TRAINING BOOK SAMPLE - Five Senses Education...MATHEMATICAL OLYMPIAD TRAINING BOOK LEVEL 2 (8 9...
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MATHEMATICAL OLYMPIAD TRAINING BOOK LEVEL 2 (8–9 years) Terry Chew Master trainer at Terry Chew Academy and Co-Founder/Academic Director of Name: Class: SAMPLE
Transcript of TRAINING BOOK SAMPLE - Five Senses Education...MATHEMATICAL OLYMPIAD TRAINING BOOK LEVEL 2 (8 9...
MATHEMATICALOLYMPIADTRAINING BOOK
LEVEL 2(8–9 years)
Terry ChewMaster trainer at Terry Chew Academy and Co-Founder/Academic Director of
Name:
Class:
Title Page_Mathematical Olympiad Training Book L2.pdf 1 31/1/2019 12:07:21 PM
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ALL RIGHTS RESERVEDAll 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-13 978-981-32-1749-2ISBN-10 981-32-1749-9
Printed in Singapore
Mathematical Olympiad Training Book Level 2
First Edition 2019
© Singapore Asia Publishers Pte Ltd and Terry Chew
Published and Distributed by: Singapore Asia Publishers Pte Ltd219 Henderson Road #10-04 Henderson Industrial Park Singapore 159556 Tel : +65 6276 8280 Fax : +65 6276 8292 Email: [email protected]: www.sapgrp.comFacebook: Singapore-Asia-Publishers
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00 Copyright_A Mathematical Olympiad Prep Book L2.indd 1 2019/7/10 10:12:14
Printed under licence in Australia by Five Senses Education Pty Ltd
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Mathematical Olympiad Training Book Level 2© Singapore Asia Publishers Pte Ltd and Terry Chew
1. Completeeachnumberpatternbelow. (a) �,2,4,5,7,8,(),(),… (b) 3,4,7,�2,�9,(),(),… (c) 2,3,5,8,�2,(),(),… (d) 2,3,5,8,�3,(),(),…
2. A lesson starts at 8.�0 am. It lasts for�hour�0minutes.Atwhattimedoesthelessonend?
3. GiventhatAandBaretwodifferentsingledigit numbers, find the values of A and B ineachofthefollowing.
(a)
A=()
B=()
(b)
A=()
B=()
4. Find the number of cubes in the figure below.
A
× A
4 B
A
× A
4 B
A
× B
3 A
A
× B
3 A
5. The sum of two numbers is �6. Thedifferencebetweenthetwonumbersis2.Findthetwonumbers.
6. Completeeachnumberpatternbelow. (a) 2,4,7,9,�2,(),(),… (b) 3,6,�2,24,48,(),(),… (c) �,�,2,3,5,(),(),… (d) �,2,3,6,7,(),(),…
7. The movie started at 2.10 pm. It finished at3.50pm.Howlongwasthemovie?
8. GiventhatAandBaretwodifferentsingledigit numbers, find the values of A and B ineachofthefollowing.
(a)
A=()
B=()
(b)
A=()
B=()
A
× B
2 B
A
× B
2 B
A
× 8
B 0
A
× 8
B 0
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9. Find the number of cubes in the figure below.
10.Sarah has 80 more marbles than Polly.Theyhave400marblesaltogether.Howmanymarblesdoeseachofthemhave?
11. Findthemissingnumbers.
12.Whatisthesumofallthenumbersontheclock?
13.GiventhatAandBaretwodifferentsingledigit numbers, find the values of A and B ineachofthefollowing.
(a) (b)
A=() A=() B=() B=()
3 7
5 5
7 94 8
6 6
3 7
5 5
7 94 8
6 6
14. Find the number of cubes in the figure below.
15.Mollyscoresatotalof�94marksintwotests. The score for the second test is4 marks more than that of the first test. Howmanymarksdoesshescoreineachtest?
16.Findthemissingnumbers.
17.Divide the clock below into halves bydrawingastraightlinesothatthesumofallthenumbersforeachpartisequal.
18.A,B,CandDrepresent5,6,7and8,butnotinthatorder.
If A × B = CD, find the values of A, B, C andD.
A=() B=() C=() D=()
9 6
3 5
�5 9
6 4
9
4 5
9
7 3
9 6
3 5
�5 9
6 4
9
4 5
9
7 3
B
B 0 7 2
B
A
B
4 0 3 B
B
A
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19. Find the number of cubes in the figure below.
20.Penny has �4 pencils. When she givesJane 2 pencils, both of them have thesame number of pencils. How manypencils does Jane have at first?
21.Completeeachnumberpattern. (a) 6,3,8,5,�0,7,(),(),… (b) �,3,9,27,(),(),(),
… (c) 4,5,7,��,�9,(),(),… (d) �,4,9,�6,25,(),(),…
22.Drawtheminuteandhourhandson thelastclock.
