What AP Calculus BC covers, what it adds beyond AB, and how much of the exam each unit is worth, based on the College Board's course description. SparklMind tutors BC 1-on-1, starting with a free 45-minute diagnostic.
BC includes every AB unit plus two more. Units 1–5 carry less of the BC exam than they do on AB, because Units 9 and 10 take up about 30% of the score. The weight is each unit's share of the BC exam.
| Unit | Exam weight | BC-only content |
|---|---|---|
| 1. Limits and Continuity | 4–7% | Same as AB |
| 2. Differentiation: Definition and Fundamental Properties | 4–7% | Same as AB |
| 3. Differentiation: Composite, Implicit, and Inverse Functions | 4–7% | Same as AB |
| 4. Contextual Applications of Differentiation | 6–9% | Same as AB |
| 5. Analytical Applications of Differentiation | 8–11% | Same as AB |
| 6. Integration and Accumulation of Change | 17–20% | Integration by parts, partial fractions with linear factors, and improper integrals |
| 7. Differential Equations | 6–9% | Euler's method and logistic growth models |
| 8. Applications of Integration | 6–9% | Arc length of a smooth curve |
| 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions | 11–12% | The whole unit is BC-only |
| 10. Infinite Sequences and Series | 17–18% | The whole unit is BC-only |
For what Units 1–8 cover in detail, and where students lose points in each, see the AP Calculus AB guide.
Source: College Board, AP Calculus AB and BC Course and Exam Description (College Board, AP Calculus BC course (opens in a new tab)).
Derivatives and arc length of parametric curves, motion described by vectors (position, velocity, speed and acceleration), and slopes and areas in polar coordinates.
Common trouble spot: confusing velocity with speed, and setting up the area between two polar curves.
Convergence tests (nth-term, integral, comparison, alternating series and ratio), power series, radius and interval of convergence, Taylor and Maclaurin series, and error bounds.
Common trouble spot: choosing the right convergence test, and forgetting to check the endpoints of an interval.
Finding the radius of convergence is usually quick. Most lost points come from the endpoints, which need a different test each.
Find the interval of convergence of the series Σ (x − 2)n ⁄ (n · 3n), for n = 1, 2, 3, …
Step 1: ratio test. The ratio of consecutive terms tends to |x − 2| ⁄ 3 as n → ∞. The series converges when |x − 2| ⁄ 3 < 1, that is |x − 2| < 3, so −1 < x < 5 and the radius is 3.
Step 2: check x = 5. The series becomes Σ 1 ⁄ n, the harmonic series, which diverges.
Step 3: check x = −1. The series becomes Σ (−1)n ⁄ n. Its terms alternate in sign, decrease, and tend to 0, so it converges by the alternating series test.
Answer: the interval of convergence is −1 ≤ x < 5.
The ratio test says nothing at the endpoints, where the ratio equals exactly 1, which is why each endpoint needs its own test. Stopping at −1 < x < 5 is the most common way to lose this point.
SparklMind tutors AP Calculus BC 1-on-1: the same tutor every session, following your child's class unit by unit, with extra time on series and on released free-response questions marked against the official scoring guidelines. It starts with a free 45-minute diagnostic; sessions are $59 each after that.
AP Calculus tutoring, exam format and prices →All of AB, plus integration by parts, partial fractions and improper integrals, Euler's method and logistic growth, arc length, and two whole extra units: parametric, polar and vector-valued functions (Unit 9) and infinite sequences and series (Unit 10).
It depends on how solid their precalculus is and what their school offers. BC covers roughly one and a half AB courses in a year, so it suits students who are fluent with functions, logarithms and trigonometry. The free diagnostic gives an honest view.
Many schools let strong students go straight from precalculus to BC; others require AB first. Tutoring follows whichever route your child's school uses.
The BC exam reports a separate AB subscore, based on the questions covering AB topics. So a student who takes BC also shows how they did on the AB portion.
Units 6 and 10, Integration and Accumulation of Change (17–20%) and Infinite Sequences and Series (17–18%). Series is also the unit students most often find hardest, so it gets extra session time.
See also: AP Calculus AB guide, Precalculus, and free practice in the AP Calculus BC exam hub.