The Princeton Review: Cracking the AP calculus AB exam (2019)

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DownloadedfromStudyXY.com[=Ww+StudyXYoias.Za\Rr'BE\StudyAnythingThisContentHasbeenPostedOnStudyXY.comassupplementarylearningmaterial.StudyXYdoesnotendroseanyuniversity,collegeorpublisher.Allmaterialspostedareundertheliabilityofthecontributors.|8)www.studyxy.com

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EditorialRobFranek,Editor-in-ChiefDavidSoto,DirectorofContentDevelopmentStephenKoch,SurveyManagerDeborahWeber,DirectorofProductionGabrielBerlin,ProductionDesignManagerSelenaCoppock,ManagingEditorAaronRiccio,SeniorEditorMeaveShelton,SeniorEditorChrisChimera,EditorSarahLitt,EditorOrionMcBean,EditorBrianSaladino,EditorEleanorGreen,EditorialAssistantPenguinRandomHousePublishingTeamTomRussell,VP,PublisherAlisonStoltzfus,PublishingDirectorAmandaYee,AssociateManagingEditorEllenReed,ProductionManagerSuzanneLee,DesignerThePrincetonReview110East42ndStreet,7thFloorNewYork,NY10017Email:editorialsupport@review.comCopyright©2019byTPREducationIPHoldings,LLC.Allrightsreserved.PublishedintheUnitedStatesbyPenguinRandomHouseLLC,NewYork,andinCanadabyRandomHouseofCanada,adivisionofPenguinRandomHouseLtd.,Toronto.TermsofService:ThePrincetonReviewOnlineCompanionTools(“StudentTools”)forretailbooksareavailableforonlythetwomostrecenteditionsofthatbook.StudentToolsmaybeactivatedonlytwicepereligiblebookpurchasedfortwoconsecutive12-monthperiods,foratotalof24monthsofaccess.ActivationofStudentToolsmorethantwiceperbookisindirectviolationoftheseTermsofServiceandmayresultindiscontinuationofaccesstoStudentToolsServices.

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TradePaperbackISBN9780525568155EbookISBN9780525568537APisatrademarkregisteredandownedbytheCollegeBoard,whichisnotaffiliatedwith,anddoesnotendorse,thisproduct.ThePrincetonReviewisnotaffiliatedwithPrincetonUniversity.Editor:AaronRiccioProductionEditors:LizDacey,LyssaMandelProductionArtist:DeborahWeberCoverartbyJimZuckerman/AlamyStockPhotoCoverdesignbySuzanneLeev5.4a+StudyXxy

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AcknowledgmentsFirstofall,|wouldliketothankArnoldFeingoldandPeterB.Kahnforonceagaindoingeveryproblem,readingeveryword,andotherwiselendingtheirinvaluableassistance.|alsowanttothankAaronRiccioforbeingaterrificeditoronthiseditionofthebook,GaryKingforhisfirst-ratereading,analysis,andcontributions,andtheproductionteamofLizRutzel,HarmonyQuiroz,andDeborahWeber.ThankstoFrank,withoutwhoseadvice|neverwouldhavetakenthispath.ThankstoJeffrey,Miriam,andVickiformoralsupport.ThanksMom.Finally,|wouldliketothankthepeoplewhoreallymadeallofthiseffortworthwhile—mystudents.|hopethat|haven'tomittedanyone,butif|have,thefaultisentirelymine.AaronandSasha,Aaron,AaronT.,AbbyB.,AbbyF.,AbbyH.,AbbyL.,Abbye,AbigailH.,Addie,Aidan,AlanM.,AlbertG.,AlecG,AlecM.,AlecR.,AlexandClaire,AlexA.,AlexB.,AlexandDanielaB.,AlexF.,AlexD.,AlexG.,AlexH.,Alex|.,AlexS.,AlexandGabe,Alexa,Alexandra,NatalieandJason,Alexes,AlexisandBrittany,AliandJon,AliandAmyZ.,AliH.,Alice,AliceC.,Alicia,Alisha,Allegra,AllieandLauren,AllisonandAndrew,AllisonH.,AllisonandMattS.,AllisonR.,Ally,AllyM.,AllyT.,AllyW.,AlyandLauren,AlyssaC.,AlyssaTDC,AlyssaandCourtney,Alvin,Amanda,Brittany,andNickA.,AmandaandPamelaB.,AmandaC.,AmandaE.,AmandaH.,AmandaM.,AmandaR.,AmandaS.,AmandaY.,AmberandTeal,Amparo,AndreaT.,AndreaV.,AndrewA.,Andrei,AndrewB.,AndrewC.,AndrewD.,AndrewE.,AndrewH.,AndrewM.,AndrewS.,AndyandSarahR.,AndyandAllison,Angela,AngelaF.,AngelaL.,Anisha,Ann,AnnaC-S.,AnnaD.,AnnaandJon,AnnaandMax,AnnaL.,AnnaM.,AnnaS.,AnnaW.,AnnabelleM.,Annerose,Annie,AnnieB.,AnnieW.,Antigone,Antonio,Anu,April,Ares,Ariadne,Ariane,Ariel,

