
4.
Sam is 7 years old. His sister is 10 years old. How many
years younger is Sam than his sister in 5 years’ time?
5.
A seaman needs to tie 6 ropes together to make a long
rope. How many knots are there altogether? Assume
both ends of the long rope are not tied together.
WEEK 3
page 1
6
WEEK 4
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
2.
Compute the sum of each series by finding the difference
in each pair first.
(a)
24 – 22 + 20 – 18 + 16 – 14 + 12 – 10
(b)
24 – 21 + 18 – 15 + 12 – 9 + 6 – 3
(c)
2 + 4 + 6 + 8 + 10 – (1 + 3 + 5 + 7 + 9)
(d)
10 + 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8
Find the missing numbers.
23
35
12
24
25
33
14
22
10
WEEK 4
Olympiad Maths Trainer - 1
page 2
18
Terry Ch
hew
3.
Given the time, draw the hour and minute hands on
each clock.
(a)
(b)
6.30
(c)
9.15
8.40
4.
Melissa is 6 years old. Mark is 9 years old. How old will
Mark be when Melissa is 15 years old?
5.
There are 15 lamp posts along a road. There is a tree
between every two lamp posts. How many trees are
there along the road?
WEEK 4
page 1
8
WEEK 5
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
2.
Use a simple method to solve the following.
(a)
63 – 61 + 59 – 57 + 55 – 53 + 4
(b)
53 + 28 – 23 – 48 + 36 – 31 + 5
(c)
40 + 52 – 48 + 46 – 42 + 40 – 36
(d)
50 + 12 – 10 + 16 – 14 + 20 – 18 + 24 – 22
Complete each number pattern.
(a)
6, 7, 9, 12, 16, (
(b)
2, 4, (
(c)
10, 11, 13, (
(d)
2, 3, 5, (
), (
), (
), 34, ...
), 10, 12, ...
), 20, (
), 13, 21, (
), 31, ...
), ...
WEEK 5
Olympiad Maths Trainer - 1
page 2
Terry Ch
hew
3.
Can you tell the time for the 4th clock?
1st clock
2nd clock
3rd clock
4th clock
4.
Nicholas will be 3 years younger than his sister in 5 years’
time. Nicholas is 9 years old. How old is his sister?
5.
8 matchsticks are lying neatly on a table. There are
2 marbles between every 2 matchsticks. How many
marbles are there altogether?
WEEK 5
page 1
10
WEEK 6
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
2.
Find the sum of each series by pairing two numbers to
make ten(s).
(a)
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 20
(b)
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29
(c)
1 + 2 + 3 + ... + 18 + 19 + 20
(d)
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
Find the missing numbers.
?
5
9
?
4
27
15
6
WEEK 6
Olympiad Maths Trainer - 1
page 2
Terry Ch
hew
3.
Which clock is not working properly?
Clock 1
Clock 2
Clock 3
4.
Michael’s cousin is 18 years old. Michael is 7 years old.
How many years older will his cousin be than Michael in
5 years’ time?
5.
It takes 5 minutes to saw a log into two pieces. How long
does it take to saw the same log into four pieces?
WEEK 6
page 1
12
WEEK 7
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
2.
Use a simple method to find the sum of the following.
(a)
18 + 82 + 40
(b)
29 + 71 + 83 + 17
(c)
24 + 76 + 54 + 43 + 57 + 46
(d)
12 + 13 + 24 + 27 + 26 + 28
Find the missing numbers.
1
1
1
1
1
3
4
(
1
3
1
1
2
)
1
6
10
4
(
)
1
5
WEEK 7
Olympiad Maths Trainer - 1
page 2
1
Terry Ch
hew
3.
The reflection of a clock in the mirror is shown below.
What is the actual time?
4.
Sarah says to her mother, “You will be 25 years older
than me in three years’ time.“ Sarah’s mother replies,
“How many years younger were you than me five years
ago?” Help Sarah answer her mother’s question.
5.
There are 9 trees from end to end along a road. Each tree
is 3 m away from the other. How long is the road?
3m
WEEK 7
page 1
14
WEEK 8
Olympiad Maths Trainer 1
Name:
Date:
Class:
Marks:
/20
Solve these questions. Show your working clearly. Each question
carries 4 marks.
1.
Distribute 15 sweets to five students in such a way that
each of them gets a different number of sweets.
2.
Find the missing numbers.
20
6
7
2
2
3.
4
10
5
2
8
9
2
4
10
A clock chimes once at 1 o’clock, twice at 2 o’clock, thrice at
3 o’clock, …. It also chimes once every half an hour. How
many times does the clock chime from 1 to 4 o’clock?
WEEK 8
Olympiad Maths Trainer - 1
page 2
Terry Ch
hew
4.
Frederick is 6 years old this year. His father is 32
years old. How old will Frederick be when his father is
38 years old?
5.
The entrance to the Chinese Garden are hung with 12 red
lanterns. There is a yellow lantern between every two red
lanterns. How many yellow lanterns are there altogether?
WEEK 8
page 1
16