AP Calculus Premium, 2022-2023 (2021)

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THETRUSTEDNAMEINTESTPREP4P12full-lengthpracticetestswithdetailedanswerexplanationsOnlinepracticewithatimedtestoptionandscoringComprehensivereviewandpracticeforalltopicsontheexamExperttipsplusBarron's“Essential5”thingsyouneedtoknowDennisDonovan,M.S.,W.ONLINEPRACTICEDavidBock,M.S.,andShirleyO.Hockett,MAP®isaTeteredple’oftheCollegeBoard,whichwasnotinvolved

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DownloadedfromStudyXY.com®+StudyXYSdYe.o>\|iF’prE\3SStudyAnythingThisContentHasbeenPostedOnStudyXY.comassupplementarylearningmaterial.StudyXYdoesnotendroseanyuniversity,collegeorpublisher.Allmaterialspostedareundertheliabilityofthecontributors.wv8)www.studyxy.com

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BARRON'STHETRUSTEDNAMEINTESTPREPPremium2022-2023DennisDonovan,M.S.DavidBock,M.S.ShirleyO.Hockett,M.A.

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ContinueYourPracticeOnlineToaccessBarron'sOnlineLearningHub,goto:online.barronsbhooks.comBARRON'S

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©Copyright2022,2019,2017,2015,2013,2012,2010,2008byKaplan,Inc.,d/b/aBarron’sEducationalSeriesPrioreditions©Copyright2005,2002,1998byKaplan,Inc.,d/b/aBarron'sEducationalSeriesunderthetitleHowtoPreparefortheAPAdvancedPlacementExaminationinCalculusand1995,1992,1987,1983,1971underthetitleHowtoPreparefortheAdvancedPlacementExamination:Mathematics.Allrightsreserved.Nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeanswithoutthewrittenpermissionofthecopyrightowner.PublishedbyKaplan,Inc.,d/b/aBarron’sEducationalSeries1515WCypressCreekRoadFortLauderdale,FL.33309www.barronseduc.comISBN:978-1-5062-7959-610987654321Kaplan,Inc.,d/b/aBarron’sEducationalSeriesprintbooksareavailableatspecialquantitydiscountstouseforsalespromotions,employeepremiums,oreducationalpurposes.Formoreinformationortopurchasebooks,pleasecalltheSimon&Schusterspecialsalesdepartmentat866-506-1949.+StudyXY

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DennisDonovanhasbeenamathteacheratXaverianBrothersHighSchoolformorethan25years,teachingAPCalculus,bothABandBC,formorethan20years.HehasservedasanAPCalculusReaderandasoneofninenationalQuestionLeadersfortheAPCalculusexam.DennisleadsprofessionaldevelopmentworkshopsformathteachersasaconsultantfortheCollegeBoardandaT®RegionalInstructorforTexasInstruments.DavidBocktaughtAPCalculusduringhis35yearsatIthacaHighSchool,andservedforseveralyearsasanExamReaderfortheCollegeBoard.HealsotaughtmathematicsatTompkins-CortlandCommunityCollege,IthacaCollege,andCornellUniversity.Arecipientofseverallocal,state,andnationalteachingawards,Davehascoauthoredfivetextbooks,andnowleadsworkshopsforAPteachers.INMEMORIAMShirleyO.Hockett(1920-2013)ShirleyHocketttaughtmathematicsfor45years,firstatCornellUniversityandlateratIthacaCollege,whereshewasnamedProfessorEmeritain1991.Anoutstandingteacher,shewonnumerousawardsandauthoredsixmathematicstextbooks.Shirley’sexperiencesasanExamReaderandTableLeaderforAPCalculusledhertowritethefirsteverAPCalculusreviewbook,publishedin1971.Herknowledgeofcalculus,attentiontodetail,pedagogicalcreativity,anddedicationtostudentscontinuetoshinethroughoutthisbook.OnbehalfofthethousandsofAPCalculusstudentswhohavebenefitedfromhertirelessefforts,wegratefullydedicatethisreviewbooktoShirley.+StudyXxy

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ReviewmaterialontopicscoveredonlyinCalculusBCisindicatedbyanasterisk(*).HowToUseThisBookBarron’sEssential5IntroductionTheCoursesTopicOutlinefortheABandBCCalculusExamsTheExaminationsTheGraphingCalculator:UsingYourGraphingCalculatorontheAPExamGradingtheExaminationsDIAGNOSTICTESTSDiagnosticTestCalculusABDiagnosticTestCalculusBCTOPICALREVIEWANDPRACTICE1FunctionsA.DefinitionsB.SpecialFunctionsC.PolynomialandOtherRationalFunctionsD.TrigonometricFunctionsE.ExponentialandLogarithmicFunctions+StudyXxy