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ArielleandGabrielle,ArthurandAnnie,Arya,AsheleyandFreddy,AshleyA.,AshleyK.,AshleyandSarah,AshleyandLauren,Aubrey,Avra,BeccaA.,BeckyB.,BeckyS.,BeckyH.,BenS.,BenandAndrewY.,BenD.,BenS.,BenjaminD.,BenjaminH.,Benji,BethandSarah,BethanyandLesley,BetsyandJon,Blythe,BiancaandIsabella,Biz,Bonnie,BonnieC.,Boris,Braedan,Brendan,Brett,BrettA.,BretteandJosh,Brian,BrianC.,BrianN.,BrianW.,BrianZ.,Brigid,Brin,BrittanyE.,BrittanyS.,Brooke,Devon,andMegan,BrookeandLindsayE.,Butch,CailynH.,Caitlin,CaitlinF.,CaitlinM.,CaitlinandAnnaS.,CamillaandEloise,Camryn,Candace,Cara,CaraG.,Carinna,CarolineA.,CarolineC.,CarolineH.,CarolineS.,CarolineandPeterW.,CarrieM.,CatherineW.,Cecilia,Celia,Chad,Channing,Charlie,Charlotte,CharlotteB.,CharlotteM.,Chase,Chelsea,Chloe,ChloeK.,ChrisB.,ChrisC.,ChrisK.,ChrisP.,Chrissie,ChristaS.,ChristenC.,Christian,ChristianC.,ChristinaF.,Christine,ChristineW.,CJ,ClaireH.,Clare,Claudia,Clio,Colette,ConorG.,Corey,Corinne,Coryn,CourtneyandKeith,CourtneyB.,CourtneyF.,CourtneyS.,CourtneyW.,Craig,DanM.,DanaJ.,DaniandAdam,Daniel,DanielandJen,Daniella,DaniellaC.,DanielleandAndreas,DanielleandNikkiD.,DanielleG.,DanielleH.,DannyK.,DaraandStacey,DaraM.,Darcy,Darya,DavidB.,DavidC.,DavidR.,DavidS.,DeborahandMatthew,DenizandDestine,Deshaun,Deval,Devin,DevonandJenna,Deyshaun,DianaH.,Dilly,Disha,DongYi,Dora,Dorrien,Eairinn,Eddy,Elana,EleanorK.,ElexaandNicky,Elisa,Eliza,Elizabeth,ElizabethandMaryC.,ElizabethF.,Ella,Ellie,EllyB.,ElyssaT.,EmilyA.,EmilyB.,EmilyandAllison,EmilyandCatieA.,EmilyC.,EmilyG.,EmilyH.,EmilyK.,EmilyL.,EmilyandPeteM.,EmilyR.,EmilyR-H.,EmilyS.,EmilyT.,Emma,EmmaandSophie,EmmaD.,EmmaS.,EricN.,EricaF.,EricaH.,EricaR.,EricaS.,EricandLauren,EricaandAnnie,Erika,Erin,ErinI.,Ernesto,Esther,Ethan,Eugenie,Eva,Evan,EveH.,EveM.,Fifi,Francesca,Frank,Franki,Gabby,Geoffrey,GeorgeandJulian.,GeorgeM.,Gloria,GraceM.,GraceP.,Gracie,GrahamandWill,Greg,GregF.,Griffin,Gussie,Gylianne,Haley,HalleR.,Hallie,HannahC.,HannahJ.,HannahR.,HannahandPaige,Harrison,AnnabelandGillian,Harry,HayleyandTimD.,Hazel,HeatherD.,

