J. Rosebush - AP® Calculus AB & BC Crash Course Book + Online

AP CALCULUS AB & BC CRASH COURSE

Flavia Banu, M.A.

Joan Rosebush, M.A.

Updated by

Stu Schwartz

Research & Education Association

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AP CALCULUS AB & BC CRASH COURSE

Copyright 2017 by Research & Education Association, Inc.

Prior edition copyright 2011 by Research & Education Association, Inc. All rights reserved. No part of this book may be reproduced in any form without permission of the publisher.

Printed in the United States of America

Library of Congress Control Number: 2016944895

ISBN-13: 978-0-7386-1219-5

ISBN-10: 0-7386-1219-7

LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: Publication of this work is for the purpose of test preparation and related use and subjects as set forth herein. While every effort has been made to achieve a work of high quality, neither Research & Education Association, Inc., nor the authors and other contributors of this work guarantee the accuracy or completeness of or assume any liability in connection with the information and opinions contained herein and in REAs companion online materials. REA and the authors and other contributors shall in no event be liable for any personal injury, property or other damages of any nature whatsoever, whether special, indirect, consequential or compensatory, directly or indirectly resulting from the publication, use or reliance upon this work.

AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. All other trademarks cited in this publication are the property of their respective owners.

Cover image: istockphoto.com/Steve Debenport

AP CALCULUS AB & BC CRASH COURSE

Access Your Online Exam

by following the instructions found at the back of this book.

REAs AP Calculus AB & BC Crash Course is a targeted test prep designed to assist you in your preparation for either version of the AP Calculus exam. This book was developed based on an in-depth analysis of both the latest AP Calculus Course Description outline as well as actual AP test questions.

Written by an AP teacher and a college professor, our easy-to-read format gives students a crash course in Calculus, for both the AB and BC exams.

Unlike other test preps, our AP Calculus AB & BC Crash Course gives you a review specifically focused on what you really need to study in order to ace the exam. The review chapters offer you a concise way to learn all the important facts, terms, and concepts before the exam. This revised edition of AP Calculus AB & BC covers all changes to the 2017 exams: LHospitals rule will now be included in Calculus AB as well as BC; absolute and conditional convergence of infinite series, the limited comparison test, and the alternating series error have been added to BC topics. In addition, multiple-choice questions will now feature four answer choices instead of five.

The introduction discusses the keys for success and shows you strategies to help you build your overall point score. Parts Two through Five are content review chapters. Here you will find the core of what you need to know for the exam. Part Six shares techniques for using the TI-83 Plus graphing calculator as well as information about the multiple-choice questions and the free-response questions. Our authors show you what you need to know in order to answer correctly the types of questions that will appear on the exams.

No matter how or when you prepare for the AP Calculus AB or BC exams, REAs Crash Course will show you how to study efficiently and strategically, so you can get a high score.

To check your test readiness for the AP Calculus AB and BC exams, either before or after studying this Crash Course, take REAs FREE online practice exams (1 each for AB & BC). To access your practice exam, visit the online REA Study Center at www.rea.com/studycenter and follow the on-screen instructions. This true-to-format test features automatic scoring, detailed explanations of all answers, and diagnostic score reporting that will help you identify your strengths and weaknesses so youll be ready on exam day!

Flavia Banu graduated from Queens College of the City University of New York with a B.A. in Pure Mathematics in 1994, and an M.A. in Pure Mathematics in 1997. From 1994 to 2008, Ms. Banu was an adjunct professor at Queens College, where she taught Algebra and Calculus II. She teaches mathematics at Bayside High School in Bayside, New York, and coaches the schools math team. Her favorite course is AP Calculus because it requires the most discipline, rigor, and creativity.

Joan Marie Rosebush teaches calculus courses at the University of Vermont. She also serves as the universitys Director of Student Success for the College of Engineering and Mathematical Sciences. Ms. Rosebush has taught mathematics to elementary, middle school, high school, and college students. She taught AP Calculus via satellite television to high school students scattered throughout Vermont. Recently, she has been teaching live/online.

Ms. Rosebush earned her bachelor of arts degree in elementary education, with a concentration in mathematics, at the University of New York in Cortland, N.Y. She received her masters degree in education from Saint Michaels College, Colchester, Vermont. She went on to earn a Certificate of Advanced Graduate Study in Administration at Saint Michaels College.

In addition to our authors, we would like to thank Larry B. Kling, Vice President, Editorial, for his overall guidance, which brought this publication to completion; Pam Weston, Publisher, for managing the publication to completion; Diane Goldschmidt, Managing Editor, for project management; and Fred Grayson of American BookWorks Corporation for overseeing manuscript development and typesetting.

We also extend our thanks to Stu Schwartz, for technically editing and reviewing this edition.

PART I

INTRODUCTION

Chapter

Keys for Success on the AP Calculus AB & BC Exams

Lets face it. The AP Calculus exams are not easy. The course itself is filled with hundreds of formulas, diagrams, and nuances that can be confusing, and by the time you take the actual AP exam, you may be overwhelmed by what you think you need to know to get a good score. But dont worry, this Crash Course focuses on the key information you really need to know for both calculus exams. However, this is not a traditional review book. During the course of the school year, you should learn most of the material that will appear on the AP Calculus exam youre taking. As you go through this book, if you discover that there is something you dont understand, consult your textbook or ask your teacher for clarification.