AP Math Revision › AP Calculus AB
AP Calculus AB: unit and topic map
The eight units of the course, with the topic numbers used in College Board's Course and Exam Description (CED) so the map can be checked against it. Topic names are our own wording. Each unit page has notes, worked examples, common traps and at least 8 original practice questions for every AB topic (multiple choice and free response with scoring guides).
573 questions in all. The Questions column counts the questions tagged with each topic (a free-response question counts for every topic its parts test). BC-only topics are listed for reference and are not part of AB.
Full practice exams
Full-length practice exams in the May 2027 exam format, made from these questions, each with its scoring guide. Practice exam 1 is free with a free account; Pro opens every one. See the practice exams
Not sure you're ready? Take the 12-question Ready for AP? check, or brush up in High school math.
Unit 1: Limits and Continuity
117 questions (113 multiple choice, 4 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 1.1 | Why calculus: change at an instant | 9 |
| 1.2 | Limit notation and meaning | 9 |
| 1.3 | Limits from graphs | 13 |
| 1.4 | Limits from tables | 10 |
| 1.5 | Limit laws | 11 |
| 1.6 | Limits by algebra | 10 |
| 1.7 | Choosing a limit method | 11 |
| 1.8 | Squeeze theorem | 8 |
| 1.9 | Limits across representations | 9 |
| 1.10 | Types of discontinuity | 10 |
| 1.11 | Continuity at a point | 12 |
| 1.12 | Continuity on an interval | 10 |
| 1.13 | Removing a discontinuity | 10 |
| 1.14 | Infinite limits and vertical asymptotes | 11 |
| 1.15 | Limits at infinity and horizontal asymptotes | 8 |
| 1.16 | Intermediate Value Theorem | 9 |
Unit 2: Differentiation: Definition and Basic Rules
72 questions (69 multiple choice, 3 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 2.1 | Average and instantaneous rate of change | 9 |
| 2.2 | The derivative and its notation | 11 |
| 2.3 | Estimating a derivative | 9 |
| 2.4 | Differentiability and continuity | 10 |
| 2.5 | Power rule | 8 |
| 2.6 | Constant, sum and constant-multiple rules | 9 |
| 2.7 | Derivatives of sin, cos, eˣ and ln x | 12 |
| 2.8 | Product rule | 9 |
| 2.9 | Quotient rule | 8 |
| 2.10 | Derivatives of tan, cot, sec and csc | 8 |
Unit 3: Differentiation: Composite, Implicit and Inverse Functions
44 questions (40 multiple choice, 4 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 3.1 | Chain rule | 11 |
| 3.2 | Implicit differentiation | 11 |
| 3.3 | Derivative of an inverse function | 9 |
| 3.4 | Derivatives of inverse trig functions | 9 |
| 3.5 | Choosing a differentiation method | 11 |
| 3.6 | Higher-order derivatives | 9 |
Unit 4: Contextual Applications of Differentiation
46 questions (42 multiple choice, 4 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 4.1 | Interpreting a derivative in context | 9 |
| 4.2 | Straight-line motion | 9 |
| 4.3 | Rates of change in other contexts | 8 |
| 4.4 | Related rates: setting up | 8 |
| 4.5 | Related rates: solving | 9 |
| 4.6 | Local linearity and linearization | 8 |
| 4.7 | L'Hospital's rule | 8 |
Unit 5: Analytical Applications of Differentiation
83 questions (78 multiple choice, 5 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 5.1 | Mean Value Theorem | 8 |
| 5.2 | Extreme Value Theorem and critical points | 9 |
| 5.3 | Increasing and decreasing intervals | 9 |
| 5.4 | First derivative test | 11 |
| 5.5 | Absolute extrema on a closed interval | 11 |
| 5.6 | Concavity | 13 |
| 5.7 | Second derivative test | 10 |
| 5.8 | Sketching f, f′ and f″ | 9 |
| 5.9 | Linking f, f′ and f″ | 11 |
| 5.10 | Optimization: setting up | 8 |
| 5.11 | Optimization: solving and justifying | 8 |
| 5.12 | Implicit relations: behavior | 8 |
Unit 6: Integration and Accumulation of Change
80 questions (76 multiple choice, 4 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 6.1 | Accumulation of change | 9 |
| 6.2 | Riemann sums | 9 |
| 6.3 | Summation and definite integral notation | 9 |
| 6.4 | FTC and accumulation functions | 8 |
| 6.5 | Behavior of accumulation functions | 8 |
| 6.6 | Properties of definite integrals | 10 |
| 6.7 | FTC and evaluating definite integrals | 8 |
| 6.8 | Antiderivatives and basic rules | 8 |
| 6.9 | Integration by substitution | 8 |
| 6.10 | Long division and completing the square | 8 |
| 6.11 | Integration by parts (BC only) | – |
| 6.12 | Linear partial fractions (BC only) | – |
| 6.13 | Improper integrals (BC only) | – |
| 6.14 | Choosing an integration method | 8 |
Unit 7: Differential Equations
47 questions (43 multiple choice, 4 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 7.1 | Modeling with differential equations | 8 |
| 7.2 | Checking a solution | 8 |
| 7.3 | Sketching slope fields | 9 |
| 7.4 | Reasoning with slope fields | 8 |
| 7.5 | Euler's method (BC only) | – |
| 7.6 | Separation of variables: general solution | 9 |
| 7.7 | Separation of variables: particular solution | 10 |
| 7.8 | Exponential growth and decay models | 8 |
| 7.9 | Logistic models (BC only) | – |
Unit 8: Applications of Integration
84 questions (78 multiple choice, 6 free response) · notes, worked examples and common traps
| CED topic | Topic (our wording) | Questions |
|---|---|---|
| 8.1 | Average value of a function | 8 |
| 8.2 | Motion with integrals | 8 |
| 8.3 | Accumulation in applied contexts | 8 |
| 8.4 | Area between curves (in x) | 8 |
| 8.5 | Area between curves (in y) | 8 |
| 8.6 | Curves crossing more than twice | 8 |
| 8.7 | Cross sections: squares and rectangles | 8 |
| 8.8 | Cross sections: triangles and semicircles | 8 |
| 8.9 | Disc method about an axis | 8 |
| 8.10 | Disc method about other lines | 8 |
| 8.11 | Washer method about an axis | 8 |
| 8.12 | Washer method about other lines | 9 |
| 8.13 | Arc length and distance traveled (BC only) | – |