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). Trong hai cuốn đầu tiên của bộ sách này, học sinh sẽ được giới thiệu 5 dạng toán trong 12 tuần. Sau đó, các em có thể áp dụng các kỹ năng tư duy khác nhau để giải từng dạng toán. Bốn cuốn sách còn lại bao gồm 6 dạng toán. Theo đó, bộ sách sẽ mở ra trước mắt các em một thế giới toán học giúp kích thích khả năng sáng tạo để giải các bài toán thách thức tư duy. Ngoài ra, với 2 bài test trong mỗi cuốn sách còn giúp các em tự hệ thống lại toàn bộ kiến thức đã học, cũng như sử dụng chính kiến thức này để giải quyết các dạng toán hóc búa đó.
Terry Chew B Sc – years o ld THẾ GIỚI PUBLISHERS OLYMPIAD MATHS TRAINER - (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 in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers ISBN: 978 - 604 - 77 - 2312 - Printed in Viet Nam Bản quyền tiếng Việt thuộc Công ty Cổ phần Giáo dục Sivina, xuất theo hợp đồng chuyển nhượng quyền Singapore Asia Publishers Pte Ltd Công ty Cổ phần Giáo dục Sivina 2016 Bản quyền tác phẩm bảo hộ, hình thức xuất bản, chụp, phân phối dạng in ấn, văn điện tử, đặc biệt phát tán mạng internet mà không cho phép đơn vị nắm giữ quyền hành vi vi phạm quyền làm tổn hại tới lợi ích tác giả đơn vị nắm giữ quyền Không ủng hộ hành vi vi phạm quyền Chỉ mua bán 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 Điện thoại: (04) 8582 5555 Hotline: 097 991 9926 Website: http://lantabra.vn http://hocgioitoan.com.vn Olympiad Maths TraineR 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 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 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 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 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 CONTENTS Week 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 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 Worked Solutions (Week to Week 50) WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks 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, ( ), ( ), … ), ( ), … ), … A lesson starts at 8.10 am It lasts for hour 10 minutes At what time does the lesson end? 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 B A A=( ) A=( ) B=( ) B=( ) Terry Chew WEEK page 1 Find the number of cubes in the figure below The sum of two numbers is 16 The difference between the two numbers is Find the two numbers Olympiad Maths Trainer WEEK page 2 WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks 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, ( ), ( ), … ), ( ), … ), … The movie started at 2.10 pm It finished at 3.50 pm How long was the movie? 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 × B B A=( ) A=( ) B=( ) B=( ) Terry Chew WEEK page Find the number of cubes in the figure below Sarah has 80 more marbles than Polly They have 400 marbles altogether How many marbles does each of them have? Olympiad Maths Trainer WEEK page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Find the missing numbers 5 6 What is the sum of all the numbers on the clock? 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 (b) B A B B A=( ) B A=( ) B=( ) B=( ) Terry Chew WEEK page Find the number of cubes in the figure below Molly scores a total of 194 marks in two tests The score for the second test is marks more than that of the first test How many marks does she score in each test? Olympiad Maths Trainer WEEK page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Find the missing numbers 15 4 9 Divide the clock below into halves by drawing a straight line so that the sum of all the numbers for each part is equal A, B, C and D represent 5, 6, 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 page Find the number of cubes in the figure below Penny has 14 pencils When she gives Jane pencils, both of them have the same number of pencils How many pencils does Jane have at first? Olympiad Maths Trainer WEEK page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks 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, ( ), ( ), … ), ( ), ( ), ( ), … ), … Draw the minute and hour hands on the last clock Given that × A = 8, A + B = 14 and B + B + C = 25, find the values of A, B and C A=( Terry Chew ) B=( WEEK page ) C=( ) 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 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 WEEK page 10 WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Find the missing numbers in the following Triangular Number Pattern 4 ( ( ) ( ) ( ) ( ) 12 ) 16 20 24 ( ( ) ) ( ) 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 ( ) h 45 ( ) If a × b = 24, b × c = 30, c × d = 35, find a + b + c + d Terry Chew WEEK page 11 Find the number of cubes in the figure below 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 WEEK page 12 WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Find the missing numbers 31 51 76 141 Sam can tell the time on each clock from the mirror Can you so? pm am A × B = 63 B × C = 42 A×B×C=( Terry Chew ) WEEK page 13 Find the number of cubes in the figure below 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 WEEK page 14 WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Find the missing numbers 13 10 18 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 Find the value of each letter A (a) A (b) A B A B + A + 1 C A A=( ) A=( ) B=( ) C=( ) WEEK Terry Chew page 15 Find the number of cubes in the figure below Mrs Howard bought 24 oranges, apples and peaches altogether She bought more apples than oranges There were more peaches than oranges How many oranges, apples and peaches of each did she buy? Olympiad Maths Trainer WEEK page 16 [...]... $22 0 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. .. 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... 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... 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,... 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... 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 ... 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... 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