AP Calculus BC review: a study guide to all 10 units
AP Calculus BC covers everything in AB plus two more units, series and parametric, polar and vector functions, and a few BC-only topics inside the AB units. This review goes through all ten units with their exam weights and gives you a plan for the months before the May 2027 exam.
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The exam you are reviewing for
The AP Calculus BC exam is on Monday 10 May 2027, in the morning session. From 2027 it has 42 multiple-choice questions (29 without a calculator in 62 minutes, then 13 with a calculator in 38 minutes) and 6 free-response questions in 90 minutes. Each section is worth 50%.
Your BC score report also includes an AB subscore, based on the AB content in the exam. In 2025, 43.9% of BC students scored a 5, so for most BC students the question is not passing but reaching a 5.
Exam weight of each unit
| Unit | Exam weight (BC) | BC-only content |
|---|---|---|
| Unit 1: Limits and Continuity | 5 to 10% | No |
| Unit 2: Differentiation: Definition and Fundamental Properties | 5 to 10% | No |
| Unit 3: Differentiation: Composite, Implicit, and Inverse Functions | 5 to 10% | No |
| Unit 4: Contextual Applications of Differentiation | 5 to 10% | No |
| Unit 5: Analytical Applications of Differentiation | 10 to 15% | No |
| Unit 6: Integration and Accumulation of Change | 15 to 20% | Yes |
| Unit 7: Differential Equations | 5 to 10% | Yes |
| Unit 8: Applications of Integration | 5 to 10% | Yes |
| Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions | 10 to 15% | Yes |
| Unit 10: Infinite Sequences and Series | 15 to 20% | Yes |
Weightings from College Board's AP Central. The two BC-only units, 9 and 10, are together 25 to 35% of the exam, and series alone is as large as integration. If you are short of time, series is where review pays most.
Unit by unit review
Unit 1: Limits and Continuity (5 to 10%)
Limits from graphs, tables and algebra, continuity, and the intermediate value theorem.
Practise: Unit 1 practice problems · Read: our guide
Unit 2: Differentiation: Definition and Fundamental Properties (5 to 10%)
The derivative as a limit, and the power, product and quotient rules.
Practise: Unit 2 practice problems · Read: our guide
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (5 to 10%)
The chain rule, implicit differentiation and derivatives of inverse functions.
Practise: Unit 3 practice problems · Read: our guide
Unit 4: Contextual Applications of Differentiation (5 to 10%)
Rates of change in context, related rates, linear approximation and L'Hôpital's rule.
Practise: Unit 4 practice problems · Read: our guide
Unit 5: Analytical Applications of Differentiation (10 to 15%)
The mean value theorem, extreme values, increasing and decreasing functions, concavity and optimisation.
Practise: Unit 5 practice problems · Read: our guide
Unit 6: Integration and Accumulation of Change (15 to 20%)
Riemann sums, the fundamental theorem, antiderivatives, and for BC, integration by parts, partial fractions and improper integrals.
Practise: Unit 6 practice problems · Read: our guide
Unit 7: Differential Equations (5 to 10%)
Slope fields, separation of variables, exponential models, and for BC, Euler's method and logistic growth.
Practise: Unit 7 practice problems · Read: our guide
Unit 8: Applications of Integration (5 to 10%)
Average value, motion, area between curves, volumes, and for BC, arc length.
Practise: Unit 8 practice problems · Read: our guide
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (10 to 15%)
BC only: derivatives and arc length of parametric curves, motion along vector paths, and polar area.
Practise: Unit 9 practice problems · Read: our guide
Unit 10: Infinite Sequences and Series (15 to 20%)
BC only: convergence tests, alternating series, Taylor and Maclaurin series, radius of convergence and error bounds.
Practise: Unit 10 practice problems · Read: our guide
The BC-only topics to check
These are the topics an AB course does not teach, and where BC students most often have gaps:
- Integration techniques: integration by parts, partial fractions with linear factors, and improper integrals.
- Differential equations: Euler's method and logistic models.
- Arc length of a curve given by y = f(x), and of a parametric curve.
- Parametric and vector motion: velocity, speed and distance travelled.
- Polar curves: slope and area, including the area between two polar curves.
- Series: every convergence test, with its conditions; Taylor and Maclaurin series; interval of convergence; the alternating series error bound and the Lagrange error bound.
See our guides to integration by parts, improper integrals, Euler's method, logistic growth, parametric equations and BC series.
A review plan for the 2027 exam
| When | What to do |
|---|---|
| Now to January | Keep each unit secure as you learn it. Do the unit's practice problems the week you finish it. |
| February | Series and Unit 9 in depth, if your class has reached them. They are a quarter to a third of the exam. |
| March | Timed multiple choice: Part A by hand, Part B with your calculator. One free-response question a week, marked with the scoring guidelines. |
| April | Two full practice exams under 2027 timing. Put each score into the BC score calculator. |
| The last week | Your error log, the standard series, and calculator routines. Rest before the exam. |
Resources: BC multiple-choice practice, AB multiple-choice practice (for the AB content), the full practice exam, official BC free-response questions and the AP Calculus BC score calculator.
Practice questions
Try each one before opening the answer.
Q1. Find the interval of convergence of ∑ xn/n for n ≥ 1.
Show answer
Q2. Find the area inside one loop of r = sin(2θ), for 0 ≤ θ ≤ π/2.
Show answer
Q3. Use Euler's method with one step of 0.1 to estimate y(1.1), given dy/dx = xy and y(1) = 2.
Show answer
Common mistakes
- Reviewing only the BC units: AB content is most of the exam, and your AB subscore depends on it.
- Applying a convergence test without checking its conditions.
- Forgetting the 1/2 in polar area.
- Rounding in the middle of a calculator question: store values instead.
Frequently asked questions
How many units are in AP Calculus BC?
Ten. Units 1 to 8 are shared with AB (with some extra BC topics), and Units 9 and 10 are BC only.
What is the hardest unit in AP Calculus BC?
Most students find Unit 10, series, the hardest. It is also 15 to 20% of the exam, so it is worth the most review time.
Do I need to review AB topics for BC?
Yes. Most of the BC exam is AB content, and your score report includes an AB subscore.
When is the 2027 AP Calculus BC exam?
Monday 10 May 2027, in the morning session.
Key takeaways
- Ten units; Units 9 and 10 are BC only and together 25 to 35% of the exam.
- Series and integration are the largest single units.
- Exam on 10 May 2027; review AB content too, for the AB subscore.
Sources: College Board, AP Central AP Calculus BC course page (unit weightings), 2027 exam schedule, and 2025 score distributions. Checked 21 October 2026.