**TI92P*MAINAppVariable file 10/03/03, 16:14Rfeb11TqĽZpúóGż§GOP]^°KĎ ŢˆZyŘ"U$d)œ*60ß57ľ9@=ď>’D†L—OlR§Tan“oCalc ABFeb 11, 2004M řŐ˘sThe materials included in  these files are intended for non-commercial use by AP* teachers for course &and exam preparation; /permission for any other 8use must be sought from Athe Advanced Placement PProgram*. Teachers may  reproduce them, in whole or in part, in limited quantities, for face-to-&face teaching purposes but /may not mass distribute 8the materials, Aelectronically or Potherwise. These materials  and any copies made of them may not be resold, and the copyright notices &must be retained as they /appear here. 8AThis permission does not Papply to any third-party  copyrights contained herein. THIS IS NOT A COMPLETE EXAMINATION. &/*College Board, Advanced 8Placement Program, and AP Aare registered trademarks Pof the College Entrance  Examination Board. Copyright (C) 2003 by the College Board. All rights &reserved. Any modification /of these electronic files 8is strictly prohibited.APP– íľƒThe following questions  come from AP Central*, the College Board's Online Home for AP* (Professionals. To find TI 1StudyCards files of AP :exam review questions for Cother subjects, please Pvisit  http://apcentral.collegeboard.com/ti/apquestions(In some cases, formatting 1these questions for this :application required some Cminor modifications to the Pquestions as they appear  on AP Central.*College Board, Advanced (Placement Program, AP, and 1AP Central are registered :trademarks of the College CEntrance Examination PBoard. PPdirections äΆqXPart A Sample Multiple- Choice QuestionsA calculator may not be used on this part of the 'examination.0Part A consists of 28 9questions. In this section Bof the examination, as aPcorrection for guessing,  one-fourth of the number of questions answeredincorrectly will be 'subtracted from the number 0of questions answered 9correctly. Following are Bthe directions for Section PI Part A and a  representative set of 13 questions.'Directions: Solve each of 0the following problems, 9using the availableBspace for scratchwork. PAfter examining the form  of the choices, decidewhich is the best of the choices given and fill in 'the corresponding oval on0the answer sheet. No 9credit will be given for Banything written in the Ptest book. Do not spend  too much time on any one problem. In this test: Unless otherwise 'specified, the domain of a 0function f is assumed to 9be the set of all real Bnumbers x for which