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HeatherE.,HeatherF.,HeatherandGillian,HernandoandVicki,HilaryandLindsay,HilaryF.,Holli,HollyG.,HollyK.,Honor,lan,lanP.,India,Ingrid,Ira,Isa,Isabel,IsabellaandSimone,IsabelleT.,Ismini,Isobel,Ivy,Jabari,JacobandKara,Jack,JackB.,JackieandVicky,Jackie,JackieA.,JackieS.,Jackson,JaclynandAdam,JacobD.,Jada,JamesS.,Jamie,JasonP.,JasonandAndrew,Jay,JayK.,JaeandGideon,JakeT.,Jarrod,JasonL.,JayneandJohnny,JedD.,JedF.,JeffreyM.,Jenna,Jen,JenM.,JennN.,JenniferB.,JenniferW.,JennyK,JennyandMissy,JeremyC.,JeremyandCaleb,Jess,JessP.,Jesse,Jessica,JessicaandEricH.,JessicaL.,JessicaT.,Jessie,JessieC.,JessieandPerryN.,Jill,Jillian,DanielandOlivia,JillianS.,Jimin,JimmyC.,JimmyP.,Joanna,JoannaC.,JoannaG.,JoannaM.,JoannaandJuliaM.,JoannaW.,Jocelyn,JodyandKim,JoeB.,Johanna,John,JohnandDan,JonahandZoe,JonathanG.,JonathanP.,JonathanW.,Jongwoo,JordanC.,JordanandBlairF.,JordanG.,JordanP.,Jordana,Jordyn,JordynK.,JoshandJesse,JoshandNoah,JudieandRob,JuliaandCaroline,Julia,JuliaF.,JuliaG.,JuliaH.,JuliaandCharlotteP.,JuliaT.,Julie,JulieH.,JulieJ.,JulieandDana,JulieP.,Juliet,JulietteR.,JustinL.,KaraB.,Kara0O.,Kasey,KasiaandAmy,KatC.,KatR.,KateD.,KateF.,KateG.,KateL.,KateP.,KateS.,KateW.,KatieC.,KatieF.,KatherineC.,Kathryn,Leslie,andTravis,Katie,KatieM.,Katrina,KeithM.,KellyC.,KenD.,Kenzie,Keri,Kerri,KimH.,Kimberly,KimberlyH.,Kirsten,KittyandAlex,Kori,Kripali,Krista,Erika,andKaroline,Kristen,Kristen,KristenY.,Magan,andAlexa,LailaandOliviaR.,LauraB.,LauraF.,LauraG.,LauraR.,LauraS.,LauraT.,LauraZ.,LaurenandEric,LaurenR.,LaurenS.,LaurenT.,LaurenandAllie,LeaK.,Leah,LeeR.,LeighandRuthie,Leigh,LexiS.,Lila,LilaM.,Lilaj,LiliC.,Lilla,Lily,LilyM-R.,LilyHayes,LisbethandCharlotte,Lina,LindsayF.,LindsayK.,LindsayL.,LindsayN.,LindsayR,LindsayandJessieS.,LindseyandKari,Lisa,LizD.,LizH.,LizM.,LizziB.,LizzieA.,LizzieM.,LizzieW.,Lizzy,LizzyC.,LizzyR.,LizzyT.,Louis,Lucas,LukeC.,Lucinda,Lucy,LucyD.,Mackenzie,MaddieandJD,MaddieH.,MaddieP.,MaddyN.,MaddyT.,MaddyW.,Madeline,Magnolia,MaggieL.,MaggieT.,Manuela,MaraandSteffie,Marcia,MargaretS.,MariaB.,MarielC.,MarielL.,MarielS.,MarielleK.,MarielleS.,

