Calculus AB Practice Exam From the 2012 Administration • This practice exam is provided by the College Board for AP Exam preparation.• Exams may not be posted on school or personal websites, nor electronically redistributed for any reason. • Teachers are permitted to download the materials and make copies to use with the students in a classroom setting only. www.mymathscloud.com
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 2011−12 AP Exam Instructions book and in the actual exam. This publication was not repaginated to begin with page 1. © 2012 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. www.mymathscloud.com
34© 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org.AP® Calculus AB ExamRegularly Scheduled Exam Date: Wednesday morning, May 9, 2012Late-Testing Exam Date: Thursday morning, May 24, 2012Section I: Multiple Choice Booklet InstructionsSection II: Free Response Booklet InstructionsSection 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.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.Section I: At a GlanceTotal Time: 1 hour, 45 minutesNumber of Questions: 45Percent of Total Score: 50%Writing Instrument:Pencil RequiredPart A: Number of Questions: 28Time: 55 minutesElectronic Device:None allowedPart B: Number of Questions: 17Time: 50 minutesElectronic Device:Graphing calculator requiredSection II: At a GlanceTotal Time: 1 hour, 30 minutesNumber of Questions: 6Percent of Total Score: 50%Writing Instrument:Either pencil or pen with black or dark blue inkWeight:The questions are weighted equally, but the parts of a question are not necessarily given equal weight.Part A: Number of Questions: 2Time: 30 minutesElectronic Device:Graphing calculator requiredPercent of Section II Score:33.3%Part B: Number of Questions: 4Time: 60 minutesElectronic Device:None allowedPercent of Section II Score:66.6%The questions for Section II are printed in this booklet. Do not break the seals on Part B until you are told to do so. Write your solution to each part of each question in the space provided. Write clearly and legibly. Cross out any errors you make; erased or crossed-out work will not be scored.Manage your time carefully. During the timed portion for Part A, work only on the questions in Part A. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. During the timed portion for Part B, you may continue to work on the questions in Part A without the use of a calculator.For each part of Section II, you may wish to look over the questions before starting to work on them. It is not expected that everyone will be able to complete all parts of all questions.• Show all of your work. Clearly label any functions, graphs, tables, or other objects that you use. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Justifications require that you give mathematical (noncalculator) reasons.• Your work must be expressed in standard mathematical notation rather than calculator syntax. For example, may not be written as .• Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If you use decimal approximations in calculations, your work will be scored on accuracy. Unless otherwise specified, your final answers should be accurate to three places after the decimal point.• Unless otherwise specified, the domain of a function is assumed to be the set of all real numbers x for which is a real number. www.mymathscloud.com
36© 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org.CalculusWhat Proctors Need to Bring to This Exam• Exam packets• Answer sheets• AP Student Packs• 2011-12 AP Coordinator’s Manual• This book — AP Exam Instructions• School Code and Home-School/Self-Study Codes• Extra graphing calculators• Pencil sharpener• Extra No. 2 pencils with erasers• Extra pens with black or dark blue ink• Extra paper• Stapler• Watch• Signs for the door to the testing room – “Exam in Progress” – “Cell phones are prohibited in the testing room” If you are giving the regularly scheduled AP Calculus AB or BC Exam:• You may seat students four feet (approximately 1.2 meters) apart because these exams have scrambled multiple-choice sections. This allows you to test more students in fewer testing rooms.• See page 8 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.• Administrators 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 less than five feet (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 42 of the 2011-12 AP Coordinator’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 41 of the 2011-12 AP Coordinator’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 48–50 Series and Casio FX-9860 graphing calculators may use cards designed for use with these 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 www.mymathscloud.com
37© 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org.AP Exam InstructionsCALCULUSthe calculator to remove exam questions and/or answers from the room may result in the cancellation of 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 for 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 scheduled exam, say:It is Wednesday morning, May 9, 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 24, 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 2011-12 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. . . .You 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. . . .Look at page 1 of your answer sheet and locate the dark blue box near the top right-hand corner that states, “Take the AP Exam label from your Section I booklet and place the label here.”. . .Now look at the front cover of your exam booklet and locate the AP Exam label near the top left of the cover. . . .Carefully peel off the AP Exam label and place it on your answer sheet on the dark blue box that we just identified. . . .Now 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? . . .www.mymathscloud.com
