Synopses & Reviews
All Access for the AP® Calculus AB & BC ExamsBook + 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 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.
Synopsis
Are You Serious About Scoring a 5 on Your Advanced Placement* exam?Then Get REAs Test Prep for the AP* Calculus AB & BC Exams with TestWare CD
REAs Calculus AB & BC test prep gives you everything you need to score a 5 on the AP* exam!
This second edition of our popular Advanced Placement* test prep is completely up-to-date and aligned with the official AP* Calculus AB & BC exams. The book contains a thorough review of all the areas covered on the AP* exams, including Limits & Continuity, Derivatives, Integrals, Sequences & Series, and Vector Valued Functions. Each review chapter is packed with equations, formulas, and examples with solutions, so you can study smarter and score a 5!
The book contains eight practice tests — five practice tests for Calculus AB and three practice tests for Calculus BC. The practice tests are composed of every type of question that can be expected on the actual AP* Calculus AB & BC exams, so you can “practice for real” and target your strengths and weaknesses before the test. Three of the practice tests (two for AB and one for BC) are included on CD in a timed format with automatic, instant scoring and detailed explanations of answers.
Our interactive TestWare CD features on-screen answers, diagnostic feedback, plus an extended time function for students with disabilities. Book comes complete with a handy study schedule for each exam, plus confidence-boosting test-taking strategies.
If youre serious about getting a 5 on your exam, then you need REAs test prep for AP* Calculus AB & BC!
REA has helped more than a million students succeed on their AP* exams! Teachers across the country consider our AP* titles to be invaluable resources and consistently recommend our books to their students.
Synopsis
ARE YOU SERIOUS ABOUT GETTING A 5 ON THE AP* CALCULUS AB & BC EXAMS?Get fully prepared with the AP* Calculus AB & BC test prep AP* teachers recommend. The Most Complete AP* Calculus AB & BC Subject Review:
Everything you need to know for the Advanced Placement* Calculus AB & BC exams, selected and presented by a seasoned high school teacher with extensive AP* Calculus AB & BC experience. The Best AP* Calculus AB & BC Practice Exams Available:
8 full-length AP* Calculus practice tests (5 tests for AP* Calculus AB and 3 tests for AP* Calculus BC) based on official AP* Calculus AB & BC exam questions released by the College Board - balanced to include every AP* Calculus AB & BC topic and type of AP* question you can expect on the Calculus AB & BC exams. Total Explanations of AP* Calculus AB & BC Exam Questions & Answers:
Each AP* Calculus AB & BC practice test comes with detailed feedback on every question. We dont just say which answers are right - but why the others are wrong, so youll be prepared for the AP* Calculus AB & BC exams! Proven Test Prep Methods:
REAs focused AP* Calculus AB & BC content and practical advice has helped millions of AP* students score higher. With our step-by-step plan, you can earn a 5 on the AP* Calculus AB & BC exams and get the credit you deserve! Recommended by AP* Calculus AB & BC Teachers:
For years, AP* Calculus AB & BC teachers have relied on REA for effective, authoritative Advanced Placement* study guides. Our authors include nationally known AP* experts who have personally coached generations of successful Advanced Placement* students. In our AP* Calculus AB & BC test prep, weve drawn on the insights of an experienced high school mathematics teacher to create one powerful volume. Get the Worlds Most Advanced AP* Calculus AB & BC Software:
REAs TestWare combines a realistic AP* test environment with the most powerful scoring analysis and diagnostic tools available. With every AP* Calculus AB & BC practice test you take, youll gain knowledge and confidence for the real AP* exam. Automatic scoring and instant reports help you zero in on the topics and types of AP* Calculus AB & BC questions that give you trouble now, so youll succeed on the AP* Calculus AB & BC exams! (CD includes 3 practice exams - 2 for AP* Calculus AB, and 1 for AP Calculus BC.)
Synopsis
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.
About the Author
Stu Schwartz taught in the Wissahickon School District, in Ambler, Pennsylvania for 35 years, specializing in AP® Calculus AB and BC and AP® Statistics. He currently teaches statistics at Chestnut Hill College in Philadelphia. Mr. Schwartz received his B.S. degree in Mathematics from Temple University, Philadelphia. He 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.
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.
Table of Contents
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