23.Giventhat2×A=8,A+B=�4andB + B + C = 25, find the values of A, B andC.
A=() B=() C=()
24.Manysmallcubesareusedtomakeabigcubeasshownbelow.Thecentreofthebigcubeishollow.Findthetotalnumberofsmallcubes.
25.Jeffreysaves$300.Hisbrother,James,saves $220. How much money mustJeffrey give to his brother so that bothof them will have the same amount ofmoney?
26.FindthemissingnumbersinthefollowingTriangularNumberPattern.
27.Drawthehourandminutehandson thethird clock. Then find the difference in timeandwritethecorrectanswers.
() 2h45min ()
�
2 43 96
4 �6�25 ()20
6 24 ()()() ()() ()
()
�
2 43 96
4 �6�25 ()20
6 24 ()()() ()() ()
()
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28.Ifa×b=24, b×c=30, c×d=35, find a + b + c + d.
29. Find the number of cubes in the figure below.
30.Astrawberryandapeachweigh�20g.Theweightofthepeachisthricethatofthestrawberry.Howmuchdoeseachfruitweigh?
31.Findthemissingnumbers.
� 6 3� 5� 76 �4�
32.Samcantellthetimeoneachclockfromthemirror.Canyoudoso?
pm am
33.A×B=63 B×C=42 A×B×C=()
34. Find the number of cubes in the figure below.
35.Two different cups weigh 320 g. Theweightofthebiggercupisfourtimesthatoftheother.Howheavyiseachcup?
36.Findthemissingnumbers.
37.Bydrawingtwostraight lines,dividetheclockintothreepartssothatthesumofallthenumbersoneachpartisthesame.
38.Findthevalueofeachletter. (a) (b)
A=() A=() B=() C=()
4�33 6
9�85
�0
7 2
4�33 6
9�85
�0
7 2
A A
+ A
9 6
A B
+ A B
� C A
A A
+ A
9 6
A B
+ A B
� C A
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Mathematical Olympiad Training Book Level 2© Singapore Asia Publishers Pte Ltd and Terry Chew
7.
From2.�0pmto3.�0pm,itis�h. From3.�0pmto3.50pm,itis40min. Themoviewasfor1 h 40 minlong.
8. (a) Sincetheproductislessthan30,thepossiblevaluesofAandBare6and4respectively.
A×B=2B 6×4=24 A=6andB=4 (b) A×8=B0 5×8=40 A=5andB=4
9.
8cubes3cubes�cube Numberofcubes=8+3+�=12
10.
400–80=320 320÷2=�60 Pollyhas160marbles. �60+80=240 Sarahhas240marbles.
11.3+7= �0 =5+5
4+8= �2 =6+6
7+9= �6 =8+8
12.�+2+3+4+5+6+...+��+�2
�3�3
Thereare6pairsof�3. 6�3=78 Thesumofallthenumbersontheclockis78.
13.(a) (b)
A=9 A=7 B=8 B=5
14.
5cubes3cubes2cubes
Numberofcubes=5+3+2=10
2.�0pm 3.�0pm 3.50pm
??
2.�0pm 3.�0pm 3.50pm
??
400Sarah
Polly
80
?
?400
Sarah
Polly
80
?
?
7 9
8 8
7 9
8 8
8
8 0
7 2
8
9 5
4 0
3 5
5
7
8
8 0
7 2
8
9 5
4 0
3 5
5
7
1. (a) �,2,4,5,7,8,(10),(11),... +�+2+� +2 +� +2 +�
(b) 3,4,7,�2,�9,(28),(39),... +� +3 +5 +7 +9 +��
(c) 2,3,5,8,�2,(17),(23),... +� +2 +3 +4 +5 +6
(d)
2,3,5,8,�3,(21),(34),...
+ + +
+ +
2.
�hafter8.�0amis9.�0am. �0minafter9.�0amis9.20am. Thelessonendsat9.20 am.
3. (a) Aismultipliedbyitselftogiveanumbergreaterthan40.
Since7×7=49, A=7andB=9. (b) Since A and B are different �-digit numbers
andtheirproductislessthan40,thepossiblevaluesofAandBare5and7respectively.
A×B=3A 5×7=35 A=5andB=7
4.
9cubes 3cubes Numberofcubes=9+3=12
5.
�6–2=�4 �4÷2=7 Thesmallernumberis7. 7+2=9 Thegreaternumberis9.
6. (a) 2,4,7,9,�2,(14),(17),... +2 +3 +2 +3 +2 +3
(b) 3,6,�2,24,48,(96),(192),... ×2 ×2 ×2 ×2 ×2 ×2
(c)
�,�,2,3,5,(8),(13),...
++
+++
(d) �,2,3,6,7,(14),(15),... +�×2+�×2+�×2
8.�0am 9.�0am
�h
?
�0min
8.�0am 9.�0am
�h
?
�0min
�6smallernumber
greaternumber 2
?
?�6
smallernumber
greaternumber 2
?
?
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