AP exam preparation

AP Calculus BC free-response practice

The AP Calculus BC exam ends with six free-response questions (FRQs), and they decide a large share of the final score. The surest way to prepare is to work through real past FRQs on the clock and mark them against the official College Board scoring guidelines, point by point.

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Section I
45 multiple-choice questions
Section II
6 free-response questions, 90 minutes
FRQ points
9 points per question
AP score
1 to 5

How the free-response section works

Section II has two parts. Part A has 2 questions in 30 minutes with a graphing calculator; Part B has 4 questions in 60 minutes without a calculator.

Each question is worth 9 points, awarded for specific steps: a correct setup, a correct answer, units, and a justification that names the theorem or reason. Clear working earns points even when a final number is wrong.

Topics that come up again and again

  • Rates of change and accumulation from a table, with Riemann and trapezoidal sums
  • Particle motion: velocity, acceleration, speed and total distance travelled
  • Parametric and vector-valued motion in the plane
  • Polar curves: area of a region and rates of change
  • Differential equations: slope fields, separation of variables and Euler’s method
  • Taylor and Maclaurin series, intervals of convergence and error bounds
  • Area and volume of solids, including cross-sections
  • Analysis of a function from its graph: extrema, concavity and points of inflection

AP Calculus BC practice on EuclidCurve

Every AP Calculus BC free-response question from 2012 to 2026 (no exam was released for 2020), arranged by year, one question at a time. Each question opens with its official scoring guideline, so students can mark their own work exactly as an AP reader would.

  • 84 free-response questions: 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2021, 2022, 2023, 2024, 2025 and 2026
  • Official College Board scoring guidelines for every question
  • Part of the University Foundations programme for IB and AP students heading to university mathematics

Frequently asked questions

Is a calculator allowed on the AP Calculus BC free-response section?

Only in Part A, which has 2 questions and needs a graphing calculator. Part B, the other 4 questions, is calculator-free.

How are AP Calculus BC FRQs scored?

Each of the six questions is worth 9 points. Points are given for the setup, the answer, units and justification, following the College Board scoring guidelines.

Which AP Calculus BC past papers can I practise here?

All free-response questions from 2012 to 2026 (2020 was not released), each with its official scoring guideline. Create an account to practise them.