Foundation maths PDF
Preview Foundation maths
Y:/Pearson/MAIN/A01/LAYOUT_A01/A01_CROF9402_05_- Foundation Maths Y:/Pearson/MAIN/A01/LAYOUT_A01/A01_CROF9402_05_- Y:/Pearson/MAIN/A01/LAYOUT_A01/A01_CROF9402_05_- Foundation Maths Sixth edition Anthony Croft Loughborough University Robert Davison Y:/Pearson/MAIN/A01/LAYOUT_A01/A01_CROF9402_05_- PearsonEducationLimited EdinburghGate HarlowCM202JE UnitedKingdom Tel:+44(0)1279623623 Web:www.pearson.com/uk Firstpublished1995(print) Thirdeditionpublished2003(print) Fourthedition2006(print) Fifthedition2010(print) Sixtheditionpublished2016(printandelectronic) #PearsonEducationLimited1995,2003,2006,2010(print) #PearsonEducationLimited2016(printandelectronic) TherightsofAnthonyCroftandRobertDavisontobeidentifiedasauthorsof thisworkhavebeenassertedbytheminaccordancewiththeCopyright,Designs andPatentsAct1988. Theprintpublicationisprotectedbycopyright.Priortoanyprohibited reproduction,storageinaretrievalsystem,distributionortransmissioninany formorbyanymeans,electronic,mechanical,recordingorotherwise,permission shouldbeobtainedfromthepublisheror,whereapplicable,alicencepermitting restrictedcopyingintheUnitedKingdomshouldbeobtainedfromthe CopyrightLicensingAgencyLtd,Barnard’sInn,86FetterLane,LondonEC4A1EN. TheePublicationisprotectedbycopyrightandmustnotbecopied,reproduced, transferred,distributed,leased,licensedorpubliclyperformedorusedinanyway exceptasspecificallypermittedinwritingbythepublishers,asallowedunderthe termsandconditionsunderwhichitwaspurchased,orasstrictlypermittedby applicablecopyrightlaw.Anyunauthoriseddistributionoruseofthistextmaybea directinfringementoftheauthors’andthepublisher’srightsandthoseresponsible maybeliableinlawaccordingly. PearsonEducationisnotresponsibleforthecontentofthird-partyinternetsites. ISBN:978-1-292-09517-2(print) 978-1-292-09519-6(PDF) 978-1-292-14419-1(ePub) BritishLibraryCataloguing-in-PublicationData AcataloguerecordfortheprinteditionisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordfortheprinteditionisavailablefromtheLibraryofCongress 10987654321 1918171615 Printeditiontypesetin10/12.5ptTimesbyLuminaDatamatics PrintedinSlovakiabyNeografia NOTETHATANYPAGECROSSREFERENCESREFERTOTHEPRINTEDITION Y:/Pearson/MAIN/A02/LAYOUT_A02/A02_CROF9402_05_SE_- Contents Preface vii List of videos ix Mathematical symbols x 1 Arithmetic of whole numbers 1 2 Fractions 14 3 Decimal numbers 26 4 Percentage and ratio 34 5 Algebra 45 6 Indices 54 7 Simplifying algebraic expressions 70 8 Factorisation 79 9 Algebraic fractions 86 10 Transposing formulae 108 11 Solving equations 114 12 Sequences and series 126 13 Sets 141 14 Number bases 154 15 Elementary logic 165 16 Functions 176 17 Graphs of functions 189 18 The straight line 211 19 The exponential function 224 20 The logarithm function 233 21 Measurement 251 22 Introduction to trigonometry 271 23 The trigonometrical functions and their graphs 279 24 Trigonometrical identities and equations 292 25 Solution of triangles 305 26 Vectors 322 27 Matrices 337 28 Complex numbers 352 29 Tables and charts 371 30 Statistics 388 31 Probability 403 32 Correlation 412 33 Regression 427 34 Gradients of curves 434 Y:/Pearson/MAIN/A02/LAYOUT_A02/A02_CROF9402_05_SE_- vi Contents 35 Techniques of differentiation 451 36 Integration and areas under curves 462 37 Techniques of integration 480 38 Functions of more than one variable and partial differentiation 495 Solutions 512 Index 592 Supporting resources Visit www.pearsoned.co.uk/croft to find valuable online resources Y:/Pearson/MAIN/A03/LAYOUT_A03/A03_CROF9402_05_SE_- Preface Today, a huge variety of disciplines require their students to have knowledge of certain mathematical tools in order to appreciate the quantitative aspects of their subjects. At the same time, higher education institutionshavewidenedaccesssothatthereismuchgreatervarietyinthe pre-university mathematical experiences of the student body. Some students are returning to education after many years in the workplace or at home bringing up families. FoundationMathshasbeenwrittenforthosestudentsinhighereducation whohavenotspecialisedinmathematicsatAorASlevel.Itisintendedfor non-specialists who need some but not a great deal of mathematics as they embark upon their courses of higher education. It is likely to be especially useful to those students embarking upon a Foundation Degree with mathematical content. It takes students from around the lower levels of GCSEtoa standardwhichwillenablethemtoparticipate fullyina degree ordiplomacourse.Itisideallysuitedforthosestudyingmarketing,business studies, management, science, engineering, social science, geography, combinedstudiesanddesign.Itwillbeusefulforthosewholackconfidence andneedcareful,steadyguidanceinmathematicalmethods.Evenforthose whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for those who wish to engage in self-study or distance learning. We have tried throughout to adopt an informal, user-friendly approach and have described mathematical processes in everyday language. Mathe- maticalideasareusuallydevelopedbyexampleratherthanbyformalproof. This