Cracking the AP Calculus BC Exam, 2020 Edition: Practice Tests & Proven Techniques to Help You Score a 5
Genres: Mathematics
Book Preface
Using This Book to Improve Your AP Score
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Preview: Your Knowledge, Your Expectations
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Your Guide to Using This Book
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How to Begin
PREVIEW: YOUR KNOWLEDGE, YOUR EXPECTATIONS
Your route to a high score on the AP Calculus BC Exam depends a lot on how you plan to use this book. Start thinking about your plan by responding to the following questions.
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Rate your level of confidence about your knowledge of the content tested by the AP Calculus BC Exam:
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Very confident—I know it all
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I’m pretty confident, but there are topics for which I could use help
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Not confident—I need quite a bit of support
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I’m not sure
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If you have a goal score in mind, choose your goal score for the AP Calculus BC Exam:
54321
I’m not sure yet
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What do you expect to learn from this book? Choose all that apply to you.
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A general overview of the test and what to expect
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Strategies for how to approach the test
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The content tested by this exam
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I’m not sure yet
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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 BC Exam.
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The remainder of Part I will provide guidance on how to use this book and help you determine your strengths and weaknesses.
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Part II of this book contains Practice Test 1, its answers and explanations, and a scoring guide. (Bubble sheets can be found online when you register your book—see this page for details.) We strongly recommend that you take this test before going any further, in order to realistically determine:
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your starting point right now
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which question types you’re ready for and which you might need to practice
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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.
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Part III of this book will:
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provide information about the structure, scoring, and content of the AP Calculus BC Exam
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help you to make a study plan
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point you towards additional resources
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Part IV of this book will explore the following strategies:
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how to attack multiple-choice questions
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how to write a high scoring free-response answer
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how to manage your time to maximize the number of points available to you
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Part V of this book covers the content you need for your exam.
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Part VI of this book contains Practice Tests 2 and 3, their answers and explanations, and a scoring guide. If you skipped Practice Test 1, we recommend that you use it, in conjunction with Tests 2 and 3 (with at least a day or two between them) to chart your progress and identify lingering issues: if you get a certain type of question wrong every time, 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 in scores 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.
HOW TO BEGIN
1. Take a Test
Before you can decide how to use this book, you need to take a practice test. Doing so will give you insight into your strengths and weaknesses, and the test will also help you make an effective study plan. If you’re feeling test-phobic, remind yourself that a practice test is a tool for diagnosing yourself—it’s not how well you do that matters but how you use information gleaned from your performance to guide your preparation.
So, before you read further, take the AP Calculus BC Practice Test 1 starting on this page. Be sure to do so in one sitting, following the instructions that appear before the test.
2. Check Your Answers
Using the answer key on this page, count how many multiple-choice questions you got right and how many you missed. Don’t worry about the explanations for now, and don’t worry about why you missed questions. We’ll get to that soon.
3. Reflect on the Test
After you take your first test, respond to the following questions:
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How much time did you spend on the multiple-choice questions?
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How much time did you spend on each free-response question?
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How many multiple-choice questions did you miss?
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Do you feel you had the knowledge to address the subject matter of the free-response questions?
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Do you feel your free responses were well organized and thoughtful?
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Circle the content areas that were most challenging for you and draw a line through the ones in which you felt confident/did well.
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Functions, Graphs, and Limits
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Differential Calculus
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Integral Calculus
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Polynomial Approximations and Series
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Applications of Derivatives
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Applications of Integrals
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4. Read Part III, and Complete the Self-Evaluation
Part III will provide information on how the test is structured and scored. It will also set out areas of content that are tested.
As you read Part III, reevaluate your answers to the questions above. At the end of Part III, you will revisit and refine the questions you answer above. You will then be able to make a study plan, based on your needs and time available, that will allow you to use this book most effectively.
5. Engage with Parts IV and V as Needed
Notice the word engage. You’ll get more out of this book if you use it intentionally than if you read it passively, hoping for an improved score through osmosis.
Strategy chapters will help you think about your approach to the question types on this exam. Part IV will open with a reminder to think about how you approach questions now and then close with a reflection section asking you to think about how/whether you will change your approach in the future.
The content chapters in Part V are designed to provide a review of the content tested on the AP Calculus BC Exam, including the level of detail you need to know and how the content is tested. You will have the opportunity to assess your mastery of the content of each chapter through test-appropriate questions and a reflection section.
6. Take Test 2 and Assess Your Performance
Once you feel you have developed the strategies you need and gained the knowledge you lacked, you should take Test 2. You should do so in one sitting, following the instructions at the beginning of the test.
When you are done, check your answers to the multiple-choice sections. See if a teacher will read your long-form calculus responses and provide feedback.
