AP Calculus AB Practice Tests

ThequestionscontainedinthisAP®CalculusABPracticeExamarewrittentothecontentspecificationsofAPExamsforthissubject.TakingthispracticeexamshouldprovidestudentswithanideaoftheirgeneralareasofstrengthsandweaknessesinpreparingfortheactualAPExam.BecausethisAPCalculusABPracticeExamhasneverbeenadministeredasanoperationalAPExam,statisticaldataarenotavailableforcalculatingpotentialrawscoresorconversionsintoAPgrades.ThisAPCalculusABPracticeExamisprovidedbytheCollegeBoardforAPExampreparation.Teachersarepermittedtodownloadthematerialsandmakecopiestousewiththeirstudentsinaclassroomsettingonly.Tomaintainthesecurityofthisexam,teachersshouldcollectallmaterialsaftertheiradministrationandkeeptheminasecurelocation.Teachersmaynotredistributethefileselectronicallyforanyreason.©2008TheCollegeBoard.Allrightsreserved.CollegeBoard,AdvancedPlacementProgram,AP,APCentral,SAT,andtheacornlogoareregisteredtrademarksoftheCollegeBoard.PSAT/NMSQTisaregisteredtrade-markoftheCollegeBoardandNationalMeritScholarshipCorporation.Allotherproductsandservicesmaybetrademarksoftheirrespectiveowners.VisittheCollegeBoardontheWeb:®CalculusABContentsDirectionsforAdministration............................................................................................iiSectionI:Multiple-ChoiceQuestions................................................................................1SectionII:Free-ResponseQuestions...............................................................................30StudentAnswerSheetforMultiple-ChoiceSection.......................................................36Multiple-ChoiceAnswerKey............................................................................................37Free-ResponseScoringGuidelines...................................................................................38TheCollegeBoard:ConnectingStudentstoCollegeSuccessTheCollegeBoardisanot-for-profitmembershipassociationwhosemissionistoconnectstudentstocollegesuccessandopportunity.Foundedin1900,theassociationiscomposedofmorethan5,000schools,colleges,universities,andothereducationalorganizations.Eachyear,theCollegeBoardservessevenmillionstudentsandtheirparents,23,000highschools,and3,500collegesthroughmajorprogramsandservicesincollegeadmissions,guidance,assessment,financialaid,enrollment,andteachingandlearning.Amongitsbest-knownprogramsaretheSAT®,thePSAT/NMSQT®,andtheAdvancedPlacementProgram®(AP®).TheCollegeBoardiscommittedtotheprinciplesofexcellenceandequity,andthatcommitmentisembodiedinallofitsprograms,services,activities,andconcerns.VisittheCollegeBoardontheWeb:®CalculusABDirectionsforAdministrationTheAPCalculusABExamis3hoursand15minutesinlengthandconsistsofamultiple-choicesectionandafree-responsesection.•The105-minutetwo-partmultiple-choicesectioncontains45questionsandaccountsfor50percentofthefinalgrade.PartAofthemultiple-choicesection(28questionsin55minutes)doesnotallowtheuseofacalculator.PartBofthemultiple-choicesection(17questionsin50minutes)containssomequestionsforwhichagraphingcalculatorisrequired.•The90-minutetwo-partfree-responsesectioncontains6questionsandaccountsfor50percentofthefinalgrade.PartAofthefree-responsesection(3questionsin45minutes)containssomequestionsorpartsofquestionsforwhichagraphingcalculatorisrequired.PartBofthefree-responsesection(3questionsin45minutes)doesnotallowtheuseofacalculator.DuringthetimedportionforPartB,studentsarepermittedtocontinueworkonquestionsinPartA,buttheyarenotallowedtouseacalculatorduringthistime.A10-minutebreakshouldbeprovidedafterSectionIiscompleted.Studentsshouldnothaveaccesstotheirgraphingcalculatorsduringthebreak.TheactualAPExamisadministeredinonesession.Studentswillhavethemostrealisticexperienceifacompletemorningorafternoonisavailabletoadministerthispracticeexam.Ifascheduledoesnotpermitonetimeperiodfortheentirepracticeexamadministration,itwouldbeacceptabletoadministerSectionIonedayandSectionIIonasubsequentday.Manystudentswonderwhetherornottoguesstheanswerstothemultiple-choicequestionsaboutwhichtheyarenotcertain.Itisimprobablethatmereguessingwillimproveascore.However,ifastudenthassomeknowledgeofthequestionandisabletoeliminateoneormoreanswerchoicesaswrong,itmaybetothestudent’sadvantagetoanswersuchaquestion.•GraphingcalculatorsarerequiredtoanswersomeofthequestionsontheAPCalculusABExam.Beforestartingtheexamadministration,makesureeachstudenthasagraphingcalculatorfromtheapprovedlistat•ItissuggestedthatSectionIofthepracticeexambecompletedusingapenciltosimulateanactualadministration.Stude