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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Document preview page 1

AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 1

Document preview content for AP Calculus: With 8 Practice Tests, 15th Edition (2020)

AP Calculus: With 8 Practice Tests, 15th Edition (2020)

Evaluate your certification readiness with AP Calculus: With 8 Practice Tests, 15th Edition (2020), a well-structured revision test.

Elijah Nelson
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 1 preview imageSoRRNA_PETUDI\VrokACK:Rs,KOICEA“ANi\|LHBFor2020&2021testsComprehensivecontentreview>DennisDonovan,M.S.,DavidBock,M.S.,andShirley0.Hockett,M.A.{AP"IsaregisteredtrademarkoftheCollegeBoard,whichwasnot1involvedintheproductionof,anddoesnotendorse,thisproduct.————TE
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 2 preview imageDownloadedfromStudyXY.com®+StudyXYSdYe.o>\|iF’prE\3SStudyAnythingThisContentHasbeenPostedOnStudyXY.comassupplementarylearningmaterial.StudyXYdoesnotendroseanyuniversity,collegeorpublisher.Allmaterialspostedareundertheliabilityofthecontributors.wv8)www.studyxy.com
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 3 preview imageLb9.99999©©9%N)AiWith8PracticeTestsFIFTEENTHEDITIONDennisDonovan,M.S.XaverianBrothersHighSchoolWestwood,MassachusettsDavidBock,M.S.IthacaHighSchool(retired)Shirley0.Hockett,M.A.Formerly,ProfessorofMathematicsIthacaCollegeBARRON'SAPisaregisteredtrademarkoftheCollegeBoard,whichwasnotinvolvedintheproductionof,anddoesnotendorse,thisproduct.©©©©©©©©©©WO)+StudyXY
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 4 preview imageAbouttheAuthorsDennisDonovanhasbeenamathteacheratXaverianBrothersHighSchoolformorethan25years,teachingAPCalculus,bothABandBC,formorethan20years.HehasservedasanAPCalculusReaderandasoneofninenationalQuestionLeadersfortheAPCalculusexam.DennisleadsprofessionaldevelopmentworkshopsformathteachersasaconsultantfortheCollegeBoardanda13RegionalInstructorforTexasInstruments.DavidBocktaughtAPCalculusduringhis35yearsatIthacaHighSchool,andservedforseveralyearsasanExamReaderfortheCollegeBoard.HealsotaughtmathematicsatTompkins-CortlandCommunityCollege,IthacaCollege,andCornellUniversity.Arecipientofseverallocal,state,andnationalteachingawards,Davehascoauthoredfivetextbooks,andnowleadsworkshopsforAPteachers.
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 5 preview imageINMEMORIAMShirleyO.Hockett(1920—2013)ShirleyHocketttaughtmathematicsfor45years,firstatCornellUniversityandlateratIthacaCollege,whereshewasnamedProfessorEmeritain1991.Anoutstandingteacher,shewonnumerousawardsandauthoredsixmathematicstextbooks.Shirley’sexperiencesasanExamReaderandTableLeaderforAPCalculusledhertowritethefirsteverAPCalculusreviewbook,publishedin1971.Herknowledgeofcalculus,attentiontodetail,pedagogicalcreativity,anddedicationtostudentscontinuetoshinethroughoutthisbook.OnbehalfofthethousandsofAPCalculusstudentswhohavebenefitedfromhertirelessefforts,wegratefullydedicatethisreviewbooktoShirley.
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 6 preview image©Copyright2019,2017,2015,2013,2012,2010,2008byKaplan,Inc.,d/b/aBarron’sEducationalSeriesPrioreditions©Copyright2005,2002,1998byKaplan,Inc.,d/b/aBarron’sEducationalSeriesunderthetitleHowtoPreparefortheAPAdvancedPlacementExaminationinCalculusand1995,1992,1987,1983,1971underthetitleHowtoPreparefortheAdvancedPlacementExamination:Mathematics.AllrightsreservedunderInternationalandPan-AmericanCopyrightConventions.Bypaymentoftherequiredfees,youhavebeengrantedthenon-exclusive,non-transferablerighttoaccessandreadthetextofthiseBookonscreen.Nopartofthistextmaybereproduced,transmitted,downloaded,decompiled,reverseengineered,orstoredinorintroducedintoanyinformationstorageandretrievalsystem,inanyformorbyanymeans,whetherelectronicormechanical,nowknownorhereinafterinvented,withouttheexpresswrittenpermissionofthepublisher.PublishedbyKaplan,Inc.,d/b/aBarron’sEducationalSeries750ThirdAvenueNewYork,NY10017www.barronseduc.comISBN:978-1-5062-7192-7InternationalStandardSerialNo.:1940-308910987654321
