Tài liệu Olympiad Maths Trainer 3

Terry Chew B. Sc 3 THẾ GIỚI PUBLISHERS d 10 years o l 9 OLYMPIAD MATHS TRAINER - 3 (9-10 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 - 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 Điện thoại: (04) 8582 5555 Hotline: 097 991 9926 Website: http://lantabra.vn http://hocgioitoan.com.vn 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 Olympiad Maths TraineR 3 CONTENTS Week 1 to Week 9  Konigsberg Bridge Problems  Geometric Patterns  IQ Maths  Solve using the Shortest Route  Logic  The Story of Gauss Week 10 to Week 18  Solve Differences and Sums  Solve Problems on Multiples  Age Problems  Working Backwards  Counting  Looking for a Pattern Week 19 to Week 24  Tricks in Multiplication  Problems from Planting Trees  Number Puzzles  Page–number Problems Week 25 Test 1 Week 26 to Week 34  Tricks in Addition and Subtraction  Catching up  Encountering  Finding Perimeter  Excess–and–Shortage Problems  Pigeonhole Principle Week 35 to Week 43  Chicken–and–Rabbit Problems  Solve By Replacement  Make a List or Table  Solve By Comparison  Geometry  Cryptarithm Week 44 to Week 49  Remainder Problems  Time  Average Problems  Areas of Square and Rectangle Week 50 Test 2 Worked Solutions (Week 1 - Week 50) Olympiad Maths Trainer 3 WEEK 1 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. Are you able to trace the figure below without lifting your fingers off the paper? You are not allowed to trace any line segments more than once. 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? Terry Chew WEEK 1 page 1 1 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? Eton library 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? If William had watched the movie, Lie If Sarah had watched the movie, Truth William Sarah Hayden Lie Truth William Sarah Hayden If Hayden had watched the movie, Lie Truth William Sarah Hayden 6. Compute each of the following using a simple method. (a) 1 + 2 + 3 + 4 + 5 + 6 (b) 2 + 4 + 6 + 8 + 10 + 12 (c) 3 + 5 + 7 + 9 + 11 + 13 (d) 3 + 8 + 13 + 18 + 23 + 28 Olympiad Maths Trainer 3 WEEK 1 page 2 2 Olympiad Maths Trainer 3 WEEK 2 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. Are you able to trace the figure below without lifting your fingers off the paper? You are not allowed to trace any line segments more than once. 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? Terry Chew WEEK 2 page 1 3 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. T R U O T N F R U E O T N R U T 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, Right Wrong A B C Right Wrong A B C If the ring is in C, Right If the ring is in B, Wrong A B C 6. Compute each of the following using a simple method. (a) 1 + 2 + 3 + 4 + ··· + 9 + 10 (b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 (c) 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 (d) 11 + 12 + 13 + ··· + 19 + 20 Olympiad Maths Trainer 3 WEEK 2 page 2 4 Olympiad Maths Trainer 3 WEEK 3 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. Is it possible to trace the figure below without lifting your fingers off the paper? You are not allowed to trace any line segments more than once. 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? Terry Chew WEEK 3 page 1 5 4. How many different ways are there for the car to travel to the city? Assume the car could only travel in the direction of South or East city 5. Alice, Beatrice and Charlene were born in Canada, Korea and Thailand, but not in that order. Alice has never been to Canada. Beatrice was not born in Canada, and neither was she born in Thailand. Find their places of birth. Canada Korea Thailand Alice Beatrice Charlene 6. Compute each of the following using a simple method. (a) 1 + 2 + 3 + 4 + ··· + 19 + 20 (b) 1 + 3 + 5 + 7 + ··· + 17 + 19 (c) 2 + 4 + 6 + 8 + ··· + 18 + 20 (d) 21 + 22 + 23 + 24 + ··· + 39 + 40 Olympiad Maths Trainer 3 WEEK 3 page 2 6 Olympiad Maths Trainer 3 WEEK 4 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. Is it possible to trace the figure below without lifting your fingers off the paper? You are not allowed to trace any line segments more than once. 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? Terry Chew WEEK 4 page 1 7 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. P M U O P T C M U E O P T M U P 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 (b) 2 + 4 + 6 + 8 + ··· + 48 + 50 (c) 1 + 3 + 5 + 7 + ··· + 47 + 49 Olympiad Maths Trainer 3 WEEK 4 page 2 8 WEEK 5 Olympiad Maths Trainer 3 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. A rat is trapped in a small maze. Help the rat to find its way, provided it must pass through each door exactly once. 2. What is the next pattern?       ? 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? Terry Chew WEEK 5 page 1 9 4. How many different ways are there for the ant to return home? Assume it could only travel towards the north and east. home 5. David, Julie and Mary are designer, writer and violinist, but not in this order. Mary is older than the violinist. David and the writer are not of the same age. The writer is younger than Julie. Find their jobs. Designer Writer Violinist David Julie Mary 6. The sum of six consecutive numbers is 123. Find the first number of this sequence. Olympiad Maths Trainer 3 WEEK 5 page 2 10 Olympiad Maths Trainer 3 WEEK 6 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. Part of a recreation park has the following path. Show how a jogger can cover the whole path exactly once. 2. Draw the missing pattern in the box below. 3. Andrew, Bryan and Charlie each draws two cards from a stack of cards numbered 1 to 8. One of Bryan’s cards has a number twice of the other. The sum of the numbers on Charlie’s cards is 9. The sum of the numbers on Andrew’s cards is 7 but the difference is not 3. Which two cards are not drawn? Terry Chew WEEK 6 page 1 11 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. B A 5. Complete the number pattern below. 16 26 2 42 2 10 178 6 110 4 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 Olympiad Maths Trainer 3 WEEK 6 page 2 12 WEEK 7 Olympiad Maths Trainer 3 Name: Date: Class: Marks: /24 Solve these questions. Show your working clearly. Each question carries 4 marks. 1. There are two small islands in the middle of a river. Seven bridges are built to link the islands to the river banks as shown below. river bank river island island river bank Show how a visitor can cross all the seven bridges exactly once. 2. What is the next pattern? ? 2 page 1 3 4 WEEK 7 1 Terry Chew 3 2 6 5 4 3. What number is opposite each number? 13 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 of → and ↑. home 5. Many years ago, the number of Saturdays was more than that of Fridays in a particular month. Similarly, the number of Sundays was more than that of Mondays. On which day of the week was the eleventh day in that month? 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? Olympiad Maths Trainer 3 WEEK 7 page 2 14