2016 AP Calculus AB Practice Exam MCQ Multiple Choice Questions with Answers Advanced Placement - Studocu

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AP

Calculus AB

Practice Exam

From the 2 016 Administration

This exam may not be posted on school or personal websites, nor
electronically redistributed for any reason. This Released Exam is provided by
the College Board for AP Exam preparation. Teachers are permitted to download the
materials and make copies to us e with their students i n 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.

Further distribution of these materials outside of the secure College Board
site disadvantages teachers who rely on uncirculated questions for
classroom testing. Any additional distribution is in violation of the College Board’s
copyright policies and may result in the termination of Practice Exam access for your
school as well as the removal of access to other online services such as the AP
Teacher Community and Online Score Reports.

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

Question Descriptors and Performance Data

Note: This publication shows the page numbers that appeared in
the 2015 − 16 AP Exam Instructions book and in the actual exam.
This publication was not repaginated to begin with page 1.

© 2016 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:
collegeboard/inquiry/cbpermit.html.

AP® Calculus AB/BC Exam

Regularly Scheduled Exam Date: Thursday morning, May 5, 2016
Late-Testing Exam Date: Thursday morning, May 19, 2016

Section I Total Time, Calculus AB: 1 hr. 45 min. Section II Total Time, Calculus AB: 1 hr. 30 min.
Section I Total Time, Calculus BC: 1 hr. 45 min. Section II Total Time, Calculus BC: 1 hr. 30 min.

Section I Total Time: 1 hour 45 minutes
Number of Questions: 45*

*The number of questions may vary slightly
depending on the form of the exam.

Percent of Total Score: 50%
Writing Instrument: Pencil required

Part A:
Number of Questions: 28
Time: 55 minutes
No calculator allowed

Part B:
Number of Questions: 17
Time: 50 minutes
Graphing calculator required

Section II Total Time: 1 hour 30 minutes
Number of Questions: 6
Percent of Total Score: 50%
Writing Instrument: Either pencil or
pen with black or dark blue ink
Note : For Section II, if students finish Part A
before the end of the timed 30 minutes for
Part A, they cannot begin working on Part B.
Students must wait until the beginning of the
timed 60 minutes for Part B. However, during
the timed portion for Part B, students may
work on the problems in Part A without the
use of a calculator.

Part A:
Number of Questions: 2
Time: 30 minutes
Percent of Section II Score:
33%
Graphing calculator required

Part B:
Number of Questions: 4
Time: 60 minutes
Percent of Section II Score:
66%
No calculator allowed

What Proctors Need to Bring to This Exam

Exam packets
Answer sheets
AP Student Packs
2015 – 16 AP Coordinator’s Manual
This book — AP Exam Instructions
AP Exam Seating Chart template(s)
School Code and Home-School/Self-
Study Codes
Extra graphing calculators
Pencil sharpener

Container for students’ electronic
devices (if needed)
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”

SEATING POLICY FOR AP CALCULUS AB AND CALCULUS BC EXAMS

Testing Window

Exams Administered at Schools in the
United States, Canada, Puerto Rico, and
the U. Virgin Islands

Exams Administered at Schools Outside
the United States, Canada, Puerto Rico,
and the U. Virgin Islands
Regularly Scheduled
Exams

Students must be seated no less than
four feet apart. Students must be seated no less than
Late-Testing Exams Students must be seated no less than five feet apart.
five feet apart.

AP Exam Instructions

####### CALCULUS

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 47 of the 2015 -1 6 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 45
of the 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
the 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. Remember, you must complete a seating
chart for this exam. See pages 305–306 for a seating chart template and instructions. See the
2015-16 AP Coordinator’s Manual for exam seating requirements (pages 49–52).

If you are giving the regularly scheduled exam, say:
It is Thursday morning, May 5, 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 19, 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 2015 – 16 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….

AP Exam Instructions

####### CALCULUS

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. You 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. You have
50 minutes for Part B. You may begin.
12
963
Note Start Time here. Note Stop Time here. Check that students have
sealed their booklets properly and are now working on Part B. The large B’s in an alternating
shaded pattern at the top of each page will assist you in monitoring their work. Proctors should
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 40 minutes, say:

There are 10 minutes remaining.

After 10 minutes, say:

Stop working and turn to page 38. You have 3 minutes to answer Questions
93–96. These are survey questions and will not affect your score. You 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. Sit quietly while I collect your answer sheets.

Collect an answer sheet from each student. Check that each answer sheet has an AP number label
and an AP Exam label. After all answer sheets have been collected, 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.
All items you placed under your chair at the beginning of this exam must stay
there, and you are not permitted to open or access them in any way. Leave
your shrinkwrapped Section II packet on top of your desk during the break.
You are not allowed to consult teachers, other students, notes, or textbooks
during the break. You may not make phone calls, send text messages, use
your calculators, check email, use a social networking site, or access any

Calculus

electronic or communication device. Remember, you may never discuss the
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?…
12
6
9 3
You 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….
You 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….
Now take an AP number label from your Student Pack and place it 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 a pen with black or dark blue ink, 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, using your pen, 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. You 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….

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….

