Olympiad Maths Trainer 4

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).

Terry Chew B Sc THẾ GIỚI PUBLISHERS d years o l 10 OLYMPIAD MATHS TRAINER - (10-11 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 - 2314 - 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 problemsolving 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  The Four Operations  Looking for a Pattern  Sequence with a Common Difference  Other Operations  Using Models for Sum or Difference  Catching up Week 10 to Week 18  The Principle of Addition  The Principle of Multiplication  Solve By Assuming  Excess and Shortage Problems  Counting  Using Models for Multiplication Week 19 to Week 24  Permutation  Combination  Problems from Planting Trees  Journey of the Train Week 25 Test Week 26 to Week 34  Encountering  Age Problems  Solve By Replacement and Comparison  Problem from Page Number  Working Backwards  Remainder Problems Week 35 to Week 43  Logic  Number Games  Solve Using Tables or Drawings  Perimeter of Square and Rectangle  Observation and Induction  Venn Diagram Week 44 to Week 49  Average  Geometry  Maximum and Minimum  Pigeonhole Principle Week 50 Test Worked Solutions (Week - Week 50) WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate each of the following (a) 376 + 285 + 124 + 715 (b) 81 + 79 + 82 + 83 + 88 (c) 173 + 123 + 877 + 327 (d) 169 + 171 + 173 + 172 + 167 Complete each number pattern (a) 2, 4, 8, 16, ( ), ( ), ( ), ··· (b) 1, 4, 9, 16, ( ), ( ), ( ), ··· (c) 1, 1, 2, 3, 5, ( (d) 2, 1, 4, 3, 6, 5, ( ), ( ), ( ), ( ), ··· ), ··· Determine whether each of the following sequences has a common difference Find the common difference if there is State the first and last terms of each sequence (a) 5, 10, 15, 20, 25, 30, 35 (b) 1, 4, 7, 10, 13, 16, 19 Terry Chew WEEK page 1 (c) 1, 4, 9, 16, 25, 36, 49 (d) 2, 4, 6, 8, 10, 12, 14 If a  b = (a + b) ÷ 2, evaluate (a) 3  7, (b) 4  (8  4) There are a total of 660 passengers on two ships 30 passengers alight from Ship A and 70 passengers board Ship B As a result, the number of passengers on the two ships becomes the same How many passengers are there on each ship at first? A car and a bicycle depart from Town A and Town B respectively at the same time Town A Town B The bicycle moves at 35 km/h and the car moves at 75 km/h How far is Town B from Town A if the car catches up with the bicycle three hours later? Olympiad Maths Trainer - WEEK page 2 Olympiad Maths Trainer WEEK Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate each of the following (a) 395 + + 197 + + 298 + 397 (b) 9998 + + 99 + 997 + + (c) 9898 + 302 + 779 + 331 (d) 5678 + 543 + 123 + 477 Find the missing numbers 15 27 45 37 57 Evaluate + + + ··· + 49 Terry Chew WEEK page If a b = × a – × b, evaluate (a) 4 (b) (5 5, 3) 20 Aloysius and Benjamin have $150 altogether Aloysius’ mother gives him another $40 and Benjamin spends $10 on a book Benjamin then has $10 more than Aloysius How much money does each of them have at first? A hound spotted its prey at a distance of 50 m away It started to run towards its prey at a speed of 12 m/s but its prey could only run at a speed of m/s How long did the hound take to catch up with its prey? Olympiad Maths Trainer - WEEK page Olympiad Maths Trainer WEEK Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate each of the following (a) 563 – 328 + 98 + 528 (b) 725 – 213 – 312 + 465 (c) 854 – (512 + 154) + 612 (d) 785 – (285 – 634) – 234 Find the missing numbers 30 29 19 Compute + + + + ··· + 98 + 100 Terry Chew WEEK page If  = + + + = 18 and  = + + = 24, (a) evaluate 2004  (b) Find the value of n when 95  n = 686 There are 120 books altogether on a bookshelf The top shelf holds 11 more books than the middle one The bottom shelf holds books fewer than the middle one How many books are there on each shelf? A The side of a square building is 10 m long A cat at Point A begins to chase a rat spotted at Point B and they run around the building The cat runs at a speed of m/s and the rat runs at a speed of m/s How soon will the cat catch up with the rat? 10 m B Olympiad Maths Trainer - WEEK page WEEK Olympiad Maths Trainer Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate each of the