OLYMPIAD MATHS TRAINER 7 8 AGE

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 - (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 in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers ISBN: 978 - 604 - 77 - 2311 - 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  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 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  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 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) + + + + (b) + + + + 10 + 12 (c) + + + + + 11 + + + + + + + + + 10 (d) 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 Olympiad Maths Trainer - page hew Write the correct time for each clock (a) (b) (c) Chloe is years old Her brother is 12 years old How many years older is her brother than Chloe in 10 years’ time? Five trees are planted from end to end along a road The distance between every two trees is m How long is the road? 3m WEEK page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks The clock chimes once at o’clock, twice at o’clock, thrice at o’clock and so on How many times does the clock chime altogether in the first six hours? Complete each number pattern (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 Olympiad Maths Trainer - page Terry Ch hew Matthew’s mother is 34 years old Matthew is years old How many years older is his mother than Matthew? 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 page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Find the sum of each series by pairing two numbers that make up a sum of tens (a) + + + + + + (b) + + + + 15 + 16 + 17 + 18 (c) (d) 12 + 14 + 16 + 24 + 26 + 28 + + + + 13 + 15 + 17 + 19 + 20 Find the missing numbers 15 10 11 18 WEEK Olympiad Maths Trainer - page Terry Ch hew Given the time, draw the hour and minute hands on each clock (a) (b) 6.00 3.00 (c) 8.00 Sam is years old His sister is 10 years old How many years younger is Sam than his sister in years’ time? A seaman needs to tie 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 page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks 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 – + – (c) (d) 10 + – + – + – + – + + + + 10 – (1 + + + + 9) Find the missing numbers 23 35 12 24 25 33 14 22 10 WEEK Olympiad Maths Trainer - page 18 Terry Ch hew Given the time, draw the hour and minute hands on each clock (a) (b) (c) 6.30 9.15 8.40 Melissa is years old Mark is years old How old will Mark be when Melissa is 15 years old? 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 page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Use a simple method to solve the following (a) 63 – 61 + 59 – 57 + 55 – 53 + (b) 53 + 28 – 23 – 48 + 36 – 31 + (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 Olympiad Maths Trainer - page Terry Ch hew Can you tell the time for the 4th clock? 1st clock 2nd clock 3rd clock 4th clock Nicholas will be years younger than his sister in years’ time Nicholas is years old How old is his sister? matchsticks are lying neatly on a table There are marbles between every matchsticks How many marbles are there altogether? 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 sum of each series by pairing two numbers to make ten(s) (a) + + + + 10 + 12 + 14 + 16 + 20 (b) 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 (c) + + + + 18 + 19 + 20 (d) + + + + + 11 + 13 + 15 + 17 + 19 Find the missing numbers ? ? 27 15 WEEK Olympiad Maths Trainer - page Terry Ch hew Which clock is not working properly? Clock Clock Clock Michael’s cousin is 18 years old Michael is years old How many years older will his cousin be than Michael in years’ time? It takes minutes to saw a log into two pieces How long does it take to saw the same log into four pieces? WEEK page 12 WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks 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 ) 10 ( ) WEEK Olympiad Maths Trainer - page Terry Ch hew The reflection of a clock in the mirror is shown below What is the actual time? 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 There are trees from end to end along a road Each tree is m away from the other How long is the road? 3m WEEK page 14 WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries marks Distribute 15 sweets to five students in such a way that each of them gets a different number of sweets Find the missing numbers 20 2 10 10 A clock chimes once at o’clock, twice at o’clock, thrice at o’clock, … It also chimes once every half an hour How many times does the clock chime from to o’clock? WEEK Olympiad Maths Trainer - page Terry Ch hew Frederick is years old this year His father is 32 years old How old will Frederick be when his father is 38 years old? The entrance to the Chinese Garden are with 12 red lanterns There is a yellow lantern between every two red lanterns How many yellow lanterns are there altogether? WEEK page 16 [...]... Olympiad Maths Trainer 1 Name: Date: Class: Marks: /20 Solve these questions Show your working clearly Each question carries 4 marks 1 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 2 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... first (a) 24 – 22 + 20 – 18 + 16 – 14 + 12 – 10 (b) 24 – 21 + 18 – 15 + 12 – 9 + 6 – 3 (c) (d) 10 + 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 2 + 4 + 6 + 8 + 10 – (1 + 3 + 5 + 7 + 9) 2 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) (c) 6.30 9.15 8. 40 4 Melissa is 6 years old... 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. .. 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 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 2 Complete each number pattern (a) 6, 7, 9,... 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 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 2 Find the missing... 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 4 10 5 2 8 9 2 4 10 3 A clock chimes once at 1 o’clock, twice... 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 ... 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. .. 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