ap calculus ab - welcome to ms. rossi's...

AP Calculus ABPractice Exam

From the 2018 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 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

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 Boardrsquos 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

copy 2018 The College Board College Board Advanced Placement Program AP AP Central and the acorn logo are registered trademarks of the College Board Visit the College Board on the Web wwwcollegeboardorg

AP Central is the official online home for the AP Program apcentralcollegeboardorg

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 2017minus18 AP Exam Instructions book and in the actual exam This publication was not repaginated to begin with page 1

copy 2018 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 wwwcollegeboardorgrequest-form

Exam Instructions

The following contains instructions taken from the 2017minus18 AP Exam Instructions book

Donrsquot delete this box

It clears one of the text variables for the footer from one subject to the next This will break down of this box gets deleted

41

AP Calculus ABBC Exam Regularly Scheduled Exam Date Tuesday morning May 15 2018

Late-Testing Exam Date Friday morning May 25 2018

Section I Total Time 1 hour and 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 30

Time 1 hour

No calculator allowed

Part B Number of Questions 15

Time 45 minutes

Graphing calculator required

Section II Total Time 1 hour and 30 minutes

Number of Questions 6Percent 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 1 hour for Part B However during the timed portion for Part B students may work on the questions in Part A without the use of a calculator


Time 30 minutes

Percent of Section II Score 3333



Time 1 hour



Before Distributing Exams Check that the title on all exam covers is Calculus AB or Calculus BC Be sure to distribute the correct exammdashAB or BCmdashto the students If there are any exam booklets with a different title contact the AP coordinator immediately

What Proctors Need to Bring to This Exam Exam packets

Answer sheets

AP Student Packs

2017-18 AP Coordinatorrsquos Manual

This bookmdash2017-18 AP Exam Instructions

AP Exam Seating Chart template

School Code and HomeschoolSelf-Study Codes

Extra graphing calculators

Pencil sharpener

Container for studentsrsquo electronic devices (if needed)

Extra No 2 pencils with erasers

Extra pens with black or dark blue ink

Extra paper

ndash

ndash

Stapler

Watch

Signs for the door to the testing room

ldquoExam in Progressrdquo

ldquoCell phones are prohibited during the testadministration including breaksrdquo

42

2017ndash18 AP Exam Instructions

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 US Virgin Islands

Exams Administered at Schools Outside the United States Canada Puerto Rico and the US Virgin Islands

Regularly Scheduled Exams

Students must be seated no less than 4 feet apart


Late-Testing Exams Students must be seated no less than 5 feet apart

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 52 of the 2017-18 AP Coordinatorrsquos 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 51 of the AP Coordinatorrsquos 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 48ndash50 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 andor 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 rsaquo 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 303ndash304 for a seating chart template and instructions See the 2017-18 AP Coordinatorrsquos Manual for exam seating requirements (pages 55ndash58)

If you are giving the regularly scheduled exam say It is Tuesday morning May 15 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 Friday morning May 25 and you will be taking either the AP Calculus AB Exam or the AP Calculus BC Exam

AP Calculus ABBC Exam


AP

Cal

culu

s A

BB

C E

xamemsp

43


If you are giving the AP Calculus AB Exam sayLook at your exam packet and confirm that the exam title is ldquoAP Calculus ABrdquo Raise your hand if your exam packet contains any title other than ldquoAP Calculus ABrdquo and I will help you

If you are giving the AP Calculus BC Exam sayLook at your exam packet and confirm that the exam title is ldquoAP Calculus BCrdquo Raise your hand if your exam packet contains any title other than ldquoAP Calculus BCrdquo and I will help you

If you are giving both the AP Calculus AB Exam and AP Calculus BC Exam sayLook at your exam packet and confirm that the exam title is ldquoAP Calculus ABrdquo or ldquoAP Calculus BCrdquo depending upon which exam you are taking today Raise your hand if your exam packet contains any other title and I will help you

Once you confirm that all students have the correct exam say

In a moment you will open the exam packet By opening this packet you agree to all of the AP Programrsquos policies and procedures outlined in the 2017-18 Bulletin for AP Students and Parents

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

Carefully remove the AP Exam label found near the top left of your exam booklet cover Place it on page 1 of your answer sheet on the light blue box near the top right corner that reads ldquoAP Exam Labelrdquo

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 can still be processed correctly

Listen carefully to all my instructions I will give you time to complete each step Please look up after completing each step Raise your hand if you have any questions

Give students enough time to complete each step Donrsquot move on until all students are ready

Read the statements on the front cover of the Section I booklet

Sign your name and write todayrsquos date

Now print your full legal name where indicated

Turn to the back cover of your exam booklet and read it completely

Are there any questions

You will now take the multiple-choice portion of the exam You should have in front of you the multiple-choice booklet and your answer sheet You may never discuss the multiple-choice exam content at any time in any form with anyone including your teacher and other students If you disclose the multiple-choice exam content through any means your AP Exam score will be canceled

Open your answer sheet to page 2 You 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

AP Calculus ABBC Exam 44


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

You have 1 hour for Part A Part A questions are numbered 1 through 30 Mark your responses for these questions on page 2 of your answer sheet Open your Section I booklet and begin

Note Start Time Note Stop Time

Check that students are marking their answers in pencil on page 2 of their answer sheets and that they are not looking beyond Part A The line of Arsquos at the top of each page will assist you in monitoring studentsrsquo work

After 50 minutes say

There are 10 minutes remaining


Stop working on Part A and turn to page 24 in your Section I booklet

On that page you should see an area marked ldquoPLACE SEAL HERErdquo 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 donrsquot 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 90 Fold your answer sheet so only page 3 is showing and mark your responses for these questions on that page You have 45 minutes for Part B You may begin


Check that students have sealed their booklets properly and are now working on Part B The large Brsquos 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 calculatorsrsquo infrared ports are not facing each other




Stop working and turn to page 38 You have 3 minutes to answer Questions 91ndash94 These are survey questions and will not affect your score Note that each survey question has five answer options 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 faceup 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


AP

Cal

culu

s A

BB

C E

xam

45


emsp

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 ldquoPLACE SEAL HERErdquo Fold each seal over the back cover When you have finished place the booklet on your desk faceup 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 electronic or communication device Remember you may never discuss the multiple-choice exam content with anyone and if you disclose the content through any means your AP Exam score will be canceled Are there any questions

You may begin your break Testing will resume at

SECTION II Free Response After the break say

May I have everyonersquos 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 donrsquot 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 todayrsquos 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 ldquoImportant Identification Informationrdquo 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


If this is your last AP Exam you may keep your Student Pack Place it under your chair for now Otherwise I will collect all Student Packs

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


Section II also has two parts that are timed separately You 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 You 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

You 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 sheet of paper you use write only your AP number and the question number you are working on Do not write your name Open your exam booklet and begin


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 1rsquos or 2rsquos at the top of each page to assist you in monitoring their work


There are 10 minutes remaining in Part A


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 You 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 You may go on to the next page and begin Part B



There are 10 minutes remaining in Part B


Stop working and close your exam booklet Place it on your desk faceup


AP

Cal

culu

s A

BB

C E

xam

47


emsp

If any students used extra paper for a question in the free-response section have those students staple the extra sheet(s) to the first page corresponding to that question in their exam booklets Complete an Incident Report after the exam (see After-Exam Tasks below)

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 their initials and todayrsquos date

Exam booklet back cover The student completed the ldquoImportant Identification Informationrdquo 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 the free-response exam content with anyone unless it is 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 content 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

After-Exam Tasks 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

NOTE If you administered exams to students with accommodations review the 2017-18 AP Coordinatorrsquos Manual and the 2017-18 AP SSD Guidelines for information about completing the NAR form and returning these exams

The exam proctor should complete the following tasks if asked to do so by the AP coordinator Otherwise the AP coordinator must complete these tasks

Complete an Incident Report for any students who used extra paper for the free-response section (Incident Report forms are provided in the coordinator packets sent with the exam shipments) These forms must be completed with a No 2 pencil It is best to complete a single Incident Report for multiple students per exam subject per administration (regular or late testing) as long as all required information is provided Include all exam booklets with extra sheets of paper in an Incident Report return envelope (see page 67 of the 2017-18 AP Coordinatorrsquos Manual for complete details)