reflects our experience that students learn better from examples than fromabstractdevelopment.Whereappropriate,theexamplescontainagreat deal of detail so that the student is not left wondering how one stage of a calculation leads to the next. In Foundation Maths, objectives are clearly stated at the beginning of each chapter, and key points and formulae are highlighted throughout the book. Self-assessment questions are provided at the end of most sections. These test understanding of important features in thesectionandanswersaregivenatthebackofthebook.Thesearefollowed byexercises;itisessentialthattheseareattemptedastheonlywaytodevelop competence and understanding is through practice. Solutions to these exercisesaregivenatthebackofthebookandshouldbeconsultedonlyafter Y:/Pearson/MAIN/A03/LAYOUT_A03/A03_CROF9402_05_SE_- viii Preface the exercises have been attempted. In this new, 6th edition of Foundation Maths, guided by user feedback, we have included in many of the chapters anumberofchallengeexercises.Theseexercisesareintentionallydemanding and require a considerable depth of understanding. Solutions to these exercises can be found at www.pearsoned.co.uk/croft. A further set of test and assignment exercises is given at the end of each chapter. These are providedsothatthetutorcansetregularassignmentsorteststhroughoutthe course. Solutions to these are not provided. Feedback from students who have used earlier editions of this book indicates that they have found the styleandpaceofthebookhelpfulintheirstudyofmathematicsatuniversity. Inordertokeepthesizeofthebookreasonablewehaveendeavouredto include topics which we think are most important, cause the most problems for students, and have the widest applicability. We have started the book with materials on arithmetic including whole numbers, fractions and decimals. This is followed by several chapters which gradually introduce important and commonly used topics in algebra. There follows chapters on sets, number bases and logic, collectively known as discrete mathematics. The remaining chapters introduce functions, trigonometry, vectors, matrices, complex numbers, statistics, probability and calculus. These will be found useful in the courses previously listed. The best strategy for those using the book would be to read through each section, carefully studying all of the worked examples and solutions. Many of these solutions develop important results needed later in the book. It is then a good idea to cover up the solution and try to work the example again independently. It is only by doing the calculation that the necessary techniques will be mastered. At the end of each section the self-assessmentquestionsshouldbeattempted.Ifthesecannotbeanswered then the previous few pages should be worked through again in order to findtheanswersinthetext,beforecheckingwithanswersgivenattheback ofthebook.Finally,theexercisesshouldbeattemptedand,again,answers should be checked regularly with those given at the back of the book. This edition is enhanced by video clips (see www.pearsoned.co.uk/croft) in which we, the authors, work through some algebraic examples and exercisestakenfromthebook,pointingouttechniquesandkeypoints.The icon next to an exercise signifies that there is a corresponding video clip. VIDEO Inconclusion,rememberthatlearningmathematicstakestimeandeffort. Carryingoutalargenumberofexercisesallowsthestudenttoexperiencea greater variety of problems, thus building up expertise and confidence. Armed with these the student will be able to tackle more unfamiliar anddemandingproblemsthatariseinotheraspectsoftheircourse. WehopethatyoufindFoundationMathsusefulandwishyoutheverybest of luck. Anthony Croft, Robert Davison 2016 Y:/Pearson/MAIN/A04/LAYOUT_A04/A04_CROF9402_05_- List of videos Thefollowingtableliststhevideoswhichaccompanyselectedexercisesandexamplesinthe book. Youcanview the videosatwww.pearsoned.co.uk/croft Name Reference Substitutionof a valueinto aquadratic expression Exercise 5.3 Q13 Simplification of expressionsrequiring useofthe first lawof indices Exercise 6.1 Q8 Simplification of expressionsrequiring useofthe second and thirdlaws ofindices Exercise 6.1 Q10 Simplification of expressionswithnegativepowers Exercise 6.2 Q4 Removingthe brackets fromexpressions 1 Example 7.18 Removingthe brackets fromexpressions 2 Example 7.24 Factorising a quadraticexpression 1 Example 8.6 Factorising a quadraticexpression 2 Example 8.12 Simplifying analgebraic fraction 1 Example 9.4 Simplifying analgebraic fraction 2 Example 9.8 Simplifying the product oftwo algebraic fractions Example 9.17 Simplifying products andquotientsof algebraic fractions Exercise 9.3 Q4 Addingalgebraic fractions1 Example 9.24 Addingalgebraic fractions2 Example 9.25 An exampleof partial fractions Example 9.28 Anotherexample ofpartial fractions Example 9.29 Transposition of aformula Example 10.7 Solvingsimultaneous equations byelimination Example 11.6 Solvinga quadratic equationbyfactorisation Example 11.10 Solvinga quadratic equationusinga formula Example 11.15
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