A-Math Revision Notes (Handwritten)

A-Math(Revision)<kaiwen:)Sec4Revision> >Algebra Al:QuadraticFunctions -3:Surds. ⊥completingthesq. ⊥Rationalisation. 13941. ☆Conjugation. y=an2tbn-1C㱺y=a(21h72-1k. 3Tp:(hik). ¥2× Eg: 9--212-6211-12 y=( ' -3,72-9+12=In-3)2-13. Flipthesign.. coeffzo ☆Trick:surdsdenominator, Expoind alwaysusecalculator. ✗2,6mExtra tI×F. I ☆coeffmustbe1. ☆coeffmustbetye ☆Qntype: 580. tIxF6_-9=2212-16N-4 y=-✗2-6×-9 ☒= ×g =2Fs' 9=21212+321--2) y=- (x2-16N-19) ~ ↑ = ✗Fg }Primefactors. factoring. Pg40. 2.Fs¥5=4 =Eo⊥y=ax4bntcalwaystve/- ve. ⊥conditions: ✓Nointersection t.to?4ac*⊥NONE. A4:Polynomials2.tile:atve degglx)>degrcx). -ve: a-ve ⊥LongDivision. A2:EquationsandInequalities f-(×)=g(×)q(×)tr(×)↑↑ ↑⊥b2_4ac(discriminant). (D) divisorquotientremainder✗Quadratic line/curve qcx)1.2.realanddistinctD>0 1.2intersectionPt D>0 gcx))fix)2-2realandequal17=02.1-intersectionpt/tangential0=0 3.Norealroots1)<0 3.Nointersection ☐<° ☆4.real. D≥o }4.Intersection D≥0 ⊥Inequalities ☆SPʳiaÉ ⊥RemainderTheorem >I≥ </≤ SHI f(×)=gC✗)qC✗)-1rcx)⊥prove, findthevalue TE_> ofD. "objective" ☆completethe ↑ ↑ %Trick Trick standhere! standhere! A8 ☆EX- fix )=(xg¥)+r( ×) ⊥coeffofN2mustbe-111C. :X__2. - K2-12N-13<0 - (R2- 2k- 3)<0 ✗2-2N- 3>0. i.

All:Polynomials(continued) Ab:PartialFractions. Findqcx)?*FactorTheorem. *2¥,:¥g. →longdiv. PIfix)=gcx)qC×)- ✓⊥ thedeg. sane.im/roper!- Factor:candividewithoutremainder' properImproper I*Ex: fix)=(2×-1)q(×) qcx)LD→ g(×))É¥5 \/:. 21=1-2 1.Linearfactor r⊥cubiceqn. *cantie-10b.2-4ac. 2.RepeatedLinear *typecalculator. ←decimals. 3.Non- factorisable = g%+qcx). I㱺1. 1-beautiful12grossquadformula. 2.3beautiful. "" laxtbxtd= -b)+¥-d)⊥Integer⊥rationalno. *smart" trialanderror" 2' ¥)(c×td=b+?d)+(x¥' pg63. 㱺case1:IuseinLD. tosolveforquadratic "¥)Ey=ia¥T+¥¥togetthe2gross. ⊥cubicidentities opp 4a'+b'=la±b)Ca¥abtbY AF:BinomialTheorem. ⊥a]- b)= (a:b)(a'+abtb'). " +no" ?" ⊥GeneralCr-11)term. *Trt=/1)an- rbn AJ:simultaneousEan. *Independenttermofn ⊥1-linear,1-non- linear. L,y(° *substitution. *nci-ri.TT.*commonmistakes 1.Avoidfractions. ⊥(7)=n (I-13N)" . 21-129=3 (1)=mn i%÷:÷÷ " - N=3-2g✓ pg103. - y=3¥✗avoid. 2.(Nff)' -139=7. * a-identity [ñ+4g]+sy=7 *( .. )*rmbto →[] "S9" ✗2-14N-14-1913g)- -917). findweffof2¥? A-7.1.3.(a)Cii)F I pg99. multiply*throughout- *(ñ4ñ+i)(aiÉ+É+¥+:) n-term?

A-8:Exponential&Logarithm. ⊥Exponential en/an¥-- lager ⊥Logarithmslgn_=logion logab. *changingbtwexpandlootpylosfor bogab-_K←→b=akarrows. ⊥sketchingofgraphs eny.nl#nYa t, >n *cannotcross *cannotcross to- veg to-veil ⊥Lawsoflogarithm. *logav+loyal/=logauv=/logalutv) *logau- loyal/= toga¥. =/logan-v) *changeofbase: logov=%§a÷ *Qnvwiwt_⊥Powers! e"tell=L }substitution! v2tu=\

⊥Gl: Trigonometry GeometryAsif S A -Rat ¥A - sin>0- sin>o S A - cos<0 - cos>O TITOACAHSOH - tanto - tan>o O. A:allratiosarepositive- sina.s.no ✗+ano=°a¥¥" S:sine"""' - a.<o - w,>o µpoÑN " T:tangentis-1K - tan>o - tanto wsO=Aµdjp%¥_u,e 0PM"" c.wine+ye T C T C )O t since-_%pP%ao,eadjacent Identity: cosO=¥ICOEO COLECOseed goor so? co