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AP Calculus AB 2005: An Apex Learning Guide

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Everything you need to score higher on the AP Calculus AB exam — Guaranteed.

Kaplan's comprehensive guide includes:

  • 2 full-length practice tests
  • Detailed answer explanations
  • Hundreds of practice questions
  • The most up-to-date information on the test
  • Focused review of all tested material, from limits of functions to differential equations
  • Explanations of important terms, concepts, and formulas
  • Powerful strategies to help you score higher
Read More Show Less

Product Details

  • ISBN-13: 9780743260534
  • Publisher: Kaplan Publishing
  • Publication date: 12/21/2004
  • Pages: 560
  • Product dimensions: 8.36 (w) x 10.74 (h) x 1.48 (d)

Table of Contents

Table of Contents

Section I: The Basics

Chapter 1: Inside the AP Calculus AB Exam

What Is the Advanced Placement (AP) Program?

An Overview of the Test Structure

What's on the Test?

How the Exam Is Scored

Registration and Fees

Additional Resources

Chapter 2: Strategies for Success: It's Not Always How Much You Know

How to Use This Book

AP Calculus AB -- Test-Taking Strategies

How to Approach Multiple-Choice Questions

How to Approach Free-Response Questions

Stress Management

Countdown to the Test

Handling Stress During the Test

Section II: AP Calculus AB Review

Chapter 3: Limits of Functions

What's A Limit?

Asymptotic and Unbounded Behavior

Chapter 4: Derivatives

Derivative at a Point

Computing and Interpreting Derivatives

Higher-Order and Implicit Derivatives

Chapter 5: Differential Calculus

Extrema and Optimization

Tangent and Normal Lines

Rates of Change and Related Rates

Chapter 6: The Definite Integral

Area Under a Curve

Chapter 7: Antiderivatives and the Fundamental Theorems of Calculus


The Fundamental Theorems of Calculus

Chapter 8: Applications of the Integral



Other Applications of the Definite Integral

Chapter 9: Inverse Functions and Transcendental Functions

Inverse Functions

Review of Logarithmic and Exponential Functions

Derivatives Involving Transcendental Functions

Integrals Involving Transcendental Functions

Chapter 10: Differential Equations

Differential Equations and Slope Fields

Section III: Full-Length Practice Tests

Practice Calculus ABTest One

Answers and Explanations

Practice Calculus AB Test Two

Answers and Explanations

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First Chapter

Chapter 1: Inside the AP Calculus AB Exam

Before you plunge into studying for the AP Calculus AB exam, let's take a step back and look at the big picture. What's the AP Calculus AB exam all about? How can I prepare for it? How's it scored? This chapter and the next will answer these questions and more.

What Is the Advanced Placement (AP) Program?

Through the Advanced Placement Program, you can take college-level courses while you are in high school. Based on your grade on an AP Exam, colleges and universities can grant you placement or college credit or both.

In addition to getting a head start on your college coursework, you can improve your chances of acceptance to competitive schools since colleges know that AP students are better prepared for the demands of college courses. There's also the money you can save on tuition if you receive credit!

An Overview of the Test Structure

The AP Calculus AB exam is administered in May by the College Board's AP Services. The exam is 3 hours and 15 minutes long, so developing your stamina is very important. The exam consists of two equally weighted sections: Section I, Multiple-Choice, and Section II, Free- Response.

Section I -- Multiple-Choice

There are 45 multiple choice questions. This section is split into two parts: part A consists of 28 questions with no calculator allowed (55 minute time limit) and part B consists of 17 questions for which a calculator is required (50 minute time limit). Each multiple choice question is worth 1 point.

Section II -- Free-Response

The second section of the examination consists of 6 free-response questions worth 9 points each.Part A consists of 3 questions for which a calculator is required (45 minutes). Part B consists of 3 questions for which calculators may be not be used (45 minutes). During Part B, you may go back to the first three questions in Part A if you have time, but you will not be permitted to use your calculator.