Return all exam materials to secure storage until they are shipped back to the AP Program (See page 26 of the 2017-18 AP Coordinatorrsquos Manual for more information about secure storage) Before storing materials check the ldquoSchool Use Onlyrdquo 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 ldquoPost-Exam Activitiesrdquo in the 2017-18 AP Coordinatorrsquos Manual

Check your list of students who are eligible for fee reductions and fill in the appropriate circle on their registration answer sheets



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 applications Date

I am aware of and agree to follow the policies and procedures in the 2017-18 Bulletin for AP Students and Parents to maintain the security of the exam and the validity of my AP score I understand and accept that my exam score may be canceled if I do not follow these policies and procedures if I disregard any exam day instructions or if my exam is administered improperly I certify that I am the person whose information appears on this answer sheet

COMPLETE THIS AREA AT EVERY EXAM USE NO 2 PENCIL ONLY

A SIGNATURE

PAGE 1AP Exam Label (from Section I Booklet)

AP Number Label (from Student Pack)

B LEGAL NAME Omit apostrophes Jr IILegal First Name mdash First 12 LettersLegal Last Name mdash First 15 Letters MI

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

E E E E E E E E E E E E E E E

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

ndash ndash ndash ndash ndash ndash ndash ndash ndash ndash ndash ndash ndash

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

E E E E E E E E E E E E E

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

ndash ndash ndash ndash ndash ndash ndash ndash ndash ndash

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

D EXAM DATECYOUR AP NUMBER

Month

AM PM

F MULTIPLE-CHOICE BOOKLET SERIAL NUMBER

H AP EXAM I AM TAKING USING THIS ANSWER SHEET

Exam Name Form CodeForm

COMPLETE THIS AREA ONLY ONCE

SCHOOL USE ONLYFee Reduction GrantedSection Number

Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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 ONLINEPROVIDER CODEDay

O STUDENT SEARCH SERVICEreg

Colleges and scholarship programs may request your information to inform you of educational opportunities and financial aid

Would you like us to supply your information

If you donrsquot answer and previously chose to participate in this service we will continue providing your information

Yes No

Answer Sheet 2018

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 (Optional)

121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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

N CURRENT GRADE LEVEL

Not yet in9th grade

9th

10th

801356

11th

12th

No longer inhigh school

AP FPO X123456789 X

Q LANGUAGE mdash 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

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

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

1 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 mdash 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

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

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

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17

18

19

20

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25

26

27

28

29

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31

32

33

34

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58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

QUESTIONS 1ndash75

Yes No

2 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 EXAMPLES OFINCOMPLETE MARKS

SELECTED MEDIA EXAMSR W O

OTHER EXAMSR W O

PT02 TOTAL

PT03 Subscore (if applicable)


FOR OFFICIAL USE ONLY

Exam

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

ndash

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

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ndash

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

ndash

0 0 0 0

1 1 1 1 1

2 2 2 2 2

3 3 3 3 3

4 4 4 4 4

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ndash

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2 2 2 2 2

3 3 3 3 3

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ndash

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

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9 9 9 9 9

For Students Taking AP Biology

ndash

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1 1 1 1 1

2 2 2 2 2

3 3 3 3 3

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5 5 5 5 5

6 6 6 6 6

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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


A B C D E

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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 76ndash120

copy 2017 The College Board College Board AP Student Search Service and the acorn logo are registered trademarks of the College Board


A B C D

A B C D

A B C D

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For Students Taking AP Computer Science Principles AP Physics 1 or AP Physics 2

Mark two responses per question You will receive credit only if both correct responses are selected



ZIP OR POSTAL CODE COUNTRY 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

E E E E E E E E E E E E E E E E E E E E E E E E E E

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

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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

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A A A A A A A A A

B B B B B B B B B

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D D D D D D D D D

E E E E E E E E E

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

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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

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0 0 0

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R 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

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE

S FOR STUDENTS OUTSIDE THE UNITED STATES ONLY

U EMAIL ADDRESS

If your address does not fit in the spaces provided in Item R fill in as many circles as you can then fill in the circle in Item S and print the remainder of your address in the spaces provided

Address City State or Province Country ZIP or Postal Code

By providing your email address you are granting the College Board permission to use your email address in accordance with the policies in the 2017-18 Bulletin for AP Students and Parents

T STUDENT IDENTIFIER (Student ID Number)

Y PARENTAL EDUCATION LEVEL

WWHICH LANGUAGE DO YOU KNOW BEST

Mother or female guardian

Father or male guardian

Grade school

Some high school

High school diploma or equivalent

Vocational or trade school

Some college

Associate or two-year degree

Bachelorrsquos or four-year degree

Some graduate or professional school

Graduate or professional degree

V SEX

Female Male

English

English and another language about the sameAnother language

In the first column indicate the highest level of education of one parentguardian and indicate whether this is your motherfemale guardian or fathermale guardian Then if applicable indicate the highest level of education of your other parentguardian in the second column and indicate whether this is your motherfemale guardian or fathermale guardian

X RACIALETHNIC GROUP

Please answer both questions about Hispanic origin and about race For the following questions about your identity Hispanic origins are not races

(You may mark all that apply)

a Are you of Hispanic Latino or Spanish origin

No not of Hispanic Latino or Spanish origin

Yes Cuban

Yes Mexican

Yes Puerto Rican

Yes another Hispanic Latino or Spanish origin

American Indian or Alaska Native

Asian (including Indian subcontinent and Philippines origin)

Black or African American (including Africa and Afro-Caribbean origin)

Native Hawaiian or other Pacific Islander

White (including Middle Eastern origin)

b What is your race


This is the multiple-choice section of the 2018 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)

APreg Calculus AB Exam 2018SECTION I Multiple Choice

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

At a Glance Total Time 1 hour and 45 minutes

Number of Questions 45

Percent of Total Score 50



Time 1 hour

Electronic Device None allowed


Time 45 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 30 on page 2 of the answer sheet For Part B fill in only the circles for numbers 76 through 90 on page 3 of the answer sheet Because Part A and Part B offer only four answer options for each question do not mark the (E) answer circle for any question The survey questions are numbers 91 through 94

Instructions

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 40BP4-S

66

CALCULUS AB

SECTION I Part A

Timemdash1 hour

Number of questionsmdash30

NO CALCULATOR IS ALLOWED FOR 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 this exam booklet 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 minusf 1 or with the

prefix ldquoarcrdquo (eg sin minus1 x = arcsin x)

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

-3- GO ON TO THE NEXT PAGE

1 If f is the function given by 4

f x = + 5x minus 1( )x

then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x



3 The graph of y = ( )f is sho wn above What is lim f x(xrarr1

(A) 0 (B) 1 (C) 3 (D) The limit does not exist

4 If f xcent( ) = 3x2 + 2x and f 2 = 1( ) 3 then f ( ) =

(A) minus10 (B) minus7 (C) 10 (D) 13


5 During an evacuation drill people leave a building at a rate of R t( ) people per minute where t is the number of

minutes since the start of the drill Selected values of R t( ) are shown in the table above Using a right Riemann

sum with three subintervals and data from the table what is the approximation of the number of people who

leave the building during the first 15 minutes of the evacuation drill

(A) 230 (B) 1150 (C) 1375 (D) 2075


6 dy2 xIf y = x (e minus 1) then = dx

(A) x2xe

(B) 2xex minus 2x

(C) 2 x xx e + 2xe minus 2x

(D) 2 x x 2x e + 2xe minus x minus 2x

7 A particle moves along the x-axis so that at any time t t ge 0 its acceleration is ( ) = minus4 sin 2t a t ( If the

velocity of the particle at t = 0 ( ) = 7is v 0 and its position at t = 0 is x( )0 = 0 then its position at time t

is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t


8 The graph of f le the second derivative of the function f is shown above Which of the following could be the graph of f

(A) (B)

(C) (D)


