AP Calculus 69-98年 选择题真题（英文版）.pdf

Table of ContentsAbout This Collection viQuestions.11969 AP Ca l c u l u s AB Ex a m,Sec t io n I.I1969 AP Ca l c u l u s BC Ex a m,Sec t io n 1.101973 AP Ca l c u l u s AB Ex a m,Sec t io n 1.201973 AP Ca l c u l u s BC Ex a m,Sec t io n 1.291985 AP Ca l c u l u s AB Ex a m,Sec t io n 1.381985 AP Ca l c u l u s BC Ex a m,Sec t io n 1.471988 AP Ca l c u l u s AB Ex a m,Sec t io n 1.571988 AP Ca l c u l u s BC Ex a m,Sec t io n 1.671993 AP Ca l c u l u s AB Ex a m,Sec t io n 1.781993 AP Ca l c u l u s BC Ex a m,Sec t io n 1.891997 AP Ca l c u l u s AB Ex a m,Sec t io n 1.100Pa r t A 100Pa r t B 1081997 AP Ca l c u l u s BC Ex a m,Sec t io n 1.113Pa r t A 113Pa r t B 1201998 AP Ca l c u l u s AB Ex a m,Sec t io n 1.125Pa r t A 125Pa r t B 1331998 AP Ca l c u l u s BC Ex a m,Sec t io n I.138Pa r t A 138Pa r t B 147A P C alculus Multiple-C hoice Question C ollectioti ivC o pyrigh t 2 0 0 5 by C o l l ege Bea rd.Al l righ ts reserved.Ava il a bl e a t a pc entra l.c o l l egebo a rd.c o m.Table of ContentsAnswer Key.153Solutions.1601969 Ca l c u l u s AB.1601969 Ca l c u l u s BC.1661973 Ca l c u l u s AB.1721973 Ca l c u l u s BC.1771985 Ca l c u l u s AB.1831985 Ca l c u l u s BC.1881988 Ca l c u l u s AB.1941988 Ca l c u l u s BC.2001993 Ca l c u l u s AB.2061993 Ca l c u l u s BC.2121997 Ca l c u l u s AB.217Pa r t A.217Pa r t B 2201997 Ca l c u l u s BC 222Pa r t A 222Pa r t B 2251998 Ca l c u l u s AB.228Pa r t A 228Pa r t B.-2311998 Ca l c u l u s BC.233Pa r t A 233Pa r t B 236A P C alculus Multiple-C hoice Question C ollection vC o pyrigh t 2 0 0 5 by C o l l ege Bea rd.Al l righ ts reserved.Ava il a bl e a t a pc entra l.c o l l egebo a rd.c o m.About This CollectionAbout This CollectionMu l t ip l e-c h o ic e q u est io n s f r o m p a st AP Ca l c u l u s Ex a ms p r o v ide a r ic h r eso u r c e f o r t ea c h in g t o p ic s in t h e c o u r se a n d r ev iew in g f o r t h e ex a m ea c h y ea r.Ov er t h e y ea r s,so me t o p ic s h a v e been a dded o r r emo v ed,bu t a l mo st a l l o f t h e o l d q u est io n s st il l o f f er in t er est in g o p p o r t u n it ies t o in v est iga t e c o n c ep t s a n d a ssess st u den t u n der st a n din g.Al w a y s c o n su l t t h e mo st r ec en t Co u r se Desc r ip t io n o n AP Cen t r a l f o r t h e c u r r en t t o p ic o u t l in es f o r Ca l c u l u s AB a n d Ca l c u l u s BC.Pl ea se n o t e t h e f o l l o w in g：Th e so l u t io n t o ea c h mu l t ip l e-c h o ic e q u est io n su ggest s o n e p o ssibl e w a y t o so l v e t h a t q u est io n.Th er e a r e o f t en a l t er n a t iv e a p p r o a c h es t h a t p r o du c e t h e sa me c h o ic e o f a n sw er,a n d f o r so me q u est io n s su c h mu l t ip l e a p p r o a c h es a r e p r o v ided.Tea c h er s a r e a l so en c o u r a ged t o in v est iga t e h o w t h e in c o r r ec t o p t io n s f o r ea c h q u est io n c o u l d be o bt a in ed t o h el p st u den t s u n der