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Marietta,MarisaB.,MarisaC.,Marissa,Marlee,MarnieandSam,MaryM.,Matt,MatthewB.,MatthewK.,MattF.,MattG.,MattandCaroline,MattV.,MatthewG.,MavisH.,MaxB.,MaxandChloeK.,MaxM.,Maxx,Ben,andSam,MayaandRohit,MayaN.,Mckyla,Meesh,MeganG.,Meliha,Melissa,MelissaandAshleyI.,Meredith,MeredithandGordieB.,MeredithandKatieD.,MeredithR.,MeredithS-K.,MichaelandDan,MichaelH.,MichaelR.,Michaela,Michal,MicheleS.,MikeC.,MikeR.,Miles,Milton,Miranda,Moira,MollyL.,MollyR.,MollyandAnnie,Morgan,MorganC.,Morgan,Zoe,andLila,MorganK.,NadiaandAlexis,NaEun,Nancy,Nanette,Naomi,NatalieandAndrewB.,NatashaandMikaelaB.,NatashaL.,Nathania,Nico,Nick,NickA.,NickyS.,NicoleB.,NicoleJ.,NicoleN.,NicoleP.,NicoleS.,Nicolette,Nidhi,NikkiG.,NinaR.,NinaV.,Noah,Nora,Nushien,Odean,Ogechi,OliandArni,Oliver,OliverW.,OliviaandDaphne,OliviaP.,Omar,Oren,Pam,Paige,Pasan,PaulA.,Peter,PhilipandPeter,Phoebe,Pierce,Pooja,Priscilla,Quanquan,QuinnandChris,RachelA,RachelB.,RachelandAdam,RachelH.,Rachel|.,RachelandJake,RachelK.,RachelL.,RachelandMitchellM.,RachelS.,RachelandEli,RachelandSteven,RachelT.,RachelW.,Rae,Ramit,RandiandSamantha,Rasheeda,RayB.,Rayna,RebeccaA.,RebeccaB.,RebeccaG.,RebeccaandGabyK.,RebeccaR.,RebeccaW.,ReneeF.,Resala,Richard,Tina,andAlice,RichieD.,Ricky,RileyC.,RobL.,RobinP.,Romanah,Rose,Ryan,RyanB.,RyanS.,Saahil,SabrinaandArianna,SabrinaO.,Sally,SamB.,SamC.,SamG.,SamL.,SamR.,SamS.,SamW.,SamZ.,SamanthaandSavannah,SamanthaM.,SamuelC.,Samar,SaraG.,SaraH.,SaraL.,SaraR.,SaraS.,SaraW.,Sarah,Patty,andKat,SarahandBeth,SarahA.,SarahC.,SarahD.,SarahF.,SarahG.,SarahandMichelleK.,SarahL.,SarahM-D.,SarahandMichael,SarahP.,SarahS.,Sascha,Samara,Saya,Sean,SelenaG.,Serena,SeungWoo,Shadae,Shannon,Shayne,Shayne,Shorty,Siegfried,SimonW.,Simone,Sinead,Siobhan,SkyeF.,SkyeL.,SofiaG.,SofiaM.,Sonja,SonjaandTalya,SophiaA.,SophiaB.,SophiaJ.,SophiaS.,SophieandTess,SophieD.,SophieS.,SophieW.,Stacey,Stacy,Steffi,Steph,Stephanie,StephanieK.,StephanieL.,StephenC.,Sumair,Sunaina,Suzie,Syd,Sydney,SydneyS.,TammyandHayley,