f(x) Pis a real number.PPone ýľ– FŒŕŕđř@@@@@@@@@@@@|@~@ţ@ţ@ţ @~ Aź B<D&H"P€"`Ŕ#"@`"Ŕ "@<@@ @`@@@ €@€0@€8˙˙˙˙˙˙˙˙˙˙˙˙˙ü @ 8@0 @ Ŕ@ €@@@p @€@@€€ @x@ŕ@@Ä €@€0@€@€ @D@x0@@@€@€@@@` @ @0@ P1. The function f, whose  graph consists of two line segments, is shownabove. Which of the &following are true for f /on the open interval8(a, b)?API. The domain of the  derivative of f is the open interval (a, b).II. f is continuous on the &open interval (a, b)./III. The derivative of f 8is positive on the open Ainterval (a, c).P (A) I only(B) II only(C) III only&(D) II and III only/(E) I, II, and IIIP DPŸtwoň ,~00 0@  Ŕ €ƀ8㌠€E@A €E@AŒ ŔD@EL 8ä@8çŒ 8ŕ  E ŒŒDŕŔ ŒD Ŕ Œ9ŕ " Œ€,  C2ú   @"  €""  "Ŕ    Ŕ  00˙˙˙˙˙˙˙˙˙˙˙đ€@@@@ 2.%.7@P řpˆÄ @ ř?˙ţ">(A) -1 (B)%(C) 0.(D) 17(E) The limit does not @exist.PAP ÂthreeÄ 3. At which of the five points on the graph in the figure below are both !G >8D€ˆ€ ˆ˘|ˆ ˘&x˘"ž"p‚,h˛˜˙‡˘ˆ˙ă˘ˆ€˘x€Ŕ˘ ” ˆ@”€˘‹ŕ&P" "Pˆ*Gnegative?3GD€@%Xis true?.X7@P(A) The function has no  relative extremum.(B) The graph of the %function has one point of .inflection and the7function has two relative @extrema.P(C) The graph of the  function has two points of inflection and thefunction has one relative %extremum..7(D) The graph of the @function has two points of Pinflection and the function has two relative extrema.%(E) The graph of the .function has two points of 7inflection and the@function has three Prelative extrema. P CPrsix (XŔ @€0@â|H€A„ř°BáČ ň‚Ařˆ@…ˆˆD„@Hˆ8H 6. If @$0@H‚" @„"ďŕ*@"ď@" @@  then%.7@P(A) -2 cos 3 (B) -2 sin 3 cos 3(C) 6 cos 3(D) 2 sin 3 cos 3%(E) 6 sin 3 cos 3PBP seven Kś5 7. The solution to the  differential equation(, where y(2)=3, is >h š Š ‚Š "yŕ Ŕ€Ŕ˙ŕ˙Ŕ"j ™@ˆ€‰@z ż€€€&(/(8AP 2˙˙˙€ů!  ‰qˆ‰đńˆ ˆ yđ@?€p? €@  (A)&/(B) y= -3:˙˙üů?>!0}˙˙P ‰ř 'Ŕq"d?AE'€ů"@9 @ @đy$@@s€ "@A$>8AP B˙˙˙€ů!  ‰qˆ'Ŕ‰đńdˆ ˆ '€yđ@> € @p$ €s€@  (C)&/8(D) 7@˙˙˙˙˙ů!  ‰qˆ>‰đń ˆ ˆ €p" €@ AP (E) D˙˙˙˙˙đů!  ‰qˆ'Ŕ‰đńdˆ ˆ '€yđ@> O€ @p$O €s€@ PEP3directions 8-9  A bug is crawling along a  straight wire. The velocity, v(t), of the bugat time t, K ,p ˆ €ˆ p€¨@ €ˆř €ˆ$€přĎ' 0is given in the graph.9Questions 8 and 9 refer to Bthe following graph and Pinformation.PP eightů FŒ!„$GH€P„P„`ˆ`Ž €€€ PČ‚„B‚€ÂđŔ `Ŕ‚€  ŕ@€€€€AŔ‚A@˙˙˙˙˙˙˙˙˙˙˙˙ü0A`ƒ@0 ((€ H €(€¤H€–X€<˘HB€ĄHB €"h‚ €ˆHń€(@”p@@‚  Ŕ ‚`‚Ŕ‡€€â‚‚‚‚P8. According to the graph,  at what time t does the bug change direction?(A) 2((B) 51(C) 6:(D) 8C(E) 10PDP žnineűƒ FŒ!