There's a five minute break between Section I and Section II.

In section II, students may go back to work on questions in Part A after timing for Part B has begun without a calculator. The proctor for the examination will remind you at the beginning of each part of the examination whether or not a calculator is permitted.

What's the AB Stand for?

There are two AP Calculus exams and the AB distinguishes this exam from the AP Calculus BC exam. The AB exam covers one semester of college-level calculus, whereas the BC exam covers a full year of college calculus, although individual colleges may differ in their course offerings and placement/credit policies. You may take only one of the two exams in any given year.

What's on the Test?

To be ready for AP Calculus, you should havea good grasp of algebra, geometry, trigonometry,analytic geometry, and elementary functions,including linear, polynomial, rational,exponential, logarithmic, trigonometric, andinverse trigonometric functions. The AP Calculus AB course itself concentrates on extending your knowledge of functions through basic differential and integral calculus. There is much emphasis on multiple representations, that is, understanding how to work with functions whether they be presented analytically (by a formula y = f(x), graphically, or as a table of data values. The breakdown of the AB course description is roughly as follows:

Limits (<10%): calculating limits using algebra, estimating limits from graphs or tables of data, and understanding the key idea of continuity, including the Intermediate and Extreme Value Theorems. (Chapter 3)

Differential calculus and its applications (<40\%): calculating derivatives using algebra (both at a point and as a function), estimating derivatives from graphs or tables of data, understanding the relationship between continuity and differentiablility, the Mean Value Theorem,higher order derivatives, implicit differentiation, using derivatives to analyze graphs, solving extremum and related rates problems. (Chapters 4, 5, and 7)

Integral calculus and its applications (<40%): calculating indefinite integrals (antiderivatives) and definite integrals using algebra , estimating integralsfrom graphs or tables of data, Riemann sum approximations, the Fundamental Theorems of Calculus, applications of integrals to finding area, volumes, distances and, in general, accumulated change. (Chapters 6-9)

Separable differential equations (<10%): solving differential equations by separation of variables, estimating solutions graphically using slope fields, geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations (application of derivatives), exponential and related models arising from differential equations. (Chapter 10)

What's New on the Test: Slope Fields Coming to Calculus AB

Effective for the 2004 examinations, slope fields will be one of the topics included on the AP Calculus AB test. What will be tested is geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations. This topic has been part of the topical outline for Calculus BC since the 1998 examinations, and is now part of the AB exam. But don't worry: You'll find plenty of practice with slope fields in Chapter 10 of this book.

How the Exam Is Scored

The AP Calculus exam is scored on a scale of 1 to 5, with 5 being the highest grade. The scores are defined as follows:

5 Extremely well qualified

4 Well qualified

3 Qualified

2 Possibly qualified

1 No recommendation

In 2002, the average grade of the 157,524 candidates who took the AB test was 3.11. Typically, to obtain a score of 3 or higher, you need to answer about 50 percent of the multiple choice section correctly, and do acceptable work on the free-response section. Remember that you can miss questions and still get a perfect 5 score.

Raw scores are calculated in points. The multiple-choice section of the AP Calculus exam is worth the same number of points as the free-response section. There is a 1.2 weighting factor used so that the multiple-choice and free-response sections of the exam have equal weight. Each section is worth 54 points, for a total of 108 points.

It would not be correct to say that the AP examination is graded on a curve. How other students do on the same exam will not affect your score. However, some multiple-choice questions are used from one year to the next to allow for a calibration of the scores so that a 4 one year reflects the same statistical strength of performance. For this reason, the cut-offs for each score level do not stay constant from year to year.

Wrong-Answer Penalty

For multiple choice questions, there is a penalty for incorrect answers as opposed to simply leaving answers blank. This is sometimes called a guessing penalty, but it is really a wrong answer penalty. If you guess right, you're in great shape!

