Online AP Calcassessment
The questions contained in this AP® Calculus AB Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Calculus AB Practice Exam has never been administered as an operational AP Exam, statistical data are not available for calculating potential raw scores or conversions into AP grades. This AP Calculus AB Practice Exam is provided by the College Board for AP Exam preparation. Teachers are permitted to download the materials and make copies to use with their students in a classroom setting only. To maintain the security of this exam, teachers should collect all materials after their administration and keep them in a secure location. Teachers may not redistribute the files electronically for any reason. © 2008 !e College Board. All rights reserved. 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Practice Exam Advanced Placement Program AP® Calculus AB Contents Directions for Administration ............................................................................................ ii Section I: Multiple-Choice Questions................................................................................ 1 Section II: Free-Response Questions ...............................................................................30 Student Answer Sheet for Multiple-Choice Section .......................................................36 Multiple-Choice Answer Key............................................................................................37 Free-Response Scoring Guidelines...................................................................................38 The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. -i- AP® Calculus AB Directions for Administration The AP Calculus AB Exam is 3 hours and 15 minutes in length and consists of a multiple-choice section and a free-response section. The 105-minute two-part multiple-choice section contains 45 questions and accounts for 50 percent of the final grade. Part A of the multiple-choice section (28 questions in 55 minutes) does not allow the use of a calculator. Part B of the multiple-choice section (17 questions in 50 minutes) contains some questions for which a graphing calculator is required. The 90-minute two-part free-response section contains 6 questions and accounts for 50 percent of the final grade. Part A of the free-response section (3 questions in 45 minutes) contains some questions or parts of questions for which a graphing calculator is required. Part B of the free-response section (3 questions in 45 minutes) does not allow the use of a calculator. During the timed portion for Part B, students are permitted to continue work on questions in Part A, but they are not allowed to use a calculator during this time. A 10-minute break should be provided after Section I is completed. Students should not have access to their graphing calculators during the break. The actual AP Exam is administered in one session. Students will have the most realistic experience if a complete morning or afternoon is available to administer this practice exam. If a schedule does not permit one time period for the entire practice exam administration, it would be acceptable to administer Section I one day and Section II on a subsequent day. Total scores on the multiple-choice section are based only on the number of questions answered correctly. No points are deducted for incorrect answers and no points are awarded for unanswered questions. Graphing calculators are required to answer some of the questions on the AP Calculus AB Exam. Before starting the exam administration, make sure each student has a graphing calculator from the approved list at http://www.collegeboard.com/ap/calculators. 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. Since graphing calculators can be used to store data, including text, it is important to monitor that students are using their calculators appropriately. It is suggested that Section I of the practice exam be completed using a pencil to simulate an actual administration. Students may use a pencil or pen with black or dark blue ink to complete Section II. Teachers will need to provide paper for the students to write their free-response answers. Teachers should provide directions to the students indicating how they wish the responses to be labeled so the teacher will be able to associate the response with the question the student intended to answer. Instructions for the Section II free-response questions are included. Ask students to read these instructions carefully at the beginning of the administration of Section II. Timing for Section II should begin after you have given students sufficient time to read these instructions. Remember that students are not allowed to remove any materials, including scratch work, from the testing site. -ii- Section I Multiple-Choice Questions -1- 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 A A A A A GO ON TO THE NEXT PAGE. 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 available space for scratch work. After examining the form of the choices, decide which is the best of the choices given and place the letter of your choice in the corresponding box on the student answer sheet. Do not spend too much time on any one problem. In this exam: (1) Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which ( )f x is a real number. (2) The inverse of a trigonometric function f may be indicated using the inverse function notation 1f - or with the prefix “arc” (e.g., 1sin arcsinx x- = ). -2- 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 A A A A A GO ON TO THE NEXT PAGE. 1. ( )cos 3x dx =Ú (A) ( )3sin 3x C- + (B) ( )1 sin 3 3 x C- + (C) ( )1 sin 3 3 x C+ (D) ( )sin 3x C+ (E) ( )3sin 3x C+ 2. 6 3 5 30 2