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 7 preview imageContentsBarron’sEssential5IntroductionTheCoursesTopicOutlinefortheABandBCCalculusExamsTheExaminationsTheGraphingCalculator:UsingYourGraphingCalculatorontheAPExamGradingtheExaminationsThisReviewBookFlashcardsDIAGNOSTICTESTSCalculusABCalculusBCTOPICALREVIEWANDPRACTICE1FunctionsA.DefinitionsB.SpecialFunctionsC.PolynomialandOtherRationalFunctionsD.TrigonometricFunctions
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 8 preview imageE.ExponentialandLogarithmicFunctionsF.ParametricallyDefinedFunctions(BCOnly)G.PolarFunctions(BCOnly)PracticeExercises2LimitsandContinuityA.DefinitionsandExamplesB.AsymptotesC.TheoremsonLimitsD.LimitofaQuotientofPolynomialsE.OtherBasicLimitsF.ContinuityPracticeExercises3DifferentiationA.DefinitionofDerivativeB.FormulasC.TheChainRule;theDerivativeofaCompositeFunctionD.DifferentiabilityandContinuityE.EstimatingaDerivativeEl.NumericallyE2.GraphicallyF.DerivativesofParametricallyDefinedFunctions(BCOnly)G.ImplicitDifferentiationH.DerivativeoftheInverseofaFunctionI.TheMeanValueTheoremJ.IndeterminateFormsandL’Hospital’sRule
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 9 preview imageK.RecognizingaGivenLimitasaDerivativePracticeExercises4ApplicationsofDifferentialCalculusA.Slope;CriticalPointsB.TangentstoaCurveC.IncreasingandDecreasingFunctionsCaseI.FunctionswithContinuousDerivativesCaseII.FunctionsWhoseDerivativesHaveDiscontinuitiesD.Maximum,Minimum,Concavity,andInflectionPoints:DefinitionsE.Maximum,Minimum,andInflectionPoints:CurveSketchingCaseI.FunctionsThatAreEverywhereDifferentiableCaseII.FunctionsWhoseDerivativesMayNotExistEverywhereF.GlobalMaximumorMinimumCaseI.DifferentiableFunctionsCaseII.FunctionsThatAreNotEverywhereDifferentiableG.FurtherAidsinSketchingH.Optimization:ProblemsInvolvingMaximaandMinimaI.RelatingaFunctionandItsDerivativesGraphicallyJ.MotionAlongaLineK.MotionAlongaCurve:VelocityandAccelerationVectors(BCOnly)L.Tangent-LineApproximations
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 10 preview imageM.RelatedRatesN.SlopeofaPolarCurve(BCOnly)PracticeExercises5AntidifferentiationA.AntiderivativesB.BasicFormulasC.IntegrationbyPartialFractions(BCOnly)D.IntegrationbyParts(BCOnly)E.ApplicationsofAntiderivatives;DifferentialEquationsPracticeExercises6DefiniteIntegralsA.FundamentalTheoremofCalculus(FTC);EvaluationofDefiniteIntegralB.PropertiesofDefiniteIntegralsC.DefinitionofDefiniteIntegralastheLimitofaRiemannSumD.TheFundamentalTheoremAgainE.ApproximationsoftheDefiniteIntegral;RiemannSumsEl.UsingRectanglesE2.UsingTrapezoidsE3.ComparingApproximatingSumsF.GraphingaFunctionfromItsDerivative;AnotherLookG.InterpretingInxasanAreaH.AverageValuePracticeExercises
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 11 preview image7ApplicationsofIntegrationtoGeometryA.AreaAl.AreaBetweenCurvesA2.UsingSymmetryB.VolumeB1.SolidswithKnownCrossSectionsB2.SolidsofRevolutionC.LengthofCurve(ArcLength)(BCOnly)D.ImproperIntegrals(BCOnly)PracticeExercises8FurtherApplicationsofIntegrationA.MotionAlongaStraightLineB.MotionAlongaPlaneCurve(BCOnly)C.OtherApplicationsofRiemannSumsD.FTC:DefiniteIntegralofaRateIsNetChangePracticeExercises9DifferentialEquationsA.BasicDefinitionsB.SlopeFieldsC.Euler’sMethod(BCOnly)D.SolvingFirst-OrderDifferentialEquationsAnalyticallyE.ExponentialGrowthandDecayCaseI:ExponentialGrowthCaseII:RestrictedGrowthCaseIII:LogisticGrowth(BCOnly)