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TaraandMax,Taryn,Tasnia,Tayler,Taylor,TenleyandGalen,Terrence,Tess,Theodora,ThomasB.,TimothyH.,Tina,Tita,Tom,Tori,Torri,Tracy,TracyK.,TrippH.,TrippW.,Tyler,Tyrik,Uma,Vana,VanessaandJohn,Veda,VeronicaM.,VickyB.,VictorZ.,Victoria,VictoriaH.,VictoriaJ.,VictoriaM.,VinnyandEric,Vivek,Vladimir,Waleed,WillA.,Will,Teddy,andEllie,WilliamM.,WilliamZ.,WyattandRyan,Wyna,Xianyuan,Yakir,Yesha,Yujin,Yuou,Zach,ZachB.,ZachS.,ZachY.,ZacharyN.,Zaria,Zoé,ZoeL.,andZoeyandRachel.

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ContentsCoverTitlePageCopyrightAcknowledgmentsGetMore(Free)ContentPartI:UsingThisBooktoImproveYourAPScorePreview:YourKnowledge,YourExpectationsYourGuidetoUsingThisBookHowtoBeginPartll:PracticeTest1PracticeTest1PracticeTest1:AnswersandExplanationsPartlll:AbouttheAPCalculusABExamABCalculusvs.BCCalculusTheStructureoftheCalculusExamHowtheAPCalculusABExamisScoredOverviewofContentTopicsGeneralOverviewofThisBookHowAPExamsAreUsedOtherResourcesDesigningYourStudyPlanPartIV:Test-TakingStrategiesfortheAPCalculusABExam

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1HowtoApproachMultiple-ChoiceQuestions2HowtoApproachFree-ResponseQuestionsPartV:ContentReviewfortheAPCalculusABExamUnit1:DifferentialCalculusEssentials3LimitsWhatisaLimit?LimitsofTrigonometricFunctionsPracticeProblemSet1EndofChapter3Drill4ContinuityTheDefinitionofContinuityTypesofDiscontinuitiesPracticeProblemSet2EndofChapter4Drill5TheDefinitionoftheDerivativeDerivingtheFormulaDifferentiabilityPracticeProblemSet3EndofChapter5Drill6BasicDifferentiationNotationThePowerRuleTheAdditionRuleHigherOrderDerivativesPracticeProblemSet4TheProductRuleTheQuotientRuleTheChainRule

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PracticeProblemSet5DerivativesofTrigFunctionsGraphicalDerivativesPracticeProblemSet6EndofChapter6Drill7ImplicitDifferentiationHowtoDoItSecondDerivativesPracticeProblemSet7EndofChapter7DrillUnit2:DifferentialCalculusApplications8BasicApplicationsoftheDerivativeEquationsofTangentLinesandNormalLinesPracticeProblemSet8TheMeanValueTheoremforDerivativesRolle’sTheoremPracticeProblemSet9EndofChapter8Drill9Maxima,Minima,andCurveStretchingAppliedMaximaandMinimaProblemsPracticeProblemSet10CurveSketchingPracticeProblemSet11EndofChapter9Drill10MotionRelatedRatesPracticeProblemSet12Position,Velocity,andAccelerationPracticeProblemSet13

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EndofChapter10Drill11DerivativesofExponentialandLogarithmicFunctionsTheDerivativeofInxTheDerivativeofeXTheDerivativeoflogxTheDerivativeofa*PracticeProblemSet14EndofChapter11Drill12OtherTopicsinDifferentialCalculusTheDerivativeofanInverseFunctionPracticeProblemSet15LinearizationPracticeProblemSet16L’Hopital’'sRulePracticeProblemSet17EndofChapter12DrillUnit3:IntegralCalculusEssentials13TheIntegralTheAntiderivativeIntegralsofTrigFunctionsAdditionandSubtractionPracticeProblemSet18u-SubstitutionPracticeProblemSet19EndofChapter13Drill14DefiniteIntegralsAreaUnderaCurveTabularRiemannSums

