Olympiad Maths Trainer 3

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).

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

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

ISBN: 978 - 604 - 77 - 2313 - 3

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

Olympiad Maths TraineR 3

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 3

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

 Solve Differences and Sums

 Solve Problems on Multiples

2 Draw the next pattern.

3 It takes 5 minutes to fry a pancake One side of the

pancake takes 3 minutes to fry and the other side takes only 2 minutes Two pancakes can be placed on the frying pan at a time What is the shortest time to fry all five pancakes?

Olympiad Maths Trainer 3 2

4 How many different ways are there for Eton to go to the

library if he can only take the routes indicated by the arrows?

5 Among William, Sarah and Hayden, only one of them

watched the movie ‘Harry Potter and the Order of the Phoenix’ When Jane asked the three friends about the

movie, they gave her the following answers

William: Sarah watched the movie already.

Sarah: I haven’t got a chance to watch it.

Hayden: Maybe I will watch it next week.

Only one of them told the truth Who had watched the movie?

Lie Truth William

Sarah

Hayden

If Sarah had watched the movie,

Lie Truth William

Sarah Hayden

If Hayden had watched the movie,

Eton

library

page 2 WEEK 1

2 Draw the missing pattern in the box below.

3 All the Primary 3 students at Russels Elementary School

subscribe to at least one magazine

150 students subscribe to Wildlife.

208 students subscribe to A-Star Maths.

88 students subscribe to both magazines.

How many Primary 3 students are there at Russels Elementary School?

Olympiad Maths Trainer 3 4

4 In the figure below, each letter is connected to another

by a straight line How many different ways are there to form the word “FORTUNE”? A straight line must connect two letters at all times

5 The prince has hidden the princess’ diamond ring in one of

the three jewellery boxes Each box is labelled as follows:

Box A: The ring is not in here.

Box B: This box is empty.

Box C: The ring is in Box A.

Only one jewellery box has the correct label Help the princess to find the ring

If the ring is in A, If the ring is in B,

Right Wrong A

B

C

Right Wrong A

B C

If the ring is in C,

Right Wrong A

B

C

6 Compute each of the following using a simple method (a) 1 + 2 + 3 + 4 + ··· + 9 + 10

page 2 WEEK 2

2 Draw the missing pattern in the box below.

3 Lina’s granny rears a hen that lays an egg every day She

then cooks 2 eggs for Lina every morning On 1st May, her granny has collected 20 eggs How long can the eggs last them?

Olympiad Maths Trainer 3 6

Alice has never been to Canada.

Beatrice was not born in Canada, and neither was she born

2 Draw the missing pattern in the box below.

3 Wilfred bought a terrier at a price of $200 He then sold it for $250 He later bought it back at a price of $280 and then sold it for $330 How much did Wilfred make in all?

Olympiad Maths Trainer 3 8

4 In the figure below, each letter is connected to another

by a straight line How many different ways are there

to form the word “COMPUTE”? Each straight line must connect two letters

5 Each of three boxes contains either two red, one blue and

one red, or two blue balls The following shows the labels

on the three boxes

Box A: Two red balls

Box B: Two blue balls

Box C: One blue and one red balls

All the boxes have been wrongly labelled George is able

to rectify the situation by picking out a ball from one of the boxes Explain how George is able to do that

6 Compute each of the following using a simple method (a) 1 + 2 + 3 + 4 + ··· + 49 + 50

page 2 WEEK 4

3 Alicia took 5 days to finish reading a book Her sister

took 8 days to finish reading the same book If Alicia were to read 15 pages more than her sister every day, what was the total pages of the book?

Olympiad Maths Trainer 3 10

Mary is older than the violinist.

David and the writer are not of the same age.

The writer is younger than Julie.

Olympiad Maths Trainer 3 12

4 How many different ways are there for the construction

worker to go to Site A if he must avoid the dangerous Site B? Assume he can go → and ↓ only

5 Complete the number pattern below.

6 Compute each of the following using a simple method (a) 100 – 99 + 98 – 97 + 96 – 95 + ··· + 50 – 49

(b) 1 + 2 + 3 + 4 + ··· + 99 + 100

(c) 200 – 196 + 192 – 188 + 184 – 180 + ··· + 128 – 124

26 2

42 2

4 110 6 178 10 16

A B

page 2 WEEK 6

Olympiad Maths Trainer 3 14

4 A spider lies in ambush for the ant as shown below How

many different ways are there for the ant to reach home safely? Assume the ant can only move in the directions

Sun Mon Tue Wed Thu Fri Sat

6 A theatre has 15 rows of seats The first row has 10

seats The second row has 3 more seats than the first row The third row has 3 more seats than the second row and so on How many seats are there altogether in the theatre?

home

page 2 WEEK 7

Terry Chew 15

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

1 Six events were held at an exhibition hall A visitor could walk from one event hall to another by passing through the doors as shown in the figure below Show how a visitor could visit all the six events by passing through each door exactly once

2 Shade the third pattern correctly

3 Anne and Betty want to buy a book Anne is short of 50¢ and Betty is short of $4.50 When they pool their money, the total amount is still not enough to buy the book How much is the book? Assume 10¢ is the smallest unit

Hall A Hall B Hall C Hall E Hall D

Olympiad Maths Trainer 3 16

4 How many different ways are there to go from A to B if only movements in the directions of → and ↑ are allowed?

5 Megan, Nikita, Patsy and Stella live on the second, third, fourth and fifth floors of a six-storey apartment, but not

in this order Their professions are artist, pianist, engineer and sales executive

Megan lives on the floor higher than that of Nikita but

lower than that of Patsy.

Stella lives on the fifth floor.

The sales executive lives one floor above the engineer but one floor lower than the pianist.

The artist lives on the lowest floor.

Find out their professions and the floor where each of them lives

6 The sum of eight consecutive odd numbers is 192 Find the last number of the sequence

A

B

page 2 WEEK 8