st a n d(a n d a v o id)c o mmo n t y p es o f mist a k es.Sc ien t if ic(n o n gr a p h in g)c a l c u l a t o r s w er e r eq u ir ed o n t h e AP Ca l c u l u s Ex a ms in 1993.Gr a p h in g c a l c u l a t o r s h a v e been r eq u ir ed o n t h e AP Ca l c u l u s Ex a ms sin c e 1995.In 1997 a n d 1998,Sec t io n I,Pa r t A did n o t a l l o w t h e u se o f a c a l c u l a t o r;Sec t io n I,Pa r t B r eq u ir ed t h e u se o f a gr a p h in g c a l c u l a t o r.Ma t er ia l s in c l u ded in t h is r eso u r c e ma y n o t r ef l ec t t h e c u r r en t AP Co u r se Desc r ip t io n a n d ex a m in t h is su bjec t,a n d t ea c h er s a r e a dv ised t o t a k e t h is in t o a c c o u n t a s t h ey u se t h ese ma t er ia l s t o su p p o r t t h eir in st r u c t io n o f st u den t s.Fo r u p-t o-da t e in f o r ma t io n a bo u t t h is AP c o u r se a n d ex a m,p l ea se do w n l o a d t h e o f f ic ia l AP Co u r se Desc r ip t io n f r o m t h e AP Cen t r a l Web sit e a t.a p c en t r a l.c o l l egebo a r d.c o mA P C alculus Multiple-C hoice Question C ollectionC o pyrigh t 2 0 0 5 by C o l l ege Bea rd.Al l righ ts reserved.Ava il a bl e a t a pc entra l.c o l l egebo a rd.c o m.1969 AP Calculus AB:Section I90 MinutesNo CalculatorNote:In t h is ex a min a t io n,In x den o t es t h e n a t u r a l l o ga r it h m o f x(t h a t is,l o ga r it h m t o t h e ba se e).1.Wh ic h o f t h e f o l l o w in g def in es a f u n c t io n f f o r w h ic h/(-%)=f(x)?(A)f(a：)=x2(B)f(x)=sin x(C)f(x)=c o s x(D)/(%)=l o gx(E)W2.In(t-2)v 0 if a n d o n l y if(A)x 3(B)0 x 3(C)2x 2(E)x 33.r,、2x+5-Jx+1/W=_,tor 2,-r 7It-x-2 a n d it j is c o n t in u o u s a t x=2,t h en k=、/T1 1 7(A)0(B)-(C)-(D)1(E)-6 3 54.r 8 dx _J。叼;3(A)1(B)-(C)2(D)4(E)65.If 3x2+2孙+)2=2,t h en t h e v a l u e o f a t x=1 isdx(A)-2(B)0(C)2(D)4(E)n o t def in edA P(C alculus Multiple-dhoice Question C ollection 1C o pyrigh t 2 c g5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bk a t a pc entra l.c a 1l egebc a rd.c o m.1969 AP Calculus AB:Section I6.8口+Wh a t is l im-Ar_1/to h(A)0(B)J(C)1(D)Th e l imit do es n o t ex ist.(E)It c a n n o t be det er min ed f r o m t h e in f bn n a t io n giv en.7.kFo r w h a t v a l u e o f A w il l x+h a v e a r el a t iv e ma x imu m a t x=-2?X(A)-4(B)-2(C)2(D)4(E)No n e o f t h ese8.If p(%)=(x+2)(x+A：)a n d if t h e r ema in der is 12 w h en p(x)is div ided by x-1,t h en k=(A)2(B)3(C)6(D)11(E)139,Wh en t h e a r ea in sq u a r e u n it s o f a n ex p a n din g c ir c l e is in c r ea sin g t w ic e a s f a st a s it s r a diu s in l in ea r u n it s,t h e r a diu s is(A)；(B):(C)-(D)1(E)冗4冗 4 it10.Th e set o f a l l p o in t s(e1,t),w h er e is a r ea l n u mber,is t h e gr a p h o f y=i(A)(B)e%(C)式标(D)(E)In xex In x11.2 1 1 Th e p o in t o n t h e c u r v e x+2y=0 t h a t is n ea r est t h e p o in t 0,o c c u r s w h er e y is、2,(A):(B)0(C)(D)1(E)n o n e o f t h e a bo v eA P(C alculus Muitiple-dhoice Question C ollection 2C o pyrigh