AP® Calculus AB & BC All Access Book + Online

AP® Calculus AB & BC All Access Book + Online

by Stu Schwartz

Paperback(Second Edition, Revised)

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Product Details

ISBN-13: 9780738612201
Publisher: Research & Education Association
Publication date: 01/13/2017
Series: Advanced Placement (AP) All Access
Edition description: Second Edition, Revised
Pages: 432
Sales rank: 515,466
Product dimensions: 8.40(w) x 10.50(h) x 1.20(d)
Age Range: 16 - 17 Years

About the Author

Stu Schwartz has been teaching mathematics since 1973. For 35 years he taught in the Wissahickon School District, in Ambler, Pennsylvania, specializing in AP® Calculus AB and BC. He has also taught at Chestnut Hill College in Philadelphia and Broward College in Fort Lauderdale. Mr. Schwartz received his B.S. degree in Mathematics from Temple University, Philadelphia.

Mr. Schwartz 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. Mr. Schwartz is always looking for ways to provide teachers with new and innovative teaching materials, believing that it should be the goal of every math teacher not only to teach students mathematics, but also to find joy and beauty in math as well.

Mr. Schwartz was a 2002 recipient of the Presidential Award for Excellence in Mathematics Teaching and also won the 2007 Outstanding Educator of the Year Award for the Wissahickon School District. He lives with his cat, Newton, in Pompano Beach, Florida. He loves to bike and swim.

Read an Excerpt

Welcome to REA’s All Access for AP Calculus AB & BC

A new, more effective way to prepare for your AP exam

There are many different ways to prepare for an AP 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 prep by testing your understanding, pinpointing your weaknesses, and delivering flashcard study materials unique to you.

Let’s get started and see how this system works.

How to Use REA’s AP All Access

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 Chapter 3 to be certain that you are strong on the essential Precalculus topics for AP Calculus. Then, study the topics tested on the AP exam and learn proven strategies that will help you tackle any question you may see on test day. This approach will maximize your score.

Test Yourself & Get Feedback: As you review the book, test yourself. 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 e-flashcards, adding to the 100 free cards (60 for Calculus AB; 40 for Calculus BC) included with this book.

Finding Your Strengths and Weaknesses: The REA Study Center

The best way to personalize your study plan and truly focus on the topics where you need the most help 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: end-of-chapter quizzes, mini-tests, and full-length practice tests. Each of these tools delivers a detailed score report that follows the topics set by the College Board.

9 End-of-Chapter Quizzes: Short online quizzes are available throughout the review and are designed to test your immediate grasp of the topics just covered.

3 Mini-Tests:Two online mini-tests for Calculus AB students and one online mini-test for Calculus BC students cover what you’ve studied in each major section of the book. These tests are like the actual AP exam, only shorter, and will help you evaluate your overall understanding of the subject material.

2 Full-Length Practice Tests: After you’ve finished reviewing the book, take our full-length exam for Calculus AB or BC (or both) to practice under test-day conditions. Available both in this book and online at the REA Study Center (www.rea.com/studycenter), these practice tests give you the most complete picture of your strengths and weaknesses. We strongly recommend that you take the online version of the exam for the added benefits of timed testing, automatic scoring, and a detailed score report.

Improving Your Score: e-Flashcards
With your score reports from our online quizzes and practice tests in hand, you’ll be able to see exactly which 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 online 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 (60 for Calculus AB; 40 for Calculus BC) included when you buy this book.

Need More Review?
Pick up a copy of REA’s Crash Course® for AP Calculus AB & BC, the fastest way to raise your score during the last few weeks before the exam. Use your All Access® score reports to focus on the topics where you still need extra review.

Table of Contents

About Our Author
About REA

Chapter 1: Welcome to REA’s 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
What’s 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
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

AP Calculus AB

Chapter 4: Basic Calculus Concepts and Limits
Graphical Approach to Limits
Algebraic Approach to Limits

Quiz 2

Chapter 5: Derivatives
Average and Instantaneous Rates 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

Quiz 3

Chapter 6: Applications of Differentiation
Related Rates
Procedure for Solving Related-Rates Problems
Straight-Line Motion
3 Important Theorems
The Intermediate Value Theorem
The Mean-Value Theorem and Rolle’s Theorem
Function Analysis
Relative (or Local) Extrema
Absolute Extrema
Procedure for Solving an Optimization Problem
L’Hospital’s Rule

Quiz 4

Mini-Test 1

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

Chapter 8: Applications of Integration
Area Between Curves
Average Value of a Function
Accumulated Change Problems
Straight-Line Motion Revisited
Solving Differential Equations
Growth and Decay

Quiz 6

Mini-Test 2

AP Calculus BC

Chapter 9: Additional Limit and Integration Problems
L’Hospital’s Rule Revisited
Integration by Parts
Integration Using Partial Fractions
Improper Integrals

Quiz 7

Chapter 10: Additional BC Calculus Applications
Euler’s Method
Logistic Growth
Arc Length
Parametric Functions
Vector-Valued Functions
Polar Equations

Quiz 8

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

Mini-Test 3

AP Calculus AB Practice Exam
Answer Key
Calculus AB Practice Exam Topic-Level Grid
Detailed Explanations of Answers

AP Calculus BC Practice Exam
Answer Key
Calculus BC Practice Exam Topic-Level Grid
Detailed Explanations of Answers

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