a word by the author -...

A Word by the AuthorRussian mathematicians have suggested that mathematics is gymnastics for the brain. Mathematics Olympiad is similarly practiced ferociously in China by a majority of the student population, all for a coveted place in one of the elite high schools.

Children who exhibit certain traits and penchant for numbers at the age of 5 or 6 years old, or even earlier, have great potential to be mathematical olympians among their peers – provided they are groomed via a systematic, rigorous and routinized training.

Singapore was ranked 3rd in Mathematics in a recent TIMSS (Trends in International Mathematics and Science Study) survey, after Hong Kong and Taiwan. Notably, China was not among the list of countries surveyed.

The most prestigious local competition is RIPMWC (Raffles Institution Primary Mathematics World Competition). Meant for primary 6 students or younger, the top 50 to 60 or so participants are selected from Round 1 to compete in Round 2. Thereafter, 6 top participants emerge to take part in the world competition for primary school mathematics in Hong Kong. Another popular competition, also for primary 6 students, is APMOPS (Asia Pacific Mathematical Olympiad for Primary Schools), which has been organized by Hwa Chong Institution since 1989. Awards are given at the end of two rounds of competition based on merit: Platinum, Gold, Silver and Bronze.

At the primary 5 level, the yearly NMOS (National Mathematical Olympiad of Singapore) competition has also captured the attention of parents, who eye NUS High as their preferred secondary school since 2006.

The first series of books Maths Olympiad: Unleash the Maths Olympian in You! published in 2007 and 2008, has served as an ideal companion to students looking to establish a strong foundation in mathematics – be it for PSLE preparation or in hope that they might one day take part in the various local and international competitions. The books are, therefore, also first-choice materials for parents of primary 3 students looking for quality content in gifted programme training.

In this edition, you will find the following new additions:• Simple Speed• Observation

The objective is to cater to increasingly intelligent children who have been exposed to a wide variety of topics. Some of these topics, which overlap with the local mathematics syllabus, have also been adopted by schools here for students to practice on.

I feel extremely privileged and honoured to be able to continue serving students in this field. My latest series Solve Exam-Type Mathematics Word Problems in 28 Essential Lessons is currently out on shelves.

For related courses and workshops, please visitterrychew.com.sg.

Terry Chew(2017)

Maths Olympiad (Junior 1).indb 2 12/7/2016 1:30:40 PM

ForewordOccasionally, in some difficult musical compositions there are beautiful,

but easy parts - parts so simple a beginner could play them. So it is with mathematics as well.

- Professor Sherman K. Stein -

Mathematical Olympiad is widely practised in some countries due to the following characteristics:

• the wide range of topics that link mathematics to most everyday events, • the witty and tricky nature of the problems that bring out the best in students’

thinking skills and creative imagination, • the ability to encourage students to use more than one method to solve the

problems, thus stimulating them to think outside the box, • and to equip them with abundant knowledge to devise their own methods in

problem-solving due to the extensive training and exposure.

This book consolidates the materials that I have used to teach my students over the years. Although the problems are of Mathematical Olympiad type, I believe all students can benefit by working on them. Built on and beyond the school syllabus, the importance of attitude and enthusiasm surpasses that of capability in learning Mathematical Olympiad.

Many children whom I have guided and their parents alike are mesmerized by the materials presented in this book.

I hope you and your child will be too!

Terry Chew(2008)


CONTENTS

Chapter 1 Tell Me the Time! ---------------------------------------------------------------------- 1

Chapter 2 Problems from Planting Trees – Intervals ----------------------------------------- 10

Chapter 3 Addition -------------------------------------------------------------------------------- 20

Chapter 4 Solve by Comparison and Replacement ------------------------------------------- 26

Chapter 5 Age Problems -------------------------------------------------------------------------- 35

Chapter 6 Division -------------------------------------------------------------------------------- 44

Chapter 7 Chicken-and-Rabbit Problems ------------------------------------------------------ 55

Chapter 8 Looking for a Pattern ----------------------------------------------------------------- 64

Chapter 9 Counting -------------------------------------------------------------------------------- 72

Chapter 10 Logic ------------------------------------------------------------------------------------ 80

Chapter 11 Make a List, Make a Table ----------------------------------------------------------- 88

Chapter 12 Using Model --------------------------------------------------------------------------- 97

Chapter 13 In Search of a Series ---------------------------------------------------------------- 105

Chapter 14 What Comes Next? ------------------------------------------------------------------117

Chapter 15 IQ Maths ----------------------------------------------------------------------------- 124

Chapter 16 Geometry ----------------------------------------------------------------------------- 132

Chapter 17 Odd and Even Numbers ------------------------------------------------------------ 141

Chapter 18 Queuing Problems ------------------------------------------------------------------ 148

Chapter 19 Working Backwards ---------------------------------------------------------------- 154

Chapter 20 Pigeonhole Principle ---------------------------------------------------------------- 161

Chapter 21 Simple Speed ------------------------------------------------------------------------ 167

Chapter 22 Observation -------------------------------------------------------------------------- 174

SOLUTIONS ------------------------------------------------------------------------------------S1 - S26


1Chapter 1

Maths Olympiad – Unleash The Maths Olympian In You! (Junior 1)© Singapore Asia Publishers Pte Ltd & Terry Chew

Tell Me the Time!1

1 For each clock, write the correct time on the line provided. (a) 12 111

10

9

87 6 5

4

3

2

(b) 12 11110

9

87 6 5

4

3

2

(c) 12 11110

9

87 6 5

4

3

2

pm am pm

Solution: (a) 7.10 (b) 10.30 (c) 1.30


10

9

87 6 5

4

3

2

(b) 12 11110

9

87 6 5

4

3

2

(c) 12 11110

9

87 6 5

4

3

2

pm am pm

Solution: (a) 12.20 (b) 3.45 (c) 10.10

EXAMPLES


2Chapter 1


3 A concert started at 8.30 pm and ended at 10.15 pm. How long did the concert last?

Solution: From 8.30 pm to 9.30 pm → 1 hour From 9.30 pm to 10.30 pm → 1 hour 1 hour + 1 hour = 2 hours 2 hours – 15 minutes = 1 hour and 45 minutes The concert lasted 1 hour and 45 minutes.

