5 Steps to a 5 AP Calculus AB & BC, 2012-2013 Edition (2011)

INTRODUCTION: THE FIVE-STEP PROGRAM

How is this Book Organized?

This book begins with an introduction to the Five-Step Program followed by 14 chapters reflecting the 5 steps.

• Step 1 provides an overview of the AP Calculus AB and BC Exams, and offers three study plans for preparing for the two AP Calculus Exams.

• Step 2 contains a diagnostic test with answers and explanations.

• Step 3 offers test-taking strategies for answering both multiple-choice and free-response questions, and for using a graphing calculator.

• Step 4 consists of 10 chapters providing a comprehensive review of all topics covered on the AP Calculus Exams, with Chapter 14 containing materials tested only on the BC exam. At the end of each chapter (beginning with Chapter 5), you will find a set of practice problems with solutions, a set of cumulative review problems with solutions, and a Rapid Review section giving you the highlights of the chapter.

• Step 5 provides four full practice AP Calculus Exams (2 AB exams and 2 BC exams) with answers, explanations, and worksheets to compute your score.

The book concludes with a summary of math formulas and theorems related to the AP Calculus Exams. (Please note that the exercises in this book are done with the TI-89 Graphing Calculator.)

Introducing the Five-Step Preparation Program

This book is organized as a five-step program to prepare you to succeed in the AP Calculus AB/BC Exams. These steps are designed to provide you with vital skills, strategies, and the practice that can lead you to that perfect 5. Here are the 5 steps.

Step 1: Set Up Your Study Program

In this step you will read an overview of the AP Calculus AB and BC Exams, including a summary of topics covered in both exams and a description of the format of both exams. You will also follow a process to help determine which of the following preparation programs is right for you:

• Full school year: September through May.

• One semester: January through May.

• Six weeks: Basic training for the exam.

Step 2: Determine Your Test Readiness

In this step you will take a diagnostic multiple-choice exam in calculus. This pre-test should give you an idea of how prepared you are to take the real exam before beginning to study for the actual AP Calculus AB and BC Exams.

Step 3: Develop Strategies for Success

In this step you will learn strategies that will help you do your best on the exam. These strategies cover both the multiple-choice and free-response sections of the exam.

• Learn to read multiple-choice questions.

• Lean how to answer multiple-choice questions.

• Learn how to plan and write answers to the free-response questions.

Step 4: Review the Knowledge You Need to Score High

In this step you will learn or review the material you need to know for the test. This review section takes up the bulk of this book. It contains:

• A comprehensive review of AP Calculus AB and BC.

• A set of practice problems.

• A set of cumulative review problems beginning with Chapter 5.

• A rapid review summarizing the highlights of the chapter.

Step 5: Build Your Test-taking Confidence

In this step you will complete your preparation by testing yourself on practice exams. We have provided you with two complete exams in AP Calculus AB and two complete exams in AP Calculus BC, and scoring guides for both of them. Although these practice exams are not reproduced questions from the actual AP calculus exams, they mirror both the material tested by AP and the way in which it is tested.

Finally, at the back of this book you will find additional resources to aid your preparation. These include:

• A brief bibliography.

• A list of websites related to the AP Calculus exam.

• A summary of formulas and theorems related to the AP Calculus exams.

Introduction to the Graphics Used in this Book

To emphasize particular skills and strategies, we use several icons throughout this book. An icon in the margin will alert you that you should pay particular attention to the accompanying text. We use these icons:

This icon points out a very important concept or fact that you should not pass over.

This icon calls your attention to a strategy that you may want to try.

This icon indicates a tip that you might find useful.

This icon identifies material covered only in the BC exam.