9 - 10 years old 9

Transcription

9 - 10 years old 9

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
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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
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
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
WEEK 1
page 2
2
WEEK 2
Name:
Date: Class:
Marks: /24
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
(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
WEEK 2
page 2
4
WEEK 3
Name:
Date: Class:
Marks: /24
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.
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
(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
WEEK 3
page 2
6
WEEK 4
Name:
Date: Class:
Marks: /24
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.
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.
(a) 1 + 2 + 3 + 4 + ··· + 49 + 50
(b) 2 + 4 + 6 + 8 + ··· + 48 + 50
(c) 1 + 3 + 5 + 7 + ··· + 47 + 49
WEEK 4
page 2
8
WEEK 5
Name:
Date: Class:
Marks: /24
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.
WEEK 5
page 2
10
WEEK 6
Name:
Date: Class:
Marks: /24
carries 4 marks.
1. Part of a recreation park has the following path.
Show how a jogger can cover the whole path exactly once.
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
(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
WEEK 6
page 2
12
WEEK 7
Name:
Date: Class:
Marks: /24
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?
WEEK 7
page 2
14
WEEK 8
Name:
Date: Class:
Marks: /24
carries 4 marks.
1. Six events were held at an exhibition hall. A visitor could
walk from one event hall to another by passing through
the doors as shown in the figure below. Show how a
visitor could visit all the six events by passing through
each door exactly once.
Hall F
Hall E
Hall A
Hall D
Hall B
Hall C
2. Shade the third pattern correctly.
3. Anne and Betty want to buy a book. Anne is short of 50¢
and Betty is short of $4.50. When they pool their money,
the total amount is still not enough to buy the book. How
much is the book? Assume 10¢ is the smallest unit.
Terry Chew
WEEK 8
page 1
15
4. How many different ways are there to go from A to B if
only movements in the directions of → and ↑ are allowed?
B
A
5. Megan, Nikita, Patsy and Stella live on the second, third,
fourth and fifth floors of a six-storey apartment, but not
in this order. Their professions are artist, pianist, engineer
and sales executive.
Megan lives on the floor higher than that of Nikita but
lower than that of Patsy.
Stella lives on the fifth floor.
The sales executive lives one floor above the engineer
but one floor lower than the pianist.
The artist lives on the lowest floor.
Find out their professions and the floor where each of
them lives.
6. The sum of eight consecutive odd numbers is 192. Find
the last number of the sequence.
WEEK 8
page 2
16

9 - 10 years old 9

Transcription

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