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AP ® Calculus AB Practice Exam From the 2 014 Administration This Practic e Exa m is provided by the Colleg e Boar d fo r AP Exam preparation . Teacher s ar e permitted to download the material s an d mak e copies to use wit h thei r student s in a classroo m settin g onl y. T o maintai n th e securit y of this exam , teacher s shoul d collec t al l material s afte r thei r administratio n an d keep the m in a secure location . Exam s ma y no t be poste d on schoo l or personal websites, no r electronically redistributed for an y reason. Fu rther distributio n of thes e material s outside of the secur e Colleg e Board sit e disadvantages teacher s wh o rel y on uncirculated questions for classroo m testing . An y additional distribution is in violation of the Colleg e Board ’s copyright policies an d ma y resul t in the terminatio n of Practic e Exa m acces s fo r you r schoo l as well as the removal of access to other online services such as the A P Teache r Communit y an d Onlin e Scor e Repo rts.

Contents Exam Instructions Student Answer Sheet for the Multiple -Choice Section Section I: Multiple -Choice Questions Section II: Free -Response Questions Multiple -Choice Answer Key Free- Response Scoring Guidelines Scoring Worksheet Note: This publication shows the page numbers that appeared in the 2013−14 AP Exam Instructions book and in th e actual exam. This publication was not repaginated to begin with page 1. © 2014 The College Board. College Board, Advanced Placement Program, AP, SAT and the acorn logo are registered trademarks of the College Board. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html.

Exam Instructions The following contains instructions taken from the 2013−14 AP Exam Instructions book.

34 What Proctors Need to Bring to This Exam • . Exam .packets • . Answer .s heets • . AP .Stude nt .Packs • . 2013-1 4 AP Coor\binator’s Manual . • . This .book .— .AP Ex am Instructions . • . School .Co de .and .Home-School/Self- Study .Codes • . Extra .gr aphing .calculators • . Pencil .s harpener • . Extra .No . .2 .pencils .with .erasers • . Extra .pe ns .with .black .or .dark .blue .ink • . Extra .pa per • . Staple r • . Watch • . Signs .fo r .the .door .to .the .testing .room . . . . .– . “Exam .i n .Progress” . . . . .– . .“Cell .phones .are .prohibited .in .the . testing .room” . If you are giving the regularly sche\bule\b AP Calculus AB or BC Exam: • . .You .may .seat .students .\bour \beet (approximately 1.2 meters) apart .because .these . exams .h ave .scrambled .multiple-choice .sections . .This .allows .you .to .test .more .students . in .fewer .testing .rooms . • . .See .pa ge .10 .for .a .sample .seating .plan, .including .form .codes .and .serial .numbers, .that . shows .how .exams .should .be .distributed .to .ensure .that .students .seated .next .to .each . other .are .not .given .the .same .form .of .the .exam . • . Admin istrators .and .proctors .must .continue .to .be .vigilant .about .opportunities . . for .cheating . If you are giving the alternate AP Calculus AB or BC Exam for late testing: • . .You .must .seat .students . no les s than five \beet (approximately 1.5 meters) apart .because . these .exams .do .not .have .scrambled .multiple-choice .sections . Graphing .calculators .are .required .to .answer .some .of .the .questions .on .the .AP .Calculus .Exams . . Before .starting .the .exam .administration, .make .sure .each .student .has .a .graphing .calculator . . from .the .approved .list .on .page .\b5 .of .the . 2013-14 AP Coor\binator’s Manual . .If .a .student .does .not . have .a .graphing .calculator .from .the .approved .list, .you .may .provide .one .from .your .supply . .If .the . student .does .not .want .to .use .the .calculator .you .provide .or .does .not .want .to .use .a .calculator .at . . all, .he .or .she .must .hand .copy, .date, .and .sign .the .release .statement .on .page .\b3 .of .the . 2013-14 AP Coor\binator’s Manual . During .the .administration .of .Section .I, .Part .B, .and .Section .II, .Part .A, .students .may .have .no . more .than .two .graphing .calculators .on .their .desks . .Calculators .may .not .be .shared . .Calculator memories do not need to be cleared before or after the exam. .Students .with .Hewlett-Packard . \b8–50 .Series .and .Casio .FX-9860 .graphing .calculators .may .use .cards .designed .for .use .with .these . AP® Calculus AB/BC Exam Regul\brly Scheduled Ex\bm D\bte: Wednesd\by morning, M\by 7, 2014 L\bte-Testing Ex\bm D\bte: Thursd\by morning, M\by 22, 2014 Section I Tot\bl Time, C\blculus AB: 1 hr. 45 min. Section II Tot\bl Time, C\blculus AB: 1 hr. 30 min. Section I Tot\bl Time, C\blculus BC: 1 hr. 45 min. Section II Tot\bl Time, C\blculus BC: 1 hr. 30 min.

