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? coto-ta-ocoseco-s.IOSeco-_¥ , IA/cSIT EI. *cscO_ tanA=¥cosB=- F- A.Bsamequadrant*specialangles g) Acute: 0>901st obtuse: 010<-18002nd Quadrant:3rd. yz, g.no go,, yang °°"" man,, go.gg,,,,, yay,,y, 3rd4th O O l ° Ext'Tso ± ¥ ¥si-ot-oexactbrn.FIas ¥ ¥ 1 =sin(600+450)¥460 ¥ ± I i.Addition Intertitles formulae. FY90 I o a Quotient: tano-%Ff-coto-9.IO Equations Pythagorean: sin"-1014=1* Sec-A=/+tan't E☒for 010<-3600 cosec'A=ItWTZA*or 0£08,. }ranges! step-by-step Addition: sinlat-B-sinAWJDIWSAI.intIfthevalueis-Ve, →cosO=⾨ Imusttakethetie. ws(A±B)=coin.ws/3T-sinAiinBII [✗(basicangle)=cos-' (E)µcannot"""""9ht tania-1-13)=,¥faI+I÷forG- =30° DoubleAngle: sin2A=2sinAcosA SA ws2A=cos'A-sin'A T C =2wiA-l |Hattingen=/-2in-A :O-_✗ or 0=3600- ✗ ' -30° =>goofy0 checkifinthe range +an2A=,?¥aa GR-torn-vay-s.noY - Amplitude1- / "° as;nA+bcosA=Roos(Attn) - verticaltranslation *as;na+bwsA=Rin(Attn) -,? on - Period 21+0 g-- asinbntc F-taba-tan"(E) y=wsO9 yooo JT "vertical lamplitudeperiodtranslation ag-ia-bwgA-Rsinln.tt)=RsinAws✗-RasAiN Howlong>0T comparecoefficient, completeasymptote> 1cycle<° Roost-- a- ① y=+anOY l # Rsin✗=b- ② " b=¥¥d. *①'+202, *¥,%¥=b_a R's;n2✗+R2coÑ=a2tb2tanabatt Y pics;ñ✗-1W)'d/=a'tbh - go a a-tai'(%)90<0-3+007-- g.as;nbn+c R=¥b' si:|3- ! a=z. i. ,-1°>n☒¥:X!i b--1180360£ - c-I- +ve-ve. <b-

62:coordinateGeometry G3:FurtherCoordinateGeometry ⊥Ean:1-grad.1-pt. *standard Eqn:(x-a)Ztly- b)'=p- centre:(a.b)4gradient: 1T¥ radius:n 4Midpt:(M+÷,Y')* *General Eqn:✗4yd-12gN-12fytc-- ow ⊥Distance:×,)2tyy centre:(- g,-f) t radius:tgifT⊥Area- - III.%.-- Y:/• *reflection. \,-1y- T 4radiusdonotchangerepeat! ⊥n- axis: n- coordinatedonotchangeI1:modulus y- coordinate- y. 㱺charge- ve→txe. y-axis:y- coordinatedonotchange > *IIlines* n- coordinate- a productofgradient=-1. ⊥Normals(calculus) ⊥normalwillcutthecentre. centre*Alternateformforline* y- y,=MIX-X.). *Ta n g e n tofapt-onthecircle. ⊥Ibisector: Pt→ +- 1grad: Ioftheline. C-1). y#centre. ?- 1pt:Midptoftheline. ⊥Ibisectorwblinein'I. - findgradd- n°L?pandcentre. - IC-1). - F-an:grad✓,pt.(x). G4:LinearLaw *y=ab" lgy= Nlgbtlga Y=mXtc⾨lookingfor. *Tip:Extrapolateallthewaytotheaxes. Ya T>a

Calculus Cl:Differentiation *2ndDerivativetest. ⊥standard: L, day ☒(differentiate1-moretime). laxn)=annn" d dayd-✗(a)=0. ☒>0:minimum In)=1 DId×2<0:maximum product: luv)=¥nlv)-1¥,/v) dd÷z=0:Inconclusive. quotient: (F)= "1¥)- u(¥,)V2 *Bothuandvmusthavea ⊥Gradient,Ta n g e n t,Normals. ⊥Identities ←diff.4. ⊥Mtan✗Mnormal=- I- (sinlaxtb))= a-cos/axtb). dTrigo :{d-✗(co,(axtb))=- a-sinlaxtb) y=MN-1C gradof p In: target. (tanlaxtb))= a-see-(axtb). grad. diff. ^ tangent(earth)= antb Exp: - Normal. d en :{d-xlennt.at, d f-'(x) dT(lnflx))= ⊥Maxima/Minima. ⊥¥=O. ⊥Increasing/Decreasingf-I. *Tip:mustshowwhymin/Max. dyTa,>0:4 ⊥use1sttest/2ndtest- dd¥<o:$. ⊥stationarypt: du ⊥Rateofchange. ☒=O. ⊥d¥=dd÷×dd÷. *Nature:2-test: 1stDerivative d¥=dI×- DNn ✗ dYdn 0 . Identical. shape - Ex:Findrateofchange0th- T t 㱺8¥. N NtO putincat. *Decreasing: . /- \:Max ,-1 \- 1:min \- y :Inflexion.

C2:Integration ⊥Areaunder- meanie. ⊥standard. A-=/baflx)dn fantndn-_%?tc Y^ fix) *Mustwrite. :; lantb)n-11 a b>N Slantb)"dn= tc F *shape- Areaorviceversa. diff.thelarltb). EI:a :[I- Areaunder*Trick: faflxldn=affix)dn. ¥"";curve. ::" ; " " ;>⊥Identities ←diff.the4. fsinlantb)dx=- cost.antb)-1C +"90. /fcoscaxtbdn-1-as.in/antb)tc(3:kinematics fseicantb)dx=tatanlatetb)-1C. Displacement Exp: feantbdn__taea"" JyArea[☒yeioc.mg/%adientddfdiff.of-power SyArea[)gradientdd¥ L f¥bdn=talnlantb)-1C Accelerationreciprocal: ffix) ☒dN=lnlfcx))-1C *Instantaneousrest:4=0. 3rdsecond:btw2ndand3rd. ⊥DefiniteIntegrals. Jbafcx)dn=f-(b)- Fla) *DistancevsDisplacement. /{flx)dn=O. I 1 fabfcx)dx=/abfcxldn €p- :Distancetravelled. ⊥Differentiation-1Integration. Pg160/161. - :Displacement. Ex: d-dxkx-ii.IE]=yz?← Find/3T¥.dk *+ve:assumetotherightFrompart(a)t - ve:assumetotheleft. Method:)dn=If}÷T dnT - T Mum: " Add"2, " remove" } t t Nun Denon. Denon: " add"3. t denom