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PracticeProblemSet20TheMeanValueTheoremforIntegralsPracticeProblemSet21EndofChapter14Drill15IntegralsofExponential,Logarithmic,andTrigFunctionsInverseTrigFunctionsPracticeProblemSet22MoreIntegralsofTrigFunctionsIntegratinge*anda*PracticeProblemSet23EndofChapter15DrillUnit4:IntegralCalculusApplications16TheAreaBetweenTwoCurvesVerticalSlicesHorizontalSlicesPracticeProblemSet24EndofChapter16Drill17TheVolumeofaSolidofRevolutionWashersandDisksCylindricalShellsVolumesofSolidswithKnownCross-SectionsPracticeProblemSet25EndofChapter17Drill18DifferentialEquationsSeparationofVariablesSlopeFieldsPracticeProblemSet26EndofChapter18Drill

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19SolutionstoPracticeProblemSets20SolutionstoEndofChapterDrillsPartVI:PracticeTests2and3PracticeTest2PracticeTest2:AnswersandExplanationsPracticeTest3PracticeTest3:AnswersandExplanationsAbouttheAuthor

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1GotoPrincetonReview.com/crackingandenterthefollowingISBNforyourbook:9780525568537

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2AnswerafewsimplequestionstosetupanexclusivePrincetonReviewaccount.(Ifyoualreadyhaveone,youcanjustlogin.)3EnjoyaccesstoyourFREEcontent!Needtoreportapotentialcontentissue?ContactEditorialSupport@review.comandinclude:

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«fulltitleofthebook*ISBNepagenumberNeedtoreportatechnicalissue?ContactTPRStudentTech@review.comandprovide:«yourfullname+emailaddressusedtoregisterthebook«fullbooktitleandISBNoOperatingsystem(Mac/PC)andbrowser(Firefox,Safari,etc.)Onceyou'veregistered,youcan...*GetourtakeonanyrecentorpendingupdatestotheAPCalculusABExam*AccessandprintPracticeTest6aswellasthecorrespondingAnswersandExplanations«Takeafull-lengthpracticeSATandACT«Getvaluableadviceaboutthecollegeapplicationprocess,includingtipsforwritingagreatessayandwheretoapplyforfinancialaid«Ifyou'restillchoosingbetweencolleges,useoursearchablerankingsofTheBest385Collegestofindoutmoreinformationaboutyourdreamschool.

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*Accesscomprehensivestudyguidesandavarietyofprintableresources,including:bonusquestions,anappendixonproperTI-84use,additionalbubblesheets,andimportantformulas«ChecktoseeiftherehavebeenanycorrectionsorupdatestothiseditionLookForTheseIconsThroughoutTheBookONLINEARTICLESPROVENTECHNIQUESAPPLIEDSTRATEGIESMOREGREATBOOKSSTUDYBREAKGOINGDEEPER

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PartI

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UsingThisBooktoImproveYourAPScore*Preview:YourKnowledge,YourExpectationseYourGuidetoUsingThisBook+HowtoBegin

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PREVIEW:YOURKNOWLEDGE,YOUREXPECTATIONSYourroutetoahighscoreontheAPCalculusABExamdependsalotonhowyouplantousethisbook.Startthinkingaboutyourplanbyrespondingtothefollowingquestions.1.RateyourlevelofconfidenceaboutyourknowledgeofthecontenttestedbytheAPCalculusABExam:A.Veryconfident—IknowitallB.I'mprettyconfident,buttherearetopicsforwhichIcouldusehelpC.Notconfident—IneedquiteabitofsupportD.I'mnotsure2.Ifyouhaveagoalscoreinmind,chooseyourgoalscorefortheAPCalculusABExam:54321I'mnotsureyet3.Whatdoyouexpecttolearnfromthisbook?Chooseallthatapplytoyou.A.AgeneraloverviewofthetestandwhattoexpectB.StrategiesforhowtoapproachthetestC.ThecontenttestedbythisexamD.I'mnotsureyet

