AP Calculus AB

Complete Course Modules & Topic Breakdown
📊 Exam Overview ⚡ Download Formulas
Unit 1: Limits and Continuity
  • 1.1 Introducing Calculus: Can Change Occur at an Instant?
  • 1.2 Defining Limits and Using Limit Notation
  • 1.3 Estimating Limit Values from Graphs
  • 1.4 Estimating Limit Values from Tables
  • 1.5 Determining Limits Using Algebraic Properties of Limits
  • 1.6 Determining Limits Using Algebraic Manipulation
  • 1.7 Selecting Procedures for Determining Limits
  • 1.8 Determining Limits Using the Squeeze Theorem
  • 1.9 Connecting Multiple Representations of Limits
  • 1.10 Exploring Types of Discontinuities
  • 1.11 Defining Continuity at a Point
  • 1.12 Confirming Continuity over an Interval
  • 1.13 Removing Discontinuities
  • 1.14 Connecting Infinite Limits and Vertical Asymptotes
  • 1.15 Connecting Limits at Infinity and Horizontal Asymptotes
  • 1.16 Working with the Intermediate Value Theorem (IVT)
📝 Practice Unit 1
Unit 2: Differentiation: Definition and Fundamental Properties
  • 2.1 Defining Average and Instantaneous Rates of Change at a Point
  • 2.2 Defining the Derivative of a Function and Using Derivative Notation
  • 2.3 Estimating Derivatives of a Function at a Point
  • 2.4 Connecting Differentiability and Continuity
  • 2.5 Applying the Power Rule
  • 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
  • 2.7 Derivatives of cos x, sin x, e^x, and ln x
  • 2.8 The Product Rule
  • 2.9 The Quotient Rule
  • 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
📝 Practice Unit 2
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
  • 3.1 The Chain Rule
  • 3.2 Implicit Differentiation
  • 3.3 Differentiating Inverse Functions
  • 3.4 Differentiating Inverse Trigonometric Functions
  • 3.5 Selecting Procedures for Calculating Derivatives
  • 3.6 Calculating Higher-Order Derivatives
📝 Practice Unit 3
Unit 4: Contextual Applications of Differentiation
  • 4.1 Interpreting the Meaning of the Derivative in Context
  • 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
  • 4.3 Rates of Change in Applied Contexts Other Than Motion
  • 4.4 Introduction to Related Rates
  • 4.5 Solving Related Rates Problems
  • 4.6 Approximating Values of a Function Using Local Linearity and Linearization
  • 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
📝 Practice Unit 4
Unit 5: Analytical Applications of Differentiation
  • 5.1 Using the Mean Value Theorem
  • 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
  • 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
  • 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
  • 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
  • 5.6 Determining Concavity of Functions over Their Domains
  • 5.7 Using the Second Derivative Test to Determine Extrema
  • 5.8 Sketching Graphs of Functions and Their Derivatives
  • 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
  • 5.10 Introduction to Optimization Problems
  • 5.11 Solving Optimization Problems
  • 5.12 Exploring Behaviors of Implicit Relations
📝 Practice Unit 5
Unit 6: Integration and Accumulation of Change
  • 6.1 Exploring Accumulations of Change
  • 6.2 Approximating Areas with Riemann Sums
  • 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
  • 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
  • 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
  • 6.6 Applying Properties of Definite Integrals
  • 6.7 The Fundamental Theorem of Calculus and Definite Integrals
  • 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
  • 6.9 Integrating Using Substitution
  • 6.10 Integrating Functions Using Long Division and Completing the Square
  • 6.14 Selecting Techniques for Antidifferentiation
📝 Practice Unit 6
Unit 7: Differential Equations
  • 7.1 Modeling Situations with Differential Equations
  • 7.2 Verifying Solutions for Differential Equations
  • 7.3 Sketching Slope Fields
  • 7.4 Reasoning Using Slope Fields
  • 7.6 Finding General Solutions Using Separation of Variables
  • 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
  • 7.8 Exponential Models with Differential Equations
📝 Practice Unit 7
Unit 8: Applications of Integration
  • 8.1 Finding the Average Value of a Function on an Interval
  • 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
  • 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
  • 8.4 Finding the Area Between Curves Expressed as Functions of x
  • 8.5 Finding the Area Between Curves Expressed as Functions of y
  • 8.6 Finding the Area Between Curves That Intersect at More Than Two Points
  • 8.7 Volumes with Cross Sections: Squares and Rectangles
  • 8.8 Volumes with Cross Sections: Triangles and Semicircles
  • 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
  • 8.10 Volume with Disc Method: Revolving Around Other Axes
  • 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
  • 8.12 Volume with Washer Method: Revolving Around Other Axes
📝 Practice Unit 8