Princeton Review AP Calculus BC Prep, 2023: 5 Practice Tests + Complete Content Review + Strategies & Techniques
Make sure you’re studying with the most up-to-date prep materials! Look for the newest edition of this title, The Princeton Review AP Calculus BC Prep, 10th Edition (ISBN: 9780593516751, on-sale August 2023).

Publisher's Note: Products purchased from third-party sellers are not guaranteed by the publisher for quality or authenticity, and may not include access to online tests or materials included with the original product.
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Princeton Review AP Calculus BC Prep, 2023: 5 Practice Tests + Complete Content Review + Strategies & Techniques
Make sure you’re studying with the most up-to-date prep materials! Look for the newest edition of this title, The Princeton Review AP Calculus BC Prep, 10th Edition (ISBN: 9780593516751, on-sale August 2023).

Publisher's Note: Products purchased from third-party sellers are not guaranteed by the publisher for quality or authenticity, and may not include access to online tests or materials included with the original product.
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Princeton Review AP Calculus BC Prep, 2023: 5 Practice Tests + Complete Content Review + Strategies & Techniques

Princeton Review AP Calculus BC Prep, 2023: 5 Practice Tests + Complete Content Review + Strategies & Techniques

by The Princeton Review, David Khan
Princeton Review AP Calculus BC Prep, 2023: 5 Practice Tests + Complete Content Review + Strategies & Techniques

Princeton Review AP Calculus BC Prep, 2023: 5 Practice Tests + Complete Content Review + Strategies & Techniques

by The Princeton Review, David Khan

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Overview

Make sure you’re studying with the most up-to-date prep materials! Look for the newest edition of this title, The Princeton Review AP Calculus BC Prep, 10th Edition (ISBN: 9780593516751, on-sale August 2023).

Publisher's Note: Products purchased from third-party sellers are not guaranteed by the publisher for quality or authenticity, and may not include access to online tests or materials included with the original product.

Product Details

ISBN-13: 9780593450697
Publisher: Random House Children's Books
Publication date: 08/02/2022
Series: College Test Preparation: AP
Pages: 768
Product dimensions: 8.30(w) x 10.80(h) x 1.40(d)

About the Author

The experts at The Princeton Review have been helping students, parents, and educators achieve the best results at every stage of the education process since 1981. The Princeton Review has helped millions succeed on standardized tests, and provides expert advice and instruction to help parents, teachers, students, and schools navigate the complexities of school admission. In addition to classroom courses in over 40 states and 20 countries, The Princeton Review also offers online and school-based courses, one-to-one and small-group tutoring as well as online services in both admission counseling and academic homework help.

