Solve EXAM-TYPE - SAP Education

PrimaryPrimary

in 28 Essential Lessons

EXAM-TYPEWORD PROBLEMS

Solve

Mathematics

Terry Chew B.Sc.

Coach and author of the celebrated series Maths Olympiad — Unleash The Maths Olympian In You! and Maths Olympiad — The Next Lap

EXAM-TYPEWORD PROBLEMS

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M

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CM

MY

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CMY

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Title Page_Solve EXAM-TYPE Maths P3.pdf 1 17/8/2018 12:01:42 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-13 978-981-32-1570-2 ISBN-10 981-32-1570-4

Printed in Singapore

For international business enquiries, email [email protected]

SAP Global Partners’ Network:

www.sapgrp.com

Solve Exam-Type Mathematics Word Problemsin 28 Essential Lessons Primary 3

First Edition 2018

© Singapore Asia Publishers Pte Ltd & 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_Solve Exam-Type Math P3.indd 1 17/8/2018 12:23:07 PM

Printed under licence in Australia by Five Senses Education Pty Ltd

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Contents

Lesson 1 Chicken and Rabbit ..................................................................................................... 1

How to Solve a Mathematical Problem .......................................................................... 10

Lesson 2 Excess and Shortage ................................................................................................ 13

Creativity ................................................................................................................... 24

Lesson 3 Geometric Pattern ..................................................................................................... 27

How to Cut a Pizza ..................................................................................................... 38

Lesson 4 Interval......................................................................................................................... 39

Shapes ....................................................................................................................... 48

Lesson 5 Age .............................................................................................................................. 51

Factors and Multiples .................................................................................................. 58

Lesson 6 Using Model (1) .......................................................................................................... 59

Pascal’s Triangle ........................................................................................................ 66


Sieve of Eratosthenes .................................................................................................. 76


Square Numbers ......................................................................................................... 84

Lesson 9 Number Pattern .......................................................................................................... 85

So Much to Say About 9 ............................................................................................... 94

Lesson 10 Replacement Method ................................................................................................ 95

The Arithmetic of Powers ............................................................................................ 102

Lesson 11 Remainder Problem ................................................................................................ 103

Palindromes and Number Symmetry ........................................................................... 114

Lesson 12 Money (1) .................................................................................................................. 115

The Magic of BODMAS .............................................................................................. 122

Lesson 13 Money (2) .................................................................................................................. 125

The Shortest Path Method .......................................................................................... 132

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Lesson 14 Time (1) ..................................................................................................................... 133

River-Crossing Problem ............................................................................................. 140

Lesson 15 Time (2) ..................................................................................................................... 141

Two Number Puzzles ................................................................................................. 148

Lesson 16 Bar Graph ................................................................................................................. 149

The Buffet Problem .................................................................................................... 160

Lesson 17 Fraction (1) – Number Line .................................................................................... 161

Chinese Remainder Problem ...................................................................................... 168

Lesson 18 Fraction (2) – Ordering the Fractions ................................................................... 169

Counterfeit Coin Problem ........................................................................................... 178

Lesson 19 Fraction (3) – Word Problems ................................................................................ 179

Imagination ............................................................................................................... 186

Lesson 20 Measurement – Volume .......................................................................................... 189

The 1089 Puzzle ........................................................................................................ 198

Lesson 21 Measurement – Mass ............................................................................................. 199

Clock and Angle ........................................................................................................ 208

Lesson 22 Measurement – Length ........................................................................................... 209

Abracadabra ............................................................................................................ 218

Lesson 23 Area and Perimeter (1) .......................................................................................... 219

Two Problems on Logic .............................................................................................. 226

Lesson 24 Area and Perimeter (2) ........................................................................................... 227

Königsberg Bridge Problem ....................................................................................... 234

Lesson 25 Area and Perimeter (3) ........................................................................................... 235

Mathematically Speaking, Are You Gifted? ................................................................... 244

Lesson 26 Non-Routine Problems (1)...................................................................................... 245



Solutions .............................................................................................................................. S1-S32

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© Singapore Asia Publishers Pte Ltd & Terry Chew All rights reserved

Lesson 2 ◙ 13

Comments

Lesson 2

Classic ExampleMs Medine bakes some cupcakes to give to her class. If she gives 3 cupcakes to each student, she will have a remainder of 5 cupcakes. If she gives 5 cupcakes to each student, she will need another 23 cupcakes.(a) How many students are there in the class?(b) How many cupcakes does she bake?

Solution Use a Simple Formula

(Excess + Shortage) ÷ Difference= Number of Items

Excess → 5 cupcakes Shortage →23 cupcakes Difference →5 – 3 = 2 cupcakes (5 + 23) ÷ 2 = 28 ÷ 2

= 14 students Number of cupcakes = 3 × 14 + 5

= 42 + 5= 47

or = 5 × 14 – 23= 70 – 23= 47

(a) 14 students (b) 47 cupcakes

In an “Excess and Excess” scenario,

Number of items =(Excess – Excess) ÷ Difference

In a “Shortage and Shortage” scenario,

Number of Items =(Shortage – Shortage) ÷ Difference

Excess and Shortage

L2_Wicked Mathematics! Workbook 13 13 1/12/2018 4:47:59 PM

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14 ◙ Lesson 2 © Singapore Asia Publishers Pte Ltd & Terry Chew All rights reserved

Practice1 Peter wants to give his marble collection to his friends. If he gives 16 marbles to

each friend, the remainder is 21 marbles. If he gives 20 marbles to each friend, he needs another 15 marbles.