35 AP Exam Instructio\Bns CALCULUS calculators . .Proctors .should .make .sure .infrared .ports .(Hewlett-Packard) .are .not .facing .each . other . .Since graphing calculators can be used to store data, including text, proctors should monitor that students are using their calculators appropriately. Attempts by students to use the calculator to remove exam questions and/or answers \brom the room may result in the cancellation o\b AP Exam scores. The .AP .Calculus .AB .Exam .and .the .AP .Calculus .BC .Exam .should .be .administered . simultaneously . .They .may .be .administered .in .separate .rooms, .or .in .the .same .room .if .it .is . . more .convenient . . SECTION I: Multiple Choice ! Do not begin the exam instructions below until you have completed the appropriate General Instructions \bor your group. These .exams .include .survey .questions . .The .time .allowed .for .the .survey .questions .is .in .addition .to . the .actual .test-taking .time . . Make .sure .you .begin .the .exams .at .the .designated .time . . If you are giving the regularly sche\bule\b exam, say: It is Wednesday morning, May 7, and you will be taking either the AP Calculus AB Exam or the AP Calculus BC Exam. If you are giving the alternate exam for late testing, say: It is Thursday morning, May 22, and you will be taking either the AP Calculus AB Exam or the AP Calculus BC Exam. In a moment, you will open the packet that contains your exam materials. By opening this packet, you agree to all of the AP Program’s policies and procedures outlined in the 2013-14 Bulletin for AP Students and Parents . Please check to make sure you have the correct exam: Calculus AB or Calculus BC. Raise your hand if you do not have the correct exam. . . . \bou may now remove the shrinkwrap from your exam packet and take out the Section I booklet, but do not open the booklet or the shrinkwrapped Section II materials. Put the white seals aside. . . . Carefully remove the AP Exam label found near the top left of your exam booklet cover. Now place it on page 1 of your answer sheet on the light blue box near the top right-hand corner that reads “AP Exam Label.” If .students .accidentally .place .the .exam .label .in .the .space .for .the .number .label .or .vice .versa, . advise .them .to .leave .the .labels .in .place . .They .should .not .try .to .remove .the .label; .their .exam .will . be .processed .correctly . . Read the statements on the front cover of Section I and look up when you have finished. . . . Sign your name and write today’s date. Look up when you have finished. . . . Now print your full legal name where indicated. Are there any questions? . . .

36 Calculus Turn to the back cover and read it completely. Look up when you have finished. . . . Are there any questions? . . . S ection I is the multiple-choice portion of the exam. \bou may never discuss these specific multiple-choice questions at any time in any form with anyone, including your teacher and other students. If you disclose these questions through any means, your AP Exam score will be canceled. Are there any questions? . . . \bou must complete the answer sheet using a No. 2 pencil only. Mark all of your responses beginning on page 2 of your answer sheet, one response per question. Completely fill in the circles. If you need to erase, do so carefully and completely. No credit will be given for anything written in the exam booklet. Scratch paper is not allowed, but you may use the margins or any blank space in the exam booklet for scratch work. Section I is divided into two parts. Each part is timed separately, and you may work on each part only during the time allotted for it. Calculators are not allowed in Part A. Please put your calculators under your chair. Are there any questions? . . . \bou have 55 minutes for Part A. Part A questions are numbered 1 through 28. Mark your responses for these questions on page 2 of your answer sheet. Open your Section I booklet and begin. 12 6 3 9 .Note .Start .Time .here . ???? ? ??????? ????????? ??? ??? ?? Stop working on Part A and turn to page 22 in your Section I booklet. . . . On that page, you should see an area marked “PLACE SEAL HERE.” Making sure all of your other exam materials, including your answer sheet, are out of the way, take one of your seals and press it on that area and then fold the seal over the open edge to the front cover. Be sure you don’t seal the Part B section of the booklet or let the seal touch anything except the marked areas. . . . After .all .students .have .sealed .Part .A, .say: Graphing calculators are required for Part B. \bou may get your calculators from under your chair and place them on your desk. Part B questions are numbered 76 through 92. Fold your answer sheet so only page 3 is showing and mark your responses for these questions on that page. \bou have 50 minutes for Part B. \bou may begin. 12 6 3 9 .Note .Start .Time .here . ???? ? ? ?????????? ????? ???

37 AP Exam Instructio\Bns CALCULUS make .sure .that .students .are .using .their .calculators .appropriately . .Proctors .should .also .make .sure . Hewlett-Packard .calculators’ .infrared .ports .are .not .facing .each .other . .After .50 .minutes, .say: Stop working and turn to page 38. \bou have 3 minutes to answer Questions 93–96. These are survey questions and will not affect your score. \bou may not go back to work on any of the exam questions. . . . Give .students .approximately .3 .minutes .to .answer .the .survey .questions . .Then .say: Close your booklet and put your answer sheet on your desk, face up. Make sure you have your AP number label and an AP Exam label on page 1 of your answer sheet. I will now collect your answer sheet. Collect .an .answer .sheet .from .each .student . .Check .that .each .answer .sheet .has .an .AP .number .label . and .an .AP .Exam .label . .Then .say: Now you must seal your Section I booklet. Remove the remaining white seals from the backing and press one on each area of your exam booklet cover marked “PLACE SEAL HERE.” Fold each seal over the back cover. When you have finished, place the booklet on your desk, face up. I will now collect your Section I booklet. . . . Collect .a .Section .I .booklet .from .each .student . .Check .that .each .student .has .signed .the .front .cover . of .the .sealed .Section .I .booklet . . There .is .a .10-minute .break .between .Sections .I .and .II . .When .all .Section .I .materials .have .been . collected .and .accounted .for .and .you .are .ready .for .the .break, .say: Please listen carefully to these instructions before we take a 10-minute break. Everything you placed under your chair at the beginning of the exam must stay there. Leave your shrinkwrapped Section II packet on top of your desk during the break. \bou are not allowed to consult teachers, other students, or textbooks about the exam during the break. \bou may not make phone calls, send text messages, use your calculators, check email, use a social networking site, or access any electronic or communication device. Remember, you are not allowed to discuss the multiple-choice section of this exam. If you do not follow these rules, your score could be canceled. Are there any questions? . . . 126 3 9 .\bou may begin your break. Testing will resume at SECTION II: Free Response After .the .break, .say: May I have everyone’s attention? Place your Student Pack on your desk. . . . \bou may now remove the shrinkwrap from the Section II packet, but do not open the Section II exam booklet until you are told to do so. . . . Read the bulleted statements on the front cover of the exam booklet. Look up when you have finished. . . .

