AP微積分BC選擇題樣卷一

APCalculusPracticeExamBCVersion-SectionI-PartACalculatorsARENOTPermittedOnThisPortionOfTheExam28Questions-55Minutes1)Given3y61y-x—4世一"'-61y-xFinddy/dx.一4"口)一.37r(3十1)d)4M+1)e)Thegraphofthederivativeoffisshownbelow.-Z5一/-2.0/E/Findtheareaboundedbetweenthegraphoffandthex-axisovertheinterval[-2,1],giventhatf(0)=1.13丁29128T311211丁Determinedy/dt,giventhaty=/+4mandx-cos(3f)—6cos(3f)sin(3￡)-3(2gb(3E)+4)sm(3f)6c(3￡)412-I8sin(3f)3(Tcos(3￡)+4)cos(3r)Thefunction/(X)=5x2+3/2')isinvertible.Givetheslopeofthenormallinetothegraphof f-1atx=3.3。+6/—2~T~~63。+6/d)e)Determine4-矛 77^~sin(24x)十C8 192a)~j~耳+表sinf12j)+Cb)'x -^—co式24x)+C8 192c)4-彳+sin(24 十e8 192d)~皿12k)+Ce)Givethepolarrepresentationforthecircleofradius2centeredat(0,2).r=2而(9)+2cos(9)a)r=4g5(9)廠二4rsin(9)-2r=4sm(0)—cos(8)e)8)Determine116T32Determine2石N一1Givetheradiusofconvergencefortheseriesjt=1jt=1上+1a)b)c)d)e)11)Determinelim工a)b)c)d)e)11)Determinelim工(W―〕Th^seriesdiv昌產(chǎn)擎sjbrallH.a)2b)15c)0d)e)12)Thepositionofaparticlemovingalongthex-axisattimetisgivenbyA(￡)=(sm(4Kf))2Atwhichofthefollowingvaluesoftwilltheparticlechangedirection?t=1/8t=1/6t=1t=2I,IIandIIIIandIII,IIIandIVII,IIIandIVIIIandIVDetermine一1十工-7U2IT-2A,1——-I--tu3 3?1 b-TV4Determinethey-interceptofthetangentlinetothecurve尸二J”+33atx=4.45~T66函-3349c)13549d)33~Te)Thefunctionfisgraphedbelow.0 1 2 3 4 5GivethenumberofvaluesofcthatsatisfytheconclusionoftheMeanValueTheoremforderivativesontheinterval[2,5].3a)2432Givetheaveragevalueofthefunctionontheinterval[1,3]. e -n3 33——7—20一3)+2e(-1)Arectanglehasbothachangingheightandachangingwidth,buttheheightandwidthchangesothattheareaoftherectangleisalways20squarefeet.Givetherateofchangeofthewidth(inft/sec)whentheheightis5feet,iftheheightisdecreasingatthatmomentattherateof1/2ft/sec.2T司

訪6CT205Thegraphofthederivativeoffisshownbelow.fhasfhasGivethenumberofvaluesofxintheinterval[-3,3]wherethegraphofe)Arectanglehasitsbaseonthex-axisanditsverticesonthepositiveportionoftheparabolaWhatisthemaximumpossibleareaofthisrectangle?20)Computettan(eC3x))e(3rJ十C4tan(e,"b(腿。相3工)))屋(2,)+Cc)"+C"+Cd)ytan(eC2xb+y+CW 4e)21)Determine1萬兀a)112^b)3Kc&67TDetermine11Ta)7b)ft?c)d)

11e)Givetheexactvalueof2”口CO5c總7T)5”sm(5)cos(5)—sin(5)Determine012卡檢檢卷混d3TGivethederivativeof

-2xx(-2x)-2工(-酎)ln(T)a)—2工工(-2])+"2])ln(r)b)—(-IT-1)_2~(-2^j—2房口—1)—2#-2幻1ngm(-a，-i)0for26)Givethefirst3nonzerotermsintheTaylorseriesexpansionaboutxthefunction0for/(ff)=g"2干)1一2f+4/a)1-2”+!b) -c)1+2r+2/d)—2”e)27)Determine—2)a+4))+CTOC\o"1-5"\h\z2yln(|x-2|)+1-ta(|x+4|)+C2 1—。砧(>—2])—Jlnrk+4|)+C2 ]—ybi(|^+4|)—yln(|^—2|)+e一 一2)O+4)|)十bwe)Whichofthefollowingseriesconverge(s)?BonlyA,BandCBandCAandBAandCd)e)b)b)e)a)c)c)b)d)c)c)c)e)a)d)a)b)a)d)b)b)a)c)d)b)b)c)a)8。口)6》4戈b)gJ7冷”+工c)8s(口〕—乃6y—kd)g小口)r67一xe)2)Give