Table of Contents

Get More (Free) Content x

Part I Using This Book to Improve Your AP Score 1

Preview: Your Knowledge, Your Expectations 2

Your Guide to Using This Book 2

How to Begin 3

Part II Practice Test 1 7

Practice Test 1 9

Practice Test 1: Diagnostic Answer Key and Explanations 39

How to Score Practice Test 1 65

Part III About the AP Calculus BC Exam 67

AB Calculus vs. BC Calculus 68

Structure of the AP Calculus BC Exam 68

How the AP Calculus BC Exam is Scored 69

Past AP Calculus BC Score Distributions 69

Overview of Content Topics 70

General Overview of This Book 73

How AP Exams Are Used 74

Other Resources 75

Designing Your Study Plan 75

Part IV Test-Taking Strategies for the AP Calculus BC Exam 77

1 How to Approach Multiple-Choice Questions 79

2 How to Approach Free-Response Questions 83

Part V Content Review for the AP Calculus BC Exam 87

3 Limits and Continuity 89

Introducing Calculus: Can Change Occur at an Instant? 90

Defining Limits and Using Limit Notation 90

Estimating Limit Values from Graphs 92

Estimating Limit Values from Tables 93

Determining Limits Using Algebraic Properties of Limits 94

Determining Limits Using Algebraic Manipulation 95

Selecting Procedures for Determining Limits 97

Determining Limits Using the Squeeze Theorem 101

Connecting Multiple Representations of Limits 103

Exploring Types of Discontinuities 105

Defining Continuity at a Point 109

Confirming Continuity over an Interval 111

Removing Discontinuities 112

Connecting Infinite Limits and Vertical Asymptotes 113

Connecting Limits at infinity and Horizontal Asymptotes 115

Working with the Intermediate Value Theorem (IVT) 116

End of Chapter 3 Drill 119

4 Differentiation: Definition and Basic Derivative Rules 121

Defining Average and Instantaneous Rates of Change at a Point 122

Defining the Derivative of a Function and Using Derivative Notation 123

Estimating Derivatives of a Function at a Point 129

Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 132

Applying the Power Rule 133

Derivative Rules: Constant, Sum, Difference, and Constant Multiple 134

Derivatives of cos x, sin x, ex, and In x 136

The Product Rule 143

The Quotient Rule 144

Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions 145

End of Chapter 4 Drill 148

5 Differentiation: Composite, Implicit, and Inverse Functions 149

The Chain Rule 150

Implicit Differentiation 154

Differentiating Inverse Functions 160

Differentiating Inverse Trigonometric Functions 164

Selecting Procedures for Calculating Derivatives 166

Calculating Higher-Order Derivatives 168

End of Chapter 5 Drill 171

6 Contextual Applications of Differentiation 173

Interpreting the Meaning of the Derivative in Context 174

Straight-Line Motion: Connecting Position, Velocity, and Acceleration 174

Rates of Change in Applied Contexts Other Than Motion 180

Introduction to Related Rates 180

Solving Related Rates Problems 181

Approximating Values of a Function Using Local Linearity and Linearization 187

Using L'Hospital's Rule for Determining Limits of Indeterminate Forms 197

End of Chapter 6 Drill 202

7 Analytical Applications of Differentiation 203

Using the Mean Value Theorem 204

Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 209

Determining Intervals on Which a Function Is Increasing or Decreasing 210

Using the First Derivative Test to Determine Relative (Local) Extrema 212

Using the Candidates Test to Determine Absolute (Global) Extrema 214

Determining Concavity of Functions over Their Domains 216

Using the Second Derivative Test to Determine Extrema 219

Sketching Graphs of Function and Their Derivatives 222

Connecting a Function, Its First Derivative, and Its Second Derivative 237

Introduction to Optimization Problems 243

Solving Optimization Problems 244

Exploring Behaviors of Implicit Relations 254

End of Chapter 7 Drill 255

8 Integration and Accumulation of Change 257

Exploring Accumulations of Change 258

Approximating Areas with Riemann Sums 259

Riemann Sums, Summation Notation, and Definite Integral Notation 272

The Fundamental Theorem of Calculus and Accumulation Functions 273

Interpreting the Behavior of Accumulation Functions Involving Area 275

Applying Properties of Definite Integrals 279

The Fundamental Theorem of Calculus and Definite Integrals 280

Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 281

Integrating Using Substitution 290

Integrating Functions Using Long Division and Completing the Square 313

Integration Using Integration by Parts 317

Using Linear Partial Fractions 323

Evaluating Improper Integrals 326

Selecting Techniques for Antidifferentiation 330

End of Chapter 8 Drill 332

9 Differential Equations 335

Modeling Situations with Differential Equations 336

Verifying Solutions for Differential Equations 336

Sketching Slope Fields 337

Reasoning Using Slope Fields 341

Approximating Solutions Using Euler's Method 343

Finding General Solutions Using Separation of Variables 349

Finding Particular Solutions Using Initial Conditions and Separation of Variables 350

Exponential Models with Differential Equations 354

Logistic Models with Differential Equations 356

End of Chapter 9 Drill 360

10 Applications of Integration 361

Finding the Average Value of a Function on an Interval 362

Connecting Position, Velocity, and Acceleration Functions Using Integrals 364

Using Accumulation Functions and Definite Integrals in Applied Contexts 365

Finding the Area Between Curves Expressed as Functions of x 366

Finding the Area Between Curves Expressed as Functions of y 368

Finding the Area Between Curves That Intersect at More Than Two Points 371

Volumes with Cross-Sections: Squares and Rectangles 372

Volumes with Cross-Sections: Triangles and Semicircles 374

Volume with Disc Method: Revolving Around the x- or y-Axis 375

Volume with Disc Method: Revolving Around Other Axes 378

Volume with Washer Method: Revolving Around the x- or y-Axis 379

Volume with Washer Method: Revolving Around Other Axes 382

The Arc Length of a Smooth, Planar Curve and Distance Traveled 385

End of Chapter 10 Drill 388

11 Parametric Equations, Polar Coordinates, and Vector-Valued Functions 391

Defining and Differentiating Parametric Equations 392

Second Derivatives of Parametric Equations 394

Finding Arc Lengths of Curves Given by Parametric Equations 395

Defining and Differentiating Vector-Valued Functions 397

Integrating Vector-Valued Functions 398

Solving Motion Problems Using Parametric and Vector-Valued Functions 400

Defining Polar Coordinates and Differentiating in Polar Form 402

Finding the Area of a Polar Region or the Area Bounded by a Single Polar Curve 403

Finding the Area of the Region Bounded by Two Polar Curves 405

End of Chapter 11 Drill 407

12 Infinite Sequences and Series 409

Defining Convergent and Divergent Infinite Series 410

Working with Geometric Series 413

The nth Term Test for Divergence 415

Integral Test for Convergence 416

Harmonic Series and p-Series 417

Comparison Tests for Convergence 419

Alternating Series Test for Convergence 422

Ratio Test for Convergence 423

Determining Absolute or Conditional Convergence 424

Alternating Series Error Bound 425

Finding Taylor Polynomial Approximations of Functions 426

Lagrange Error Bound 428

Radius and Interval of Convergence of Power Series 429

Finding Taylor or Maclaurin Series for a Function 430

Representing Functions as Power Series 432

End of Chapter 12 Drill 437

13 Answers to Practice Problem Sets 439

14 Answers to End of Chapter Drills 601

Part VI Practice Tests 2 and 3 635

15 Practice Test 2 637

16 Practice Test 2: Answers and Explanations 667

How to Score Practice Test 2 691

17 Practice Test 3 693

18 Practice Test 3: Answers and Explanations 725

How to Score Practice Test 3 743

About the Author 745

Practice Test 4 online

Practice Test 4: Answers and Explanations online

Practice Test 5 online

Practice Test 5: Answers and Explanations online

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