9

ln(x h minus ( + ) ln x)

When x = 2e lim is hrarr0 h

(A)1

2e (B) 1 (C) ln 2e ( ) (D) nonexistent

10 3dy d y4 3If = x minus 2x + 3x minus 1 then 3 evaluated at x = 2 is

dx dx

(A) 11 (B) 24 (C) 26 (D) 125



⎧⎪ 2⎪x for x lt 0⎪f x =( ) ⎨minus1 for x = 0⎪⎪⎩⎪x for x gt 0

11 Let f be the function defined above What is 1

int f x d( ) xminus1

(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent



12 Given that 3x minus tan y = 4 what is dy

dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+

13 For time t ge 1 the position of a particle moving along the x-axis is given by p t( ) = t minus 2 At what time t in

the interval 1 pound poundt 16 is the instantaneous v elocity of the particle equal to the average velocity of the particle

over the interval 1 pound poundt 16

(A) 1 (B)121

25 (C)

25

4 (D) 25

)14 If f is a differentiable function and ( 2 ( )y = sin f x what is dy

dx when x = 3

(A) cos ( ( )9 )f cent

(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )



15 The graph of g cent the first derivative of the function g consists of a semicircle of radius 2 and two line segments

as shown in the figure above If g( ) = 0 1 what is (g 3)

(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2

16 Let f be the function given by ( ) x 3 minus 6x 2 minus xf x = 15 What is the maximum v alue of f on the interval [0 6]

(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5

(A) arctan (x + 2) + C

(B) arcsin (x + 2) + C

(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3

18 Let f be the function defined by ( )f x = x3 What is the approximation for f 10( ) found by using the line

tangent to the graph of f at the point (8 2)

(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x

lim is4x xrarr0 e minus 4x minus 1

(A) 0 (B)1

2 (C) 8 (D) nonexistent

20 Let g be a twice-differentiable increasing function of t If g 0 = 20 and g 10 220( ) ( ) = which of the following

must be true on the interval 0 t lt lt 10

(A) g t( ) = 0cent for some t in the interval

(B) g tcent( ) = 20 for some t in the interval

(C) g t( ) = 0le for some t in the interval

(D) g t( ) le 0 for all gt t in the interval



21 3d x 2ln + 1) dt =int (t dx e

(A) 6 +ln x 1( ) (B) 2 2 +x3 ln (x 1) (C) 2x3 ln (x6 + 1) (D)



6 2ln x + 1 minus ln e + 1( ) ( )

22 Shown above is a slope field for which of the following differential equations

(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy

23 Using the substitution ⌠ x

u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1

(B) minus1 2int u du (C) 1 2 1 2 int (u minus uminus ) du (D) 1 2u 1 int u du( minus ) minus

24 Let f be the function given by 22x + 14x minus

f x = 2( )x minus 9x + 8

16 For what values of x does f have a removable

discontinuity

(A) 1 only (B) 8 only (C) minus8 and 1 (D) 1 and 8



25 Which of the following is a solution to the differential equation y le minus 4y = 0

(A) y = e 2x (B) y = 2ex (C) y = (sin 2x ) (D)



y = cos 2( )x

26 The table above gives values of the continuous function f at selected values of x If f has exactly two critical

points on the open interval (10 14) which of the following must be true

(A) f x ( ) gt 0 for all x in the open interval (10 14 )

(B) f cent( )x )e xists for all x in the open interval (10 14

(C) cent( ) lt 0 f x for all x in the open interval 10 11)(

(D) f ( ) π 0 cent 12





27 The positive variables p and c change with respect to time t The relationship between p and c is given by the

equation p2 = (20 minus c)3 At the instant when dp

= 41 dt

and c = 15 what is the value ofdc

dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+

lim x is xrarrminusinfin 4 minus 5

(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent

29 The graphs of the function g and the line y = x are shown in the figure above The graphs intersect at the points

(0 0) (1 1) and (2 2) Which of the following expressions give the area enclosed by the graphs

I x g x ) dx( minus ( )int02

II 2

int x g x minus ( ) dx 0

III 1 2

int g x x dx + ( minus ( )g x ) dx( ( ) minus ) x 0 int1

(A) II only

(B) III only

(C) I and II only

(D) II and III only



30 A student attempts to solve the differential equation dy

= xy3

dx with the initial condition that y = 2 when x = 0

The steps of the studentrsquos solution are shown below In which of the following steps does an error first appear

Step 1


⌠ 1 ⎮ dy = x dx y3 int

-23-

Step 2 2x3ln y = + C

2

Step 3 3 2 2 y = Kex

Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e

(A) Step 1 (B) Step 2 (C) Step 3 (D) Step 4

END OF PART A

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

PART B STARTS ON PAGE 26

-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes


A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAM


BE SURE YOU ARE USING PAGE 3 OF THE ANSWER SHEET TO RECORD YOUR ANSWERS TO QUESTIONS NUMBERED 76ndash90

YOU MAY NOT RETURN TO PAGE 2 OF THE ANSWER SHEET


In this exam

(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 that best approximates the exact numerical value


f x( is a real number


prefix ldquoarcrdquo 1(eg sin minus x = arcsin x)

76 The graph of f cent the derivative of the function f is shown above for minus3 pound x 3pound On what intervals is fincreasing

(A) 3 [minus minus1] only (B) [minus1 3 ] (C) [minus2 0 ] and [2 3 ] (D)

B B B B B B B B B


3 [[minus minus1] and 1 3 ]

B B B B B B B B B

77 The rate at which water leaks from a tank in gallons per hour is modeled by R a differentiable function of the

number of hours after the leak is discovered Which of the following is the best interpretation of Rcent(3 )

(A) The amount of water in gallons that has leaked out of the tank during the first three hours after the leak is discovered

(B) The amount of change in gallons per hour in the rate at which water is leaking during the three hours after the leak is discovered

(C) The rate at which water leaks from the tank in gallons per hour three hours after the leak is discovered

(D) The rate of change of the rate at which water leaks from the tank in gallons per hour per hour three hours after the leak is discovered


78 A particle moves along the x-axis The velocity of the particle at time t is given by

4v t( ) =

3 t + 1 If the

position of the particle is x = 1 when t = 2 what is the position of the particle when t = 4

(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B

79 The graph of the function f is shown above Of the following intervals on which is f continuous but not differentiable

(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B

80 The first derivative of the function f is defined by cent xf x( ) = ( 2 + 1 sin 3) ( x minus 1) for minus x 1515 lt lt On which

of the following intervals is the graph of f concave up

(A) (minus15 minus1341) and (minus0240 0964)

(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)


81 During a rainfall the depth of water in a rain gauge increases at a rate modeled by ⎛ 3 ⎞pt⎜R t( ) = 05 + t cos⎜ ⎝ 80

⎟⎟⎟⎟⎟⎜⎜ ⎠

where t is the time in hours since the start of the rainfall and R t( is measured in centimeters per hour How

much did the depth of water in the rain gauge increase from t = 0 to t = 3 hours

(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm

82 Let f be a function such that f 1( ) = 2minus and f 5( ) = 7 Which of the following conditions ensures that

f c( ) = 0 for some value c in the open interval 1 5( )

(A) 5

int (1

f x) d x exists

(B) f is increasing on the closed interval 1 5[ ]

(C) f is continuous on the closed interval 1 5[ ]

(D) f is defined for all values of x in the closed interval 1 5[ ]

B B B B B B B B B

83 The acceleration of a particle moving along the x-axis is given by a t = ( minus ) ( ) t 8 sin for pound poundt 80 At what t

value of t is the particlersquos velocity decreasing most rapidly

(A) 0 (B) 1420 (C) 3142 (D) 4439


84 If the average value of the function f over the closed interval [2 4 ] is 3 and if f x in [2 4 ( ) ge 0 for all x ] what

is the area of the region enclosed by the graph of ) y = (f the lines = 2 and x = 4x and the x-axis x

(A) 12 (B) 6 (C) 3 (D) 3

2

85 The function f is continuous and increasing for x gt minus1 The table above gives values of f at selected values

of x Of the following which is the best approximation for minus (lim e 2f x

xrarr0

)