38 Calculus Now place an AP number label on the shaded box. If you don’t have any AP number labels, write your AP number in the box. Look up when you have finished. . . . Read the last statement. . . . Using your pen, print the first, middle and last initials of your legal name in the boxes and print today’s date where indicated. This constitutes your signature and your agreement to the statements on the front cover. . . . Turn to the back cover and complete Item 1 under “Important Identification Information.” Print the first two letters of your last name and the first letter of your first name in the boxes. Look up when you have finished. . . . In Item 2, print your date of birth in the boxes. . . . In Item 3, write the school code you printed on the front of your Student Pack in the boxes. . . . Read Item 4. . . . Are there any questions? . . . I need to collect the Student Pack from anyone who will be taking another AP Exam. \bou may keep it only if you are not taking any other AP Exams this year. If you have no other AP Exams to take, place your Student Pack under your chair now. . . . While Student Packs are being collected, read the information on the back cover of the exam booklet, paying careful attention to the bulleted statements in the instructions. Do not open the exam booklet or break the seals in the exam booklet until you are told to do so. Look up when you have finished. . . . Collect .the .Student .Packs . .Then .say: . Are there any questions? . . . Section II also has two parts that are timed separately. \bou are responsible for pacing yourself, and may proceed freely from one question to the next within each part. Graphing calculators are required for Part A, so you may keep your calculators on your desk. \bou must write your answers in the appropriate space in the exam booklet using a No. 2 pencil or a pen with black or dark blue ink. Do not break the seals for Part B at this time. Are there any questions? . . . \bou have 30 minutes to answer the questions in Part A. If you need more paper during the exam, raise your hand. At the top of each extra piece of paper you use, be sure to write only your AP number and the number of the question you are working on. Do not write your name. Open your exam booklet and begin.

39 AP Exam Instructio\Bns CALCULUS 126 3 9 .Note .Start .Time .here . . .Note .Stop .Time .here . . .Check .that .students .are . working .on .Part .A .only .and .writing .their .answers .in .their .exam .booklets .using .pencils .or .pens . with .black .or .dark .blue .ink . .The .pages .for .the .Part .A .questions .are .marked .with .large .1s .or .2s .at . the .top .of .each .page .to .assist .you .in .monitoring .their .work . .After .20 .minutes, .say: There are 10 minutes remaining in Part A. After .10 .minutes, .say: Stop working on Part A. Calculators are not allowed for Part B. Please put all of your calculators under your chair. . . . Turn to page 13. \bou have 1 hour for Part B. During this time you may go back to Part A, but you may not use your calculator. Remember to show your work, and write your answer to each part of each problem in the appropriate space in the exam booklet. Are there any questions? . . . Using your finger, break open the seals on Part B. Do not peel the seals away from the booklet. \bou may begin Part B. 12 6 3 9 .Note .Start .Time .here . . .Note .Stop .Time .here . . .After .50 .minutes, .say: There are 10 minutes remaining in Part B. After .10 .minutes, .say: Stop working and close your exam booklet. Place it on your desk, face up. . . . If .any .students .used .extra .paper .for .the .free-response .section, .have .those .students .staple .the .extra . sheet/s .to .the .first .page .corresponding .to .that .question .in .their .exam .booklets . .Then .say: . Remain in your seat, without talking, while the exam materials are collected. . . . Collect .a .Section .II .exam .booklet .from .each .student . .Check .for .the .following: . • .Exam .booklet .front .cover: .The .student .placed .an .AP .number .label .on .the .shaded .box, . . and .printed .his .or .her .initials .and .today’s .date . . • .E xam .booklet .back .cover: .The .student .completed .the .“Important .Identification . Information” .area . When .all .exam .materials .have .been .collected .and .accounted .for, .return .to .students .any .electronic . devices .you .may .have .collected .before .the .start .of .the .exam . . If you are giving the regularly sche\bule\b exam, say: \bou may not discuss or share these specific free-response questions with anyone unless they are released on the College Board website in about two days. \bour AP score results will be available online in July. If you are giving the alternate exam for late testing, say: None of the questions in this exam may ever be discussed or shared in any way at any time. \bour AP score results will be available online in July.

40 Calculus If .any .students .completed .the .AP .number .card .at .the .beginning .of .this .exam, .say: Please remember to take your AP number card with you. \bou will need the information on this card to view your scores and order AP score reporting services online. Then .say: \bou are now dismissed. All .exam .materials .should .be .put .in .secure .storage .until .they .are .returned .to .the .AP .Program . after .your .school’s .last .administration . .Before .storing .materials, .check .the .“School .Use .Only” . section .on .page .1 .of .the .answer .sheet .and: . . • .Fill .in .the .appropriate .section .number .circle .in .order .to .access .a .separate .AP . . I nstructional .Planning .Report .(for .regularly .scheduled .exams .only) .or .subject . . score .roster .at .the .class .section .or .teacher .level . .See .“Post-Exam .Activities” .in .the . . 2013-14 AP Coor\binator’s Manual . . . • .Check .your .list .of .students .who .are .eligible .for .fee .reductions .and .fill .in .the . . appropriate .circle .on .their .registration .answer .sheets . .

