AP Calculus BC: Units, Exam Format, Study Guide and Free Practice

AP Calculus BC is College Board's faster calculus course. It includes all of AP Calculus AB plus parametric and polar curves and infinite series, and it matches about two semesters of college calculus. This guide covers all 10 units, how much each one counts, how the exam and the AB subscore work, and where to practice every topic with instant feedback.

The 2027 AP Calculus BC exam

The exam is on Monday, May 10, 2027. It is a hybrid digital exam: you answer multiple-choice questions and read the free-response questions in the Bluebook app, then write your free-response work by hand in a paper booklet.

In total that is 3 hours 10 minutes: 42 multiple-choice and 6 free-response questions. You get two scores from 1 to 5: your BC score and an AB subscore, which comes from the part of the exam that covers AB topics. Colleges can use the subscore like an AB exam score.

AP Calculus BC units and what to practice

BC has 10 units. Units 1 to 8 share their names with AB but add BC topics such as integration by parts, partial fractions, improper integrals, Euler's method, logistic growth and arc length. Units 9 and 10 are only in BC.

Units 6 and 10 can each be up to a fifth of the exam. Series in particular is new to most students and builds slowly: geometric series first, then convergence tests, then power series, Taylor polynomials and error bounds. Give it several weeks.

What the BC free-response questions look like

Free response is half of the score. BC students meet the same question types as AB, often with a BC twist, plus questions only BC asks:

• A particle in the plane. Given x'(t) and y'(t), find the velocity vector, the speed, the total distance traveled and the slope \dfrac{dy}{dx} at a point.
• A polar curve. Find the area inside a region with \frac{1}{2}\int r^2\,d\theta, and decide whether the point is moving toward or away from the origin.
• A Taylor polynomial. Write the first terms of a series, find its interval of convergence, and bound the error with the alternating series or Lagrange error bound.
• A differential equation. Use Euler's method for an estimate, then decide whether it is too high or too low from the concavity.

As with AB, every claim needs a reason. Name the test or theorem, check its conditions, and connect the answer to the question in a short sentence.

Example problems at the AP Calculus BC level

1. Integration by parts (Unit 6). Evaluate \int x e^x\,dx with u = x and dv = e^x\,dx:

2. A parametric slope (Unit 9). For x = t^2 and y = t^3 - 3t, find \dfrac{dy}{dx} at t = 2.

3. A geometric series (Unit 10). Find the sum.

How to prepare for AP Calculus BC

• Do not neglect the AB topics. They are most of the exam and the whole AB subscore. Keep practicing derivatives, integrals and accumulation alongside the new BC units.
• Start series early. Work through sequences, geometric series and the ratio test well before spring, so there is time for power series and Taylor polynomials.
• Practice a little every day. Every lesson here gives new numbers each time, so you can repeat a topic until it feels automatic.
• Keep the formulas close. The calculus formula sheet has every derivative, integral and series on one page. No formula sheet is provided on the exam.
• Take timed practice exams in the final weeks using practice exams, and review every mistake.

Not sure BC is right for you? Read our comparison of AP Calculus AB vs BC or the AP Calculus AB guide.

AP and Advanced Placement are registered trademarks of College Board, which is not affiliated with PracticeCalculus and does not endorse this guide. Exam details come from College Board's AP Calculus BC pages; check them for any changes.