t 2 c g5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bk a t a pc entra l.c a 1l egebc a rd.c o m.1969 AP Calculus AB:Section I12.If f(%)=-a n d g(x)=2x,t h en t h e so l u t io n set o f/(g(%)=g(/(%)isx 1(A)出(B)2(C)3(D)-1,2(E)卷213.Th e r egio n bo u n ded by t h e x-a x is a n d t h e p a r t o f t h e gr a p h o f y=c o sx bet w een x=-a n d%=(is sep a r a t ed in t o t w o r egio n s by t h e l in e x=左.If t h e a r ea o f t h e r egio n f o r y xk isnt h r ee t imes t h e a r ea o f t h e r egio n f o r k g(x)f o r a l l r ea l x,t h en t h e gr a p h o f y=f(x)a n d t h e gr a p h o f y=g(x)(A)(R)(C)(D)(E)in t er sec t ex a c t l y o n c e.in t er sec t n o mo r e t h a n o n c e.do n o t in t er sec t.c o u l d in t er sec t mo r e t h a n o n c e.h a v e a c o mmo n t a n gen t a t ea c h p o in t o f in t er sec t io n.A P C alculus Multiple-C hoice Question C ollection3C o pyrigh t 2 D 0 5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bl e a t a pc en t r a l.c o l I eg ebo a rd.c o m.1969 AP Calculus AB:Section I16.If v is a f u n c t io n o f x su c h t h a t y 0 f o r a l l x a n d y 0)is giv en by v=At w h a t v a l u e o f t do es v a t t a in it s ma x imu m?1 3(A)1(B)e，(C)e(D)/(E)Th er e is n o ma x imu m v a l u e f o r v.AP C alculus Multiple-C hoice Question C ollectionC o pyrigh t 2 D 0 5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bl e a t a pc en t r a l.c o l I eg ebo a rd.c o m.41969 AP Calculus AB:Section I20.An eq u a t io n f o r a t a n gen t t o t h e gr a p h o f y-a r c s in a t t h e o r igin is(A)x-2y=0(B)x-=0(C)x=0(D)y=0(E)nx-2y=021.At x=0,w h ic h o f t h e f o l l o w in g is t r u e o f t h e f u n c t io n f def in ed by/(x)=x 2+ex?(A)f is in c r ea sin g.(B)f is dec r ea sin g.(C)f is disc o n t in u o u s.(D)f h a s a r el a t iv e min imu m.(E)f h a s a r el a t iv e ma x imu m.22.lne2x=1 2(A)(B)(C)2x(D)1(E)2e e23.Th e a r ea o f t h e r egio n bo u n ded by t h e c u r v e y=e,t h e x-a x is,t h e y-a x is,a n d t h e l in e%=2 is eq u a l t o/e4 e4 1(A)丁 e(B)-1(C)-z 工 z z(D)2e4-e(E)2e4-224.If sin x=e,0 x 0.Th e a r ea o f t h is r egio n(A)is in dep en den t o f m.(B)in c r ea ses a s m in c r ea ses.(C)dec r ea ses a s m in c r ea ses.(D)dec r ea ses a s m in c r ea ses w h en m.2 2(E)in c r ea ses a s m in c r ea ses w h en m .2 2j o(A)(B)(C)(D)26.1 Jx 2-2x+1 dx is-121n o n e o f t h e a bo v e27.Tf=t a n x,t h en y=dx.(A)tan2x+C(B)sec2 x+C(C)In|sec x|+C2(D)In|c o sx|+C(E)sec t a n x+C28.Th e f u n c t io n def in ed by f(x)=73 c o sx+3sinx h a s a n a mp l it u de o f(A)3-3(B)省(C)2a/5(D)3+5/3(E)3 6AP C alculus Multiple-C hoice Question C ollection 6C o pyrigh t 2 D 0 5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bl e a t a pc en t r a l.c o l I eg ebo a rd.c o m.1969 AP Calculus AB:Section If ir/2 COSX29.-ax=J 4 sin x(A)In V2(B)In 弓(C)In Q(D)l n-(E)h ie30.If a f u n c t io n f is c o n t in u o u s f o r a l l x a n d if/h a s a r el a t iv e ma x imu m a t(-1,4)a n d a r el a t iv e min imu m a t(3,-2),w h ic h o f t h e f o l l o w in g st a t emen t s mu st be t r u e?