Tài liệu Olympiad Maths Trainer 2

Terry Chew B. Sc 9 – 8 years o ld 2 THẾ GIỚI PUBLISHERS OLYMPIAD MATHS TRAINER - 2 (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 - 6 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 2 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 2 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 2 CONTENTS Week 1 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 1 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 2 Worked Solutions (Week 1 to Week 50) WEEK 1 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 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, ( ), ( ), … ), ( ), … ), … 2. A lesson starts at 8.10 am. It lasts for 1 hour 10 minutes. At what time does the lesson end? 3. 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 4 B 3 A A=( ) A=( ) B=( ) B=( ) Terry Chew WEEK 1 page 1 1 4. Find the number of cubes in the figure below. 5. The sum of two numbers is 16. The difference between the two numbers is 2. Find the two numbers. Olympiad Maths Trainer 2 WEEK 1 page 2 2 WEEK 2 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 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, ( ), ( ), … ), ( ), … ), … 2. The movie started at 2.10 pm. It finished at 3.50 pm. How long was the movie? 3. 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 × 8 2 B B 0 A=( ) A=( ) B=( ) B=( ) Terry Chew WEEK 2 page 1 3 4. Find the number of cubes in the figure below. 5. Sarah has 80 more marbles than Polly. They have 400 marbles altogether. How many marbles does each of them have? Olympiad Maths Trainer 2 WEEK 2 page 2 4 WEEK 3 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. 3 7 4 8 5 5 6 6 7 9 2. What is the sum of all the numbers on the clock? 3. 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 0 7 2 (b) B A 4 0 3 B B A=( ) B A=( ) B=( ) B=( ) Terry Chew WEEK 3 page 1 5 4. Find the number of cubes in the figure below. 5. Molly scores a total of 194 marks in two tests. The score for the second test is 4 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 all the numbers for each part is equal. 3. A, B, C and D represent 5, 6, 7 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 4 page 1 7 4. Find the number of cubes in the figure below. 5. Penny has 14 pencils. 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, 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 shown below. The center of the big cube is hollow. Find the total number of small cubes. 5. 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 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 ) 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 peach is thrice that of the 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 4. Find the number of cubes in the 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 the clock into three parts so that the sum of all the numbers on each part is the same. 3. Find the value of each letter. A (a) A (b) A B A B + A + 6 1 C A 9 A=( ) A=( ) B=( ) C=( ) WEEK 8 Terry Chew page 1 15