following (a) 77 × ÷ 11 (b) 96 × ÷ 12 (c) 65 × ÷ 13 (d) 120 × ÷ 15 Find the missing number in each of the following (a) 12 24 20 16 26 28 16 12 34 18 (b) Terry Chew WEEK page Compute + + + ··· + 99 + 100 If a b = the remainder when a ÷ b, evaluate (a) 2008 2007, (b) 2010 (2000 300) If a student is transferred from Class 3A to Class 3B, the two classes will have the same number of students If a student is transferred from Class 3B to Class 3C, Class 3C will have two more students than Class 3B Between Class 3A and Class 3C, which class has more students? A fish swims past a kingfisher at a speed of m/s The fish is m away from the kingfisher when the kingfisher gives chase and catches it in seconds At what speed is the kingfisher gliding? Olympiad Maths Trainer - WEEK page Olympiad Maths Trainer WEEK Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate each of the following (a) + 99 + 999 + 9999 + 99 999 (b) 28 + 298 + 2998 + 29 998 + 299 998 Observe the number pattern below: 3 ​ , ​  3 ​ , ​  1 ​ , ​  1 ​ , ​  2 ​ , ​  1 ​ , ​  2 ​ , ​  1 ​ , ​  2 ​ , ​  4 ​ , ​  2 3 4 4 ··· What fraction is the 35th term? Compute + + 11 + ··· + 95 + 99 Terry Chew WEEK page If a U b = a × b – a + b, evaluate (a) 2 U 4, (b) 3 U 5 Catherine and Molly have $320 altogether Molly and Tom have $360 in all Tom and Catherine have $240 altogether How much does each of them have? Mark and Nigel were jogging along a circular track They started their jog from the same place and at the same time Mark jogged at a speed of 220 m/min and Nigel jogged at a speed of 180 m/ What was the circumference of the track if Mark caught up with Nigel in 30 minutes? Mark Nigel Olympiad Maths Trainer - WEEK page 10 Olympiad Maths Trainer WEEK Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use distributive law to calculate each of the following (a) 42 × 34 + 58 × 34 (b) 37 × 54 + 63 × 54 (c) 156 × 32 – 56 × 32 (d) 233 × 46 – 133 × 46 The first three terms of a three-number pattern are (1, 3, 6), (2, 6, 9) and (3, 9, 12) Find the sum of the three numbers in the 100th term Find the sum of all multiples of from to 200 Terry Chew WEEK page 11 If a  b = a × b – (a + b), evaluate (a) 5  6, (b) 8  (3  4) Some PE teachers bought a total of 83 balls for the school The number of basketballs is twice the number of footballs The number of volleyballs is less than the number of footballs How many balls of each type did the teachers buy? start end 1200 m A train, which is 200 m long, travels at a speed of 20 m/s How long does it take to pass a bridge that is 1200 m long? Olympiad Maths Trainer - WEEK page 12 Olympiad Maths Trainer WEEK Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate each of the following (a) 999 × 222 + 333 × 334 (b) 999 × 778 + 333 × 666 Observe the number pattern below: 16, 23, 28, 38, 49, ··· What is the 6th term? Find the sum of all multiples of between 100 and 200 Terry Chew WEEK page 13 If a  b = a + (a + 1) + (a + 2) + ··· + (a + b), evaluate (a) 3  8, (b) 8  A family has four members The father is years older than the mother The sister is years older than the brother The sum of all their present ages is 64 Three years ago, the sum of their ages was 53 How old is each of them now? Betty and Celine were jogging along a circular track surrounding a lake The track measured 640 m If they started from the same place and jogged in the same direction, Betty would take 16 minutes to catch up with Celine If they jogged in the opposite direction, they would meet every minutes How long did Betty take to jog one round of the track? Olympiad Maths Trainer - WEEK page 14 Olympiad Maths Trainer WEEK Name: Date: Class: Marks: /24 Solve these questions Show your working clearly Each question carries marks Use a simple method to calculate 99 999 × 12 345 Observe the number pattern below: 121, 12 321, 234 321, 123 454 321, ··· What number is the 5th term? Compute + + + ··· + 49 + 50 + 49 + ···+ + + Terry Chew WEEK page 15 If m  n = m + (m – 1) + (m – 2) + ··· + (m – n), evaluate (a) 7  5, (b) m when m  = 20 In the figure below, the big square is made up of a small square and four identical rectangles The area of the big square is 196 cm2 The area of the small square is 36 cm2 What is the width of each rectangle? 