Once you have taken the test, reflect on what areas you still need to work on, and revisit the chapters in this book that address those topics. Through this type of reflection and engagement, you will continue to improve.
7. Keep Working
After you have revisited certain chapters in this book, continue the process of testing, reflecting, and engaging with Practice Test 3. You want to be increasing your readiness by carefully considering the types of questions you are getting wrong and how you can change your strategic approach to different parts of the test.
As discussed in Part III, there are other resources available to you, including a wealth of information on AP Central. You can continue to explore areas that can stand to improve and engage in those areas right up to the day of the test.
Contents
Cover
Title Page
Copyright
Acknowledgments
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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 BC Exam
AB Calculus vs. BC Calculus
Structure of the Exam
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 BC Exam
1 How to Approach Multiple-Choice Questions
2 How to Approach Free-Response Questions
Part V: Content Review for the AP Calculus BC Exam
Unit 1: Differential Calculus Essentials
3 Limits
What is a Limit?
Limits of Trigonometric Functions
Practice Problem Set 1
End of Chapter 3 Drill
4 Continuity
The Definition of Continuity
Types of Discontinuities
Practice Problem Set 2
End of Chapter 4 Drill
5 The Definition of the Derivative
Deriving the Formula
Differentiability
Practice Problem Set 3
End of Chapter 5 Drill
6 Basic Differentiation
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
End of Chapter 6 Drill
7 Implicit Differentiation
How to Do It
Second Derivatives
Practice Problem Set 7
End of Chapter 7 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
End of Chapter 8 Drill
9 Maxima, Minima, and Curve Stretching
Applied Maxima and Minima Problems
Practice Problem Set 10
Curve Sketching
Practice Problem Set 11
End of Chapter 9 Drill
10 Motion
Related Rates
Practice Problem Set 12
Position, Velocity, and Acceleration
Practice Problem Set 13
End of Chapter 10 Drill
11 Derivatives of Exponential and Logarithmic Functions
The Derivative of In x
The Derivative of ex
The Derivative of logax
The Derivative of ax
Practice Problem Set 14
End of Chapter 11 Drill
12 Other Topics in Differential Calculus
The Derivative of an Inverse Function
Practice Problem Set 15
Derivatives of Parametric Functions
Practice Problem Set 16
L’Hôpital’s Rule
Practice Problem Set 17
Linearization
Practice Problem Set 18
Logarithmic Differentiation
Practice Problem Set 19
End of Chapter 12 Drill
Unit 3: Integral Calculus Essentials
13 The Integral
The Antiderivative
Integrals of Trig Functions
Addition and Subtraction
Practice Problem Set 20
u-Substitution
Practice Problem Set 21
End of Chapter 13 Drill
14 Definite Integrals
Area Under a Curve
Tabular Riemann Sums
Practice Problem Set 22
The Mean Value Theorem for Integrals
Practice Problem Set 23
End of Chapter 14 Drill
15 Integrals of Exponential, Logarithmic, and Trig Functions
More Integrals of Trig Functions
Integrating ex and ax
Practice Problem Set 24
End of Chapter 15 Drill
16 Integration by Parts
The Formula
Practice Problem Set 25
End of Chapter 16 Drill
17 Advanced Integrals of Trig Functions
Inverse Trig Functions
Practice Problem Set 26
Advanced Integrals of Trig Functions
Practice Problem Set 27
End of Chapter 17 Drill
Unit 4: Integral Calculus Applications
18 The Area Between Two Curves
Vertical Slices
Horizontal Slices
Practice Problem Set 28
End of Chapter 18 Drill
19 The Volume of a Solid of Revolution
Washers and Disks
Cylindrical Shells
Volumes of Solids with Known Cross-Sections
Practice Problem Set 29
End of Chapter 19 Drill
20 Other Applications of the Integral
Length of a Curve
Parametric Functions
Practice Problem Set 30
The Method of Partial Fractions
Practice Problem Set 31
Improper Integrals
Practice Problem Set 32
Calculus of Polar Curves
Practice Problem Set 33
End of Chapter 20 Drill
21 Differential Equations
Separation of Variables
Euler’s Method
Slope Fields
Practice Problem Set 34
End of Chapter 21 Drill
22 Infinite Series
Sequences and Series
Geometric Series
The Ratio Test
Comparison Test
Limit Comparison Test
Conditional Convergence
Alternating Series
Integral Test
Error Bound
Power Series
Taylor Series and Polynomials
Practice Problem Set 35
End of Chapter 22 Drill
23 Answers to Practice Problem Sets
24 Answers to End of Chapter Drills
Part VI: Practice Tests
25 Practice Test 2
26 Practice Test 2 Answers and Explanations
27 Practice Test 3
28 Practice Test 3 Answers and Explanations
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Read Now | Epub | November 19, 2020 |
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