Olympiad Maths Trainer 4

Olympiad Maths Trainer là bộ sách bài tập Toán gồm 6 cuốn, dành cho học sinh từ 7 13 tuổi. Bộ sách được biên soạn bởi Terry Chew – thầy giáo có nhiều năm kinh nghiệm trong việc ôn luyện cho học sinh tham gia các kỳ thi Toán quốc tế và là tác giả nổi tiếng tại Singapore. Ông luôn hướng tới việc tìm kiếm giải pháp để giải quyết các bài toán khó một cách đơn giản và hiệu quả nhất. Các cuốn sách sẽ cung cấp bài tập thực hành cho các dạng toán khác nhau đã được giới thiệu trong bộ sách đầu tiên của tác giả là bộ “Đánh thức Tài năng Toán học” (Unleash the Maths Olympian in You).

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Terry Chew B Sc

THẾ GIỚI PUBLISHERS

410- 11 years old 10- 11 ye y arsr oldd

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in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers.

ISBN: 978 - 604 - 77 - 2314 - 0

Printed in Viet Nam

Bản quyền tiếng Việt thuộc về Công ty Cổ phần Giáo dục Sivina, xuất bản theo hợp đồng chuyển nhượng bản quyền giữa Singapore Asia Publishers Pte Ltd và Công ty Cổ phần Giáo dục Sivina 2016.

Bản quyền tác phẩm đã được bảo hộ, mọi hình thức xuất bản, sao chụp, phân phối dưới dạng in ấn, văn bản điện tử, đặc biệt là phát tán trên mạng internet mà không được sự cho phép của đơn vị nắm giữ bản quyền

là hành vi vi phạm bản quyền và làm tổn hại tới lợi ích của tác giả và đơn vị đang nắm giữ bản quyền Không ủng hộ những hành vi vi phạm bản quyền Chỉ mua bán bản in hợp pháp.

ĐƠN VỊ PHÁT HÀNH:

Công ty Cổ phần Giáo dục Sivina

Địa chỉ: Số 1, Ngõ 814, Đường Láng, Phường Láng Thượng, Quận Đống Đa, TP Hà Nội

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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 solving techniques with other students, parents and teachers

problem-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 4

FOREWORD

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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

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Week 1 to Week 9

 The Four Operations

 Looking for a Pattern

 Sequence with a Common Difference  Other Operations

 Using Models for Sum or Difference

 Catching up

 The Principle of Addition

 The Principle of Multiplication

 Problems from Planting Trees

 Journey of the Train

Week 25 Test 1

CONTENTS

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 Encountering

 Age Problems

 Solve By Replacement and Comparison

 Problem from Page Number

 Solve Using Tables or Drawings

 Perimeter of Square and Rectangle

 Observation and Induction

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Terry Chew 1

page 1WEEK 1

Solve these questions Show your working clearly Each question carries 4 marks.

1 Use a simple method to calculate each of the following.

3 Determine whether each of the following sequences has a

common difference Find the common difference if there is State the first and last terms of each sequence

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Olympiad Maths Trainer - 4 2

page 2WEEK 1

5 There are a total of 660 passengers on two ships 30 passengers

alight from Ship A and 70 passengers board Ship B As a result, the number of passengers on the two ships becomes the same How many passengers are there on each ship at first?

6 A car and a bicycle depart from Town A and Town B respectively

at the same time

The bicycle moves at 35 km/h and the car moves at 75 km/h How far is Town B from Town A if the car catches up with the bicycle three hours later?

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Terry Chew 3

page 1WEEK 2

4557

Name: Date:

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page 2

4 If a b = 6 × a – 3 × b, evaluate

5 Aloysius and Benjamin have $150 altogether Aloysius’ mother

gives him another $40 and Benjamin spends $10 on a book Benjamin then has $10 more than Aloysius How much money does each of them have at first?

6 A hound spotted its prey at a distance of 50 m away It started

to run towards its prey at a speed of 12 m/s but its prey could only run at a speed of 7 m/s How long did the hound take to catch up with its prey?

WEEK 2

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Terry Chew 5

page 1WEEK 3

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page 2

4 If 3  4 = 3 + 4 + 5 + 6 = 18 and 7  3 = 7 + 8 + 9 = 24,

5 There are 120 books altogether on a bookshelf The top shelf

holds 11 more books than the middle one The bottom shelf holds 5 books fewer than the middle one How many books are there on each shelf?

6 The side of a square building is 10 m long A cat at Point A begins

to chase a rat spotted at Point B and they run around the building The cat runs at a speed of 2 m/s and the rat runs at a speed of 1 m/s How soon will the cat catch up with the rat?

10 m

A

BWEEK 3

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5 If a student is transferred from Class 3A to Class 3B, the two

classes will have the same number of students If a student is transferred from Class 3B to Class 3C, Class 3C will have two more students than Class 3B Between Class 3A and Class 3C, which class has more students?

6 A fish swims past a kingfisher at a speed of 1 m/s The fish is 4

m away from the kingfisher when the kingfisher gives chase and catches it in 2 seconds At what speed is the kingfisher gliding?

WEEK 4

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Terry Chew 9

page 1WEEK 5

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page 2

4 If a U b = a × b – a + b, evaluate

$360 in all Tom and Catherine have $240 altogether How much does each of them have?

6 Mark and Nigel were jogging along a circular track They started

their jog from the same place and at the same time Mark jogged

at a speed of 220 m/min and Nigel jogged at a speed of 180 m/min What was the circumference of the track if Mark caught up with Nigel in 30 minutes?

MarkNigel

WEEK 5

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Terry Chew 11

page 1WEEK 6

1 Use distributive law to calculate each of the following.

Find the sum of the three numbers in the 100th term

3 Find the sum of all multiples of 5 from 5 to 200.

Name: Date:

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page 2

4 If a  b = a × b – (a + b), evaluate

5 Some PE teachers bought a total of 83 balls for the school The

number of basketballs is twice the number of footballs The number of volleyballs is 5 less than the number of footballs How many balls of each type did the teachers buy?

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Terry Chew 13

page 1WEEK 7

2 Observe the number pattern below:

16, 23, 28, 38, 49, ···

What is the 6th term?

3 Find the sum of all multiples of 7 between 100 and 200.

Name: Date:

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page 2

4 If a  b = a + (a + 1) + (a + 2) + ··· + (a + b), evaluate

5 A family has four members The father is 2 years older than the

mother The sister is 2 years older than the brother The sum of all their present ages is 64 Three years ago, the sum of their ages was 53 How old is each of them now?

6 Betty and Celine were jogging along a circular track surrounding

a lake The track measured 640 m If they started from the same place and jogged in the same direction, Betty would take 16 minutes to catch up with Celine If they jogged in the opposite direction, they would meet every 4 minutes How long did Betty take to jog one round of the track?

WEEK 7

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Terry Chew 15

page 1WEEK 8

1 Use a simple method to calculate 99 999 × 12 345.

2 Observe the number pattern below:

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page 2

4 If m  n = m + (m – 1) + (m – 2) + ··· + (m – n), evaluate

5 In the figure below, the big square is made up of a small square

and four identical rectangles The area of the big square is 196

cm2 The area of the small square is 36 cm2 What is the width

of each rectangle?

6 A train takes 27 s to cross a bridge 420 m long It takes 30 s to

pass through a tunnel 480 m long at the same speed

(a) What is the speed of the train?

(b) What is the length of the train?

36 cm2

WEEK 8

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