(A) minus2

(B) 0

(C) 1

(D) The limit does not exist

B B B B B B B B B


B B B B B B B B B

86 Let R be the region in the first quadrant bounded by the graphs of ( )px y = 4 cos and y = ( minusx 2 2

4 ) as sho wn

in the figure above The region R is the base of a solid For the solid each cross section perpendicular to the

x-axis is an isosceles right triangle with a leg in region R What is the volume of the solid

(A) 1775 (B) 3549 (C) 4800 (D) 5575


87 Let f and g be continuous functions If 6

int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36

88 Let f be a twice-differentiable function such that f xle( ) lt 0 for all x The graph of y = S(x) is the secant line

passing through the points 5 f 5 (3 f ( ))3 and ( ( )) The graph of y (= T )x is the line tangent to the graph of f at

x = 4 Which of the following is true

(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B


89 The number of insects in a certain population at time t days is modeled by the function P with first derivative

P t = 2 + 12 t + 210cent( ) 03t At time t = 0 the number of insects in the population is 40 Which of the following

statements are true

I At time t = 10 the number of insects in the population is 2840

II At time t = 10 the number of insects in the population is increasing at a rate of 360 insects per day

III At time t = 10 the rate of change of the number of insects in the population is increasing at a rate of 18 insects per day per day

(A) I only (B) II only (C) III only (D) I II and III

B B B B B B B B B


90 Selected values of the increasing function h and its derivative hcent are shown in the table above If g is a

differentiable function such that h g x ( ( )) = x for all x what is the value of g 7cent( )

(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I

IF YOU FINISH BEFORE TIME IS CALLED YOU MAY CHECK YOUR WORK ON PART B ONLY

DO NOT GO ON TO SECTION II UNTIL YOU ARE TOLD TO DO SO

MAKE SURE 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 91ndash94

-37-


This is the free-response section of the 2018 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)

APreg Calculus AB Exam 2018SECTION II Free Response

DO NOT OPEN THIS BOOKLET OR BREAK THE SEALS ON PART B UNTIL YOU ARE TOLD TO DO SO





Weight The questions are weighted equally but the parts of a question are not necessarily given equal weight


Time 30 minutes




Time 1 hour



Instructions 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 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 Part B you may continue to work on the questions in Part A without the use of a calculator

As you begin each part 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 even though a question may not explicitly remind you to do so Clearly label any functions graphs tables or other objects that you use Justifications require that you give mathematical reasons and that you verify the needed conditions under which relevant theorems properties definitions or tests are applied 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

Your work must be expressed in standard mathematical notation rather than calculator

syntax For example 5 x2 dx may not be written as

1 fnInt(X2 X 1 5)

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 f is assumed to be the set of all real numbers x for which fx is a real number


66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes


A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS


1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r

1 Grain is being added to a silo At time t = 0 the silo is empty The rate at which grain is being added is

modeled by the differentiable function g where g t( ) is measured in cubic feet per minute for 0 tpound pound 8 minutes Selected values of g t( ) are given in the table above

(a) Using the data in the table approximate g cent 3 ( ) Using correct units interpret the meaning of (g cent 3 ) in the

context of the problem

(b) Write an integral expression that represents the total amount of grain added to the silo from time t = 0 to time t = 8 Use a right Riemann sum with the four subintervals indicated by the data in the table to approximate the integral

Do not w

rite beyond this border

-4- Continue question 1 on page 5

1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r

(c) The grain in the silo is spoiling at a rate modeled by p t

w t( ) = 32 loz sin ⎛⎜⎜

⎞⎟⎟⎟⎝ 74 ⎠ where w t( ) is measured in

cubic feet per minute for 0 tpound pound 8 minutes Using the result from part (b) approximate the amount of

unspoiled grain remaining in the silo at time t = 8

(d) Based on the model in part (c) is the amount of unspoiled grain in the silo increasing or decreasing at time t = 6 Show the work that leads to your answer

Do not w



2 2 2 2 2 2 2 2 2 2

2 A snail is traveling along a straight path The snailrsquos velocity can be modeled by 2v t( ) = 14 ln (1 + t ) inches

per minute for

Do

not w

rite

bey

ond

this

bor

der

0 t pound pound 15 minutes

(a) Find the acceleration of the snail at time t = 5 minutes

(b) What is the displacement of the snail over the interval 0 t pound pound 15 minutes

Do not w



2 2 2 2 2 2 2 2 2 2

(c) At what time t 0 tpound pound 15 is the snailrsquos instantaneous v elocity equal to its average velocity over the interval 0 t pound pound 15

(d) An ant arrives at the snailrsquos starting position at time

Do

not w

rite

bey

ond

this

bor

der

t = 12 minutes and follows the snailrsquos path During the interval 12 t 15 pound pound minutes the ant travels in the same direction as the snail with a constant acceleration of 2 inches per minute per minute The ant catches up to the snail at time t = 15 minutes The antrsquos velocity at time t = 12 is B inches per minute Find the value of B

Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour


NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS

DO NOT BREAK THE SEALS UNTIL YOU ARE TOLD TO DO SO

-13-

3 3 3 3 3 3 3 3 3 3 NO CALCULATOR ALLOWED

Do

not w

rite

bey

ond

this

bor

der

3 The function g is defined on the closed interval [minus4 8 ] The graph of g consists of two linear pieces and a

semicircle as shown in the figure above Let f be the function defined by f x = 3x + g t ( ) ( ) tint0

x d

(a) Find f 7( ) and f cent(7 )

(b) Find the value of x in the closed interval [minus4 3 ] at which f attains its maximum value Justify youranswer

Do not w




(c) For each of lim gminus

cent(xrarr0

x) and lim g+

cent(xrarr0

x) f ind the value or state that it does not exist

Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )

lim x+ 3 6xrarrminus2 e minus 1

Do not w




4 Let f be the function defined by6

f x = 2( )1 + x

Let R be the shaded region bounded by the graph of f and

the horizontal line y = 3 as shown in the figure above

(a) Find the area of R

Do

not w

rite

bey

ond

this

bor

der

Do not w




(b) Write but do not evaluate an integral expression for the volume of the solid generated when R isrotated about the horizontal line y = 7

Do

not w

rite

bey

ond

this

bor

der

(c) Let h x( ) be the vertical distance between the point x f x( ( )) and the horizontal line = 3y Find the rate of

change of h x( ) with respect to x at = 2x

Do not w




Do

not w

rite

bey

ond

this

bor

der

5 During a chemical reaction the function y = f ( )t models the amount of a substance present in grams at

time t seconds At the start of the reaction (t = 0) there are 10 grams of the substance present The function

y = f ( )t satisfies the differential equation dy

= minus002y 2dt

(a) Use the line tangent to the graph of y = f ( )t at t = 0 to approximate the amount of the substance

remaining at time t = 2 seconds

(b) Using the given differential equation determine whether the graph of f could resemble the following graph Give a reason for your answer

Do not w




(c) Find an expression for y = f (t ) by solving the differential equation dy

= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10

(d) Determine whether the amount of the substance is changing at an increasing or a decreasing rate Explain your reasoning

Do not w



6 Consider the curve given by the equation 2 x y( minus ) 3= + ycos For all points on the curv e


2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2

there is a point P on the curve through which the line tangent to the curve has slope 1

Find the coordinates of the point P

Do not w




(c) Determine the concavity of the curve at points for which minusp

y p

lt lt2 2

Give a reason for your answer

(d) Let

Do

not w

rite

bey

ond

this

bor

der

y = f x( ) be a function defined implicitly by 2 x y y( minus ) = +3 cos that is continuous on the closed

interval [2 21 ] and differentiable on the open interval (2 21) Use the Mean Value Theorem on the

interval [2 21 ] to show that 1 1

pound f (21 f 2 pound) minus ( )15 5

Do not w



____________________________________

STOP

END OF EXAM

THE FOLLOWING INSTRUCTIONS APPLY TO THE COVERS OF THE SECTION II BOOKLET

MAKE SURE YOU HAVE COMPLETED THE IDENTIFICATION INFORMATION AS REQUESTED ON THE FRONT AND BACK COVERS OF THE SECTION II BOOKLET

