AP Calculus AB/BC All Access (Advanced Placement (AP) All Access)

Book + Web + Mobile

Everything you need to prepare for the Advanced Placement* exam, in a study system built around you!

There are many different ways to prepare for an Advanced Placement* exam. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.

This book, and the free online tools that come with it, will help you personalize your AP* Calculus AB & BC prep by testing your understanding, pinpointing your weaknesses, and delivering flashcard study materials unique to you.

The REA AP* All Access system allows you to create a personalized study plan through three simple steps: targeted review of exam content, assessment of your knowledge, and focused study in the topics where you need the most help.

Here's how it works:

Review the Book:

Study the topics tested on the AP* Calculus AB & BC exams and learn proven AP* strategies that will help you tackle any question you may see on test day.

Test Yourself and Get Feedback:

As you review the book, test yourself with 9 end-of-chapter quizzes, plus 2 mini-tests (1 for each exam). Score reports from your free online tests and quizzes give you a fast way to pinpoint what you really know and what you should spend more time studying.

Improve Your Score:

Armed with your score reports, you can personalize your study plan. Review the parts of the book where you are weakest, and use the REA Study Center to create your own unique AP* Calculus AB & BC e-flashcards, adding to the 100 free cards included with this book.

Visit The REA Study Center for a suite of online tools:

The best way to personalize your study plan and truly focus on your weaknesses is to get frequent feedback on what you know and what you don't. At the online REA Study Center, you can access three types of assessment: topic-level quizzes, mini-tests, and 2 full-length practice tests (1 for AP* Calculus AB and 1 for AP* Calculus BC). Each of these tools provides true-to-format questions and delivers a detailed score report that follows the topics set by the College Board.

Topic-Level Quizzes

Short, 15-minute online quizzes are available throughout the review and are designed to test your immediate grasp of the topics just covered.

Mini-Tests

Two online mini-tests cover what you've studied for AP* Calculus AB & BC. These tests are like the actual AP* exams, only shorter, and will help you evaluate your overall understanding of the subject.

2 Full-Length Practice Tests

After you've finished reviewing the book, take 2 full-length practice tests (1 for AP* Calculus AB and 1 for AP* Calculus BC) to practice under test-day conditions. Available both in the book and online, these tests give you the most complete picture of your strengths and weaknesses. We strongly recommend that you take the online versions of the exams for the added benefits of timed testing, automatic scoring, and a detailed score report.

Improving Your Score: e-Flashcards

With your score reports from the quizzes and tests, you'll be able to see exactly which AP* Calculus AB & BC topics you need to review. Use this information to create your own flashcards for the areas where you are weak. And, because you will create these flashcards through the REA Study Center, you'll be able to access them from any computer or smartphone. Not quite sure what to put on your flashcards? Start with the 100 free cards included when you buy this book.

This complete AP* test prep package comes with a customized study schedule and expert test-taking strategies and tips.

AP* Calculus AB/BC All Access™

Anytime, Anywhere Access to AP Prep

Make the most of your time with a new kind of study system built around you.

You need a high score on the AP Calculus AB/BC exam to get the college credit or placement youre counting on. We know prepping efficiently is important to you. So were here to help you stay flexible and focused with REAs All Access study system.

AP Calculus AB/BC All Access offers you seamless access to targeted Advanced Placement Calculus AB/BC assessment with e-flashcards, quizzes, and practice tests—just pick up wherever you leave off from whatever device youre on! Whether youre on your computer, smartphone, or other mobile device, All Access is there for you.

3 Study Tools Working Together to Help You Succeed

Book: Targeted review of the AP Calculus AB/BC material youll be expected to know on exam day, plus proven tips and strategies for answering every question type.

Web: Diagnostic tools at the online REA Study Center help you pinpoint your strengths and weaknesses, so you know exactly where to focus your study.

Mobile: Customizable e-flashcards mean personalized prep—practice where you need it most.

Outside the classroom, Mr. Schwartz does consulting work with the Math and Science Partnership of Greater Philadelphia, focusing on factors affecting success in college in STEM (science, technology, engineering, math) degrees. He is well-known in the AP community, having developed the website www.mastermathmentor.com, which is geared toward helping educators teach AP Calculus, AP Statistics, and other math courses.

