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Be Prepared
for the AP Calculus Exam

Mark Howell, Gonzaga High School, Washington, D.C.,
Martha Montgomery, Fremont City Schools, Fremont, Ohio

Practice Exam Contributors:

Benita Albert, Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick, Oregon State University
Joe Milliet, St. Mark's School of Texas, Dallas, Texas

Reviewers:

Ray Cannon, Barbara Currier, Maria Litvin, Bernard Madison, Steven Olson, Nancy Stephenson, JT Sutcliffe.

Copyright © 2005 by Skylight Publishing.

ISBN 978-0-9727055-5-4.  List price: $17.95.  12+ copies: $14.50 each.

430 pages. Dimensions 8-1/2" x 11" x 1". Soft cover.

800 Questions in Calculus:
25 Years of
Continental Mathematics League Contests

Copyright © 2005 by Skylight Publishing.

ISBN 978-0-9727055-4-7.  List price: $14.95.  12+ copies: $11.95 each.

208 pages. Dimensions 8-1/2" x 11" x 1/2". Soft cover.

800 Solutions Part# 978-0-9727055-C-D.  $24.95.    

Brief Contents

Contents

Acknowledgments

How to Use This Book

Introduction

Chapter 1. Exam Format, Grading, and Tips

Chapter 2. Limits and Continuity

Chapter 3. Derivatives

Chapter 4. Applications of Derivatives

Chapter 5. Integration

Chapter 6. Applications of Integrals

Chapter 7. Differential Equations

Chapter 8. Parametric, Vector, and Polar Functions

Chapter 9. Series

Chapter 10. Annotated Solutions to Past Free-Response Questions

Appendix: Calculator Skills

Practice Exams (AB1, AB2, AB3, BC1, BC2)

Answers and Solutions

Index

On the Back Cover

Be Prepared for the AP Calculus Exam is your indispensable guide to scoring well on the Advanced Placement Calculus AB or BC exam.  This book features an outstanding team of authors and practice exam contributors: veteran AP Calculus teachers who have served on the AP Calculus Test Development Committee and are College Board consultants, exam grading leaders, and AP award recipients.  The book expands Skylight's Be Prepared series, and it is crafted with the same care, attention to detail, and respect for the student as our Be Prepared for the AP Computer Science Exam, which has helped many thousands of students get a good grade on AP exams in that subject. 

A serious introductory chapter describes the exam format and requirements and offers important tips for successful exam taking.  Eight review chapters thoroughly cover all of the AB and BC material.  Embedded in these chapters are 200+ multiple-choice and free-response questions with solutions that show you effective strategies and shortcuts.  Five complete practice exams with answers and solutions (three AB and two BC exams) will give you plenty of practice material and help you decide whether to take the AB or BC exam.  This book's companion web site contains annotated solutions to free-response questions from past AP exams. Whether you sit in the front row, the back row, or anywhere in between, Be Prepared will help you focus on the AP Calculus exam requirements, review the material, and fill the gaps in your knowledge.  Review, practice, and take the AP Calculus exam with confidence, knowing that you are well prepared.

About This Book

The Continental Mathematics League has been bringing us fun competitions in mathematics and computer science since 1980.  The annual calculus contest includes 32 questions divided into four rounds.  We are delighted to be able to offer you one book that brings together 800 questions from the past 25 years of CML calculus.  (Actually, we weren't able to include the last 32 questions from the 2004-2005 contest -- sorry! They will appear on this web site after the contest is completed.) 

These questions offer a great opportunity to test your knowledge of calculus and practice for the AP exam.  They stay within the range of the standard AP Calculus curriculum (mostly AB but also some BC).  Most are of average difficulty, but a few questions may be slightly more challenging: each round includes 6 one-point questions and 2 two-pointers. 

The questions are presented in order by year.  The book also includes an index of all questions by subject. Answers are included at the end of the book.  Complete solutions are available (see the order form).  E-mail support@skylit.com about licensing this collection of questions and solutions in digital format.

2003-2004, Question 16:

Chord AB of the parabola y = x² moves up from the vertex at 3/4 units/sec, always remaining parallel to the x-axis.  Triangle ABC is formed by AB and the two tangents to the parabola at A and at B.  The triangle increases in area as AB moves up.  Find the rate at which the area is increasing in units²/sec at the instant when AB is 4 units above the vertex.