CHECK TO SEE THAT YOUR AP NUMBER LABEL APPEARS IN THE BOX ON THE FRONT COVER

MAKE SURE YOU HAVE USED THE SAME SET OF AP NUMBER LABELS ON ALL AP EXAMS YOU HAVE TAKEN THIS YEAR

-22-


The following contains the answers to the multiple-choice questions in this exam

Answer Key for AP Calculus AB Practice Exam Section I

Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C


The following contains the scoring guidelines for the free-response questions in this exam

copy 2018 The College Board Visit the College Board on the Web wwwcollegeboardorg

(a) ( ) ( ) ( )5 1 205 1513 1355 1 4g gg minus minusasympprime = =

minus

At time 3t = minutes the rate at which grain is being added to the silo is increasing at a rate of 135 cubic feet per minute per minute

1 approximation2

1 interpretation with units

(b) The total amount of grain added to the silo from time t 0= to time 8t =

is ( )8

0g t dtint cubic feet

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608

g t dt g g g gasymp sdot minus + sdot minus + sdot minus + sdot minus

= sdot + sdot + sdot + sdot =int

1 integral expression3 1 right Riemann sum

1 approximation

(c) ( )8

099051497w t dt =int

The approximate amount of unspoiled grain remaining in the silo at

time 8t = is ( )8

01608 61749w t dtminus =int (or 61748) cubic feet

1 integral2

1 answer

(d) ( ) ( )6 6 183 16063173 2236827 0g wminus = minus = gt

Because ( ) ( )6 6 0g wminus the amount of unspoiled grain is increasing atgttime 6t =

( ) ( ) 1 considers 6 62

1 answerg wminus

APreg CALCULUS AB2018 SCORING GUIDELINES

Question 1

APreg CALCULUS AB 2018 SCORING GUIDELINES


Question 2

(a) ( )5 0538462vprime =

The acceleration of the snail at time t = 5 minutes is 0538 inches perminute per minute

1 answer

(b) ( )15

076043074v t dt =int

The displacement of the snail over the interval 0 15tle le minutes is 76043 inches

1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int

( )214ln 1 5069538 6031t t+ = rArr = minutes

1 average value expression2

1 answer

(d) The velocity of the ant at time t 12 15tle le is 2 dt t c= +int 2 inches

per minute for some constant c

For 12 15tle le the displacement of the ant is

( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=

=+ = + = +int inches

Thus 81 3 76043074 1652309c+ = rArr = minusc

The velocity of the ant at time 12t = is B = 2 sdot minus12 1652309 82= 2 43 (or 22347) inches per minute

mdash OR mdash

The velocity of the ant at time t 12 15tle le is ( )2 12t minus B+ inches per minute


( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=

=minus minus + =+ =int 12 3+ inches

9 3 76043074 22348B B+ = rArr = (or 22347) inches per minute

1 antrsquos velocity 1 antrsquos displacement

4 1 equation 1 answer



Question 3

(a) ( ) ( )7

097 3 7 21 3 242f g t dt π= + = =sdot minus + minusint 9

2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime

(b) On the interval 4 3xminus le le ( ) ( )3f x g xprime = + Because ( ) 0f xprime ge for 4 3xminus le le f is nondecreasing overthe entire interval and the maximum must occur when 3x =

2 answer with justification

(c) ( )0

1lim 2xg x

minusrarrprime = minus

( )0

limx

g x+rarr

prime does not exist 1 left-hand limit

2 1 right-hand limit

(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus

rarrminus+ = minus + + =int

( )3 62

lim 1 0xx

e +rarrminus

minus =

Using LrsquoHospitalrsquos Rule ( ) ( ) ( )

3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x

f x f x ge e+ +rarrminus rarrminus

prime+ + minus += = = = 43minus

1 limits equal 03 1 applies LrsquoHospitalrsquos Rule

1 answer

Note max 1 3 [1-0-0] if no limit notation attached to a ratio of derivatives



Question 4

(a) ( ) 3 1 and 1f x x x= rArr = minus =

( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus

= minus minus minus +

= sdot minus minus sdot minus +

= minus

⌠⌡int

1 6

The area of R is 3 6π minus

1 integral3 1 antiderivative

1 answer

(b) ( ) ( )( )( )1 221

Volume 7 3 7 f x dxπminus

= minus minus minusint 2 integrand3

1 limits and constant

(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5

(a) ( ) ( )20 002 10 2prime = minus = minusy

An equation for the line tangent to the graph of ( )y f t=at t = 0 is y = 10 minus t2

( ) ( )2 10 2 2 6y asymp minus = grams

( ) 1 02

1 approximationprime

y

(b) 2002 0dy ydt = leminus so the graph of f is nonincreasing

The graph of f cannot resemble the given graph because the given graph is increasing on a portion of its domain

1 answer with reason

(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +

Note this solution is valid for 5t gt minus

1 separation of variables 1 antiderivatives

4 1 constant of integrationand uses initial condition

1 answer

Note max 2 4 [1-1-0-0] if no constant of integration

Note 0 4 if no separation of variables

(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=

Because 0y gt 300008 0y gt The amount of substance is changing at an increasing rate

mdash OR mdash

From part (c) 50( ) 5f t t=+

and from context 0t ge

( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge

The amount of substance is changing at an increasing rate

2

2 1 2 1 answer with reason

d ydt



Question 6

(a) ( )( ) ( )2 3 cosd dx y ydx dxminus = +

( )2 2 sindy dyydx dxminus = minus

( )2 2 sin dyy dx= minus

22 sin

dydx y=

minus

1 implicit differentiation2

1 verification

(b) 2 1 sin 0 02 sindy y ydx y= = rArr = rArr =

minus

( )2 0 3 cos 0 2 4 2x xminus = + rArr = xrArr =

Point P has coordinates ( )2 0

1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos

2 sin 2 sinyd y dyy dxdx y

minus= minus =minus yminus

2

2 0d ydx

gt for all y in the interval 2 yπminus lt lt 2π

Therefore the curve is concave up for 2 yπminus lt lt 2π

2


d ydx

(d) By the Mean Value Theorem for some value c in the

interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=

For all points on the curve ( )2 23 f xprime lele

Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus

le le rArr le minus 1le

1 applies Mean Value Theorem2

1 verification

Scoring Worksheet

The following provides a scoring worksheet and conversion table used for calculating a composite score of the exam

2018 AP Calculus AB Scoring Worksheet

Section I Multiple Choice

times 12000 = Number Correct Weighted Section I Score (out of 45) (Do not round)

Section II Free Response

Question 1 times 10000 = (out of 9) (Do not round)






Sum = Weighted Section II

Score (Do not round)

Composite Score

+ = Weighted Weighted Composite Score

Section I Score Section II Score (Round to nearest whole number)

AP Score Conversion Chart Calculus AB

Composite Score Range AP Score

66-10854-6541-5326-40

0-25

5 4 3 2 1


The following contains tables showing the content assessed the correct answer and how AP students performed on each question

2018 AP Calculus AB Question Descriptors and Performance Data

Multiple-Choice Questions

Question Learning Objective

Essential Knowledge

Mathematical Practice for AP Calculus 1


Key Correct

1 21C 21C1 Implementing algebraic computational processes Building notational fluency A 76

2 33B(a) 33B1 Implementing algebraic computational processes Building notational fluency A 65

3 11B 11B1 Connecting multiple representations Reasoning with definitions and theorems

D 84

4 33B(b) 33B2 Implementing algebraic computational processes

Building notational fluency B 79

5 32B 32B2 Implementing algebraic computational processes

Connecting multiple representations B 81

6 21C 21C3 Connecting concepts Implementing algebraic computational processes C 87

7 35A 35A1 Connecting concepts Implementing algebraic computational processes A 44

8 22A 22A3 Connecting concepts Connecting multiple representations D 60

9 21A 21A3 Reasoning with definitions and theorems Building notational fluency A 47

