Math sec2 tips

Chap1 linearequation axbyklinearequation ymxc positivegradient negativegradient rise run yinterceptgradient ofaline straightlineformulagammachorizontal yintercept straightlineformula xavertical xintercept simultaneousequationmethods graphicalmethod drawoutequationandfindrespectivex yintercepts eliminationmethod cancelout1coefficient mustbe1positiveInegative substitutionmethod findvaluesofcoefficientsandsubinvaluesintoequation eg 3x7y17 3x6y4left3x7yrightleft3x6yright1743x7y3x6y1313y13y1xfrac103

Chap2 inequalitysigns aIb aismorethanbacbaislessthanba.IS aismorethanequaltob AIb aislessthanequaltob whenapositivenegativenumberisaddedsubtractedonbothsidesofaninequalitysigndoesnotchange whenapositivenumberismultiplieddividedonbothsidesofaninequalitysigndoesnotchange whenanegativenumberismultiplieddividedonbothsidesofaninequalitysignisreversed tosolveainequality egx 2 Finpossiblevalueof tofittheinequality IFPossible notpossiblevalue 2 321012 possiblevalue 2 32 10 12

Chap3 algebraicexpressions expressioncontaininglettersnumbersandoroperations linearexpressioninonevariable onlyonevariable nopowers quadraticexpressions highestpoweris2 eg.axtbxtca.b.ciconstants a o ifa Oitslinear expansionofatb ctd MEETactadtbetbd ALWAYSSOLVEBRACKETSFIRST formpxtqrxts factorisationofax bx c Cco a 1 5 22 7 15 forrows2x22 100 I302 sighpaidsÉmI3 37 15 uptoQ

factorisingatb Ctd abtad2bct2cd commonfactorsabtad 2bct2cd abtd 2cbtd at2c btd

Chap4 stspecialalgebraicidentity1stperfectsquareidentity atb a 2abtb 2ndspecialalgebraicidentity2ndperfectsquareidentity ab as 2abtb rdspecialalgebraicidentity3rdperfectsquareidentity atb ab 92b

Chap5 ZeroProductPrinciple ab0 a0bo yxopensupwardsindefinitelyandhasaminimumpointI 1turning yxopensdownwardsindefinitelyandhasamaximumpointPoints stymmetrical aboutyaxislineofsymmetryis O y Ilineofsymmetry mtmx quadraticfunctions nonlinearyx yx2 familyofcurvesparabolas minimumpoint symmetry jugglers yaxtbxtc a oin ircept atwidergraph intercept'd minimumpoint yax2 y 012intercept lyinterceptmaximumpoint yaxtbxtcoo aco intercept x lineofsymmetry

Chap6 simplifyingalgebraicfractions ie fracabfracatimescbtimesc fracabadivcbdivccancelnumeratordenominatorbytheircommonfactors multiplydivide 1factorisenumeratordenominatorwherepossible 2cancelcommonfactors 3multiplyremainingterms 1factorisenumeratordenominatorwherepossible 2flipsecondfractionformultiplication 3cancelcommonfactors 4multiplyremainingterms addsubtract 1factorisenumeratordenominatorwherepossible 2cancelcommonfactors 3findLCMofdenominators 4makecommondenominators 5 fractionstakenoteofnegatives solvingequationsinvolvingalgebraicfractionsifonly2algebraicfractionsarewithintheequationusecrossmultiplicationMETHOD1expressaslikefractionsMETHOD2multiplythroughout byLCMof denom.ifthereare3algebraicfractionswithinequationuseoneoftwomethods 1expressallfractionsaslikefractionsusingtheLemofdenominatorseliminatedenominatorsbymultiplyingeachtermbyLCMof denominators2ensureLHSRHSare expressedasasinglefractionsolveas usual3crossmultiplytogetridoffractionssubsolutionstocheckfor validity4solveas usual5subsolutionstocheckforvalidity

Chap7 directproportion ykx inverseproportion yfrackx changingthesubjectofaformula ie Vpir2h Visthesubject performalgebraicmanipulationexpansiontaking outcommonfactor factorising

Chap 9AbcBCaΔ ABCisarightangledtriangle inAABC thelongestsidebisoppositethelargestangle90thelongestsideiscalledthehypotenuseofthetriangle A bcBCa PythagorasTheorem Thesquareofthelengthofahypotenuseofatriangle totalofthesquaresofthelengthsoftheother2sides inarightangledtriangleABC AB2AC2BC2 whereABisthelengthofthehypotenuse ie c2a2b2

Chap 10hypotenuseOppadj TOA tanfracOPPadj CAH cosahdyjp SOH sinefracopphyp