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Ch-ch-ch-changesTheorganizationalstructureoftheAPCalculusABExamischangingforthe2019-2020course.Thematerialinthisbookcoversallcurrentlyannouncedcontentforthecourseandexam,butpleasecheckyouronlinestudenttoolsforanylate-breakingnews.YOURGUIDETOUSINGTHISBOOKThisbookisorganizedtoprovideasmuch—oraslittle—supportasyouneed,soyoucanusethisbookinwhateverwaywillbemosthelpfulforimprovingyourscoreontheAPCalculusABExam.oTheremainderofPartIwillprovideguidanceonhowtousethisbookandhelpyoudetermineyourstrengthsandweaknesses.oPartIIofthisbookcontainsPracticeTest1anditsanswersandexplanations.(Bubblesheetscanbeprintedoutfromyourfreeonlinestudenttoolsforeasyuse.)Westronglyrecommendthatyoutakethistestbeforegoinganyfurther,inordertorealisticallydetermine:oyourstartingpointrightnowowhichquestiontypesyou'rereadyforandwhichyoumightneedtopracticeowhichcontenttopicsyouarefamiliarwithandwhichyouwillwanttocarefullyreviewOnceyouhavenaileddownyourstrengthsandweaknesseswithregardtothisexam,youcanfocusyourtestpreparation,buildastudyplan,andbeefficientwithyourtime.

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oPartIIIofthisbookwill:oprovideinformationaboutthestructure,scoring,andcontentoftheAPCalculusABExamohelpyoutomakeastudyplanopointyoutowardsadditionalresourcesoPartIVofthisbookwillexplorethefollowingstrategies:ohowtoattackmultiple-choicequestionsohowtowriteahighscoringfree-responseanswerohowtomanageyourtimetomaximizethenumberofpointsavailabletoyouoPartVofthisbookcoversthecontentyouneedforyourexam.oPartVIofthisbookcontainstwoadditionalPracticeTestsandtheiranswersandexplanations.IfyouskippedPracticeTest1,werecommendthatyoudoallthree(withatleastadayortwobetweenthem)sothatyoucancompareyourprogressbetweenthem.Additionally,thiswillhelptoidentifyanyexternalissues:ifyougetacertaintypeofquestionwrongbothtimes,youprobablyneedtoreviewit.Ifyouonlygotitwrongonce,youmayhaverunoutoftimeorbeendistractedbysomething.Ineithercase,thiswillallowyoutofocusonthefactorsthatcausedthediscrepancyandtobeaspreparedaspossibleonthedayofthetest.Youmaychoosetousesomepartsofthisbookoverothers,oryoumayworkthroughtheentirebook.Thiswilldependonyourneedsandhowmuchtimeyouhave.Let'snowlookathowtomakethisdetermination.

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Onceyouregisteryourbookonline,youcandownloadandprintoutthebubblesheetsforallthreepracticetests.YoucanalsofindahandyAppendixthatcontainsalltheformulasyoushouldknow.HOWTOBEGIN1.TakeaTestBeforeyoucandecidehowtousethisbook,youneedtotakeapracticetest.Doingsowillgiveyouinsightintoyourstrengthsandweaknesses,andthetestwillalsohelpyoumakeaneffectivestudyplan.Ifyou'refeelingtest-phobic,remindyourselfthatapracticetestisatoolfordiagnosingyourself—it’snothowwellyoudothatmattersbuthowyouuseinformationgleanedfromyourperformancetoguideyourpreparation.So,beforeyoureadfurther,taketheAPCalculusABPracticeTest1startingatthispageofthisbook.Besuretodosoinonesitting,followingtheinstructionsthatappearbeforethetest.2.CheckYourAnswersUsingtheanswerkeyonthispage,counthowmanymultiple-choicequestionsyougotrightandhowmanyyoumissed.Don’tworryabouttheexplanationsfornow,anddon’tworryaboutwhyyoumissedquestions.We'llgettothatsoon.3.ReflectontheTestAfteryoutakeyourfirsttest,respondtothefollowingquestions:

