资源描述：
《2010年高考压轴题数学跟踪演练系列六》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
2010年高考压轴题数学跟踪演练系列六Preparingforthe2010collegeentranceexaminationmathematics一一thefinaltitletrackingexercisesseriessix(theonly1.outof14)Asshowninthediagram,thefocusoftheparabolaisF,andthepointPmovesinthestraightline,andthetwotangentPAandPBoftheparabolaCaretangenttotheAandCrespectivelyatthePandBpoints(1)thetrajectoryequationofgravitycenterGDeltaAPB・(2)proof/PFA=/PFB.Solution:(1)setthetangentpoint,AandBcoordinates,respectively,TheAPequationforthetangentformula:ThetangentBPequationis:Coordinatesolutionforp:SothecoordinatesofthegravitycenterGforDeltaAPB,Therefore,themotionofthepointPonthelineLisobtained,andthelocusequationofthecenterofgravityGisobtained:(2)method1:becauseBecausePinparabola,then LSimilarlyL/AFP二/PFB.Method2:whenpispsocoordinates,distancetothelineAF:ThatisSothedistancePtothelineBF:Sodl二d2/AFP二/PFB.,i.e.TheequationoflinearAFatthattime:EquationoflinearBF:SothedistancePtothelineAF:Similarly,availablePtoastraightlinedistanceofBF,thuscanbeobtainedbydl二d2/AFP二/PFB..(theonly2.outof12)LetAandBbetwopointsontheellipse・ThepointN(1,3)isthemidpointofthelinesegmentAB.TheverticalbisectorofthelinesegmentABintersectstheellipseatCandDtwopoints(I)determinetherangeofvalues,andfindtheequationofthelineAB; (I)trytodeterminewhetherthereissuchawaythatA,B,C,andDareonthesamecircleatfourpointsAndexplainthereasons(thisquestiondoesnotrequiredrawingontheanswersheet)Thistextmainlyexaminesthebasicknowledgeofstraightline,circleandellipseplaneanalyticgeometryandreasoningabilityandcomprehensivesolutiontotheproblem・(I)1solutions:accordingtothemeaningofproblems,alinearABequation,finishing1.Settwodifferentrootsofanequation,StarIIAndtheN(1,3)isthemidpointofthelineABThesolutionisk二-1,andthevaluerangeis(12++)Thus,theequationofthelinearABisSolution2:lettherebeAccordingtoa.,DreamsofN(1,3)isthecenteroftheAB,RTheN(1,3)intheelliptic,triangular TherangeisR(12,+2).TheequationofthelinearABisY-3二-(x-1),thatis,x+y-4二0.(I)for1CD:dreamsperpendicularbisectorofthelineCDAB,frequencyequationwasy3二x1,Xy+2二0,Bysubstitutingtheellipticequation,itissortedoutThemidpointoftheCDistwooftheequations,LSobythechordformulaavailable・ThelinearABequationX+y4=0,ellipticequation,substitutionSimilarlyavailable・Atthetimeofimprisonment,Supposethatthereis>12,sothatA,B,CandDarefourpointstogether,thenCDmustbethediameterofthecircle,andthepointMisthecenterofthecircleMABisthedistancetothelineThen,by4,and,andthePythagoreantheoremcanbeSowhen>12,A,B,C,D,fourpointsevenlyinMasthecenterof