About Our Author

About Research & Education Association

Acknowledgments

Chapter 1: Welcome to REAs All Access for AP Calculus AB/BC

Chapter 2: Strategies for the Exams

Content of the AP Calculus AB & BC Exams

Format of the Exams

Whats the Score?

The Focus of Our Review Chapters

General Strategies for the AP Calculus Exams

Section I: Strategies for the Multiple-Choice Section

Section II: Strategies for the Free-Response Section

Calculators

Using the Calculator

Chapter 3: A Precalculus Review

1. Functions

2. Domain and Range

3. The Function Toolbox

4. Even and Odd Functions

5. Transformation of Graphs

6. Special Factorization

7. Linear Equations

8. Solving Quadratic Equations

9. Asymptotes

10. Inverses

11. Negative and Fractional Exponents

12. Eliminating Complex Fractions

13. Solving Fractional Equations

14. Solving Absolute Value Equations

15. Solving Inequalities

16. Exponential Functions and Logs

17. Right Angle Trigonometry

18. Special Angles

19. Trigonometric Identities

20. Solving Trigonometric Equations or Inequalities

Quiz 1....................................................available online at www.rea.com/studycenter

AP Calculus AB

Chapter 4: Basic Calculus Concepts and Limits

Introduction

Graphical Approach to Limits

Algebraic Approach to Limits

Continuity

Quiz 2....................................................available online at www.rea.com/studycenter

Chapter 5: Derivatives

Average and Instantaneous Rate of Change

The Derivative

Derivatives of Algebraic Functions

The Chain Rule

Tangent Line Approximations

Derivatives of Trigonometric Functions

Derivatives of Exponential, Logarithmic, and Inverse Trig Functions

Implicit Differentiation

Derivatives of Inverse Functions

Horizontal and Vertical Tangent Lines

Differentiability

Quiz 3....................................................available online at www.rea.com/studycenter

Chapter 6: Applications of Differentiation

Related Rates

Procedure for Solving Related Rates Problems

Straight-Line Motion

The Intermediate Value Theorem

The Mean-Value Theorem and Rolles Theorem

Function Analysis

Increasing/Decreasing

Concavity

Relative (or Local) Extrema

Absolute Extrema

Optimization

Procedure for Solving an Optimization Problem

Quiz 4....................................................available online at www.rea.com/studycenter

Mini-Test 1............................................available online at www.rea.com/studycenter

Chapter 7: Integration

Antidifferentiation and Indefinite Integrals

Area and the Definite Integral

The Accumulation Function

Riemann Sums and the Trapezoidal Rule

The Fundamental Theorem of Calculus

The Second Fundamental Theorem of Calculus

Quiz 5....................................................available online at www.rea.com/studycenter

Chapter 8: Applications of Integration

Area Between Curves

Average Value of a Function

Accumulated Change Problems

Straight-Line Motion Revisited

Volume

Solving Differential Equations

Growth and Decay

Quiz 6....................................................available online at www.rea.com/studycenter

Mini-Test 2............................................available online at www.rea.com/studycenter

Chapter 9: Additional Limit and Integration Problems

LHospitals Rule

Integration by Parts

Integration Using Partial Fractions

Improper Integrals

Quiz 7....................................................available online at www.rea.com/studycenter

Chapter 10: Additional BC Calculus Applications

Eulers Method

Logistic Growth

Arc Length

Parametric Functions

Vector-Valued Functions

Polar Equations

Quiz 8....................................................available online at www.rea.com/studycenter

Chapter 11: Sequences and Series

Basic Series and Convergence Tests

Power Series and Interval of Convergence

Taylor Polynomial Approximations

Error Bounds

Taylor and Maclaurin Series

Functions Defined as Power Series

Quiz 9....................................................available online at www.rea.com/studycenter

Mini-Test 3............................................available online at www.rea.com/studycenter

AP Calculus AB Practice Exam (also available online at www.rea.com/studycenter )

Answer Key

Detailed Explanations of Answers

AP Calculus BC Practice Exam (also available online at www.rea.com/studycenter )

Answer Key

Detailed Explanations of Answers

Answer Sheets

Index