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«Howmuchtimedidyouspendonthemultiple-choicequestions?«Howmuchtimedidyouspendoneachfree-responsequestion?eHowmanymultiple-choicequestionsdidyoumiss?¢Doyoufeelyouhadtheknowledgetoaddressthesubjectmatterofthefree-responsequestions?«Doyoufeelyourfreeresponseswerewellorganizedandthoughtful?eoCirclethecontentareasthatweremostchallengingforyouanddrawalinethroughtheonesinwhichyoufeltconfident/didwell.oFunctions,Graphs,andLimitsoDifferentialCalculusoIntegralCalculusoApplicationsofDerivativesoApplicationsofIntegrals4.ReadPartIIIandCompletetheSelf-EvaluationPartIIIwillprovideinformationonhowthetestisstructuredandscored.Itwillalsosetoutareasofcontentthataretested.AsyoureadPartIII,reevaluateyouranswerstothequestionsabove.AttheendofPartIII,youwillrevisitthequestionsaboveandrefineyouranswerstothem.Youwillthenbeabletomakeastudyplan,basedonyourneedsandtimeavailable,thatwillallowyoutousethisbookmosteffectively.

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5.EngagewithPartsIVandVasNeededNoticethewordengage.You'llgetmoreoutofthisbookifyouuseitintentionallythanifyoureaditpassively,hopingforanimprovedscorethroughosmosis.Strategychapterswillhelpyouthinkaboutyourapproachtothequestiontypesonthisexam.PartIVwillopenwitharemindertothinkabouthowyouapproachquestionsnowandthenclosewithareflectionsectionaskingyoutothinkabouthow/whetheryouwillchangeyourapproachinthefuture.ContentchaptersinPartVaredesignedtoprovideareviewofthecontenttestedontheAPCalculusABExam,includingthelevelofdetailyouneedtoknowandhowthecontentistested.Youwillhavetheopportunitytoassessyourmasteryofthecontentofeachchapterthroughtest-appropriatequestionsandareflectionsection.6.TakeAnotherTestandAssessYourPerformanceOnceyoufeelyouhavedevelopedthestrategiesyouneedandgainedtheknowledgeyoulacked,youshouldtakeTest2.Youshoulddosoinonesitting,followingtheinstructionsatthebeginningofthetest.Whenyouaredone,checkyouranswerstothemultiple-choicesections.Seeifateacherwillreadyourlong-formcalculusresponsesandprovidefeedback.Onceyouhavetakenthetest,reflectonwhatareasyoustillneedtoworkon,andrevisitthechaptersinthisbookthataddressthosetopics.Throughthistypeofreflectionandengagement,youwillcontinuetoimprove.7.KeepWorking

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Afteryouhaverevisitedcertainchaptersinthisbook,continuetheprocessoftesting,reflecting,andengagingwithPracticeTest3onthispage.Youwanttobeincreasingyourreadinessbycarefullyconsideringthetypesofquestionsyouaregettingwrongandhowyoucanchangeyourstrategicapproachtodifferentpartsofthetest.AswewilldiscussinPartIII,thereareotherresourcesavailabletoyou,includingawealthofinformationontheCollegeBoard'sAPStudentswebsite:https://apstudent.collegeboard.org/apcourse/ap-calculus-ab.Youcancontinuetoexploreareasthatcanstandtoimproveandengageinthoseareasrightuptothedayofthetest.Ifyoucan’tgetenoughAPCalculusABandwanttoreviewthismaterialwithanexpert,wealsoofferanonlineCramCoursethatyoucansignupforhere:https://www.princetonreview.com/college/ap-test-prep

The Princeton Review: Cracking the AP calculus AB exam (2019) - Page 30 preview image

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PartIIPracticeTest1*PracticeTest1*PracticeTest1:AnswersandExplanations

The Princeton Review: Cracking the AP calculus AB exam (2019) - Page 31 preview image

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