Tài liệu Olympiad Maths Trainer 1

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 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 - 9 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 Điện thoại: (04) 8582 5555 Hotline: 097 991 9926 Website: http://lantabra.vn http://hocgioitoan.com.vn 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. 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 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 (d) 2. 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. (a) 2, 3, 5, 8, 13, ( ), ... (b) 1, 2, 4, 7, ( (c) 1, 6, 7, 12, 13, ( ), ( (d) 1, 1, 2, 3, 5, ( ), ... ), ( ), ( ), ... ), ... 3. 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. 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) (d) 12 + 14 + 16 + 24 + 26 + 28 1 + 3 + 5 + 7 + 13 + 15 + 17 + 19 + 20 2. 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. 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) (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. 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. 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, 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. 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 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. 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 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 4 10 5 2 8 9 2 4 10 3. 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