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*F.ParametricallyDefinedFunctions*G.PolarFunctionsPracticeExercises2LimitsandContinuityA.DefinitionsandExamplesB.AsymptotesC.TheoremsonLimitsD.LimitofaQuotientofPolynomialsE.OtherBasicLimitsF.ContinuityPracticeExercises3DifferentiationA.DefinitionofDerivativeB.FormulasC.TheChainRule:TheDerivativeofaCompositeFunctionD.DifferentiabilityandContinuityE.EstimatingaDerivativeE1.NumericallyE2.Graphically*F.DerivativesofParametricallyDefinedFunctionsG.ImplicitDifferentiationH.DerivativeoftheInverseofaFunctionI.TheMeanValueTheoremJ.IndeterminateFormsandL’Hospital’sRuleK.RecognizingaGivenLimitasaDerivativePracticeExercises4ApplicationsofDifferentialCalculusA.Slope;CriticalPointsB.TangentstoaCurveC.IncreasingandDecreasingFunctionsCaseI.FunctionswithContinuousDerivatives

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CaseII.FunctionsWhoseDerivativesHaveDiscontinuitiesD.Maximum,Minimum,Concavity,andInflectionPoints:DefinitionsE.Maximum,Minimum,andInflectionPoints:CurveSketchingCaseI.FunctionsThatAreEverywhereDifferentiableCaseII.FunctionsWhoseDerivativesMayNotExistEverywhereF.GlobalMaximumorMinimumCaseI.DifferentiableFunctionsCaseII.FunctionsThatAreNotEverywhereDifferentiableG.FurtherAidsinSketchingH.Optimization:ProblemsInvolvingMaximaandMinimaI.RelatingaFunctionandItsDerivativesGraphicallyJ.MotionAlongaLine*K.MotionAlongaCurve:VelocityandAccelerationVectorsL.Tangent-LineApproximationsM.RelatedRates*N.SlopeofaPolarCurvePracticeExercises5AntidifferentiationA.AntiderivativesB.BasicFormulas*C.IntegrationbyPartialFractions*D.IntegrationbyPartsE.ApplicationsofAntiderivatives;DifferentialEquationsPracticeExercises6DefiniteIntegralsA.FundamentalTheoremofCalculus(FTC);EvaluationofDefiniteIntegralsB.PropertiesofDefiniteIntegralsC.DefinitionofDefiniteIntegralastheLimitofaRiemannSumD.TheFundamentalTheoremAgainE.ApproximationsoftheDefiniteIntegral;RiemannSumsEl.UsingRectanglesE2.UsingTrapezoidsE3.ComparingApproximatingSums

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F.GraphingaFunctionfromItsDerivative;AnotherLookG.InterpretingInxasanAreaH.AverageValuePracticeExercises7ApplicationsofIntegrationtoGeometryA.AreaAl.AreaBetweenCurvesA2.UsingSymmetry*A3.RegionBoundedbyPolarCurveB.VolumeB1.SolidswithKnownCrossSectionsB2.SolidsofRevolution*C.LengthofCurve(ArcLength)*D.ImproperIntegralsPracticeExercises8FurtherApplicationsofIntegrationA.MotionAlongaStraightLine*B.MotionAlongaPlaneCurveC.OtherApplicationsofRiemannSumsD.FTC:DefiniteIntegralofaRateIsNetChangePracticeExercises9DifferentialEquationsA.BasicDefinitionsB.SlopeFields*C.Euler'sMethodD.SolvingFirst-OrderDifferentialEquationsAnalyticallyE.ExponentialGrowthandDecayCaseI:ExponentialGrowthCaseII:RestrictedGrowth*CaseIII:LogisticGrowthPracticeExercises

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10*SequencesandSeriesA.SequencesofRealNumbersB.InfiniteSeriesB1.DefinitionsB2.TheoremsAboutConvergenceorDivergenceofInfiniteSeriesB3.TestsforConvergenceofInfiniteSeriesB4.TestsforConvergenceofNonnegativeSeriesB5.AlternatingSeriesandAbsoluteConvergenceC.PowerSeriesC1.Definitions;ConvergenceC2.FunctionsDefinedbyPowerSeriesC3.FindingaPowerSeriesforaFunction:TaylorandMaclaurinSeriesC4.ApproximatingFunctionswithTaylorandMaclaurinPolynomialsC5.Taylor’sFormulawithRemainder;LagrangeErrorBoundC6.ComputationswithPowerSeriesC7.PowerSeriesoverComplexNumbersPracticeExercises11MiscellaneousMultiple-ChoicePracticeQuestions12MiscellaneousFree-ResponsePracticeExercisesABPRACTICETESTSABPracticeTest1ABPracticeTest2ABPracticeTest3BCPRACTICETESTSBCPracticeTest1BCPracticeTest2BCPracticeTest3Appendix:FormulasandTheoremsforReference+StudyXxy