Here's how the scoring works: You receive 1 point for a correct answer, 0 points for no answer, and -1/4 point for a wrong answer. For example, getting 30 correct and 15 wrong would give you a score of 30-(15x1/4) = 26.25. We'll talk more about guessing on the AP Calculus AB multiple-choice section in the next chapter, Taking AP Calculus AB -- Strategies for Success.

What You Need to Bring

  • Two calculators (see below) and batteries
  • Photo I.D. (driver's license, school I.D., or a valid passport are acceptable)
  • Your secondary school code number (see your Guidance Counselor or AP Coordinator)
  • Your Social Security number
  • Several sharpened No. 2 pencils
  • Pencil sharpener
  • Eraser
  • A watch (in case your exam room doesn't have a clock you can see easily. You need to be able to pace yourself during this long test!)

What NOT to Bring

  • DON'T bring scratch paper. You'll make your notes in the test booklet in the spaces provided.
  • Don't bring books, compasses, correction fluid, dictionaries, highlighters, notes, or rulers.
  • Don't bring beepers or cellular phones, or watches that have beepers or alarms.
  • Don't bring food or drinks.
  • Don't even wear a T-shirt with math of any kind on it!


You can only bring two calculators, both of which must be approved types. To be an approved calculator, it should be able to:

  • Produce the graph of a function within an arbitrary viewing window.
  • Find the zeros of a function.
  • Compute the derivative of a function numerically.
  • Compute definite integrals numerically.

You can't use a calculator with a QWERTY keypad, because it makes it too easy to type text (such as test questions) into the calculator. Visit the AP Calculus Website at or see the AP Bulletin for Students and Parents for a listing of approved calculators.

How Are Exams Graded?

The multiple-choice section of the exam is graded by computer. The free-response booklets are graded by faculty consultants. These are college professors and AP teachers who are specially trained to assess the questions. Usually about six faculty consultants review each free-response booklet.

How Do I Get My Grade?

AP Grade Reports are sent in July to each student's home, high school, and any colleges designated by the student. Students may designate the colleges they would like to receive their grade on the answer sheet at the time of the test. Students may also contact AP Services to forward their grade to other colleges after the exam, or to cancel or withhold a grade.

AP Grades by Phone

AP Grades by phone are available for $15 a call beginning in early July. A touch-tone phone is needed. The toll-free number is (888) 308-0013.

Registration and Fees


To register for the AP Calculus AB exam, contact your school guidance counselor or AP Coordinator. If your school does not administer the exam, contact AP Services for a listing of schools in your area that do.


The fee for each AP Exam is $80. The College Board offers a $22 credit to qualified students with acute financial need. A portion of the exam fee may be refunded if a student does not take the test. There is a $20 late fee for late exam orders. Check with AP Services for applicable deadlines.

Additional Resources

The College Board offers a number of publications about the Advanced Placement Program, including: Advanced Placement Program Course Description -- Calculus, A Guide to the Advanced Placement Program, and the AP Bulletin for Students and Parents. You can download these and other publications online at at the Library link, or call AP Services.

For More Information

For more information about the AP Program and/or the AP Calculus AB exam, contact your school's AP Coordinator or guidance counselor, or contact AP Services at:

AP Services

P.O Box 6671

Princeton, NJ 08541-6671

(609) 771-7300

Toll-free: (888) CALL-4-AP (888-225-5427)

Fax: (609) 530-0482

TTY: (609) 882-4118


Website: www.

Copyright © 2005 by Apex Learning Inc.

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  • Anonymous

    Posted January 23, 2005


    Well, I haven't gone through this book cover to cover yet, but from the 40 or so pages I have read through, I can tell you this: WHAT KIND OF EDITOR DID THEY HIRE? THERE ARE SO MANY TYPOS! I've used Kaplan before, and they have always proved the effective as a study aide. Yet, I think they made a bit of a mistake here . . .

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