36 cm2 A train takes 27 s to cross a bridge 420 m long It takes 30 s to pass through a tunnel 480 m long at the same speed (a) What is the speed of the train? (b) What is the length of the train? Olympiad Maths Trainer - WEEK page 16 [...]... Nigel in 30 minutes? Mark Nigel Olympiad Maths Trainer - 4 WEEK 5 page 2 10 Olympiad Maths Trainer 4 WEEK 6 Name: Date: Class: Marks: / 24 Solve these questions Show your working clearly Each question carries 4 marks 1 Use distributive law to calculate each of the following (a) 42 × 34 + 58 × 34 (b) 37 × 54 + 63 × 54 (c) 156 × 32 – 56 × 32 (d) 233 × 46 – 133 × 46 2 The first three terms of a three-number... m B Olympiad Maths Trainer - 4 WEEK 3 page 2 6 WEEK 4 Olympiad Maths Trainer 4 Name: Date: Class: Marks: / 24 Solve these questions Show your working clearly Each question carries 4 marks 1 Use a simple method to calculate each of the following (a) 77 × 6 ÷ 11 (b) 96 × 9 ÷ 12 (c) 65 × 7 ÷ 13 (d) 120 × 8 ÷ 15 2 Find the missing number in each of the following (a) 12 8 24 20 16 26 28 8 16 12 34 9.. .Olympiad Maths Trainer 4 WEEK 3 Name: Date: Class: Marks: / 24 Solve these questions Show your working clearly Each question carries 4 marks 1 Use a simple method to calculate each of the following (a) 563 – 328 + 98 + 528 (b) 725 – 213 – 312 + 46 5 (c) 8 54 – (512 + 1 54) + 612 (d) 785 – (285 – 6 34) – 2 34 2 Find the missing numbers 9 4 30 7 6 5 29 8 3 19 3 Compute 2 + 4 + 6 + 8 + ···... past a kingfisher at a speed of 1 m/s The fish is 4 m away from the kingfisher when the kingfisher gives chase and catches it in 2 seconds At what speed is the kingfisher gliding? Olympiad Maths Trainer - 4 WEEK 4 page 2 8 Olympiad Maths Trainer 4 WEEK 5 Name: Date: Class: Marks: / 24 Solve these questions Show your working clearly Each question carries 4 marks 1 Use a simple method to calculate each... bridge that is 1200 m long? Olympiad Maths Trainer - 4 WEEK 6 page 2 12 Olympiad Maths Trainer 4 WEEK 7 Name: Date: Class: Marks: / 24 Solve these questions Show your working clearly Each question carries 4 marks 1 Use a simple method to calculate each of the following (a) 999 × 222 + 333 × 3 34 (b) 999 × 778 + 333 × 666 2 Observe the number pattern below: 16, 23, 28, 38, 49 , ··· What is the 6th term?... The track measured 640 m If they started from the same place and jogged in the same direction, Betty would take 16 minutes to catch up with Celine If they jogged in the opposite direction, they would meet every 4 minutes How long did Betty take to jog one round of the track? Olympiad Maths Trainer - 4 WEEK 7 page 2 14 Olympiad Maths Trainer 4 WEEK 8 Name: Date: Class: Marks: / 24 Solve these questions... clearly Each question carries 4 marks 1 Use a simple method to calculate 99 999 × 12 345 2 Observe the number pattern below: 121, 12 321, 1 2 34 321, 123 45 4 321, ··· What number is the 5th term? 3 Compute 1 + 2 + 3 + ··· + 49 + 50 + 49 + ···+ 3 + 2 + 1 Terry Chew WEEK 8 page 1 15 4 If m  n = m + (m – 1) + (m – 2) + ··· + (m – n), evaluate (a) 7  5, (b) m when m  4 = 20 5 In the figure below,... 1 ​ , ​  2 ​ , ​  1 ​ , ​  2 ​ , ​  1 ​ , ​  2 ​ , ​  4 ​ , ​  1 2 2 3 3 3 4 4 4 4 ··· What fraction is the 35th term? 3 Compute 3 + 7 + 11 + ··· + 95 + 99 Terry Chew WEEK 5 page 1 9 4 If a U b = a × b – a + b, evaluate (a) 2 U 4, (b) 3 U 5 5 Catherine and Molly have $320 altogether Molly and Tom have $360 in all Tom and Catherine have $ 240 altogether How much does each of them have? 6 Mark and... + 1 54) + 612 (d) 785 – (285 – 6 34) – 2 34 2 Find the missing numbers 9 4 30 7 6 5 29 8 3 19 3 Compute 2 + 4 + 6 + 8 + ··· + 98 + 100 Terry Chew WEEK 3 page 1 5 4 If 3  4 = 3 + 4 + 5 + 6 = 18 and 7  3 = 7 + 8 + 9 = 24, (a) evaluate 20 04  4 (b) Find the value of n when 95  n = 686 5 There are 120 books altogether on a bookshelf The top shelf holds 11 more books than the middle one The bottom shelf... of the small square is 36 cm2 What is the width of each rectangle? 36 cm2 6 A train takes 27 s to cross a bridge 42 0 m long It takes 30 s to pass through a tunnel 48 0 m long at the same speed (a) What is the speed of the train? (b) What is the length of the train? Olympiad Maths Trainer - 4 WEEK 8 page 2 16