Student Answer Sheet for the Multiple -Choice Section Use this section to capture student responses. (Note that the following answer sheet is a sample, and may differ from one used in an actual exam. )

Sign your legal name as it will\. appear on your college applic\.ations. Date To maintain the security of the exam and the validity of my AP score, \b will allow no one else to see the multiple-choice questions. \b will seal the multiple-choice booklet when asked to do so, and \b will not discuss these questions with anyone at any time after completing the section. \b am aware of and agree to the AP Program’s policies and procedures as outlined in the 2013-14 Bulletin for AP Students and Parents, including using testing accommodations (e.g., extended time, computer, etc.) only if \b have been preapproved by College Board Services for Students with \vDisabilities.COMPLETE THIS AREA AT EVERY EXAM. USE NO. 2 PENCIL ONLY A. SIGNATURE GE 1AP anuyC\bFu \bGHI JKLMFueHNOPMQuluRMMTIHOU\. anu.VFGHLu \bGHIuJKLMFueOVWHQOun\bNTU OHHZeuLHY 1 X B Q – a D Rpu yAa u.agy iFPOu\b2MXOLM2ZHX3u4Lp3ullp H5\bIu6PLXOu.\bFHu7u6PLXOuBDu HOOHLX H5\bIu \bXOu.\bFHu7u6PLXOuB8u HOOHLX gl A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b F F F F F F F F F F F F F F F G G G G G G G G G G G G G G G H H H H H H H H H H H H H H H I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J K K K K K K K K K K K K K K K L L L L L L L L L L L L L L L M M M M M M M M M M M M M M M N N N N N N N N N N N N N N N O O O O O O O O O O O O O O O P P P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R R R S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T U U U U U U U U U U U U U U U V V V V V V V V V V V V V V V W W W W W W W W W W W W W W W X X X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z – – – – – – – – – – – – – 1 2 3 4 5 6 7 8 9 A A A A A A A A A A A A A B B B B B B B B B B B B B C C C C C C C C C C C C C D D D D D D D D D D D D D \b \b \b \b \b \b \b \b \b \b \b \b \b F F F F F F F F F F F F F G G G G G G G G G G G G G H H H H H H H H H H H H H I I I I I I I I I I I I I J J J J J J J J J J J J J K K K K K K K K K K K K K L L L L L L L L L L L L L M M M M M M M M M M M M M N N N N N N N N N N N N N O O O O O O O O O O O O O P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R S S S S S S S S S S S S S T T T T T T T T T T T T T U U U U U U U U U U U U U V V V V V V V V V V V V V W W W W W W W W W W W W W X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z – – – – – – – – – – 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 0 0 1 1 2 2 3 3 4 5 6 7 8 9 6 12 7 1 8 2 9 3 10 4 11 5 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 S 9puuywagu9aoy Spuuticmuanu.cgRym Month AM PM F. MULTIPLE-CHOICE BOOKL\NET SERIAL NUMBER rpuuanuywaguluagu oahl.Aucel.Auorleu a.exymueryyo \bxam Name: Form Code: Form: COMPLETE THIS AREA ONLY ONCE. SCHOOL USE ONLY Fee Reduction Gr\bnted Section Number Option 1 Option 2 E. EXAM START TIME 0 0 1 1 2 3 4 5 6 7 8 9 1 2 773898 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 G. ONLINE PROVIDER CODE Day 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 L. SOCIAL SECURITY NUMBER (Option\bl) 99735-00657• UNLW\bB114 Q3779/1-4 COLLEGE CODE 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 M. COLLEGE TO RECEIVE YOUR AP SCORE REPORT College Name State Country Using the college \.code listed in the AP Student Pack, indicate the ONE college that you want to receive your AP score report. City SCHOOL CODE 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 School Name State Country J. SCHOOL YOU ATTEND City 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 INTERNATIONAL PHONE I. AREA CODE AND PHONE NUMBER 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Day Year K. DATE OF BIRTH .puuScmmy.ou Ama9yu ysy Not yet in 9th grade 9th 10th 11th 12th No longer in high school B123456789T

P. LANGUAGE — Do not complete this section unle\Nss instructed to do so. 1 2 34 5 67 8 9 A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I A B C D \b F G H I If this \bnswer sheet is for the French L\bngu\bge \bnd Culture, Germ\bn L\bngu\bge \bnd Culture, It\bli\bn L\bngu\bge \bnd Culture, Sp\bnish L\bngu\bge \bnd Culture, or Sp\bnish Liter\bture \bnd Culture Ex\bm, ple\bse \bnswer the following questions. Your responses will not \bffect your score. 1. Have you lived or studied for one month or mo\.re in a country where the language of \.the exam you are now taking is spoken? Yes No DO NOT WRITE IN THIS AREA O. SURVEY QUESTIONS — Answer the survey questions in the \NAP Student P\bck. Do not put responses to ex\bm questions in this\N section. PAGE 2 COMPLETE THIS AREA AT EACH EXAM (IF APPLICABLE) Indic\bte your \bnswers to the ex\bm questions in this\N section (p\bges 2 \bnd 3). M\brk only one response per question\N. If \b question h\bs onl\Ny four \bnswer options, do not m\brk option E. Answers written in the multiple-choice booklet will not be scored. A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 QUESTIONS 1–75 Yes No 2. Do you regularly speak or hear th\.e language at home\.? L GL 1L xL 2 L GL 1L xL 2 You must use \b No. 2 pencil \bnd m\brks must be complete. Do not use \b mech\bnic\bl pencil. It is very important that you fill in the entire circle darkly and completely. If you change your response, erase as completely as possible. Incomplete marks or erasures may affect your score. COMPLETE MARK EXAMPLES OF INCOMPLETE MARKS

