Table of Contents

Step 1 Set up Your Study Plan
 1 What You Need to Know about the AP Calculus AB Exam
 2 How to Plan Your Time

Step 2 Determine Your Test Readiness
 3 Take a Diagnostic Exam

Step 3 Develop Strategies for Success
 4 How to Approach Each Question Type

Step 4 Review the Knowledge You Need to Score High

5 Review of Precalculus

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

5.1 Lines

Big Idea 1: Limits

6 Limits and Continuity

6.1 The Limit of a Function
 Definition and Properties of Limits
 Evaluating Limits
 OneSided Limits
 Squeeze Theorem

6.2 Limits Involving Infinities
 Infinite Limits (as 𝑥 → 𝑎)
 Limits at Infinity (as 𝑥 → ±∞)
 Horizontal and Vertical Asymptotes

6.3 Continuity of a Function
 Continuity of a Function at a Number
 Continuity of a Function over an Interval
 Theorems on Continuity

6.1 The Limit of a Function

6 Limits and Continuity

Big Idea 2: Derivatives

7 Differentiation

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

7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential,
and Logarithmic Functions
 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’s Rule for Indeterminate Forms

7.1 Derivatives of Algebraic Functions

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
 8.4 Graphs of Derivatives

8.1 Rolle’s Theorem, Mean Value Theorem, and Extreme Value Theorem

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
 General Procedure for Solving Applied Maximum and Minimum Problems
 Distance Problem
 Area and Volume Problems
 Business Problems

9.1 Related Rate
 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 the 𝑛th 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

7 Differentiation

Big Idea 3: Integrals and the Fundamental Theorems of Calculus

11 Integration

11.1 Evaluating Basic Integrals
 Antiderivatives and Integration Formulas
 Evaluating Integrals

11.2 Integration by USubstitution
 The USubstitution Method
 USubstitution and Algebraic Functions
 USubstitution and Trigonometric Functions
 USubstitution and Inverse Trigonometric Functions
 USubstitution and Logarithmic and Exponential Functions

11.1 Evaluating Basic Integrals

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
 Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions
 Definite Integrals Involving Odd and Even Functions

12.1 Riemann Sums and Definite Integrals

13 Areas and Volumes
 13.1 The Function 𝐹(𝑥) = ∫_𝑎^𝑥 𝑓(𝑡)d𝑡

13.2 Approximating the Area Under a Curve
 Rectangular Approximations
 Trapezoidal Approximations

13.3 Area and Definite Integrals
 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

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

14.1 Average Value of a Function

11 Integration

5 Review of Precalculus