Cambridge Mathematics Year 11 2 Unit Pdf

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Cambridge 2 Unit Mathematics Year 11

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YEAR112 Uni tSecondEdi t i onCAMBRIDGEMat hemat icsBI LL PENDERDAVI D SADLERJ ULI A SHEADEREK WARDCOLOURVERSION WITHSTUDENT CD- ROMNow i n col our wi t h anel ect r oni c ver si on of t he book on CDCAMBRIDGE UNIVERSITY PRESS Cambri dge, New York, Mel bourne, Madri d, Cape Town, Si ngapore, So Paul o, Del hi Cambri dge Uni versi ty Press 477 Wi l l i amstown Road, Port Mel bourne, VIC 3207, Austral i a www.cambri dge.edu.au Informati on on thi s ti tl e: www.cambri dge.org/ 9780521147170 Bi l l Pender, Davi d Sadl er, Jul i a Shea, Derek Ward 2009 Fi rst edi ti on 1999 Repri nted 2001, 2004 Second edi ti on 2005 Col our versi on 2009 Cover desi gn by Syl vi a Wi tte Typeset by Aptara Corp. Pri nted i n Chi na by Pri ntpl us Nat i onal Li br ar y of Aust r al i a Cat al ogui ng i n Publ i cat i on dat a Bi l l Pender Cambri dge mathemati cs 2 uni t : year 11 / Bi l l Pender [et al .] . 2nd ed. 9780521147170 (pbk.) Incl udes i ndex. For secondary school age. Mathemati cs. Mathemati cs--Probl ems, exerci ses, etc. Sadl er, Davi d. Shea, Jul i a. Ward, Derek. 510 ISBN 978-0-521-14717-0 paperback Reproducti on and Communi cati on f or educati onal purposes The Austral i an Copyr i ght Act 1968 (the Act) al l ows a maxi mum of one chapter or 10% of the pages of thi s publ i cati on, whi chever i s the greater, to be reproduced and/ or communi cated by any educati onal i nsti tuti on for i ts educati onal purposes provi ded that the educati onal i nsti tuti on (or the body that admi ni sters i t) has gi ven a remunerati on noti ce to Copyri ght Agency Li mi ted (CAL) under the Act. For detai l s of the CAL l i cence for educati onal i nsti tuti ons contact: Copyri ght Agency Li mi ted Level 15, 233 Castl ereagh Street Sydney NSW 2000 Tel ephone: (02) 9394 7600 Facsi mi l e: (02) 9394 7601 Emai l : i nfo@copyri ght.com.au Reproducti on and Communi cati on f or other purposes Except as permi tted under the Act (for exampl e a fai r deal i ng for the purposes of study, research, cri ti ci sm or revi ew) no part of thi s publ i cati on may be reproduced, stored i n a retri eval system, communi cated or transmi tted i n any form or by any means wi thout pri or wri tten permi ssi on. Al l i nqui ri es shoul d be made to the publ i sher at the address above. Cambri dge Uni versi ty Press has no responsi bi l i ty for the persi stence or accuracy of URLS for external or thi rd-party i nternet websi tes referred to i n thi s publ i cati on and does not guarantee that any content on such websi tes i s, or wi l l remai n, accurate or appropri ate. Informati on regardi ng pri ces, travel ti metabl es and other factual i nformati on gi ven i n thi s work are correct at the ti me of fi rst pri nti ng but Cambri dge Uni versi ty Press does not guarantee the accuracy of such i nformati on thereafter. Student CD-ROM l i cence Pl ease see the fi l e 'l i cence.txt' on the Student CD-ROM that i s packed wi th thi s book. ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viHow to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAbout the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xChapter One Methods in Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 11A Arithmetic with Pronumerals . . . . . . . . . . . . . . . . . . . . . . . 11B Expanding Brackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41C Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61D Algebraic Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91E Factoring the Sum and Dierence of Cubes . . . . . . . . . . . . . . . 131F Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 141G Solving Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . 171H Solving Simultaneous Equations . . . . . . . . . . . . . . . . . . . . . . 201I Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . 231J Chapter Review Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . 25Chapter Two Numbers and Surds . . . . . . . . . . . . . . . . . . . . . . . . . . 272A Integers and Rational Numbers . . . . . . . . . . . . . . . . . . . . . . 272B Terminating and Recurring Decimals . . . . . . . . . . . . . . . . . . . 302C Real Numbers and Approximations . . . . . . . . . . . . . . . . . . . . 332D Surds and their Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . 362E Further Simplication of Surds . . . . . . . . . . . . . . . . . . . . . . 382F Rationalising the Denominator . . . . . . . . . . . . . . . . . . . . . . 402G Chapter Review Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . 42Chapter Three Functions and their Graphs . . . . . . . . . . . . . . . . . . . . . 453A Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . 453B Review of Linear Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 503C Review of Quadratic Graphs . . . . . . . . . . . . . . . . . . . . . . . . 523D Higher Powers of x and Circles . . . . . . . . . . . . . . . . . . . . . . 553E Two Graphs that have Asymptotes . . . . . . . . . . . . . . . . . . . . 573F Transformations of Known Graphs . . . . . . . . . . . . . . . . . . . . 593G Chapter Review Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . 63Chapter Four Graphs and Inequations . . . . . . . . . . . . . . . . . . . . . . . . 664A Inequations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 664B Solving Quadratic Inequations . . . . . . . . . . . . . . . . . . . . . . . 694C Intercepts and Sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704D Odd and Even Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 744E The Absolute Value Function . . . . . . . . . . . . . . . . . . . . . . . 77r riv Contents4F Using Graphs to Solve Equations and Inequations . . . . . . . . . . . . 814G Regions in the Number Plane . . . . . . . . . . . . . . . . . . . . . . . 854H Chapter Review Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . 89Chapter Five Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925A Trigonometry with Right-Angled Triangles . . . . . . . . . . . . . . . . 925B Problems Involving Right-Angled Triangles . . . . . . . . . . . . . . . 975C Trigonometric Functions of a General Angle . . . . . . . . . . . . . . . 1015D The Quadrant, the Related Angle and the Sign . . . . . . . . . . . . . 1055E Given One Trigonometric Function, Find Another . . . . . . . . . . . . 1115F Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . 1135G Trigonometric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 1175H The Sine Rule and the Area Formula . . . . . . . . . . . . . . . . . . . 1235I The Cosine Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295J Problems Involving General Triangles . . . . . . . . . . . . . . . . . . . 1335K Chapter Review Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . 138Appendix Proving the Sine, Cosine and Area Rules . . . . . . . . . 141Chapter Six Coordinate Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 1436A L