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AP Calculus AB

Limits, derivatives and accumulation

AP Calculus AB is about change: how fast a quantity changes at one instant, and how much it changes over a stretch of time. Each lesson asks you to predict before it explains, and every wrong answer says which mistake it comes from. The lessons are being written one unit at a time.

AP Calculus AB Exam Monday, May 10, 2027

Start Lesson 1.1 Introducing Calculus: Can Change Occur at an Instant?

Units

Eight units, numbered as College Board numbers them. Each unit's share of the multiple-choice section is printed beside it, as College Board publishes it. Topics that belong only to AP Calculus BC are not part of this course, so a few topic numbers are skipped.

  1. Unit 1 Limits and Continuity 10–15% of the multiple-choice section · 16 topics
    1. 1.1Introducing Calculus: Can Change Occur at an Instant?
    2. 1.2Defining Limits and Using Limit Notation
    3. 1.3Estimating Limit Values from Graphs
    4. 1.4Estimating Limit Values from Tables
    5. 1.5Determining Limits Using Algebraic Properties of Limits
    6. 1.6Determining Limits Using Algebraic Manipulation
    7. 1.7Selecting Procedures for Determining Limits
    8. 1.8Determining Limits Using the Squeeze Theorem
    9. 1.9Connecting Multiple Representations of Limits
    10. 1.10Exploring Types of Discontinuities
    11. 1.11Defining Continuity at a Point
    12. 1.12Confirming Continuity over an Interval
    13. 1.13Removing Discontinuities
    14. 1.14Connecting Infinite Limits and Vertical Asymptotes
    15. 1.15Connecting Limits at Infinity and Horizontal Asymptotes
    16. 1.16Working with the Intermediate Value Theorem (IVT)

    Unit 1 overviewUnit 1 check

  2. Unit 2 Differentiation: Definition and Fundamental Properties 10–15% of the multiple-choice section · 10 topics
    1. 2.1Defining Average and Instantaneous Rates of Change at a Point
    2. 2.2Defining the Derivative of a Function and Using Derivative Notation
    3. 2.3Estimating Derivatives of a Function at a Point
    4. 2.4Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
    5. 2.5Applying the Power Rule
    6. 2.6Derivative Rules: Constant, Sum, Difference, and Constant Multiple
    7. 2.7Derivatives of cos x, sin x, eˣ, and ln x
    8. 2.8The Product Rule
    9. 2.9The Quotient Rule
    10. 2.10Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

    Unit 2 overviewUnit 2 check

  3. Unit 3 Differentiation: Composite, Implicit, and Inverse Functions 5–10% of the multiple-choice section · 6 topics
    1. 3.1The Chain Rule
    2. 3.2Implicit Differentiation
    3. 3.3Differentiating Inverse Functions
    4. 3.4Differentiating Inverse Trigonometric Functions
    5. 3.5Selecting Procedures for Calculating Derivatives
    6. 3.6Calculating Higher-Order Derivatives

    Unit 3 overviewUnit 3 check

  4. Unit 4 Contextual Applications of Differentiation 10–15% of the multiple-choice section · 7 topics
    1. 4.1Interpreting the Meaning of the Derivative in Context
    2. 4.2Straight-Line Motion: Connecting Position, Velocity, and Acceleration
    3. 4.3Rates of Change in Applied Contexts Other Than Motion
    4. 4.4Introduction to Related Rates
    5. 4.5Solving Related Rates Problems
    6. 4.6Approximating Values of a Function Using Local Linearity and Linearization
    7. 4.7Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

    Unit 4 overviewUnit 4 check

  5. Unit 5 Analytical Applications of Differentiation 15–20% of the multiple-choice section · 12 topics
    1. 5.1Using the Mean Value Theorem
    2. 5.2Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
    3. 5.3Determining Intervals on Which a Function Is Increasing or Decreasing
    4. 5.4Using the First Derivative Test to Determine Relative (Local) Extrema
    5. 5.5Using the Candidates Test to Determine Absolute (Global) Extrema
    6. 5.6Determining Concavity of Functions over Their Domains
    7. 5.7Using the Second Derivative Test to Determine Extrema
    8. 5.8Sketching Graphs of Functions and Their Derivatives
    9. 5.9Connecting a Function, Its First Derivative, and Its Second Derivative
    10. 5.10Introduction to Optimization Problems
    11. 5.11Solving Optimization Problems
    12. 5.12Exploring Behaviors of Implicit Relations

    Unit 5 overviewUnit 5 check

  6. Unit 6 Integration and Accumulation of Change 15–20% of the multiple-choice section · 11 topics
    1. 6.1Exploring Accumulations of Change
    2. 6.2Approximating Areas with Riemann Sums
    3. 6.3Riemann Sums, Summation Notation, and Definite Integral Notation
    4. 6.4The Fundamental Theorem of Calculus and Accumulation Functions
    5. 6.5Interpreting the Behavior of Accumulation Functions Involving Area
    6. 6.6Applying Properties of Definite Integrals
    7. 6.7The Fundamental Theorem of Calculus and Definite Integrals
    8. 6.8Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
    9. 6.9Integrating Using Substitution
    10. 6.10Integrating Functions Using Long Division and Completing the Square
    11. 6.14Selecting Techniques for Antidifferentiation

    Unit 6 overviewUnit 6 check

  7. Unit 7 Differential Equations 5–10% of the multiple-choice section · 7 topics
    1. 7.1Modeling Situations with Differential Equations
    2. 7.2Verifying Solutions for Differential Equations
    3. 7.3Sketching Slope Fields
    4. 7.4Reasoning Using Slope Fields
    5. 7.6Finding General Solutions Using Separation of Variables
    6. 7.7Finding Particular Solutions Using Initial Conditions and Separation of Variables
    7. 7.8Exponential Models with Differential Equations

    Unit 7 overviewUnit 7 check

  8. Unit 8 Applications of Integration 10–15% of the multiple-choice section · 12 topics
    1. 8.1Finding the Average Value of a Function on an Interval
    2. 8.2Connecting Position, Velocity, and Acceleration of Functions Using Integrals
    3. 8.3Using Accumulation Functions and Definite Integrals in Applied Contexts
    4. 8.4Finding the Area Between Curves Expressed as Functions of x
    5. 8.5Finding the Area Between Curves Expressed as Functions of y
    6. 8.6Finding the Area Between Curves That Intersect at More Than Two Points
    7. 8.7Volumes with Cross Sections: Squares and Rectangles
    8. 8.8Volumes with Cross Sections: Triangles and Semicircles
    9. 8.9Volume with Disc Method: Revolving Around the x- or y-Axis
    10. 8.10Volume with Disc Method: Revolving Around Other Axes
    11. 8.11Volume with Washer Method: Revolving Around the x- or y-Axis
    12. 8.12Volume with Washer Method: Revolving Around Other Axes

    Unit 8 overviewUnit 8 check

Labs

Labs for this course are being built.

The exam

The exam is hybrid digital: you answer the multiple-choice questions in the Bluebook app and handwrite your free-response answers in a paper booklet. Each section has a part where a graphing calculator is required and a part where no calculator is allowed.

Exam format and practice