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Index

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HowToUseThisBookDiagnosticTestsThediagnostictestsforbothABandBCCalculusarepracticeAPtests.Theyarefollowedbysolutionskeyedtothecorrespondingtopicalreviewchapter.ReviewandPractice“TopicalReviewandPractice”includes10chapterswithnotesonthemaintopicsoftheCalculusABandBCsyllabiandnumerouscarefullyworked-outexamples.Eachchapterconcludeswithasetofmultiple-choicequestions,usuallydividedintocalculatorandno-calculatorsections,followedimmediatelybyanswersandsolutions.Thisreviewisfollowedbyfurtherpractice:(1)Chapter11,whichincludesasetofmultiple-choicequestionsonmiscellaneoustopicsandananswerkeyandanswerexplanations;(2)Chapter12,asetofmiscellaneousfree-responseproblemsthatareintendedtobesimilartothoseinSectionIIoftheAPexaminations.Theyarefollowedbydetailedsolutions.Inthisebook,reviewmaterialontopicscoveredonlyinCalculusBCisindicatedbyanasterisk(*),asarebothmultiple-choicequestionsandfree-response-typeproblemsthatarelikelytooccuronlyonaBCexamination.PracticeTestsThenextpartofthisbook,titled“ABPracticeTests”and“BCPracticeTests,”hasthreeABandthreeBCpracticeteststhatsimulatetheactualAPexaminations.Eachisfollowedbyanswersandexplanations.

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OnlinePracticeInadditiontothetwodiagnostictestsandsixpracticetestswithinthisbook,therearealsofourfull-lengthonlinepracticetests.Youmaytakethesetestsinpractice(oruntimed)modeorintimedmode.TwooftheseonlinetestsmirrortheABtest,andtheothertwomirrortheBCtest.Detailedanswersandexplanationsareprovidedforeveryquestion.Refertothecardatthebeginningofthisbook,whichprovidesinstructionsforaccessingtheseonlinetests.ForTeachersTheteacherwhousesthisbookwithaclassmayprofitablydosoinanyofseveralways.Ifthebookisusedthroughoutayear’scourse,theteachercanassignallorpartofeachsetofmultiple-choicequestionsandsomemiscellaneousexercisesafterthetopichasbeencovered.Thesesetscanalsobeusedforreviewpurposesshortlybeforeexaminationtime.Thepracticetestswillalsobeveryhelpfulwhenreviewingtowardtheendoftheyear.TeachersmayalsoassembleexaminationsbychoosingappropriateproblemsfromthesamplemiscellaneouspracticequestionsinChapters11and12.ForStudentsStudentswhousethisbookindependentlywillimprovetheirperformancebystudyingtheillustrativeexamplescarefullyandtryingtocompletepracticeproblemsbeforereferringtothesolutions.

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bdBARRON’SESSENTIAL5Asyoureviewthecontentinthisbooktoworktowardearningthat5onyourAPCALCULUSABexam,herearefivethingsthatyouMUSTknowaboveeverythingelse:1Learnthebasicfacts:+derivatives(p.115)andantiderivatives(p.213)ofcommonfunctions;+theProduct(p.115),Quotient(p.115),andChainRules(p.116)forfindingderivatives;+themidpoint,leftandrightrectangle,andtrapezoidapproximationsforestimatingdefiniteintegrals(p.248);+findingantiderivativesbysubstitution(p.224);+theimportanttheorems:Rolle’sTheorem(p.132),theMeanValueTheorem(p.131),andespeciallytheFundamentalTheoremofCalculus(p.241).2Understandthataderivativeisaninstantaneousrateofchange,andbeabletoapplythatconceptto:+useL’Hospital’sRuletofindlimitsofindeterminateforms(only2and2)(p.133);+findequationsoftangentlines(p.161);+determinewhereafunctionisincreasing/decreasing(p.163),isconcaveup/down(p.164),orhasmaxima,minima,orpointsofinflection(pp.165,170);+analyzethespeed,velocity,andaccelerationofanobjectinmotion(p.180);+solverelatedratesproblems(p.188),usingimplicitdifferentiation(p.128)whennecessary.

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3Understandthatintegralsrepresentaccumulationfunctionsbasedonantiderivatives,andbeabletoapplythoseconceptsto:+theaveragevalueofafunction(p.261);+area(p.283)andvolume(p.290);+thepositionofobjectsinmotionanddistancetraveled(p.337);+totalamountwhengiventherateofaccumulation(p.344);+differentialequations,includingsolutionsandslopefields(p.357).4Beabletoapplyanyoftheabovecalculusconceptstofunctionsdefinedalgebraically,graphically,orintables.5Beabletomaximizeyourscoreontheexamby:+answeringallthemultiple-choicequestions;+knowinghowandwhentouseyourcalculator,andwhennotto;+understandingwhatworkyouneedtoshow;+knowinghowtoexplain,interpret,andjustifyanswerswhenaquestionrequiresthat.(Thefree-responsesolutionsinthisbookmodelsuchanswers.)

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