AP Math Revision › AP Calculus BC
AP Calculus BC: unit and topic map
BC is the whole AB course plus a set of BC-only topics in Units 6 to 8 and two more units: parametric, polar and vector-valued functions (Unit 9) and infinite series (Unit 10). The topic numbers are the ones in College Board's Course and Exam Description (CED), so you can check the map against it; the topic names are our own wording.
For Units 1 to 8, the shared material is on the AB pages. The BC pages below hold the BC-only topics, each with notes, worked examples, common traps and at least 8 original practice questions (multiple choice, and free response with scoring guides).
224 BC questions in all. The Questions column counts the questions tagged with each topic (a free-response question counts for every topic its parts test).
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
Unit 1: Limits and continuity
16 topics shared with AB: AB Unit 1 notes and practice.
No BC-only topics in this unit.
Unit 2: Differentiation: definition and basic rules
10 topics shared with AB: AB Unit 2 notes and practice.
No BC-only topics in this unit.
Unit 3: Differentiation: composite, implicit and inverse functions
6 topics shared with AB: AB Unit 3 notes and practice.
No BC-only topics in this unit.
Unit 4: Derivatives in context
7 topics shared with AB: AB Unit 4 notes and practice.
No BC-only topics in this unit.
Unit 5: Analyzing functions with derivatives
12 topics shared with AB: AB Unit 5 notes and practice.
No BC-only topics in this unit.
Unit 6: Integration and accumulation of change
11 topics shared with AB: AB Unit 6 notes and practice.
BC page: 24 questions (22 multiple choice, 2 free response) · notes, worked examples and common traps
| CED topic | BC topic (our wording) | Questions |
|---|---|---|
| 6.11 | Integration by parts | 10 |
| 6.12 | Linear partial fractions | 9 |
| 6.13 | Improper integrals | 11 |
Unit 7: Differential equations
7 topics shared with AB: AB Unit 7 notes and practice.
BC page: 17 questions (15 multiple choice, 2 free response) · notes, worked examples and common traps
| CED topic | BC topic (our wording) | Questions |
|---|---|---|
| 7.5 | Euler's method | 9 |
| 7.9 | Logistic models | 9 |
Unit 8: Applications of integration
12 topics shared with AB: AB Unit 8 notes and practice.
BC page: 9 questions (8 multiple choice, 1 free response) · notes, worked examples and common traps
| CED topic | BC topic (our wording) | Questions |
|---|---|---|
| 8.13 | Arc length and distance traveled | 9 |
Unit 9: Parametric equations, polar coordinates and vector-valued functions
BC page: 66 questions (63 multiple choice, 3 free response) · notes, worked examples and common traps
| CED topic | BC topic (our wording) | Questions |
|---|---|---|
| 9.1 | Parametric curves and dy/dx | 9 |
| 9.2 | Second derivative of a parametric curve | 8 |
| 9.3 | Arc length of a parametric curve | 10 |
| 9.4 | Vector-valued functions and their derivatives | 8 |
| 9.5 | Integrating vector-valued functions | 10 |
| 9.6 | Motion in the plane | 10 |
| 9.7 | Polar coordinates and polar derivatives | 8 |
| 9.8 | Area inside one polar curve | 8 |
| 9.9 | Area between two polar curves | 8 |
Unit 10: Infinite sequences and series
BC page: 108 questions (105 multiple choice, 3 free response) · notes, worked examples and common traps
| CED topic | BC topic (our wording) | Questions |
|---|---|---|
| 10.1 | Convergent and divergent series | 8 |
| 10.2 | Geometric series | 10 |
| 10.3 | The nth-term test | 8 |
| 10.4 | The integral test | 8 |
| 10.5 | Harmonic series and p-series | 8 |
| 10.6 | Comparison tests | 8 |
| 10.7 | Alternating series test | 9 |
| 10.8 | Ratio test | 8 |
| 10.9 | Absolute and conditional convergence | 8 |
| 10.10 | Alternating series error bound | 8 |
| 10.11 | Taylor polynomials | 8 |
| 10.12 | Lagrange error bound | 8 |
| 10.13 | Radius and interval of convergence | 9 |
| 10.14 | Taylor and Maclaurin series | 10 |
| 10.15 | Power series of new functions | 9 |