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Ma, William. 5 Steps to a 5 AP Calculus AB&BC 2012-2013 4/E. McGraw-Hill, 2011.

5 Steps to a 5 AP Calculus AB&BC 2012-2013 4/E

Authors: William Ma

Published:  June 2011

eISBN: 9780071751735 0071751734 | ISBN: 9780071751728
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  • Contents
  • About the Authors
  • Preface
  • Introduction: The Five-Step Program
  • Step 1 Set Up Your Study Plan
  • 1 What You Need to Know About the AP Calculus AB/BC Exams
  • 1.1 What Is Covered on the AP Calculus Exams?
  • 1.2 What Is the Format of the AP Calculus AP/BC Exams?
  • 1.3 What Are the Advanced Placement Exam Grades?
  • 1.4 Which Graphing Calculators Are Allowed for the Exam?
  • 2 How to Plan Your Time
  • 2.1 Three Approaches to Preparing for the AP Calculus Exam
  • 2.2 Calendar for Each Plan
  • Step 2 Determine Your Test Readiness
  • 3 Take a Diagnostic Exam
  • 3.1 Getting Started!
  • 3.2 Diagnostic Test
  • 3.3 Answers to Diagnostic Test
  • 3.4 Solutions to Diagnostic Test
  • 3.5 Calculate Your Score
  • Step 3 Develop Strategies for Success
  • 4 How to Approach Each Question Type
  • 4.1 The Multiple-Choice Questions
  • 4.2 The Free-Response Questions
  • 4.3 Using a Graphing Calculator
  • 4.4 Taking the Exam
  • Step 4 Review the Knowledge You Need to Score High
  • 5 Limits and Continuity
  • 5.1 The Limit of a Function
  • 5.2 Limits Involving Infinities
  • 5.3 Continuity of a Function
  • 5.4 Rapid Review
  • 5.5 Practice Problems
  • 5.6 Cumulative Review Problems
  • 5.7 Solutions to Practice Problems
  • 5.8 Solutions to Cumulative Review Problems
  • 6 Differentiation
  • 6.1 Derivatives of Algebraic Functions
  • 6.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions
  • 6.3 Implicit Differentiation
  • 6.4 Approximating a Derivative
  • 6.5 Derivatives of Inverse Functions
  • 6.6 Higher Order Derivatives
  • 6.7 Indeterminate Forms
  • 6.8 Rapid Review
  • 6.9 Practice Problems
  • 6.10 Cumulative Review Problems
  • 6.11 Solutions to Practice Problems
  • 6.12 Solutions to Cumulative Review Problems
  • 7 Graphs of Functions and Derivatives
  • 7.1 Rolle’s Theorem, Mean Value Theorem, and Extreme Value Theorem
  • 7.2 Determining the Behavior of Functions
  • 7.3 Sketching the Graphs of Functions
  • 7.4 Graphs of Derivatives
  • 7.5 Parametric, Polar, and Vector Representations
  • 7.6 Rapid Review
  • 7.7 Practice Problems
  • 7.8 Cumulative Review Problems
  • 7.9 Solutions to Practice Problems
  • 7.10 Solutions to Cumulative Review Problems
  • 8 Applications of Derivatives
  • 8.1 Related Rate
  • 8.2 Applied Maximum and Minimum Problems
  • 8.3 Rapid Review
  • 8.4 Practice Problems
  • 8.5 Cumulative Review Problems
  • 8.6 Solutions to Practice Problems
  • 8.7 Solutions to Cumulative Review Problems
  • 9 More Applications of Derivatives
  • 9.1 Tangent and Normal Lines
  • 9.2 Linear Approximations
  • 9.3 Motion Along a Line
  • 9.4 Parametric, Polar, and Vector Derivatives
  • 9.5 Rapid Review
  • 9.6 Practice Problems
  • 9.7 Cumulative Review Problems
  • 9.8 Solutions to Practice Problems
  • 9.9 Solutions to Cumulative Review Problems
  • 10 Integration
  • 10.1 Evaluating Basic Integrals
  • 10.2 Integration by U-Substitution
  • 10.3 Techniques of Integration
  • 10.4 Rapid Review
  • 10.5 Practice Problems
  • 10.6 Cumulative Review Problems
  • 10.7 Solutions to Practice Problems
  • 10.8 Solutions to Cumulative Review Problems
  • 11 Definite Integrals
  • 11.1 Riemann Sums and Definite Integrals
  • 11.2 Fundamental Theorems of Calculus
  • 11.3 Evaluating Definite Integrals
  • 11.4 Improper Integrals
  • 11.5 Rapid Review
  • 11.6 Practice Problems
  • 11.7 Cumulative Review Problems
  • 11.8 Solutions to Practice Problems
  • 11.9 Solutions to Cumulative Review Problems
  • 12 Areas and Volumes
  • 12.1 The Function F(x) = ∫[sup(x)][sub(a)]f(t)dt
  • 12.2 Approximating the Area Under a Curve
  • 12.3 Area and Definite Integrals
  • 12.4 Volumes and Definite Integrals
  • 12.5 Integration of Parametric, Polar, and Vector Curves
  • 12.6 Rapid Review
  • 12.7 Practice Problems
  • 12.8 Cumulative Review Problems
  • 12.9 Solutions to Practice Problems
  • 12.10 Solutions to Cumulative Review Problems
  • 13 More Applications of Definite Integrals
  • 13.1 Average Value of a Function
  • 13.2 Distance Traveled Problems
  • 13.3 Definite Integral as Accumulated Change
  • 13.4 Differential Equations
  • 13.5 Slope Fields
  • 13.6 Logistic Differential Equations
  • 13.7 Euler’s Method
  • 13.8 Rapid Review
  • 13.9 Practice Problems
  • 13.10 Cumulative Review Problems
  • 13.11 Solutions to Practice Problems
  • 13.12 Solutions to Cumulative Review Problems
  • 14 Series (For Calculus BC Students Only)
  • 14.1 Sequences and Series
  • 14.2 Types of Series
  • 14.3 Convergence Tests
  • 14.4 Alternating Series
  • 14.5 Power Series
  • 14.6 Taylor Series
  • 14.7 Operations on Series
  • 14.8 Rapid Review
  • 14.9 Practice Problems
  • 14.10 Cumulative Review Problems
  • 14.11 Solutions to Practice Problems
  • 14.12 Solutions to Cumulative Review Problems
  • Step 5 Build Your Test-Taking Confidence
  • AP Calculus AB Practice Exam 1
  • AP Calculus AB Practice Exam 2
  • AP Calculus BC Practice Exam 1
  • AP Calculus BC Practice Exam 2
  • Appendixes
  • Formulas and Theorems
  • Bibliography and Web Sites