Cracking the AP Calculus AB Exam, 2018 Edition
Book Preface
YOUR GUIDE TO USING THIS BOOK
This book is organized to provide as much—or as little—support as you need, so you can use this book in whatever way will be most helpful for improving your score on the AP Calculus AB Exam.
• The remainder of Part I will provide guidance on how to use this book and help you determine your strengths and weaknesses.
• Part II of this book contains Practice Test 1, and its answers and explanations. (Bubble sheets can be downloaded as PDFs here.) We strongly recommend that you take this test before going any further, in order to realistically determine
your starting point right now
which question types you’re ready for and which you might need to practice
which content topics you are familiar with and which you will want to carefully review
Once you have nailed down your strengths and weaknesses with regard to this exam, you can focus your test preparation, build a study plan, and be efficient with your time.
• Part III of this book will
provide information about the structure, scoring, and content of the AP Calculus AB Exam.
help you to make a study plan.
point you towards additional resources.
• Part IV of this book will explore the following strategies:
how to attack multiple-choice questions
how to write a high scoring free-response answer
how to manage your time to maximize the number of points available to you
• Part V of this book covers the content you need for your exam.
• Parts VI and VII of this book contain four additional Practice Tests, their answers and explanations, and an Appendix containing formulas you should know. If you skipped Practice Test 1, we recommend that you do all five (with at least a day or two between them) so that you can compare your progress between them. Additionally, this will help to identify any external issues: if you get a certain type of question wrong both times, you probably need to review it. If you only got it wrong once, you may have run out of time or been distracted by something. In either case, this will allow you to focus on the factors that caused the discrepancy and to be as prepared as possible on the day of the test.
You may choose to use some parts of this book over others, or you may work through the entire book. This will depend on your needs and how much time you have. Let’s now look at how to make this determination.
Contents
Cover
Title Page
Copyright
Acknowledgments
Register Your Book Online!
Part I: Using This Book to Improve Your AP Score
Preview: Your Knowledge, Your Expectations
Your Guide to Using This Book
How to Begin
Part II: Practice Test 1
Practice Test 1
Practice Test 1: Answers and Explanations
Part III: About the AP Calculus AB Exam
AB Calculus vs. BC Calculus
The Structure of the Calculus Exam
How the AP Calculus AB Exam is Scored
Overview of Content Topics
General Overview of This Book
How AP Exams Are Used
Other Resources
Designing Your Study Plan
Part IV: Test-Taking Strategies for the AP Calculus AB Exam
1 How to Approach Multiple-Choice Questions
2 How to Approach Free-Response Questions
Part V: Content Review for the AP Calculus AB Exam
Unit 1: Differential Calculus Essentials
3 Limits
What is a Limit?
Limits of Trigonometric Functions
Practice Problem Set 1
4 Continuity
The Definition of Continuity
Types of Discontinuities
Practice Problem Set 2
5 The Definition of the Derivative
Deriving the Formula
Differentiability
Practice Problem Set 3
6 Differentiability
Notation
The Power Rule
The Addition Rule
Higher Order Derivatives
Practice Problem Set 4
The Product Rule
The Quotient Rule
The Chain Rule
Practice Problem Set 5
Derivatives of Trig Functions
Graphical Derivatives
Practice Problem Set 6
7 Implicit Differentiation
How to Do It
Second Derivatives
Practice Problem Set 7
Unit 1 Drill
Unit 2: Differential Calculus Applications
8 Basic Applications of the Derivative
Equations of Tangent Lines and Normal Lines
Practice Problem Set 8
The Mean Value Theorem for Derivatives
Rolle’s Theorem
Practice Problem Set 9
9 Maxima and Minima
Applied Maxima and Minima Problems
Practice Problem Set 10
Curve Sketching
Practice Problem Set 11
10 Motion
Related Rates
Practice Problem Set 12
Position, Velocity, and Acceleration
Practice Problem Set 13
11 Exponential and Logarithmic Functions, Part One
The Derivative of ln x
The Derivative of ex
The Derivative of logax
The Derivative of ax
Practice Problem Set 14
12 Other Topics in Differential Calculus
The Derivative of an Inverse Function
Practice Problem Set 15
Differentials
Practice Problem Set 16
L’Hôpital’s Rule
Practice Problem Set 17
Unit 2 Drill
Unit 3: Integral Calculus Essentials
13 The Integral
The Antiderivative
Integrals of Trig Functions
Addition and Subtraction
Practice Problem Set 18
u-Substitution
Practice Problem Set 19
14 Definite Integrals
Area Under a Curve
Tabular Riemann Sums
Practice Problem Set 20
The Mean Value Theorem for Integrals
Practice Problem Set 21
15 Exponential and Logarithmic Functions, Part Two
Inverse Trig Functions
Practice Problem Set 22
More Integrals of Trig Functions
Integrating ex and ax
Practice Problem Set 23
Unit 3 Drill
Unit 4: Integral Calculus Applications
16 The Area Between Two Curves
Vertical Slices
Horizontal Slices
Practice Problem Set 24
17 The Volume of a Solid of Revolution
Washers and Disks
Cylindrical Shells
Volumes of Solids with Known Cross-Sections
Practice Problem Set 25
18 Differential Equations
Separation of Variables
Slope Fields
Practice Problem Set 26
Unit 4 Drill
19 Solutions to Practice Problem Sets and Unit Drills
Part VI: Practice Tests 2 and 3
Practice Test 2
Practice Test 2: Answers and Explanations
Practice Test 3
Practice Test 3: Answers and Explanations
Part VII: Additional Practice Tests
Practice Test 4
Practice Test 4: Answers and Explanations
Practice Test 5
Practice Test 5: Answers and Explanations
Appendix
About the Author
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Epub | September 4, 2018 |
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