/ / / – . . . . . 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 / / / – . . . . . 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 / / / – . . . . . 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 / / / – . . . . . 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 / / / – . . . . . 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 For Students T\bking AP Biology / / / – . . . . . 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 121123 122 124125 126 Write your \bnswer in the boxes \bt the top of the gridd\bble \bre\b \bnd fill in the corresponding circles. M\brk only one circle in \bny column. You will receive credit only if the circles \bre filled in correctly. SELECTED MEDIA EXA\NMS R W O OTHER EXAMS R W O PT02 TOTAL PT03 Subscore (if \bpplic\bble) PT04 Subscore (if \bpplic\bble) PAGE 3 ETS USE ONLY DO NOT WRITE IN THIS AREA A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b A B C D \b 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110111 112 113 114 115 116 117 118 119 120 Be sure e\bch m\brk is d\brk \bnd completely fills the circle. If \b question h\bs on\Nly four \bnswer options, do not m\brk option E. QUESTIONS 76–120 © 2013 The College Board. College Board, AP, Student Search Service and the acorn logo are registered trademarks of the College Board. \bxam \bxam 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

COMPLETE THIS AREA ONLY ONCE. ZIP OR POSTAL CODECOUNTRY CODE PAGE 4 STREET ADDRESS (include street number, street name, apartment number, etc.) CITY A A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D D D D D D D D D D D D \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b \b F F F F F F F F F F F F F F F F F F F F F F F F F F G G G G G G G G G G G G G G G G G G G G G G G G G G H H H H H H H H H H H H H H H H H H H H H H H H H H I I I I I I I I I I I I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J J J J J J J J J J J J K K K K K K K K K K K K K K K K K K K K K K K K K K L L L L L L L L L L L L L L L L L L L L L L L L L L M M M M M M M M M M M M M M M M M M M M M M M M M M N N N N N N N N N N N N N N N N N N N N N N N N N N O O O O O O O O O O O O O O O O O O O O O O O O O O P P P P P P P P P P P P P P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R R R R R R R R R R R R R R S S S S S S S S S S S S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T T T T T T T T T T T T U U U U U U U U U U U U U U U U U U U U U U U U U U V V V V V V V V V V V V V V V V V V V V V V V V V V W W W W W W W W W W W W W W W W W W W W W W W W W W X X X X X X X X X X X X X X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 / / / / / / / / / / / / / / / / / / / / / / / / A A A A A A A A A A A A A B B B B B B B B B B B B B C C C C C C C C C C C C C D D D D D D D D D D D D D \b \b \b \b \b \b \b \b \b \b \b \b \b F F F F F F F F F F F F F G G G G G G G G G G G G G H H H H H H H H H H H H H I I I I I I I I I I I I I J J J J J J J J J J J J J K K K K K K K K K K K K K L L L L L L L L L L L L L M M M M M M M M M M M M M N N N N N N N N N N N N N O O O O O O O O O O O O O P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R S S S S S S S S S S S S S T T T T T T T T T T T T T U U U U U U U U U U U U U V V V V V V V V V V V V V W W W W W W W W W W W W W X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z A A A A A A A A A B B B B B B B B B C C C C C C C C C D D D D D D D D D \b \b \b \b \b \b \b \b \b F F F F F F F F F G G G G G G G G G H H H H H H H H H I I I I I I I I I J J J J J J J J J K K K K K K K K K L L L L L L L L L M M M M M M M M M N N N N N N N N N O O O O O O O O O P P P P P P P P P Q Q Q Q Q Q Q Q Q R R R R R R R R R S S S S S S S S S T T T T T T T T T U U U U U U U U U V V V V V V V V V W W W W W W W W W X X X X X X X X X Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 / / / / / / / 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 Q. YOUR MAILING ADDRESS Use the address abbreviations from your AP Student Pack. Fill in only one circle per column. Indicate a space in your address by leaving a blank box; do not grid that column. AK AL AR AZ CA CO CT DC D\b FL GA HI IA ID IL IN KS KY LA MA MD M\bMI MN MO MS MT NC ND N\b NH NJ NM NV NY OH OK OR PA RI SC SD TN TX UT VAVT WA WI WV WY Puerto Rico AA A\b AP Other STATE R. FOR STUDENTS OUTSIDE THE UNITED STATES ONLY T. EMAIL ADDRESS If your address does not fit in the spaces provided in Item Q, fill in as many circles as you can, then fill in the circle in Item R and print the remainder of your address in the spaces provided. Address City State or Province Country ZIP or Postal Code 1EL.HTQO6OPMLET HLSRAOILA66HSVVyLET LAHSLMHAPYOPMLYKSLxTIISMSL1TAH6L .SHROVVOTPLYTL VSLET HLSRAOILOPLAUUTH6APUSLXOYKLYKSL.TIOUOSVLOPLYKSL 2013-14 Bulletin for AP Students and Parents. S. STUDENT IDENTIFIER (Student ID Number) U. 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Section I: Multiple -Choice Questions This is the multiple -choice section of the 2014 AP exam. It includes cover material and other administrative instructions to help familiarize students with the mechanics of the exam. (Note that future exams may differ in look from the following content.)