(A)Th e gr a p h o f f h a s a p o in t o f in f l ec t io n so mew h er e bet w een x=-1 a n d x=3.(B)r(-i)=o(C)Th e gr a p h o f f h a s a h o r izo n t a l a sy mp t o t e.(D)Th e gr a p h o f/h a s a h o r izo n t a l t a n gen t l in e a t x=3.(E)Th e gr a p h o f f in t er sec t s bo t h a x es.31.If/(X)=-jx)a n d/(I)=1,t h en f(x)=(A)ge iz(B)e-x-(C)或一”(D)1 尤(E)32.If a,b,c,d,a n d e a r e r ea l n u mber s a n d w 0,t h en t h e p o l y n o mia l eq u a t io n ax7+bx5+ex3+c/x+e=0 h a s(A)o n l y o n e r ea l r o o t.(B)a t l ea st o n e r ea l r o o t.(C)a n o dd n u mber o f n o n r ea l r o o t s.(D)n o r ea l r o o t s.(E)n o p o sit iv e r ea l r o o t s.33.Wh a t is t h e a v er a ge(mea n)v a l u e o f 3厂-广 o v er t h e in t er v a l 1 /2?(A)j(B)I(C)8(D)(E)16AP C alculus Multiple-C hoice Question C ollectionC o pyrigh t 2 D 0 5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bl e a t a pc en t r a l.c o l I eg ebo a rd.c o m.1969 AP Calculus AB:Section I34.Wh ic h o f t h e f o l l o w in g is a n eq u a t io n o f a c u r v e t h a t in t er sec t s a t r igh t a n gl es ev er y c u r v e o f t h e f a mil y y=+A：(w h er e k t a k es a l l r ea l v a l u es)?x(A)尸 T 片”(C)v=(D)(E).y=l n x35.At?=0 a p a r t ic l e st a r t s a t r est a n d mo v es a l o n g a l in e in su c h a w a y t h a t a t t ime t it s a c c el er a t io n is 24?2 f eet p er sec o n d p er sec o n d.Th r o u gh h o w ma n y f eet do es t h e p a r t ic l e mo v e du r in g t h e f ir st 2 sec o n ds?(A)32(B)48(C)64(D)96(E)19236.Th e a p p r o x ima t e v a l u e o f y=4+sin x a t x=0.12,o bt a in ed f r o m t h e t a n gen t t o t h e gr a p h a tx=0,is(A)2.00(B)2.03(C)2.06(D)2.12(E)2.2437.Wh ic h is t h e best o f t h e f o l l o w in g p o l y n o mia l a p p r o x ima t io n s t o c o s 2x n ea r;t=0?(A),x1+-2(B)1+x(C)1-2(D)l-2x2(E)l-2x+x23&J.dx=(A)-lnexc 3(B)一乙 3(C)-y+C3e*(D)1 9-xer+C 3(E)3ex39.If v-=t a n u,u=v-,a n d v=In,Vw h a t is t h e v a l u e o f dxa t x=e?(A)0(B)-(C)1(D)2(E)sec2 eA P(laiculus Muitiple-dhoice Question(ollectiongC o pyrigh t 2 c g5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bk a t a pc entra l.c a 1l egebc a rd.c o m.1969 AP Calculus AB:Section I40.If 71 is a n o n-n ega t iv e in t eger,t h en x 服=(1 一%)“dx f br(A)n o n(B)n ev en,o n l y(C)n o dd,o n l y(D)n o n zer o n,o n l y(E)a l l n41.f(x)=8-x2 f br-2x 0(B)Al l k4(C)左=0,4(D)0左 4(E)Al l k43.j sin(2x+3)dx=(A)gc o s(2x+3)+C(B)c o s(2x+3)+C(C)-c o s(2x+3)+C(D)；c o s(2x+3)+C(E)-j c o s(2x 4-3+C44.p 71工Th e f u n da men t a l p er io d o f t h e f u n c t io n def in ed by/(x)=3-2 c o s is3(A)1(B)2(C)3(D)5(E)645.If 3(/(x)=g(x)a n d(g(x)=/(d),t h en a(马卜 dx ax dx v 7(A)/(x6)(B)g(.x3)(C)3%2g 1 3)(D)9*卜 6)+6x g(-)(E)/(x6)+g(.x3)A P(laiculus Midtiple-C hoice Question(ollectionC o pyrigh t 2 c g5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bk a t a pc entra l.c a l l egebc a rd.c o m.1969 AP Calculus BC:Section I90 MinutesNo CalculatorNote:In t h is ex a min a t io n,In x den o t es t h e n a t u r a l l o ga r it h m o f x(t h a t is,l o ga r it h m t o t h e ba se e).1.Th e a sy mp t o t es o f t h e gr a p h o f t h e p a r a met r ic eq u a t io n s x=,y=a r e i t+(A).