SAT2数学Level_2常用公式

SATII数学LevelII常用公式MATHLEVELIIINTRODUCTIONTOFUNCTIONS(f+g)(x)=f(x)+g(x)(f·g)(x)=f(x)·g(x)(f/g)(x)=f(x)/g(x)(fg)(x)=f(x)g(x)=f(g(x))POLYNOMIALFUNCTIONSLinearFunctionsDistance=221212(x-x)+(y-y)Distance=1122AxByCABTan=12121mmmm（mistheslopeofl.）242bbacxaSumofzeros(roots)=baProductofzeros(roots)=caTRIGONOMETRICFUNCTIONSGraphs:()istheamplitudeistheperiodofthegraphCisthephaseshiftByAfBxCAfBsincsc1cossec1tancot1sintancoscoscotsinQuadrantIIIIIIIVFunction:sin,csc++--cos,sec+--+tan,cot+-+-ArcsandAngles212srArSpecialAngles02322sine010-10cosine10-101tangent0und0und0cotangentund0und0undsecant1und-1und1cosecantund1und-1und*und:meansthatthefunctionisundefinedbecausethedefinitionofthefunctionnecessitatesdivisionbyzero.306or454or603orsine122232cosine322212tangent3313cotangent3132secant23322cosecant22233Formulas:2222221.sincos12.tan1sec3.cot1csc4.sin()sincoscossin5.sin()sincoscossin6.cos()coscossinsin7.cos()coscossinsintantan8.tan()1tantan9.taxxxxxxABABABABABABABABABABABABABABABtantann()1tantanABABAB2222210.sin22sincos11.cos2cossin12.cos22cos113.cos212sin2tan14.tan21tan11cos15.sin2211cos16.cos2211cos17.tan21cos1cos18.sinsin19.1cosAAAAAAAAAAAAAAAAAAAAAAAA*ThecorrectsignforFormulas15through17isdeterminedbythequadrantinwhichangle12Alies.TrianglesLawofsines:sinsinsinABCabcLawofcosines:2222222222cos2cos2cosabcbcAbacacBcababCAreaofa:1sin21sin21sin2AreabcAAreaacBAreaabCMISCELLANEOUSRELATIONSANDFUNCTIONSThegeneralquadraticequation220AxBxyCyDxEyFIf240BACandAC,thegraphisacircle.If240BACandAC,thegraphisanellipse.If240BAC,thegraphisaparabola.If240BAC,thegraphisahyperbola.Circle:222()()xhykrEllipse:ifCA,2222()()1xhykab,transverseaxishorizontalifCA,2222()()1xhykba,transverseaxisvertical,where222abcVertices:aunitsalongmajoraxisfromcenterFoci:cunitsalongmajoraxisfromcenterLength=2bEccentricity=ca1Lengthoflatusrectum=22baParabola:ifC=0,2()4()xhpykopensupanddown---axisofsymmetryisverticalifA=0,2()4()ykpxhopenstotheside---axisofsymmetryishorizontalEquationofaxisofsymmetry:x=hifverticaly=kifhorizontalFocus:punitsalongtheaxisofsymmetryfromvertexEquationofdirectrix:y=-pifaxisofsymmetryisverticalx=-pifaxisofsymmetryishorizontalEccentricity=ca=1Lengthoflatusrectum=4pHyperbola:2222()()1xhykab,transverseaxishorizontal2222()()1ykxhab,transverseaxisvertical,where222cabVertices:aunitsalongthetransverseaxisfromcenterFoci:cunitsalongthetransversefromcenterLengthoflatusrectum=22baEccentricity=ca1theslopesoftheasymptotesareab(vertical)orba(horizontal).ExponentialandLogarithmicFunctions0log11()()log()logloglog10loglogloglog1log()loglogloglogbababaabbaaababaaabbbbpbbbbxbbabaxxxxxxxxxxxxyxypqpqbpppqqbpxpppbGreatestIntegerFunctions:,whereiisanintergerand1xiixiPolarCoordinates:222cossinxryrxyrMISCELLANEOUSTOPICS!(1)(2)...321nnnnPermutations:Circularpermutation(e.g.,aroundatable)ofnelements=(1)!nCircularpermutation(e.g.,beadsonabracelet)ofnelements=(1)!2nPermutationsofnelementswitharepetitionsandwithbrepetitions=!!!nab!!nrnPnrtheproductofthelargestrfactorsofn!!!nrnPrrrThenumberofcombinationsofnthingstakenratatimeisdenotedbynrCorC(n,r)ornr.nnrnrBinomialTheorem:1nrrrnrTCabProbability:Independentevents:()()()PABPAPBMutuallyexclusiveevents:()0()()()PABandPABPAPBSequencesandSeriesIngeneral,anarithmeticsequenceisdenotedby11111,,2,3......(1)ttdtdtdtnd11()2[2(1)]2nnnnSttornStndIngeneral,ageometricsequenceisdenotedby23111111,,,,...,nttrtrtrtr1(1)1nntrSr1lim1nntSrGeometryandVectorsIf12(,)Vvvand12(,)Uuu,1122(,)UVuvuv2212()()Vvv1122VUvuvuTwovectorsareperpendicularifandonlyif0VULogic:()()Ifistrue,then''isalsotrue.conjunctionABdisjunctionABABBADeterminates:acadbcbd,axbycIfdxeyfcbacfedfxyababdedeGeometry:Distancebetweentwopointswithcoordinates111222222121212(,,),,()()()xyzandxyzxxyyzzThedistancebetweenapointandaplane:Distance=111222AxByCzDABCTriange:Heron’sformular:A=()()();,,arethethreesidesofthetriangle,1s=()2ssasbscabcabcRhombus:Area=bh=121;,,2ddbbasehheightddiagonalCylinderVolume=2rhLatersurfacearea=2rhTotalsurfacearea=222rhrCone:Thevolumeofthecone:213VrhLatersurfacearea22rrh12clTotalsurfacearea222rrhrSphereVolume=343rSurfacearea=24r