4 Trains arrive at a subway station every 5 minutes. How many trains would have arrived at the subway station in 30 minutes?

Solution:

0 5 10 15 20 25 30

1st 2nd 3rd 4th 5th 6th 7th

minutes

trains

7 trains would have arrived at the subway station in 30 minutes.

5 The clocks below are images in the mirror. Write the correct time on the lines provided. (a) 12

• ••

•

••••

•

•

•

(b) 12• •

•

•

••••

•

•

•

am pm

Solution: (a) 7.10 (b) 2.30


3Chapter 1


PRACTICE


10

9

87 6 5

4

3

2

(b) 12 11110

9

87 6 5

4

3

2

(c) 12 11110

9

87 6 5

4

3

2

am pm am

(d) 12 11110

9

87 6 5

4

3

2

(e) 12 11110

9

87 6 5

4

3

2

(f) 12 11110

9

87 6 5

4

3

2

pm am pm

2 Draw the hour and minute hands on the face of each clock to show the correct time. Write the correct time on the lines provided.

(a) 25 minutes later

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

2 pm pm

(b) 40 minutes ago

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

5.45 pm pm


4Chapter 1


3 A movie started at 2.30 pm and ended at 4.05 pm. How long was the movie?

4 The signboard shown on the right is placed outside a shop. For how many hours is the shop open daily?

Business Hours11 am — 9.30 pm


5Chapter 1


5 Carl attended a birthday party. The time that the birthday party started and ended are shown on the two clocks below.

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

starting time ending time How long did the birthday party last?

6 Benson played for 10 minutes after reaching home. He watched television for another 20 minutes before taking his lunch. His lunch, which lasted for 20 minutes, was finished at 2.50 pm. At what time did Benson reach home?


6Chapter 1


7 In the pattern below, draw the hour and minute hands on the face of each clock. Write down the correct time on the lines provided.

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

7.20 am 8.10 am 8.50 am

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

am am

8 Buses arrived at a bus stop every 15 minutes. Lincoln needed to board the bus at 8.30 am but he was late for 8 minutes. At what time did Lincoln arrive at the bus stop? How long did he have to wait for the next bus?


S�Maths Olympiad – Unleash The Maths Olympian In You! (Junior 1)© Singapore Asia Publishers Pte Ltd & Terry Chew

1CHAPTERCHAPTER

Chapter 1

1. (a) 7.15 (b) 2.45 (c) 4.55 (d) 10.40 (e) 5.50 (f) 6.15

2. (a) 12 11110

9

87 6 5

4

3

2

(b) 12 11110

9

87 6 5

4

3

2

2.25 5.05

3. 2.30 pm to 3.30 pm → 1 hour 3.30 pm to 4.00 pm → half an hour

or 30 minutes 4.00 pm to 4.05 pm → 5 minutes 1 hour + 30 minutes + 5 minutes = 1 hour 35 minutes The movie was 1 hour and 35 minutes.

4. 11.00 am to 12.00 pm → 1 hour 12.00 pm to 9.00 pm → 9 hours 9.00 pm to 9.30 pm → half an hour

or 30 minutes 1 hour + 9 hours + 30 minutes = 10 hours and 30 minutes The shop is open for 10 hours 30 minutes daily.

5. 2.30 pm to 5.30 pm → 3 hours 5.30 pm to 5.45 pm → 15 minutes 3 hours + 15 minutes = 3 hours 15 minutes The birthday party lasted 3 hours 15 minutes.

6. 10 minutes + 20 minutes + 20 minutes = 50 minutes 50 minutes before 2.50 pm is 2 pm. Benson reached home at 2 pm.

7. 7.20 am to 8.10 am → 50 minutes 8.10 am to 8.50 am → 40 minutes 8.50 am to 9.20 am → 30 minutes 9.20 am to 9.40 am → 20 minutes

12 11110

9

87 6 5

4

3

2

12 11110

9

87 6 5

4

3

2

9.20 9.40

8. 8 minutes after 8.30 am is 8.38 am. Lincoln arrived at the bus stop at 8.38 am.

15 minutes after 8.30 am is 8.45 am. From 8.38 am to 8.45 am → 7 minutes. He had to wait another 7 minutes for the next bus.

9. (a) 2.50 (b) 8.15 (c) 7.30 (d) 5.45

10. 40 minutes after 6.30 am → 7.10 am 40 minutes after 7.10 am → 7.50 am The third train would leave at 7.50 am.

11. Method 1

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th

0 6 12 18 24 30 36 42 48 54 60trainsminutes

Method 2 60 ÷ 6 = 10 10 + 1 = 11 11 trains would have arrived at the subway station

in 60 minutes.

12. 1st coach → 5.00 am 2nd coach → 6.30 am 3rd coach → 8.00 am 4th coach → 9.30 am The fourth coach leaves the station at 9.30 am.

13. 1 + 2 + 3 + 4 + 5 + 6

777

7 × 3 = 21 It would have chimed 21 times by 6 o’clock.

14. starting time → 2 pm ending time → 5.40 pm Her birthday party was 3 hours and 40 minutes

long.


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