=0,v=0(B)x=0 o n l y(C)x=-1,y=0(D)x=1 o n l y(E)=0,y=12.Wh a t a r e t h e c o o r din a t es o f t h e in f l ec t io n p o in t o n t h e gr a p h o f 夕=(x+1)a r c t a n x?/(A)(-1,0)(B)(0,0)(C)(0,1)(D)11,1(E)3.Th e Mea n Va l u e Th eo r em gu a r a n t ees t h e ex ist en c e o f a sp ec ia l p o in t o n t h e gr a p h o f y=-Jx bet w een(0,0)a n d(4,2).Wh a t a r e t h e c o o r din a t es o f t h is p o in t?(A)(2,1)(B)(1,1)(C)(2/(E)No n e o f t h e a bo v e3(A)1(B)-(C)2(D)4(E)65.If 3x2+2xy+y=2,t h en t h e v a l u e o f a t x=1 is一 dx(A)-2(B)0(C)2(D)4(E)n o t def in edA P C alculus Multiple-C hoice Question C ollectionC o pyrigh t 2 D 0 5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bl e a t a pc en t r a l.c o l I eg ebo a rd.c o m.101969 AP Calculus BC:Section I6.Wh a t is l im-旦-?/to h(A)0(B)；(C)1(D)Th e l imit do es n o t ex ist.(E)It c a n n o t be det er min ed f r o m t h e in f o r ma t io n giv en.7.kFo r w h a t v a l u e o f A:w il l x+h a v e a r el a t iv e ma x imu m a t x=-2?X(A)-4(B)-2(C)2(D)4(E)No n e o f t h ese8.If，2(x)=/2(x)-g2(x),/(x)=-g(x),a n d g(x)=/(x),t h en hx)=(A)0(B)1(C)-4/(x)g(x)(D)(-g(x)2-(/(x)2(E)-2(-g(x)+/(x)9.Th e a r ea o f t h e do sed r egio n bo u n ded by t h e p o l a r gr a p h o f r=v 3+c o s 0 is giv en by t h e in t egr a l(A)J；*,3+c o s。49(B)J：J3十c o se de(C)22(3+c o se)/e(D)J：(3+c o s9)d9(E)2；=j3+c o sC dH10.dx=J。r+i4 1 4+兀(A)(B)In 2(C)0(D)-In 2(E)-4 2 4A P C alculus Multiple-C hoice Question C ollectionC o pyrigh t 2 D 0 5 by C o l l ege Bo a rd.Al l righ ts reserved.Ava il a bl e a t a pc en t r a l.c o l I eg ebo a rd.c o m.111969 AP Calculus BC:Section I11.Th e p o in t o n t h e c u r v e x2+2y=0 t h a t is n ea r est t h e p o in t|0,o c c u r s w h er e y is闻3(B)0(Q-1(D)-1(E)n o n e o f t h e a bo v e12.If F(x)=2一 dt,t h en Fx)=2 2 e(A)2x e-“(B)-lxex(C)+1(D)-1(E)13.Th e r egio n bo u n ded by t h e x-a x is a n d t h e p a r t o f t h e gr a p h o f y-c o sx bet w een x-a n d71 TCx=2 is sep a r a t ed in t o t w o r egio n s by t h e l in e x=左.Tf t h e a r ea o f t h e r egio n f o r-x k is t h r ee t imes t h e a r ea o f t h e r egio n f o r k x g(x)f o r a l l r ea l x,t h en t h e gr a p h o f y=/(x)a n d t h e gr a p h o f y=g(x)(A)in t er sec t ex a c t l y o n c e.(B)in t er sec t n o mo r e t h a n o n c e.(C)do n o t in t er sec t.(D)c o u l d in t er sec t mo r e t h a n o n c e.(E)h a v e a c o mmo n t a n gen t a t ea c h p o in t o f in t er sec t io n.16.If j is a f u n c t io n x su c h t h a t y 0 f o r a l l x a n d y 0)is giv en by v=.At w h a t v a l u e o f t do es v a t t a in it s ma x imu m?1 3(A)1(B)/(C)e(D)/(E)Th er e is n o ma x imu m v a l u e f o r v.20.An e