Table Of Content

Competitive Math for Middle School Pan Stanford Series on Renewable Energy — Volume 2 Competitive Math for Middle School Algebra, Probability, and Number Theory Vinod Krishnamoorthy editors Preben Maegaard Anna Krenz Wolfgang Palz The Rise of Modern Wind Energy Wind Power for the World February9,2018 14:42 PSPBook-9inx6in 00-Prelims Publishedby PanStanfordPublishingPte.Ltd. PenthouseLevel,SuntecTower3 8TemasekBoulevard Singapore038988 Email:[email protected] Web:www.panstanford.com BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary. CompetitiveMathforMiddleSchool:Algebra,Probability, andNumberTheory Copyright(cid:2)c 2018PanStanfordPublishingPte.Ltd. Coverimage:CourtesyofNirmalaMoorthy Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinany form or by any means, electronic or mechanical, including photocopying, recordingoranyinformationstorageandretrievalsystemnowknownorto beinvented,withoutwrittenpermissionfromthepublisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not requiredfromthepublisher. ISBN978-981-4774-13-0(Paperback) ISBN978-1-315-19663-3(eBook) February6,2018 13:35 PSPBook-9inx6in 00-Prelims Contents Preface ix 1 Algebra 1 Part1 LinearEquations 1 Part2 CrossMultiplication 6 Part3 SystemsofEquations 8 Part4 ExponentsandRoots 13 Part5 SimplifyingRadicalExpressions 21 Part6 Proportions 23 Part7 Inequalities 28 Part8 CountingNumbers 31 Part9 SequencesandSeries 32 Part10 Distance,Rate,andTime 36 Part11 Rates 38 Part12 UnitConversionandAnalysis 42 Part13 Percentages 45 Part14 Mixtures 48 Part15 PolynomialExpansions 50 Part16 EquivalentExpressions 53 Part17 Factoring 54 Part18 SpecialFactorizations 59 Part19 TheQuadraticFormula 60 Part20 SolvingforWholeExpressions 65 Part21 InfiniteSeries 66 Part22 Sets 70 Part23 Mean,Median,Mode,andRange 74 SolutionsManual 76 Part1 LinearEquations 76 Part2 CrossMultiplication 82 February6,2018 13:35 PSPBook-9inx6in 00-Prelims vi Contents Part3 SystemsofEquations 84 Part4 RootsandExponents 89 Part5 SimplifyingRadicalExpressions 94 Part6 Proportions 95 Part7 Inequalities 100 Part8 CountingNumbers 104 Part9 SequencesandSeries 105 Part10 Distance,Rate,andTime 110 Part11 Rates 113 Part12 UnitConversionandAnalysis 119 Part13 Percentages 120 Part14 Mixtures 123 Part15 PolynomialExpansions 124 Part16 EquivalentExpressions 129 Part17 Factoring 130 Part18 SpecialFactorizations 135 Part19 TheQuadraticFormula 137 Part20 SolvingforWholeExpressions 142 Part21 InfiniteSeries 144 Part22 Sets 146 Part23 Mean,Median,ModeandRange 147 2 CountingandProbability 151 Part1 BasicProbability 151 Part2 BasicCounting 155 Part3 MultipleEvents 157 Part4 Orderings 160 Part5 DependentEvents 162 Part6 Subsets 168 Part7 OrganizedCounting 169 Part8 PermutationsandCombinations 171 Part9 ExpectedValue 176 Part10 WeightedAverage 178 Part11 Generality 180 SolutionsManual 183 Part1 BasicProbability 183 Part2 BasicCounting 185 Part3 MultipleEvents 187 February6,2018 13:35 PSPBook-9inx6in 00-Prelims Contents vii Part4 Orderings 189 Part5 DependentEvents 192 Part6 Subsets 200 Part7 OrganizedCounting 202 Part8 PermutationsandCombinations 206 Part9 ExpectedValue 211 Part10 WeightedAverage 212 Part11 Generality 214 3 NumberTheory 219 Part1 BasicNumberTheory 219 Part2 CountingFactors,GCF,LCM 224 Part3 Bases 229 Part4 ModularArithmetic 231 Part5 DivisibilityTricks 235 SolutionsManual 237 Part1 BasicNumberTheory 237 Part2 CountingFactors,GCF,LCM 239 Part3 Bases 243 Part4 ModularArithmetic 247 Part5 DivisibilityTricks 252 Index 255 February6,2018 13:35 PSPBook-9inx6in 00-Prelims February6,2018 13:35 PSPBook-9inx6in 00-Prelims Preface I originally began writing this textbook after teaching creative math to middle school students, who were endlessly fascinated, just as I had been, with the ﬁeld of mathematics. This book is a compilationofimportantconceptsusedincompetitionmathematics in Algebra, Counting/Probability, and Number Theory. Over 420 problems are provided with detailed solutions found at the end of each chapter. These solutions are intended to guide students to identify a promising approach and to execute the necessary math. I recommend that students try all of the problems, even if they seem intimidating, and use the solutions to the problems as part of the learning process; they are as essential to learning as the teachingsandexamplesgiveninthebodyofthetext.Afterreading the solution, students should try to reproduce it themselves. My hope is to provide notonlymathematical facts andtechniques but alsoexamplesofhowtheymaybeapplied,sothatthestudentgains a thorough understanding of the material and conﬁdence in their problem-solvingabilities. Creativemathisbecomingincreasinglyimportantinschoolsall overtheworld.Thenewtrendisconspicuousintheremodelingof standardizedtestssuchastheAmericanSAT,thestandardentrance exam for U.S. colleges. Advanced middle school students and high schoolstudentscanusethisbooktogainanadvantageinschooland developcriticalthinkingskills. VinodKrishnamoorthy