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.
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Practice Exam
Advanced Placement
Program
AP® Calculus AB
Contents
Directions for Administration ......................................................................... XXXXXXXXXXii
Section I: Multiple-Choice Questions............................................................. XXXXXXXXXX1
Section II: Free-Response Questions ........................................................... XXXXXXXXXX30
Student Answer Sheet for Multiple-Choice Section ................................... XXXXXXXXXX36
Multiple-Choice Answer Key........................................................................ XXXXXXXXXX37
Free-Response Scoring Guidelines............................................................... XXXXXXXXXX38
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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
eak should be provided after Section I is completed. Students should not have access to their
graphing calculators during the
eak.
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 co
ectly. No
points are deducted for inco
ect 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
e 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.
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Section I
Multiple-Choice Questions
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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
co
esponding 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- = ).
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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.
XXXXXXXXXXcos 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