Table of Contents

Part 1 The Basics
 Chapter 1 Inside the AP Calculus AB Exam
 Chapter 2 Strategies for Success
 Chapter 3 Calculator Basics

Part 2 Fundamental Concepts

Big Idea 1 Limits

Chapter 4 Basic Limits
 4.1 Evaluating Limits Graphically
 4.2 Evaluating Limits Algebraically
 4.3 Limits of Composite Functions
 4.4 Limits That Don’t Exist

Chapter 5 More Advanced Limits
 5.1 Infinite Limits
 5.2 Limits at Infinity
 5.3 Horizontal and Vertical Asymptotes
 5.4 Limits Involving Trig Functions
 5.5 L’Hopital’s Rule

Chapter 6 Continuity
 6.1 Continuity and Limits
 6.2 Types of Discontinuities
 6.3 Piecewise Functions
 6.4 The Intermediate Value, Extreme Value, and Mean Value Theorems

Chapter 4 Basic Limits

Big Idea 2 Derivatives

Chapter 7 Derivatives—The Basics
 7.1 The Limit Definition of the Derivative
 7.2 Estimating Derivatives from Graphs and Tables
 7.3 The Power Rule
 7.4 The Product and Quotient Rules
 7.5 The Chain Rule
 7.6 Derivatives of Logarithmic and Exponential Functions

Chapter 8 More Advanced Derivatives
 8.1 Derivatives of Trig Functions
 8.2 Derivatives of Inverse Trig Functions
 8.3 Higher Order Derivatives
 8.4 Implicit Differentiation
 8.5 Derivatives of Inverse Functions

Chapter 9 Applications of the Derivative
 9.1 The Slope of a Curve at a Point
 9.2 Tangent Lines and Normal Lines
 9.3 Local Linear Approximations
 9.4 Derivatives as Rates of Change
 9.5 First Derivatives and Curve Sketching
 9.6 Second Derivatives and Curve Sketching

Chapter 10 More Advanced Applications
 10.1 The Relationship between Differentiability and Continuity
 10.2 Using the Graphs of 𝑓, 𝑓′ and 𝑓′′
 10.3 Optimization
 10.4 Rectilinear Motion
 10.5 Related Rates

Chapter 7 Derivatives—The Basics

Big Idea 3 Integrals and the Fundamental Theorem of Calculus

Chapter 11 Integration—The Basics
 11.1 Antiderivatives and the Indefinite Integral
 11.2 Antiderivatives Subject to an Initial Condition
 11.3 USubstitution and Algebraic Functions
 11.4 Trig Functions
 11.5 Exponential and Logarithmic Functions

Chapter 12 The Definite Integral
 12.1 The Fundamental Theorems of Calculus
 12.2 Reimann Sums and Definite Integrals
 12.3 Properties of Definite Integrals
 12.4 USubstitution and Definite Integrals
 12.5 Equivalent Forms of Definite Integrals

Chapter 13 Geometric Applications of Integration
 13.1 Area Under a Curve
 13.2 Area between or Bounded by Curves
 13.3 Volumes of Solids with Known Cross Sections
 13.4 Volume of Solids of Revolution

Chapter 14 Further Applications of Integration
 14.1 Average Value of a Function
 14.2 Net Change over an Interval
 14.3 Motion along a Line
 14.4 Differential Equations
 14.5 Exponential Growth and Decay
 14.6 Slope Fields

Chapter 11 Integration—The Basics

Big Idea 1 Limits

Part 3 Graphing Calculators and Free Response Questions

Chapter 15 Problems That Require Graphing Calculators
 15.1 Graphing Functions and Finding Critical Points
 15.2 Finding a Derivative at a Point
 15.3 Evaluating a Definite Integral
 Chapter 16 Answering Free Response Questions

Chapter 15 Problems That Require Graphing Calculators

Part 4 Calculus BC Topics

Chapter 17 Parametric, Polar, and Vector Functions
 17.1 Define and Graph Parametric Functions
 17.2 Differentiate and Integrate Parametric Functions
 17.3 Define and Graph Polar Functions
 17.4 Differentiate and Integrate Polar Functions
 17.5 Define and Graph Vector Functions
 17.6 Differentiate and Integrate Vector Functions

Chapter 18 Additional Techniques of Differentiation and
Integration
 18.1 Solve Differential Equations via Euler’s Method
 18.2 Apply Integration by Parts to Integrands with Two Functions
 18.3 Evaluate Fractional Integrands Using Simple Partial Fractions
 18.4 Perform Antidifferentiation of Improper Integrals
 18.5 Solve Logistic Differential Equations and Use Them in Modeling

Chapter 19 Series
 19.1 Evaluate the Limits of Series Using Partial Sums
 19.2 Define Convergence in a Series and Identify Geometric and Harmonic Series
 19.3 Apply the Integral Test and Determine Convergence in 𝑝Series
 19.4 Determine Convergence with the Comparison Test and the Ratio Test
 19.5 Evaluate Alternating Series for Convergence and Estimate Their Limit

Chapter 20 Power Series
 20.1 Find the Radius and Interval of Convergence of Functions Defined by Power Series
 20.2 Use Taylor Polynomial Expansion to Approximate Nonpolynomial Functions
 20.3 Apply the Maclaurin Series of Special Functions to More Complex Functions
 20.4 Find the Lagrange Error Bound for Taylor Polynomials

Chapter 17 Parametric, Polar, and Vector Functions
 Part 5 Practice Exams