10 21D 21D1 Implementing algebraic computational processes Building notational fluency B 90

11 32C 32C3 Implementing algebraic computational processes Connecting concepts A 37

12 21C 21C5 Implementing algebraic computational processes Connecting concepts B 50

13 23C 23C1 Implementing algebraic computational processes

Connecting concepts C 68


Connecting concepts D 63

15 32C 32C1 Connecting multiple representations Implementing algebraic computational processes B 45

16 22A 22A1 Implementing algebraic computational processes Building notational fluency A 43


18 23B 23B2 Connecting concepts Implementing algebraic computational processes C 56


Reasoning with definitions and theorems B 46

20 24A 24A1 Reasoning with definitions and theorems Connecting concepts B 54

21 33A 33A2 Implementing algebraic computational processes Building notational fluency C 49

22 23F 23F1 Connecting multiple representations Connecting concepts D 71

23 33B(a) 33B5 Implementing algebraic computational processes


24 12A 12A3 Implementing algebraic computational processes

Reasoning with definitions and theorems A 56

25 23E 23E2 Implementing algebraic computational processes Building notational fluency A 51

26 22A 22A1 Connecting multiple representations Reasoning with definitions

and theorems D 22

27 23C 23C2 Implementing algebraic computational processes Connecting concepts D 45

28 11D 11D1 Building notational fluency Implementing

algebraiccomputational processes

C 26

29 34D 34D1 Connecting multiple representations Connecting concepts D 34

30 35A 35A2 Reasoning with definitions

and theorems Implementing algebraic computational processes B 46


Question Learning

Objective Essential

Knowledge Mathematical Practice

for AP Calculus 1 Mathematical Practice

for AP Calculus 2 Key Correct

76 22A 22A3 Connecting multiple representations Connecting concepts B 81

77 23A 23A2 Connecting concepts Building notational fluency D 69

78 34C 34C1 Implementing algebraic computational processes Connecting concepts C 66

79 22B 22B1 Connecting multiple representations Connecting concepts C 80


81 34E 34E1 Implementing algebraic computational processes


82 12B 12B1 Reasoning with definitions and theorems

Building notational fluency C 68

83 23C 23C1 Connecting concepts Implementing algebraic computational processes B 56

84 34B 34B1 Connecting concepts Implementing algebraic computational processes B 71

85 11B 11B1 Connecting multiple representations Implementing algebraic computational processes C 60

86 34D 34D2 Implementing algebraic computational processes

Connecting multiple representations A 43

87 32C 32C2 Reasoning with definitions and theorems Connecting concepts B 79

88 23B 23B1 Connecting concepts Reasoning with definitions and theorems C 41

89 23D 23D1 Implementing algebraic computational processes Connecting concepts D 68

90 21C 21C6 Connecting concepts Connecting multiple representations C 36


Free-Response Questions

Question Learning Objective Essential Knowledge Mathematical Practice for AP Calculus

Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2

Reasoning with definitions and theorems|Connecting

concepts|Implementing algebraiccomputational

processes|Connecting multiple representations|Building notational

fluency|Communicating

498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1



processes|Building notational fluency|Communicating

331

3 11A(b)|11B|11C|22A|32C|32C|33A 11A3|11B1|11C3|22A1|32C1|32C3|33A2





234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board

The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity Founded in 1900 the College Board was created to expand access to higher education Today the membership association is made up of over 6000 of the worldrsquos leading educational institutions and is dedicated to promoting excellence and equity in education Each year the College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success mdash including the SATreg and the Advanced Placement Programreg The organization also serves the education community through research and advocacy on behalf of students educators and schools 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

Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover

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ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt DAN 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 ESP 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 FRA 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger) NOR 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 PTB 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 SUO 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 SVE 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later) gtgt Namespace [ (Adobe) (Common) (10) ] OtherNamespaces [ ltlt AsReaderSpreads false CropImagesToFrames true ErrorControl WarnAndContinue FlattenerIgnoreSpreadOverrides false IncludeGuidesGrids false IncludeNonPrinting false IncludeSlug false Namespace [ (Adobe) (InDesign) (40) ] OmitPlacedBitmaps false OmitPlacedEPS false OmitPlacedPDF false SimulateOverprint Legacy gtgt ltlt AddBleedMarks false AddColorBars false AddCropMarks false AddPageInfo false AddRegMarks false ConvertColors ConvertToCMYK DestinationProfileName () DestinationProfileSelector DocumentCMYK Downsample16BitImages true FlattenerPreset ltlt PresetSelector MediumResolution gtgt FormElements false GenerateStructure false IncludeBookmarks false IncludeHyperlinks false IncludeInteractive false IncludeLayers false IncludeProfiles false MultimediaHandling UseObjectSettings Namespace [ (Adobe) (CreativeSuite) (20) ] PDFXOutputIntentProfileSelector DocumentCMYK PreserveEditing true UntaggedCMYKHandling LeaveUntagged UntaggedRGBHandling UseDocumentProfile UseDocumentBleed false gtgt ]gtgt setdistillerparamsltlt HWResolution [2400 2400] PageSize [612000 792000]gtgt setpagedevice

Contents

Exam Instructions






Scoring Worksheet


Note This publication shows the page numbers that appeared in the 2017minus18 AP Exam Instructions book and in the actual exam This publication was not repaginated to begin with page 1

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Exam Instructions




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Time 1 hour



Time 45 minutes







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Time 1 hour





Answer sheets

AP Student Packs






Pencil sharpener




Extra paper

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Testing Window

















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A SIGNATURE































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Answer Sheet 2018

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121586-00657 bull TF

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rinted in US

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COLLEGE CODE

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INTERNATIONAL PHONE


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Not yet in9th grade

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AP FPO X123456789 X


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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

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

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



Yes No



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QUESTIONS 1ndash75

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A B C D

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OTHER EXAMSR W O

PT02 TOTAL




Exam

Exam

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ndash

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A B C D E

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A B C D

A B C D

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PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover

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ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt DAN 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 DEU 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 ESP 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 FRA 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger) NOR 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 PTB ltFEFF005500740069006c0069007a006500200065007300730061007300200063006f006e00660069006700750072006100e700f50065007300200064006500200066006f0072006d00610020006100200063007200690061007200200064006f00630075006d0065006e0074006f0073002000410064006f0062006500200050004400460020006d00610069007300200061006400650071007500610064006f00730020007000610072006100200070007200e9002d0069006d0070007200650073007300f50065007300200064006500200061006c007400610020007100750061006c00690064006100640065002e0020004f007300200064006f00630075006d0065006e0074006f00730020005000440046002000630072006900610064006f007300200070006f00640065006d0020007300650072002000610062006500720074006f007300200063006f006d0020006f0020004100630072006f006200610074002000650020006f002000410064006f00620065002000520065006100640065007200200035002e0030002000650020007600650072007300f50065007300200070006f00730074006500720069006f007200650073002egt SUO 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 SVE ltFEFF0041006e007600e4006e00640020006400650020006800e4007200200069006e0073007400e4006c006c006e0069006e006700610072006e00610020006f006d002000640075002000760069006c006c00200073006b006100700061002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e007400200073006f006d002000e400720020006c00e4006d0070006c0069006700610020006600f60072002000700072006500700072006500730073002d007500740073006b00720069006600740020006d006500640020006800f600670020006b00760061006c0069007400650074002e002000200053006b006100700061006400650020005000440046002d0064006f006b0075006d0065006e00740020006b0061006e002000f600700070006e00610073002000690020004100630072006f0062006100740020006f00630068002000410064006f00620065002000520065006100640065007200200035002e00300020006f00630068002000730065006e006100720065002egt ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later) gtgt Namespace [ (Adobe) (Common) (10) ] OtherNamespaces [ ltlt AsReaderSpreads false CropImagesToFrames true ErrorControl WarnAndContinue FlattenerIgnoreSpreadOverrides false IncludeGuidesGrids false IncludeNonPrinting false IncludeSlug false Namespace [ (Adobe) (InDesign) (40) ] OmitPlacedBitmaps false OmitPlacedEPS false OmitPlacedPDF false SimulateOverprint Legacy gtgt ltlt AddBleedMarks false AddColorBars false AddCropMarks false AddPageInfo false AddRegMarks false ConvertColors ConvertToCMYK DestinationProfileName () DestinationProfileSelector DocumentCMYK Downsample16BitImages true FlattenerPreset ltlt PresetSelector MediumResolution gtgt FormElements false GenerateStructure false IncludeBookmarks false IncludeHyperlinks false IncludeInteractive false IncludeLayers false IncludeProfiles false MultimediaHandling UseObjectSettings Namespace [ (Adobe) (CreativeSuite) (20) ] PDFXOutputIntentProfileSelector DocumentCMYK PreserveEditing true UntaggedCMYKHandling LeaveUntagged UntaggedRGBHandling UseDocumentProfile UseDocumentBleed false gtgt ]gtgt setdistillerparamsltlt HWResolution [2400 2400] PageSize [612000 792000]gtgt setpagedevice