thecircle,Fortheradiusofthecircle(Note:thelaststepintheabovesolutioncanbeobtainedasfollows:)A,B,C,DcircleDeltaACDrighttriangle,A|DN|angle|AN|2二|CN|,ThatistheFromthetypeofknowledge,andontheleftBythepeopleandknowtherighttypeThestartypewasestablished,namelyA,B,C,Droundtotaloffourpoints・Solution2:(II)solution1andlambda>12,DreamsCDperpendicularbisectorAB,linearCDequationintotriangular,ellipticequation,tidy3ThelinearABequationX+y4=0substitution,ellipticequation,tidy5. SolutionandformulacanbeobtainedMightaswellsetLCanbecalculated,henceAinCDdiametercircle・BasasymmetricalpointaboutCDA,A,B,C,RDroundtotaloffourpoints・(Note:alsoavailableproofofthePythagoreantheoremACtAD)(theonly3.outof14)Theknowninequalityisanintegergreaterthan2,whichmeansnomorethanthelargestinteger(I)prove(II)whetherthereisalimittoguessthesequence?Ifyouhave,writethelimit(don，tproveit);(III)trytodetermineapositiveintegerN,whichmakesanyb>0availableatthattimeThecomprehensiveapplicationofthemaintestsequence,andtheylimitinequalityandrecursivethoughtissummedup.(I)method1:whendreams ThatisHenceAllinequalitiescanbesummeduponbothsidesBytheknowninequalities,whenn=3is,DreamsLaw2:setup,firstofall,usemathematicalinductiontoproveinequality(I)whenn二3,byKnowledgeinequalityisestablished(II)whenn=k(k二3),inequality,i・e.beThatis,inequalityisalsoestablishedwhenn二k+1isappliedBy(I),(II)knowledge,Bytheknowninequalities(I)havingalimit;and(II)dreams IsthereTherefore,N=1024canbeusedwhenn>Nisavailable4.asshowninfigure,thecenteroftheellipseisknownatthecoordinateorigin,thefocusisFl,F2isontheXaxis,thelengthofthelongaxisA1A2is4,andtheintersectionpointoftheleftquasilineLandtheXaxisisM,and|IA11二|A1F1二2:1.(I)theequationfortheellipse;(II)ifPisontheL/F1PF2point,seekingthemaximumvalue・Themaintopicofthisarticleistoexaminethegeometricpropertiesofellipse,theellipticequation,theangleoftwostraightlinesandotherbasicknowledge,toexaminethebasicideasandmethodsofanalyticgeometryandcomprehensiveproblem-solvingability・14marksSolution:(I)theellipticequationisset,andthehalffocallengthis(II)5.theimageofafunctionanditsoriginissymmetricabouttheorigin(I)theanalyticexpressionofthefunction;(II)solvinginequalities; (3)iftheupperisanincreasingfunction,therangeoftherealnumberisdeterminedThispapermainlyexaminesthebasicfunctionsofthesymmetryofthefunctionimage,thebasicpropertiesofthetwofunctionandtheapplicationofinequality,andtheabilitytoanalyzeandsolvetheproblemcomprehensivelybyusingtheknowledgelearned・Thescoreis14Solution:(I)anypointontheimageofafunction,thepointofsyminetryontheoriginis,thenIntheimageonthefunctionofdreamsL(II)byThen,,AtthispointthereisnosolutiontoinequalityAtthattime,thesolutionTherefore,thesolutionsetoftheoriginalinequalityis(Ill)1.2 I)II)(the6.outof16)inatotalof3items,firstitemsoutof4points,secondoutof6items,thirditemsoutof6points・ThedomainsdefinedarefunctionsofDf,Dg,y二f(x),andy二g(x),F(x)-G(x)x,DfandX,whenDgRequirements:functionH(x)二f(x)x,DfandxDgwhenG(x)x,DgandxDfwhen(1)ifthefunctionf(x)=g(x),=x2,x,R,H(x)writefunctionanalyticformula;(2)findtherangeofthefunctionH(x)intheproblem(1);(3)ifG(x)二f(x+alpha),isaconstant,andalpha二[0,PI],pleasedesignadomainasafunctionofRy二f(x),andanalphavalue,theH(x)二cos4x,andtoproveit.[solution](1)II(x)=x(=infty,1),(1+2)1x=l(2)whenx=1,H二=xT++2(x),Ifx>l,thenH(x)二4,whichequalswhenx=2wasestablishedIf x