Calculus

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.
– Exam 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 scheduled exam, say:
You 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. Your AP
Exam 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. Your AP Exam score results will be available online in July.

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. You will need the
information on this card to view your scores and order AP score reporting
services online.

Then say:

You are now dismissed.

All exam materials must be placed 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
Instructional Planning Report (for regularly scheduled exams only) or subject
score roster at the class section or teacher level. See “Post-Exam Activities” in the
2015-16 AP Coordinator’s Manual.
– Check your list of students who are eligible for fee reductions and fill in the
appropriate circle on their registration answer sheets.

Be sure to give the completed seating chart to the AP Coordinator. Schools must retain seating
charts for at least six months (unless the state or district requires that they be retained for a
longer period of time). Schools should not return any seating charts in their exam shipments
unless they are required as part of an Incident Report.

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Student Answer Sheet for

the Multiple-Choice Section

null

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.)

Q. LANGUAGE — Do not complete this section unless instructed to do so.

1
2
3

4
5
6

7
8
9

A B C D E F G H I
A B C D E F G H I
A B C D E F G H I

If this answer sheet is for the French Language and Culture, German Language and Culture, Italian Language and Culture, Spanish Language
and Culture, or Spanish Literature and Culture Exam, please answer the following questions. Your responses will not affect your score.

Have you lived or studied for one month or more in a country where the language of the
exam you are now taking is spoken?
Yes No

DO NOT WRITE IN THIS AREA

P. SURVEY QUESTIONS — Answer the survey questions in the AP Student Pack. Do not put responses to exam questions in this section.

PAGE 2

COMPLETE THIS AREA AT EACH EXAM (IF APPLICABLE).

Indicate your answers to the exam questions in this section (pages 2 and 3). Mark only one response per question
for Questions 1 through 120. If a question has only four answer options, do not mark option E. Answers written in
the multiple-choice booklet will not be scored.

A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E

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
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31
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51
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66
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70
71
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73
74
75

QUESTIONS 1–

Yes No

Do you regularly speak or hear the language at home?

A B C D
A B C D

You must use a No. 2 pencil and marks must be complete. Do not use a mechanical 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 INCOMPLETE MARKSEXAMPLES OF

SELECTED MEDIA EXAMS
R W O
OTHER EXAMS
R W O

PT02 TOTAL
PT03 Subscore (if applicable)
PT04 Subscore (if applicable)

ETS USE ONLY

Exam

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

/ / /
-…..
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 Taking 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

121 123122 124 125 126

Write your answer in the boxes at the top of the griddable area and fill in the corresponding circles.
Mark only one circle in any column. You will receive credit only if the circles are filled in correctly.

PAGE 3

DO NOT WRITE IN THIS AREA

A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E

76
77
78
79
80
81
82
83
84
85
86
87
88
89
90

91
92
93
94
95
96
97
98
99
10 0
101
102
103
104
105

106
107
108
109
110
111
112
113
114
115
116
117
118
119
120

Be sure each mark is dark and completely fills the circle. If a question has only four answer options, do not mark option E.

QUESTIONS 76–

QUESTIONS 121–

A B C D
A B C D
A B C D
A B C D

131
132
133
134

135
136
137
138

139
140
141
142

For Students Taking AP Physics 1 or AP Physics 2
Mark two responses per question. You will receive credit only if both correct responses are selected.

QUESTIONS 131–

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Section I: Multiple-Choice Questions

null

This is the multiple-choice section of the 2016 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.)

®
Calculus AB
Exam

SECTION I: Multiple Choice 2016

DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.

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

Instructions
Section I of this exam contains 45 multiplechoice 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 multiplechoice 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 multiplechoice questions.
Your total score on the multiplechoice 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 4LBP6-S

66

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Unauthorized copying or reuse of
any part of this page is illegal. GO ON TO THE NEXT PAGE.
-4-

If y =cos 2 , x then =
dy
dx
(A) -2sin 2 x (B)-sin 2 x (C) sin 2 x (D)2sin 2 x (E) 2sin x
()
23 10
Ú xx – 1 dx =

(A)

34 10
34

Êˆ
Á ̃-+
Ë ̄

xx xC

(B)

()
3 11
1
11

x
C

(C)

()
23 11
1
11

xx
C

(D)

()
3 11
1
33

x
C

(E)

()
33 11
1
33

xx
C

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Unauthorized copying or reuse of
any part of this page is illegal. GO ON TO THE NEXT PAGE.
-5-

4
2
lim 91
x 43

x
Æ• x

(A) 1
3
(B) 3
4
(C) 3
2
(D) 9
4
(E) infinite

4. If ()

5
,
1
=
+
y x
x
then =
dy
dx

(A) 51 ()+ x 4 (B)
()

x
x

4
4

5
+ 1

x
x
)

(D)
(

4
6

5
+ 1

x
x
)

(E)
(
()

4
6

52 1
1

xx
x

)

2016 AP Calculus AB Practice Exam MCQ Multiple Choice Questions with Answers Advanced Placement – Studocu

AP

Calculus AB

Practice Exam

From the 2 016 Administration

AP® Calculus AB/BC Exam

!

Student Answer Sheet for

the Multiple-Choice Section

Section I: Multiple-Choice Questions

66

4. If ()