„$GH€P„P„`ˆ`Ž €€€ PČ‚„B‚€ÂđŔ `Ŕ‚€  ŕ@€€€€AŔ‚A@˙˙˙˙˙˙˙˙˙˙˙˙ü0A`ƒ@0 ((€ H €(€¤H€–X€<˘HB€ĄHB €"h‚ €ˆHń€(@”p@@‚  Ŕ ‚`‚Ŕ‡€€â‚‚‚‚P9. According to the graph,  at what time t is the speed of the buggreatest?((A) 21(B) 5:(C) 6C(D) 8P(E) 10 P EPŁten? KPŔ @€0ŕPÁ đ@@řC AAA˙˙˙˙˙˙ţă‘8D…ˆJ€Sę€p Eˆ P€""|ˆ|  ˆ@ř"" 10. What is&/8AP(A) -2 (B) -1/4(C) 1/2&(D) 1/(E) The limit does not 8exist.PBP elevenV 11. The area of the region  in the first quadrant between the graph of K A˙˙˙˙ ˆ|"Ÿˆ$ˆ|>x"€p(Kand the 1x-axis is: :8Dţ |8D˙| |(D8C(A)P 8DD8DD8˙|D8(B)  ř@p@ŕˆA@@ Ŕ@@@€řAó (C) # ř@pGŔˆ@ƒA@€ Ŕ@@D@řCƒ((D) 7 !€b$'€$@$@s€Ŕ>"1:(E)PBP €twelve ĆY 12. Which of the  following are antiderivatives of%#? $` "Ŕ"# " " r "˙˙˙"".#7#P  I. €€`€ "Ŕ"# " " r "˙˙˙%.7@P ",€€`€ "Ŕ"# " " Ŕr "Ŕ˙˙˙‚/ Ŕ II. %. 0(@€€ `XD €d("Ŕ"D8# D(" DD" r "?˙˙˙˙˙˙ţpˆ @"ř"7III. @ P (A) I only(B) III only(C) I and II only%(D) I and III only.(E) II and III onlyPCP ¤thirteenÂN 13. If r is positive and  increasing, for what value of r is the rate of P ŕ@€@  ąßČ€€€%increase of. 7 twelve times that of r?@P  ř ˙€ ‰q $=>(A) (B) 2%.7(C) 7 ř ˙ü ‰Ăq2  }@€;ŕ@P  ř@pGŔˆ@‡A@€ Ŕ@@D@řC‡ (D)%.(E) 6P BPždirectionsĺËœ‡S8Part B Sample Multiple- Choice QuestionsA graphing calculator is required for some &questions on this part of/the examination.8Part B consists of 17 Aquestions. In this section Pof the examination, as a correction for guessing, one-fourth of the number of questions answered&incorrectly will be /subtracted from the number 8of questions answeredAcorrectly. Following are Pthe directions for Section  I Part B and a representativeset of 7 questions.&Directions: Solve each of /the following problems, 8using the availableAspace for scratchwork. PAfter examining the form  of the choices, decidewhich is the best of the choices given and fill in &the corresponding oval on/the answer sheet. No 8credit will be given for Aanything written in the Ptest book. Do not spend  too much time on any one problem.In this test:&(1) The exact numerical /value of the correct 8answer does not alwaysAappear among the choices Pgiven. When this happens,  select from amongthe choices the number that best approximates the &exact numerical value./(2) Unless otherwise 8specified, the domain of a Afunction f is assumed toPbe the set of all real  numbers x for which f(x) is a real number.PP éfourteen wĚ[° 14. The volume generated  by revolving about the x-axis the region enclosed by the graphs of y=2x and(),for ( ŕˆˆř@ˆ"€xřA‚€pô@ -F%pˆD0ˆ (¨@ ˆř(|ˆDpř|?1t, is:CP R08€@ ŕ@‰€„€ ů€@?Q‡p€?Qˆ€ˆ…đ?Q€˘ Ô™@2ż‚8 €„A@€˘ú ô@@ ŕPŕ (A)(1:CP L08€@@ŔH€ Ä Bů@BQ€âQB5Q ŕBLŻ™ˆ DDO$P(D > =P(ˆD€ŕ@Pŕ (B)(1:CP Z ` p €pŔ?