Exam Instructions




41







Time 1 hour



Time 45 minutes







Time 30 minutes




Time 1 hour





Answer sheets

AP Student Packs






Pencil sharpener




Extra paper

ndash

ndash

Stapler

Watch




42



Testing Window

















AP

Cal

culu

s A

BB

C E

xamemsp

43







































Then say



AP

Cal

culu

s A

BB

C E

xam

45


emsp





















Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

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75

QUESTIONS 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




41







Time 1 hour



Time 45 minutes







Time 30 minutes




Time 1 hour





Answer sheets

AP Student Packs






Pencil sharpener




Extra paper

ndash

ndash

Stapler

Watch




42



Testing Window

















AP

Cal

culu

s A

BB

C E

xamemsp

43







































Then say



AP

Cal

culu

s A

BB

C E

xam

45


emsp





















Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


42



Testing Window

















AP

Cal

culu

s A

BB

C E

xamemsp

43







































Then say



AP

Cal

culu

s A

BB

C E

xam

45


emsp





















Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



AP

Cal

culu

s A

BB

C E

xamemsp

43







































Then say



AP

Cal

culu

s A

BB

C E

xam

45


emsp





















Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover






















Then say



AP

Cal

culu

s A

BB

C E

xam

45


emsp





















Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



AP

Cal

culu

s A

BB

C E

xam

45


emsp





















Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover





Read Item 4





Then say


















AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

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40

41

42

43

44

45

46

47

48

49

50

51

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54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

QUESTIONS 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



AP

Cal

culu

s A

BB

C E

xam

47


emsp


Then say









Then say
















A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover












A SIGNATURE































1 2 3 4 5 6 7 8 9




























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


Month

AM PM






Option 1 Option 2

E EXAM START TIME

0 0

1 1

2

3

4

5

6

7

8

9

1 2

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






Yes No

Answer Sheet 2018

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


121586-00657 bull TF

11017E5500 bull P

rinted in US

A

Q45461-4

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


College Name

State

Country


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


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


Not yet in9th grade

9th

10th

801356

11th

12th


AP FPO X123456789 X


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

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

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



Yes No



PAGE 2



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

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

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

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28

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46

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63

64

65

66

67

68

69

70

71

72

73

74

75

QUESTIONS 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



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

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

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



Yes No



PAGE 2



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

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

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

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

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 1ndash75

Yes No


A B C D

A B C D




OTHER EXAMSR W O

PT02 TOTAL




Exam

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

ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


ndash

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

ndash

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

ndash

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

ndash

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

ndash

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


ndash

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


PAGE 3


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

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

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

110

111

112

113

114

115

116

117

118

119

120





A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

A B C D

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






PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




PAGE 4




























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

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

E E E E E E E E E

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


AK

AL

AR

AZ

CA

CO

CT

DC

DE

FL

GA

HI

IA

ID

IL

IN

KS

KY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT

WA

WI

WV

WY

Puerto Rico

AA

AE

AP

Other

STATE


U EMAIL ADDRESS









Grade school

Some high school



Some college





V SEX

Female Male

English








Yes Cuban

Yes Mexican

Yes Puerto Rican







b What is your race










Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover











Time 1 hour



Time 45 minutes



Instructions





66

CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


CALCULUS AB

SECTION I Part A

Timemdash1 hour




In this exam









then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




then cent( ) =f 2

(A) 4 (B) 6 (C) 7 (D) 11

2 3xint 6e dx =

(A) 2e3x + C

(B) 6e3x + C

(C) 18e3x + C

(D)



x+6e 3 1

+ C 3x + 1

)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


)x






(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



(A) minus10 (B) minus7 (C) 10 (D) 13






(A) 230 (B) 1150 (C) 1375 (D) 2075



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



(A) x2xe

(B) 2xex minus 2x





is x t( ) =

)

(A) sin 2t( ) + 5t

(B) sin 2t( ) + 7t

(C) sin 2t( ) + 9t

(D)



16 sin 2t( ) + 7t



(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




(A) (B)

(C) (D)


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


9



(A)1



dx dx

(A) 11 (B) 24 (C) 26 (D) 125






(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover





(A) 5

6 (B)

2

3 (C) minus

1

6 (D) nonexistent




dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



dx in terms of y

(A) dy

= 3 sin2 ydx

(B) dy

= 3 cos2 ydx

(C) dy

= 3 cos ycot ydx

(D)



dy 3= 2dx 1 9y+




(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover





(A) 1 (B)121

25 (C)

25

4 (D) 25


dx when x = 3


(B) 6 cos ( ( )f 9 )

(C) f cent( ) f 9 )9 cos ( ( )

(D) 6f cent 9 f 9 )( )cos ( ( )





(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




(A) p + 1 (B) p + 2 (C) 2p + 1 (D) 2p + 2


(A) 0 (B) 5 (C) 6 (D) 8



17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


17

⌠ 1 ⎮ dx = x2 + 4x + 5



(C) ln x2 + 4x + 5 + C

(D)



1 1

+ C 3 2x + 2x + 5x

3



(A)11

6(B)

25

12 (C)

13

6(D)

7

3

19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


19 24x


(A) 0 (B)1














6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover






6 2ln x + 1 minus ln e + 1( ) ( )


(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



(A) dy

dx =

x

y

(B) dy

dx = minus

x

y

(C) dy

dx = xy

(D)



dy

dx = minusxy


u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



u = +x 1 ⎮ dx x + 1

is equivalent to

(A) ⌠ 1

⎮ du u + 1



f x = 2( )x minus 9x + 8


discontinuity








y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover






y = cos 2( )x






(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover







(D) f ( ) π 0 cent 12







= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover






= 41 dt


dt

(A)

82minus

75(B)

2 5minus

3 (C)

3 5minus

2 (D)

82 5minus

15

28 3 2x+


(A) 2

minus 5

(B) 0 (C)3

4 (D) nonexistent




II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover





II 2


III 1 2


(A) II only

(B) III only

(C) I and II only

(D) II and III only




= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



= xy3



Step 1



-23-


2


Step 4 23 x 2y = 4e

Step 5 23 x 2y = 4e


END OF PART A




-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



-25-

)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


)

B B B B B B B B B

CALCULUS AB

SECTION I Part B

Timemdash45 minutes







In this exam








B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




B B B B B B B B B



B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


B B B B B B B B B









4v t( ) =

3 t + 1 If the


(A) 0617 (B) 0647 (C) 1353 (D) 5713

B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


B B B B B B B B B


(A) (0 1) (B) (1 2) (C) (2 3) (D) (3 4)


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


)

B B B B B B B B B




(B) (minus1341 minus0240) and (0964 15)

(C) (minus0714 0333) and (1381 15)

(D) (minus15 minus0714) and (0333 1381)



⎟⎟⎟⎟⎟⎜⎜ ⎠



(A) 1233 cm (B) 1466 cm (C) 1966 cm (D) 5401 cm



(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




(A) 5

int (1

f x) d x exists




B B B B B B B B B



(A) 0 (B) 1420 (C) 3142 (D) 4439




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




(A) 12 (B) 6 (C) 3 (D) 3

2



xrarr0

)

