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1、InthischapteryouAlgebraicwilllearn:somestandardalgebraicstrategiesfor3structuressolvingequationshowtosketchgraphs,andsomelimitationsofgraphicalcalculatorsIntroductoryproblemhowtouseagraphicalcalculatortosolve1Solvetheequation=lnx.equationsx2howtoworkwithi
2、dentities.Equationsarethebuildingblocksofmathematics.Therearemanydifferenttypes:somehavenosolutions;somehavemanysolutions;somehavesolutionswhichcannotbeexpressedintermsofanyfunctionyouhavemet.Graphsareanalternativewayofexpressingarelationshipbetweentwovar
3、iables.Ifyouunderstandtheconnectionbetweengraphsandequations,andcanswitchreadilybetweenthetworepresentations,youwillhaveawidervarietyoftoolsforsolvingmathematicalproblems.TheInternationalBaccalaureate®placesgreatemphasisonusinggraphicalcalculatorstoanalys
4、egraphs.Identitiesareusedtorewriteanexpressioninadifferentform,whichcanbeveryusefulwhensolvingequations.Inmuchofmathematicswedonotdistinguishbetweenequationsandidentities,althoughtheyarefundamentallydifferent.Inthischapterweshallexploresomeofthesedifferen
5、cesandlookatthedifferenttechniqueswecanapplytoequationsandidentities.Veryfewexaminationquestionsaresetonthistopicalone,butthetechniquesofthischapterareinvolvedinvirtuallyeveryexaminationquestion.©CambridgeUniversityPress2012.3Algebraicstructures71Notforpr
6、inting,sharingordistribution.3ASolvingequationsbyfactorisingWestartbylookingatsomecommonalgebraicmethodsforsolvingequations.Youhavealreadyseenhowfactorisingcanbeusedtohelpsketchthegraphsofquadraticfunctions;inthischapterwewillapplythesameprinciplesinawide
7、rcontext.Iftwonumbersmultiplytogethertogive5,whatcanyousayThisistrueforrealaboutthosetwonumbers?Theycouldbeand5,10numbers,butifthe15numbersyouareand,πand,….Infact,thereareaninfinitenumberlookingforareintegers,then2πknowingthattheymultiplyofpossibilities.S
8、o,justknowingthattwonumbersmultiplytogethertogiveanon-zerotogethertogive5isnotofmuchhelpindeterminingwhattheconstantisextremelyuseful.numbersactuallyare.Forexample,canyousolvexy=14ifxandyareHowever,ifyouknowthattwo(