ˆ"  ň$D$@Ô@˘D(B€ 2ż ˘„ŕ @˘D(€ €ů2$>Dä@ô Ŕ     Ŕ (C)(1:CP J"8D>€@˙Ŕ €|‘!‘!ů‘!?Qá?Q!?QŽÁ™€Ôż‡ń4@€ŔŽÁ@‘!ó€!ŕ‚A„ˆPŸâ€ŕ (D)(1:CP B€€    đŕ@  ŕŔ€Ѐůóđ 4@€ @ř€pŕ P€ˆóŔP€@P€ €˜€ @€@€€řđ€8DDT DD8 (E)P BP fifteençž 15. Let f be defined as follows, where a0 6'O€p@ˆ@€  @!Ŕř   @  !$    ůË‚#˙˙˙Ŕ",… "( "("!Ŕ!Čˆ    Cáŕ`  ŕ`  $ !Ŕ " ůË€" ",…" "(" "(""(!Č€!Č%.f(x)=7@P Which of the following are  true about f?I. Á@CAAA㑉P'ĎP‘‰6f(x) exists % .II.f(a) exists.7III.f(x) is continuous at @x=a.P (A)None(B)I only(C)II only%(D)I and II only.(E)I, II, and III PDP Ęsixteen j˙˙˙˙˙˙˙˙˙˙˙˙˙˙€ @€ @€ AÁ @€D 0 Â!0`@€( @! @€ @A @€( @đ@€D A @€¸ ëáN: @€ @˙˙˙˙˙˙˙˙˙˙˙˙˙˙€ @€ @Œ "‡!9řČGß’H’1ˆŁEŔB@… PˆĽE(ň @„@¸‚ ‡)9H ĘA… řˆŻE| +â@H’ˆĄEŠ(B@ "Ç!N9 qČR@€ @€ @˙˙˙˙˙˙˙˙˙˙˙˙˙˙16. Let f be a function such (that f"(x) < 0 for all x 1in the closed [1, 2], with :selected values shown in Cthe table above. Which of Pthe following must be true  about f'(1.2)?(A) f'(1.2) < 0((B) 0 < f'(1.2) < 1.61(C) 1.6 < f'(1.2) < 1.8:(D) 1.8 < f'(1.2) < 2.0C(E) f'(1.2) > 2.0P DP0seventeenŻ 17. If the function g is  defined by ] SD((D€Ŕ"(@$€Bp€€€‚‰"@ Š/‚‹â Š ŒXˆk€z/‚dœ™ "@„Dˆ‰p€€DDˆ‰?ŽD‰xŔF Ŕ     Ŕ]']on the 0]9Bclosed interval -1 œ x œ 3 Pthen g has a local minimum  at x=(A) 0'(B) 1.0840(C) 1.7729(D) 2.171B(E) 2.507P EP Żeighteen ŢŇĆ şŽ 18. The graphs of five  functions are shown below. Which function has a nonzero average value over %the closed interval .7(? 7 ŕ€€€řĀP„œP„€PB„€˜DĀ€ŕ@P FŒpřüü     €  € Ŕ  €ř€ 0€  @Ŕ @ Ŕ €            € `€ Ŕ€!€@@.``8<p˙˙˙˙˙˙˙˙˙˙˙˙˙ř` p ` @ 0 ~@ ü@ €$€ ?đ(€ ,€ d F  €      P € €` Ŕ@x<A€ >  8 P F@přř     ŕ$ >x  H Œ „ „đ    < $ €đ€ Ŕ @ @ $@ (  đ 0 ` Ŕ € €˙˙˙˙˙˙˙˙˙˙˙˙˙˙€+€ Ŕ ` 0 đţ  üŕ  ţh `4ŕH @$H @$Hř@ @$΀ €gÄđ€bŕ €     ‚đ‚@ ‚Ŕ BŔ D@ lĄ@ 8˘Ŕ°``@ @ P FŒ€  5€$@D „ € €`@ @@@ ˙˙˙˙˙˙˙˙˙˙˙ţ€0  řü°Ř  P đP Đ¸Ü0ˆ €`@@`€ €Ą<AŔ P„P FŒ€ ?€€€€@@`  0l‚ƒ€€@@ ˙˙˙˙˙˙˙˙˙˙˙˙€€ 0€@ @   4ř~$°ěd („ ŕ(„ h¸nD€€ @@ >   P FŒ@€ Ŕ Ŕ$   Á€@Á°0!`0 @ `€€€€Ŕ?˙˙˙˙˙˙˙˙˙˙ŕ€Ŕ€€€Ŕ?@üvAŘ P P4 Đ7܈   @@@@€€€€€P EP 'nineteenÍ19. The region in the  first quadrant enclosed by the y-axis and the graphs of y=cosx and 'y=x is rotated about the 0x-axis. The volume of 9the solid generated isBP(A) 0.484 (B) 0.877(C) 1.520(D) 1.831'(E) 3.0400P CP UtwentyŰ20. Oil is leaking from a  tanker at the rate of R(t)= 2,000e^-0.2t gallons per hour, where t is %measured in hours. How .much oil has leaked out of 7the tanker after 10 hours?@P(A) 54 gallons (B) 271 gallons(C) 865 gallons(D) 8,647 gallons%(E) 14,778 gallons.P DPSTDYřwU