5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 24, 2018 14:

1 What You Need to Know About the AP Calculus AB Exam STEP 1 Set Up Your Study Plan
- 1.1 What Is Covered on the AP Calculus AB Exam?
- 1.2 What Is the Format of the AP Calculus AB Exam?
- 1.3 What Are the Advanced Placement Exam Grades?
  - How Is the AP Calculus AB Exam Grade Calculated?
- 1.4 Which Graphing Calculators Are Allowed for the Exam?
  - Calculators and Other Devices Not Allowed for the AP Calculus AB Exam
  - Other Restrictions on Calculators

2 How to Plan Your Time
- 2.1 Three Approaches to Preparing for the AP Calculus AB Exam
  - Overview of the Three Plans
- 2.2 Calendar for Each Plan
  - Summary of the Three Study Plans

3 Take a Diagnostic Exam STEP 2 Determine Your Test Readiness
- 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
  - Short-Answer Questions
  - AP Calculus AB Diagnostic Test

4 How to Approach Each Question Type STEP 3 Develop Strategies for Success
- 4.1 The Multiple-Choice Questions
- 4.2 The Free-Response Questions
- 4.3 Using a Graphing Calculator
- 4.4 Taking the Exam
  - What Do I Need to Bring to the Exam?
  - Tips for Taking the Exam

MA 3972-MA-Book May 24, 2018 14:

5 Review of Precalculus STEP 4 Review the Knowledge You Need to Score High
- 5.1 Lines
  - Slope of a Line
  - Equations of a Line
  - Parallel and Perpendicular Lines
- 5.2 Absolute Values and Inequalities
  - Absolute Values
  - Inequalities and the Real Number Line
  - Solving Absolute Value Inequalities
  - Solving Polynomial Inequalities
  - Solving Rational Inequalities
- 5.3 Functions
  - Definition of a Function
  - Operations on Functions
  - Inverse Functions
  - Trigonometric and Inverse Trigonometric Functions
  - Exponential and Logarithmic Functions
- 5.4 Graphs of Functions
  - Increasing and Decreasing Functions
  - Intercepts and Zeros
  - Odd and Even Functions
  - Shifting, Reflecting, and Stretching Graphs
- 5.5 Rapid Review
- 5.6 Practice Problems
- 5.7 Cumulative Review Problems
- 5.8 Solutions to Practice Problems
- 5.9 Solutions to Cumulative Review Problems

6 Limits and Continuity Big Idea 1: Limits
- 6.1 The Limit of a Function
  - Definition and Properties of Limits
  - Evaluating Limits
  - One-Sided Limits
  - Squeeze Theorem
- 6.2 Limits Involving Infinities
  - Infinite Limits (asx→a)
  - Limits at Infinity (asx→±∞)
  - Horizontal and Vertical Asymptotes
- 6.3 Continuity of a Function
  - Continuity of a Function at a Number

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Continuity of a Function over an Interval Contents v

Theorems on Continuity

6.4 Rapid Review

6.5 Practice Problems

6.6 Cumulative Review Problems

6.7 Solutions to Practice Problems

6.8 Solutions to Cumulative Review Problems

7 Differentiation Big Idea 2: Derivatives
- 7.1 Derivatives of Algebraic Functions
  - Definition of the Derivative of a Function
  - Power Rule
  - The Sum, Difference, Product, and Quotient Rules
  - The Chain Rule
  - Exponential, and Logarithmic Functions 7.2 Derivatives of Trigonometric, Inverse Trigonometric,
  - Derivatives of Trigonometric Functions
  - Derivatives of Inverse Trigonometric Functions
  - Derivatives of Exponential and Logarithmic Functions
- 7.3 Implicit Differentiation
  - Procedure for Implicit Differentiation
- 7.4 Approximating a Derivative
- 7.5 Derivatives of Inverse Functions
- 7.6 Higher Order Derivatives
- 7.7 L’Hôpital’sRule for Indeterminate Forms
- 7.8 Rapid Review