(a) How many friends does he give the marbles to?

(b) How many marbles does he have?

Ans: (a) friends

(b) marbles


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Challenging Problems

9 There are some black and white beads in a box. If 1 black bead and 1 white bead are removed each time, there will still be 40 white beads left when the black beads finish. If 1 black bead and 3 white beads are removed each time, there will still be 40 black beads left when the white beads finish.

(a) How many white beads are there?

(b) How many black beads are there?

Ans: (a) white beads

(b) black beads


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Counterfeit Coin ProblemTheCounterfeitCoinProblemhascroppedupinmanyguisesovertheyears.Hereisoneversionofit.

Ali Baba has 12 gold coins, but one of them is a fake. A fake coin is slightly lighter than a real one. Using only a two-pan balance, can you help him to find the fake coin in only 3 weighings?

Answer:Therearemanywaystodothis.Listedbelowarejusttwoofthem.

Method 1Firstweighing:Put6coinsoneachsideofthebalance.Thelightersidecontainsthefakecoin.

Secondweighing:Splitthe6coinsfromthelightersideinto2groupsof3coinsandweighthem.Again,thefakecoinisonthelightersideofthebalance.

Thirdweighing:Onecoineachonbothsidesofthebalance.Thefakecoinisonthelightersideofthebalance.Ifthebalanceisstraight,thenthefakecoinistheonenotbeingweighed.

Method 2Firstweighing:Put4coinsoneachsideofthebalance.Thelightersidecontainsthefakecoin.Ifthebalanceisstraight,then thefakecoinisinthegroupnotbeingweighed.

Secondweighing:Splitthe4coinsfromthe‘suspicious’groupintogroupsof2coinsandweighthem.Thefakecoinisonthelightersideofthebalance.

Thirdweighing:Thefakecoinisonthelightersideofthebalanceinthis lastweighing.

Youmaywanttothinkaboutweighing3coinseachtime,or5coinseachtime!

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© Singapore Asia Publishers Pte Ltd & Terry Chew All rights reserved

Lesson 27 ◙ 253

Lesson 27

Non-Routine Problems (2)Practice1 Useasimplemethodtocomputethefollowing.

(a) (2+4+6+...+98+100)–(1+3+5+...+97+99)

(b) 100–98+96–94+92–90+...+8–6+4–2

Ans:(a)

(b)

2 50studentstookpartin50-mfreestyleand50-mbackstrokeswimmingevents. 32studentstookpartinfreestyleand28studentstookpartinbackstroke. Howmanystudentstookpartinbackstrokeonly?

Ans: students

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◙ S�© Singapore Asia Publishers Pte Ltd & Terry Chew All rights reserved

Lesson 1

Lesson � Chicken and Rabbit1. M1:Ifallweretricycles, 34×3=102wheels 102–86=16wheels Diff:3–2=1wheel Ans:(a)16÷1=16bicycles

(b)34–16=18tricycles

M2:Ifallwerebicycles, 34×2=68wheels 86–68=18wheels Diff:3–2=1wheel Ans:(b)18÷1=18tricycles

(a)34–18=16bicycles

M3

No.oftricycles No.ofwheels No.ofbicycles No.ofwheels Total

17 17×3=51 17 17×2=34 85

18 18×3=54 16 16×2=32 86

2. Ifallwerecows, 26×4=104legs 104–78=26legs Diff:4–2=2legs Ans:(a)26÷2=13ducks

(b)26–13=13cows

3. Ifallweregirls, 29×5=145stickers 145–113=32stickers Diff:5–3=2stickers

32÷2=16boys Ans:16boys

4. Ifallwereboys, 34×3=102balloons 156–102=54balloons Diff:6–3=3balloons

54÷3=18girls34–18=16boys

Ans:(a)16boys(b)18girls

5. Comment:Thequestion requiresadifferentapproach.

4+2=6wheels 216÷6=36carsand36motorcycles Check:36×4=144wheels

36×2=72wheels144+72=216wheels

Ans:36cars

6. 5×2=10legs 3×4=12legs 10+12=22legsforevery5chickensand3

goats. 132÷22=6 or6×22=132legs Themultiplieris6. 5×6=30chickens 3×6=18goats Ans:(a)30chickens

(b)18goats

7. Ifallquestionswereansweredcorrectly, 40×4=160marks Tomlost(160–124)=36marks. Eachwronganswerwas(4+2)=6marks. 36÷6=6wrong 40–6=34correct Ans:34questions

8. Ifallquestionswereansweredcorrectly, 20×5=100marks Dannylost(100–79)=21marks. Eachwronganswerwas(5+2)=7marks. 21÷7=3wrong 20–3=17correct Ans:17questions

9. M1:WriteTwoStatements A+B=39 ——(1) 2A+3B=91 ——(2) Makethemcomparable. From(1),2A+2B=78 ——(3) Comparing(2)and(3), B=91–78=13 A=39–13=26 Ans:A=26 M2:MakeaTable

A 2×A B 3×B Total

20 40 19 57 40+57=97

22 44 17 51 44+51=95

24 48 15 45 48+45=93

26 52 13 39 52+39=91

Important: The solution should be cut shortafter the first guess.

97–91=6togo Diff:3–2=1

6÷1=620+6=26

Ans:A=26

02 Solution_Wicked Mathematics! 1 1 1/15/2018 4:33:01 PM

Solve Exam‑Type Mathematics Word Problemsin 28 Essentials Lessons Primary 3

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