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 12 preview imagePracticeExercisesl0SequencesandSeries(BCOnly)A.SequencesofRealNumbersB.InfiniteSeriesB1.DefinitionsB2.TheoremsAboutConvergenceorDivergenceofInfiniteSeriesB3.TestsforConvergenceofInfiniteSeriesB4.TestsforConvergenceofNonnegativeSeriesB5.AlternatingSeriesandAbsoluteConvergenceC.PowerSeriesC1.Definitions;ConvergenceC2.FunctionsDefinedbyPowerSeriesC3.FindingaPowerSeriesforaFunction:TaylorandMaclaurinSeriesC4.ApproximatingFunctionswithTaylorandMaclaurinPolynomialsC5.Taylor’sFormulawithRemainder;LagrangeErrorBoundC6.ComputationswithPowerSeriesC7.PowerSeriesoverComplexNumbersPracticeExercises[1MiscellaneousMultiple-ChoicePracticeQuestions2MiscellaneousFree-ResponsePracticeExercisesABPRACTICEEXAMINATIONS
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 13 preview imageAB1AB?2AB3BCPRACTICEEXAMINATIONSBC1BC2BC3Appendix:FormulasandTheoremsforReferenceIndex
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 14 preview image5.Barron’sEssential5Asyoureviewthecontentinthisbooktoworktowardearningthat5onyourAPCALCULUSABexam,herearefivethingsthatyouMUSTknowaboveeverythingelse:Learnthebasicfacts:®derivatives(p.119)andantiderivatives(p.217)ofcommonfunctions;eotheProduct(p.119),Quotient(p.119),andChainRules(p.120)forfindingderivatives;othemidpoint,leftandrightrectangle,andtrapezoidapproximationsforestimatingdefiniteintegrals(p.254);ofindingantiderivativesbysubstitution(p.219);otheimportanttheorems:Rolle’sTheorem(p.135),theMeanValueTheorem(p.134),andespeciallytheFundamentalTheoremofCalculus(p.247).(Barron’sAPCalculusFlashcardsareanothergreatwaytostudythese!)Understandthataderivativeisaninstantaneousrateofchange,andbeabletoapplythatconceptto:eusingL’Hospital’sRuletofindlimitsofindeterminateforms(onlygand2)(p.136);eofindequationsoftangentlines(p.165);
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 15 preview image®determinewhereafunctionisincreasing/decreasing(p.166),isconcaveup/down(p.167),orhasmaxima,minima,orpointsofinflection(pp.168,173);®analyzethespeed,velocity,andaccelerationofanobjectinmotion(p.183);®solverelatedratesproblems(p.191),usingimplicitdifferentiation(p.131)whennecessary.Understandthatintegralsrepresentaccumulationfunctionsbasedonantiderivatives,andbeabletoapplythoseconceptsto:eotheaveragevalueofafunction(p.267);®area(p.287)andvolume(p.294);®positionofobjectinmotionanddistancetraveled(p.341);eototalamountwhengiventherateofaccumulation(p.346);eodifferentialequations,includingsolutionsandslopefields(p.359).Beabletoapplyanyoftheabovecalculusconceptstofunctionsdefinedalgebraically,graphically,orintables.Beabletomaximizeyourscoreontheexamby:eansweringallthemultiple-choicequestions;
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AP Calculus: With 8 Practice Tests, 15th Edition (2020) - Page 16 preview image®knowinghowandwhentouseyourcalculator,andwhennotto;ounderstandingwhatworkyouneedtoshow;®knowinghowtoexplain,interpret,andjustifyanswerswhenaquestionrequiresthat.(Thefree-responsesolutionsinthisbookmodelsuchanswers.)Asyoureviewthecontentinthisbooktoworktowardearningthat5onyourAPCALCULUSBCexam,herearefivethingsthatyouMUSTknowaboveeverythingelse:MastertheEssential5listedfortheABCalculusExam.TheseformthecoreforquestionsthatdetermineyourABsubscore,andprovidetheessentialknowledgebaseyou’llneedforquestionsrelatedtotheadditionalBCtopics.UnderstandhowtoextendABCalculusconceptstomoreadvancedsituations,including:®usinglimitstoanalyzeimproperintegrals(p.303);®solvinglogisticdifferentialequations(p.379)andestimatingsolutionsusingEuler’smethod(p.365);ofindingantiderivativesusingintegrationbyparts(p.225)orpartialfractions(p.224);ofindinglengthofcurve(arclength)(p.301).
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