OXFORDUNIVERSITY PRESSASPIRESUCCEEDPROGRESSCompleteMathematicsfor Cambridge IGCSEFifth EditionExtendedDavid Raynerlan BettisonMathew TaylorOxford excellence for Cambridge IGCSEOXFORDOXFORDCambridge Assessment International Education bears noresponsibility for the example answers to questions takenUNIVERSITY PRESSfrom its past question papers which are contained in thisGreat Clarendon Street,Oxford,OX2 6DP,United Kingdompublication.Oxford University Press is a department of the Universityp1:DeAgostini/Getty Images;p15:patrimonio designs Itdof Oxford.Shutterstock;p16:EvgenySHCH/Shutterstock;p19:NPeter/It furthers the University's objective of excellence inShutterstock:p24:Eric Isselee/Shutterstock;p25:Donresearch,scholarship,and education by publishingBendickson/Shutterstock;p29:Mike Flippo/Shutterstock:worldwide.Oxford is a registered trade mark of Oxfordp29:Leena Robinson/Shutterstock;p31:TonyV3112University Press in the UK and in certain other 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is a natural,PHYSICS/SCIENCE PHOTO LIBRARY;p389:Monkey Businessrecyclable product made from wood grown in sustainableImages/Shutterstock;p398:Vlademareous/Shutterstock:forests.The manufacturing process conforms to thep399:chotwit piyapramote/Shutterstockpiyapramote/environmental regulations of the country of origin.ShutterstockPrinted in Italy by L.E.G.O.SpACover image:ShutterstockAlthough we have made every effort to trace and contactAcknowledgementsThe publishers would like to thank the following forall copyright holders before publication this has not beenpermissions to use copyright material:possible in all cases.If notified,the publisher will rectify anyerrors or omissions at the earliest opportunity.IGCSE is the registered trademark of CambridgeAssessment International Education.Links to third party websites are provided by Oxford ingood faith and for information only.Oxford disclaims anyPast paper examination material reproduced by permissionresponsibility for the materials contained in any third partyof Cambridge Assessment International Education.website referenced in this work.ContentsSyllabus matching gridv-ix3.6Surface area125IntroductionXRevision exercise 3A1281Number1-54Examination-style exercise 3B 1311.1 Arithmetic21.2Number facts and sequences7Geometry136-1721.3Approximations and4.1 Fundamental results137estimation144.2Pythagoras'theorem1411.4Standard form194.3Symmetry1441.5Ratio and proportion214.4Similarity1471.6Percentages284.5Congruence1561.7Speed,distance and time364.6Circle theorems1581.8Mixed problems404.7Constructions1661.9Calculator424.8Nets167Revision exercise 1A47Revision exercise 4A168Examination-style exercise 1B 49Examination-style exercise 4B 1702Algebra 155-1025Algebra 2173-2072.1 Negative numbers565.1 Algebraic fractions1732.2Directed numbers575.2Changing the subject2.3Formulae59of a formula1762.4Brackets and simplifying645.3Variation1832.5Linear equations675.4Indices1892.6Problems solves by linear5.5Inequalities193equations725.6Linear programming1982.7Simultaneous equations77Revision exercise 5A2032.8Problems solved by simultaneousExamination-style exercise 5B 204equations812.9Factorising846Trigonometry208-2372.10 Quadratic equations876.1 Right-angled triangles2082.11 Problems solved by quadratic6.2 Scale drawing219equations932.12 Non-linear simultaneous6.4Sine,cosine and tangentequations96for any angle222Revision exercise 2A986.5 The sine rule225Examination-style exercise 2B.1006.6The cosine rule227Revision exercise 6A2313Mensuration103-135Examination-style exercise 6B 2333.1 Area1043.2 The circle1087Graphs238-2793.3 Arc length and sector area1127.1 Drawing accurate graphs2393.4 Chord of a circle1157.2 Gradients2413.5Volume1187.3 The form y=mx +c243