AP ® Calculus AB Exam SECTION I: Multiple Choice 2014 DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions At a Glance Total Time 1 hour, 45 minutes Number of Questions 45 Percent of Total Score 50% Writing Instrument Pencil required Part A Number of Questions 28 Time 55 minutes Electronic Device None allowed Part B Number of Questions 17 Time 50 minutes Electronic Device Graphing calculator required Section I of this exam contains 45 multiple-choice questions and 4 survey questions. For Part A, fill in only the circles for numbers 1 through 28 on page 2 of the answer sheet . For Part B, fill in only the circles for numbers 76 through 92 on page 3 of the answer sheet. The survey questions are numbers 93 through 96. Indicate all of your answers to the multiple- choice questions on the answer sheet. No credit will be given for anything written in this exam booklet, but you may use the booklet for notes or scratch work. After you have decided which of the suggested answers is best, completely fill in the corresponding circle on the answer sheet. Give only one answer to each question. If you change an answer, be sure that the previous mark is erased completely. Here is a sample question and answer. Use your time effectively, working as quickly as you can without losing accuracy. Do not spend too much time on any one question. Go on to other questions and come back to the ones you have not answered if you have time. It is not expected that everyone will know the answers to all of the multiple- choice questions. Your total score on the multiple- choice section is based only on the number of questions answered correctly. Points are not deducted for incorrect answers or unanswered questions. Form I Form Code 4JBP6-S 66

( fx ) f-1 AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -3- CALCULUS AB SECTION I, Part A Time — 55 minutes Number of questions — 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM. Directions: Solve each of the following problems, using the av ailable space for scratch work. After examining the form of the choices, decide which is the best of the choices given and fill in the corresponding circle on the answer sheet. No credit will be given for anything written in the exam book. Do not spend too much time on any one problem. In this exam : (1) Unless other wise specified, the domain of a function fis assumed to be the set of all real numbers xfor which is a real number. (2) The inverse of a trigonometric function fmay be indicated using the inverse function notation or with the prefix “arc” (e.g., 1 sin arcsinx - = ). x

() 2 231 - Ú x t = dt 3 6 -- xx 3- xx 2 31 - x 2 3 - x 1 61- x ( = ln 2 y x ) 1 8 1 4 1 2 3 4 AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -4- 1. (A) (B ) (C) 2 (D ) (E) 2 2. What is the slope of the line tangent to the graph of at the point where x= 4? (A) (B ) (C) (D) (E) 4

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -5- 3. If (A) 62 - (B ) 58 - (C) 3 - (D) 0 (E) 1 4. 2 1 21 = + Ú dx x (A) (B ) (C) (D) (E) (1 ln 5 ln 3 2 - ) ln 5 ln 3 - (2ln 5 ln 3 - ) 1 ln 2 2 2ln2 fx() x- 1 22 x 44 =++ 4 , thenf ¢ 2() =

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -6- () () 2 lim 2 - Æ = x fx f () () 6 lim lim - Æ = xx fx fx () () 6 lim 6Æ = x fx f 5. The figure above shows the graph of the function f . Which of the following statements are true? I. II. 6+ Æ III. (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -7- 6. () (32 sin d x dx = (32 cos x ()22 3sin x ()22 6sinxx () ()22 2 3sin cos xx () (22 2 6sin cosxx ) (A) ) (B) (C) (D) (E) ) x

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -8- 7. 3 3 lim x x x e Æ• is (A) 0 (B) 2 9 (C ) 23 ( sin 2 , u = x ) () () 2 5 6sin 2 cos 2 x p p Ú xdx (D) 1 (E) infinite 8. Using the substitution is equivalent to (A) 1 5 12 2 udu -Ú (B) 1 5 12 1 2 udu Ú (C) 32 5 0 1 2 udu Ú (D) 0 5 32 1 2 ud Ú u (E) 0 5 32 2 udÚ u

() ( )( 2 fx xx x =- ¢ ) + 31 . At what values of x does f have - 1 -1 -1 -1 , 0, and 3 AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -9- 9. The function f has a first derivative given by a relative maximum? (A) only (B) 0 only (C) and 0 only (D) and 3 only (E) () () 2 710 for 2 2 for 2 xx x fx bx bÏ -+ π Ô = - Ì Ô = Ó - 3 2 x 10. Let f be the function defined above. For what value of b is f continuous at x = 2? (A) (B ) (C) 3 (D) 5 (E) There is no such value of b.

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -10- 0 x ££ 6, the graph of , the derivative of f, is piecewise linear as shown above. If f ¢ ()0 f =1, what is the 11. For maximum value of f on the interval? (A) 1 (B) 1.5 (C) 2 (D) 4 (E) 6 () 9 =x fx . If four subintervals of equal length are used, what is the value of the () 2 0 ? Ú fx dx 12. Let f be the function given by right Riemann sum approximation for (A) 20 (B) 40 (C) 60 (D) 80 (E) 120

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -11- 13. 2 1 1 + ʈ = Á˜ ˯ + dx dx x (A) () 2 2 2 21 1 +- + xx x (B) -- + + xx x (C) () 2 2 2 21 1 -- + + xx x (D) () 2 2 2 321 1 ++ + xx x (E) x

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -12- 14. The velocity of a particle moving along the x-axis is given by at time t. If the particle is at x = 4 when t= 0, what is the position of the particle when 2 p = t ? () ( ) sin 2 vt t = (A) 2 (B) 3 (C) 4 (D) 5 (E) 6

( ygx = ) (3 6 y gx x = )2 - AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -13- 15. The function is differentiable and increasing for all real numbers. On what intervals is the function increasing? (A) ( ] -•,0 [ • 4, ) and [ ]0, 4 [ )• 2, [ )• 6, (-••, ) only (B) only (C) only (D) only (E) 16. 3 3 lim 3 x x x - Æ - - 3 - 1 - is (A) (B ) (C) 1 (D) 3 (E) nonexistent

() ax fx ae - = 0 > a , then ()fx =¢ ax e- ax ae - 2 ax ae - ax ae - - 2 ax ae - - AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -14- 17. If for (A) (B) (C) (D) (E)

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -15- 18. A student attempted to solve the differential equation dy xy dx = with initial condition y= 2 when x=0. In which step, if any, does an error first appear? Step 1 : 1 dy x dx y = Û Ù ı Ú Step 2 : 2 ln 2 x y C =+ Step 3 : 22 x y e =+ C Step 4: Since y=2 when x= 0, 0 2 e =+ . C Step 5 : 22 1 x ye =+ (A) Step 2 (B) Step 3 (C) Step 4 (D) Step 5 (E) There is no error in the solution.