(A) minus2

(B) 0

(C) 1


B B B B B B B B B


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


B B B B B B B B B


4 ) as sho wn



(A) 1775 (B) 3549 (C) 4800 (D) 5575



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



int f x dx = 5 ( ) 2

and 2

int g x d ( ) x = 76

then 6

int ( ( ) ( )) d3f x + g x x = 2

(A) minus6 (B) 8 (C) 22 (D) 36




(A) f (42) lt S(42 ) lt T(42)

(B) f (42) lt T(42 ) lt S(42)

(C) S(42) lt f (42 ) lt T(42)

(D) T(42) lt f (42 ) lt S(42)

B B B B B B B B B




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




statements are true





B B B B B B B B B




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




(A) 1

minus 10

(B)1

10 (C)

1

5(D)

B B B B B B B B B


7

5

_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


_______________________________________________________

B B B B B B B B B

END OF SECTION I








-37-











Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover












Time 30 minutes




Time 1 hour








1 fnInt(X2 X 1 5)




66

CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


CALCULUS AB

SECTION II Part A

Timemdash30 minutes




1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r






Do not w



1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


1 1 1 1 1 1 1 1 1 1 D

o no

t wri

te b

eyon

d th

is b

orde

r


w t( ) = 32 loz sin ⎛⎜⎜





Do not w



2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


2 2 2 2 2 2 2 2 2 2


per minute for

Do

not w

rite

bey

ond

this

bor

der




Do not w



2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


2 2 2 2 2 2 2 2 2 2



Do

not w

rite

bey

ond

this

bor

der


Do not w



END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


END OF PART A



-8-

CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


CALCULUS AB

SECTION II Part B

Timemdash1 hour




-13-


Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



Do

not w

rite

bey

ond

this

bor

der



x d



Do not w





cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




cent(xrarr0

x) and lim g+

cent(xrarr0


Do

not w

rite

bey

ond

this

bor

der

(d) Find f x + 7( )


Do not w





f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




f x = 2( )1 + x




Do

not w

rite

bey

ond

this

bor

der

Do not w





Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




Do

not w

rite

bey

ond

this

bor

der



Do not w




Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



Do

not w

rite

bey

ond

this

bor

der




= minus002y 2dt




Do not w





= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




= minus002y2

dt with the initial

condition

Do

not w

rite

bey

ond

this

bor

der

f ( )0 = 10


Do not w





2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




2 3 pound

dy

dx pound 2

(a) Show that

Do

not w

rite

bey

ond

this

bor

der

dy 2=

dx 2 minus si y

n

(b) For p

y p

minus lt lt2 2



Do not w





y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




y p

lt lt2 2


(d) Let

Do

not w

rite

bey

ond

this

bor

der





Do not w



____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


____________________________________

STOP

END OF EXAM





-22-




Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover





Question 1 A

Question 2 A

Question 3 D

Question 4 B

Question 5 B

Question 6 C

Question 7 A

Question 8 D

Question 9 A

Question 10 B

Question 11 A

Question 12 B

Question 13 C

Question 14 D

Question 15 B

Question 16 A

Question 17 A

Question 18 C

Question 19 B

Question 20 B

Question 21 C

Question 22 D

Question 23 C

Question 24 A

Question 25 A

Question 26 D

Question 27 D

Question 28 C

Question 29 D

Question 30 B

Question 76 B

Question 77 D

Question 78 C

Question 79 C

Question 80 A

Question 81 D

Question 82 C

Question 83 B

Question 84 B

Question 85 C

Question 86 A

Question 87 B

Question 88 C

Question 89 D

Question 90 C





minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover






minus


1 approximation2



is ( )8


( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )8

01 1 0 5 5 1 6 6 5 8 8 6

151 1 205 4 183 1 227 2 1608




1 approximation

(c) ( )8

099051497w t dt =int


time 8t = is ( )8


1 integral2

1 answer



( ) ( ) 1 considers 6 62

1 answerg wminus


Question 1



Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




Question 2

(a) ( )5 0538462vprime =


1 answer

(b) ( )15

076043074v t dt =int


1 integral2

1 answer

(c) ( )15

01 506953815 v t dt =int



1 answer




( ) ( )15 1521212

2 81 3t

tt c dt t ct c

=




mdash OR mdash



( )( ) ( )( )2

15212

15

12 2 91

t

tt B dt Bt Bt

=







Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




Question 3

(a) ( ) ( )7


2π

( ) ( )7 3 7 3 3f gprime = + = + = 6

( )( )

1 72

1 7ff

prime



(c) ( )0

1lim 2xg x


( )0

limx

g x+rarr



(d) ( )( ) ( )2

02lim 7 6 7 0

xf x g t dt

minus


( )3 62

lim 1 0xx

e +rarrminus

minus =


3 6 3 62 2

7 3 2 3 1lim lim 3 31 3x xx x




1 answer




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




Question 4


( )( )

( )( ) ( )( )( ) ( )( )

1

21 111

11 1

3 31

6 tan 3

6 tan 1 3 6 tan 1 3

6 3 6 34 43 6

f x dx dxx

x x

π π

π

minus minus

minusminus

minus minus

minus = minus +

= minus



= minus

⌠⌡int

1 6



1 answer

(b) ( ) ( )( )( )1 221




(c) ( ) ( ) 263 3

1h x f x

x= minus = minus

+ for 1x gt

( )( )221

h xx

prime =+

for 1x gt12x

( ) 212 2 242 255

h sdotprime = =

( )( )( )

1 3 1

1 2

h xh xh

prime prime



Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




Question 5




( ) 1 02


y




(c) 2

1 002dy dty

minus =

⌠⌡ int1 002t Cy = +

( )1 002 0 0110 C C= + rArr =

1 1 50002 01 002 01 5t yy t t= + rArr = =+ +




1 answer



(d)

( )

2

2

2

3

004

004 002

00008

d y dyy dtdty y

y

= minus

= minus minus

=


mdash OR mdash



( )( )2

50 5

ft

t minus=+

prime and ( )( )3

100 05

f tt

primeprime = gt+

for 0t ge


2


d ydt



Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover




Question 6




22 sin

dydx y=

minus


1 verification


minus



1 12 1 answer

dydx

=

(c) ( )

( )( )

2

2 2 34cos2 cos



2

2 0d ydx



2


d ydx


interval ( )2 21 ( ) ( ) ( )21 201

ff c minusprime f=


Thus ( ) ( ) ( ) ( )21 22 12 21 23 01 15 5f f f fminus



1 verification

Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


Scoring Worksheet














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover














Composite Score





66-10854-6541-5326-40

0-25

5 4 3 2 1






Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover







Essential Knowledge



Key Correct




D 84































and theorems D 22




C 26





Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover



Question Learning

Objective Essential

























Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover





Mean

1 21B|23A|23A|32B|33B(b)|34A 21B1|23A1|23A2|32B2|33B2|34A2





498

2 23C|33B(b)|34B|34C 23C1|33B2|34B1|34C1




331






234

4 21C|23A|33B(b)|34D|34D 21C4|23A2|33B2|34D1|34D2





263

5 21C|21D|22A|23B|35A 21C4|21D1|22A1|23B2|35A2





234

6 12B|21C|21D|22A|23B|24A 12B1|21C5|21D1|22A1|23B1|24A1




278

AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


AP Calculus AB

The College Board


Cover

Contents

Exam Instructions



SECTION I Part A

Questions 1 and 2

Question 3

Questions 4 and 5

Questions 6 and 7

Question 8

Questions 9 and 10

Question 11

Question 12

Questions 13 and 14

Questions 15 and 16

Questions 17 and 18

Questions 19 and 20

Question 21

Question 22

Questions 23 and 24

Question 25

Question 26

Questions 27 and 28

Question 29

Question 30

SECTION I Part B

Question 76

Questions 77 and 78

Question 79

Questions 80 and 81

Questions 82 and 83

Questions 84 and 85

Question 86

Questions 87 and 88

Question 89

Question 90


SECTION II Part A

Question 1

Question 2

SECTION II Part B

Question 3

Question 4

Question 5

Question 6



Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Scoring Worksheet


Back Cover


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