8 Graphs of Functions and Derivatives
- 8.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem
  - Rolle's Theorem
  - Mean Value Theorem
  - Extreme Value Theorem
- 8.2 Determining the Behavior of Functions
  - Test for Increasing and Decreasing Functions
  - First Derivative Test and Second Derivative Test for Relative Extrema
  - Test for Concavity and Points of Inflection
- 8.3 Sketching the Graphs of Functions
  - Graphing without Calculators
  - Graphing with Calculators

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8.4 Graphs of Derivatives vi Contents

8.5 Rapid Review

9 Applications of Derivatives
- 9.1 Related Rate
  - General Procedure for Solving Related Rate Problems
  - Common Related Rate Problems
  - Inverted Cone (Water Tank) Problem
  - Shadow Problem
  - Angle of Elevation Problem
- 9.2 Applied Maximum and Minimum Problems
  - and Minimum Problems General Procedure for Solving Applied Maximum
  - Distance Problem
  - Area and Volume Problems
  - Business Problems
- 9.3 Rapid Review

10 More Applications of Derivatives

10.1 Tangent and Normal Lines
- Tangent Lines
- Normal Lines

10.2 Linear Approximations
- Tangent Line Approximation (or Linear Approximation)
- Estimating thenth Root of a Number
- Estimating the Value of a Trigonometric Function of an Angle

10.3 Motion Along a Line
- Instantaneous Velocity and Acceleration
- Vertical Motion
- Horizontal Motion

10.4 Rapid Review

MA 3972-MA-Book May 24, 2018 14:

11 Integration Big Idea 3: Integrals and the Fundamental Theorems of Calculus

11.1 Evaluating Basic Integrals
- Antiderivatives and Integration Formulas
- Evaluating Integrals

11.2 Integration by U-Substitution
- The U-Substitution Method
- U-Substitution and Algebraic Functions
- U-Substitution and Trigonometric Functions
- U-Substitution and Inverse Trigonometric Functions
- U-Substitution and Logarithmic and Exponential Functions

11.3 Rapid Review

12 Definite Integrals

12.1 Riemann Sums and Definite Integrals
- Sigma Notation or Summation Notation
- Definition of a Riemann Sum
- Definition of a Definite Integral
- Properties of Definite Integrals

12.2 Fundamental Theorems of Calculus
- First Fundamental Theorem of Calculus
- Second Fundamental Theorem of Calculus

12.3 Evaluating Definite Integrals
- Definite Integrals Involving Algebraic Functions
- Definite Integrals Involving Absolute Value
- and Exponential Functions Definite Integrals Involving Trigonometric, Logarithmic,
- Definite Integrals Involving Odd and Even Functions

12.4 Rapid Review

13 Areas and Volumes

af(t)dt ∫x

13.2 Approximating the Area Under a Curve
- Rectangular Approximations
- Trapezoidal Approximations

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13.3 Area and Definite Integrals viii Contents
- Area Under a Curve
- Area Between Two Curves

13.4 Volumes and Definite Integrals
- Solids with Known Cross Sections
- The Disc Method
- The Washer Method

13.5 Rapid Review

14 More Applications of Definite Integrals

14.1 Average Value of a Function
- Mean Value Theorem for Integrals
- Average Value of a Function on [a, b]

14.2 Distance Traveled Problems

14.3 Definite Integral as Accumulated Change
- Business Problems
- Temperature Problem
- Leakage Problem
- Growth Problem

14.4 Differential Equations
- Exponential Growth/Decay Problems
- Separable Differential Equations

14.5 Slope Fields

14.6 Rapid Review

- AP Calculus AB Practice Exam STEP 5 Build Your Test-Taking Confidence
- AP Calculus AB Practice Exam
- Appendix
- Bibliography
- Websites

5 Steps to a 5 AP Calculus AB 2019 - William Ma

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