5 3 =+ y x 4 10x 8 3 =- x 2 =- x 8 3 =- x 2 =- x () 2 ln 3 ln 5 lim 2 x x x Æ +-- () 15 1 2 AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -16- 19. For what values of x does the graph of have a point of inflection? (A) only (B) only (C) x = 0 only (D) x = 0 and (E) x = 0 and 20. is (A) 0 (B) (C ) (D) 1 (E) nonexistent

2 wx= y 240 - 96 - () 32 2 3 12 18 fx x x x =--+ . On which of the following intervals is the graph () 1 1, 2 - ( ) 1, 2 - ,1 ,2 2 ( )2, • AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -17- 21. Functions w, x, and y are differentiable with respect to time and are related by the equation . If x is decreasing at a constant ra te of 1 unit per minute and y is increasing at a constant rate of 4 units per minute, at what rate is w changing with respect to time when x= 6 and y= 20 ? (A) 384 - (B) (C) (D) 276 (E) 384 22. Let f be the function defined by of f both decreasing and concave up? (A) ( ) ,1 --• (B ) (C) (D ) (E)

() 2 35when 1 3when 1x fx x+ Ï = Ì -+ ≥- Ó x x < - ( 1 f - ¢) , , , , 2 385 21 x fx x + = + 4. Which of the following is a horizontal asymptote to -x 6 y=- 3 y=- 1 2 y =- 3 2 y = AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -18- 23. If f is the function defined above, then is (A) 3 - (B ) 2- (C) 2 (D) 3 (E) nonexistent 24. Let f be the function defined by the graph of f ? (A) (B) (C) (D) y = 0 (E)

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -19- 25. If and 2 2 =- y xx 2 = ux + 1 = dy du ( () 2 2 221 +-+ xx x )1 2 63 - x - x 2 1 - x 1 1 - x 0,> x 2 1 1 1 = + Ú x d dt dx t ( 1 21 + xx ) 1 21 + xx ) 1 1 + x 1+x x 1 1 + x , then (A) (B ) (C) 4x ( D) (E) 26. For (A) (B) (C) (D) (E)

0££t 1 () ( ) sin 2 2 . p p = xt t t + 1 8 1 4 1 2 AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -20- 27. A particle moves on the x-axis so that at any time t, , its position is given by For what value of t is the particle at re st? (A) 0 (B) (C) (D) (E) 1

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Unauthorized copying or reuse of any part of this page is illegal. -21- dyxy x dx =- dy xy x dx =+ 2 dy y x dx =- 2 1 dy y x dx =-) 31 dy y dx =-) 28. Shown above is a slope field for which of the following differential equations? (A) (B) (C) (D) (E) END OF PART A OF SECTION I IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON PART A ONLY. DO NOT GO ON TO PART B UNTIL YOU ARE TOLD TO DO SO.

( fx ) 1f- 1 sin arcsin x - = x BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -24- CALCULUS AB SECTION I, Part B Time — 50 minutes Number of questions — 17 A GRAPHING CALCULATOR IS RE QUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAM. Directions: Solve each of the following problems, using the available space for scratch work. After examining the form of the choices, decide which is the best of the choices given and fill in the corresponding circle on the answer sheet. No credit will be given for anything written in the exam book. Do not spend too much time on any one problem. BE SURE YOU ARE USING PAGE 3 OF THE ANSWER SHEET TO RECORD YOUR ANSWERS TO QUESTIONS NUMBERED 76–92. YOU MAY NO T RETURN TO PAGE 2 OF THE ANSWER SHEET. In this e xam: (1) The exact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among the choices the number th at best approximates the exact numerical value. (2) Unless otherwise specified, the domain of a function fis assumed to be the set of all real numbers xfor which is a real number. ( 3) The inverse of a trigonometric function fmay be indicated using the inverse function notation or with the prefix “arc” (e.g., ). B B

0 t > (st ), the (vt ) () at [ ]2, 8 BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -25- 76. A particle moves along a straight line so that at time the position of the particle is given by velocity is given by , and the acceleration is given by . Which of the following expressions gives the average velocity of the particle on the interval ? (A) () 8 2 1 6 at dt Ú (B) ()8 2 1 6 st dt Ú () ()8 6 ss -2 () ()8 6 v -2 v () ()8 vv -2 SIN Ê Á Ë + x ˆ ˜ ¯ (fx ) () 2 1 = Ú fxdx 0.281 - 0.102 - (C) (D) (E) 77. If is an antiderivative for , then (A) (B ) (C) 0.102 (D) 0.260 (E) 0.282 BB

f¢ BB B B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -26- 78. The function f is differentiable and increasing for all real numbers x, and the graph of f has exactly one point of inflection. Of the following, which could be the graph of , the derivative of f ? (A) (B) (C) (D) (E) B B

79. A vase has the shape obtained by revolving the curve 2sin =+ y x BB B B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -27- from x = 0 to x= 5 about the x-axis, where x and y are measured in inches. What is the volume, in cubic inches, of the vase? (A) 10.716 (B) 25.501 (C) 33.666 (D) 71.113 (E) 80.115 x (fx ) 1 2.4 3 3.6 5 5.4 80. The table above gives sele cted values of a function f. The function is twice differentiable with () 0. > ¢¢ fx Which of the following could be the value of ()3 ¢ f ? (A) 0.6 (B) 0.7 (C) 0.9 (D) 1.2 (E) 1.5 BB

BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -28- 81. At time t = 0 years, a forest preserve has a population of 1500 deer. If the rate of growth of the population is modeled by () 0.23 2000 = t Rt e deer per year, what is the population at time t = 3? (A) 3987 (B) 5487 (C) 8641 (D) 10,141 (E) 12,628 B B

BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -29- f ¢ 6 x -< < 8 82. The figure above shows the graph of , the derivative of function f, for . Of the following, which best describes the graph of f on the same interval? (A) 1 relative minimum, 1 relative maximum, and 3 points of inflection (B) 1 relative minimum, 1 relative maximum, and 4 points of inflection (C) 2 relative minima, 1 relative maximum, and 2 points of inflection (D) 2 relative minima, 1 relative maximum, and 4 points of inflection (E) 2 relative minima, 2 relative maxima, and 3 points of inflection B B

() 6 0 9, fx dx = Ú () 6 3 5, fx dx = Ú () 0 3 7 gx dx =- Ú . What is BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -30- 83. Let f and g be continuous functions such that and the value of () () ( 3 0 1 3 2 fx gx dx - Û Ù ı ) 23 - ? (A) (B ) 19 - 17 2 - (C) (D) 19 (E) 23 B B

BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -31- [ ]0, 8 40 3 80 3 84. The regions A, B, and C in the figure above are bounded by the graph of the function f and the x-axis. The area of region A is 14, the area of region B is 16, and the area of region C is 50. What is the average value of f on the interval ? (A) 6 (B) 10 (C) 0 t≥ () 2 2 1 1 t vt t- = + (D) (E) 48 85. A particle moves along the x-axis so that its velocity at time is given by . What is the total distance traveled by the particle from t=0 to t= 2? (A) 0.214 (B) 0.320 (C) 0.600 (D) 0.927 (E) 1.600 B B

 x y e= (, k ke )  1 2 () 3 fx £¢ 1x ££ 8 ()5 f =6 ()20 f = ()6 f =-2 ()713 f = BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -32- 86. Line is tangent to the graph of at the point . What is the positive value of k for which the y-intercept of is ? (A) 0.405 (B) 0.768 (C) 1.500 (D) 1.560 (E) There is no such value of k. 87. A differentiable function f has the property that for and . Which of the following could be true? I. II. III. (A) I only (B) II only (C) I and II only (D) I and III only (E) II and III only B B

BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -33- () () 0 x hx f t d = Ú . Which of the following correctly orders t ()2 h ()2 h ¢ (2 h ¢¢ 22 hh

2, x ye=- sin , y x = () 32 2 - =- + + t vt t t 20 ≥ t . For what values BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -34- 89. What is the area of the region enclosed by the graphs of and x= 0? (A) 0.239 (B) 0.506 (C) 0.745 (D) 2.340 (E) 3.472 (0, 0.177 ) () 1.256, • (0, 1.256 ) ( 0, 2.057 ) (0.177, 1.256 ) ( 0.177, 1.256 ) 90. A particle moves along a line so that its velocity is given by for of t is the speed of the particle increasing? (A) and (2.057, •) (B) only (C) only (D) only (E) and BB

91. Let F be a function defined for all real numbers x such that () 0 Fx >¢ BBB B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -35- and () 0 Fx > ¢¢ . Which of the following could be a table of values for F ? (A) x ()Fx 1 –3 2 – 4 3 – 6 4 –9 (B) x ()Fx 1 –3 2 –1 3 3 4 19 (C) x ()Fx 1 –3 2 0 3 3 4 6 (D) x ()Fx 1 –3 2 5 3 11 4 13 (E) x ()Fx 1 –3 2 – 4 3 –3 4 0 B B

BB x ()fx ()gx ¢()fx – 4 0 –9 5 –2 4 –7 4 0 6 – 4 2 2 7 –3 1 4 10 –2 3 92. The table above gives values of the differentiable functions f and g, and f¢, the derivative of f, at selected values of x. If () ( 1 gx f x - = ), what is the value of ()4 g ¢ ? (A) 1 3 - (B 1 4 - (C) 3 100 - (D 1 4 (E) 1 3 BB B B BB B Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -36-

BBB B BB B -37- END OF SECTION I IF YOU FINISH BEF ORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON PART B ONLY. DO NOT GO ON TO S ECTION II UNTIL YOU ARE TOLD TO DO SO. ____________________ ____________________________ MAKE SU RE YOU HAVE DONE THE FOLLOWING. • PLACED YOUR AP NUMBER LABEL ON YOUR ANSWER SHEET • WRITTEN AND GRIDDED YOUR AP NUMBER CORRECTLY ON YOUR ANSWER SHEET • TAKEN THE AP EXAM LABEL FROM THE FRONT OF THIS BOOKLET AND PLACED IT ON YOUR ANSWER SHEET AFTER TIME HAS BEEN CALLED, TURN TO PAGE 38 AND ANSWER QUESTIONS 93–96. B B

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