AP Calculus BC practice test: free questions, exam format and 2027 date

Each daily paper has 8 original questions worth 25 to 35 marks. Be clear about the fit. The AP Calculus AB paper is the better daily match: differentiation rules, integration techniques including by parts, parametric differentiation and differential equations. The AP Calculus BC paper overlaps only on series, polar curves and volumes; its complex numbers, matrices, hyperbolic functions and proof by induction are not in AP Calculus, so skip those questions.

AP Calculus BC exam format for 2027

More than two thirds of the score comes from parts with no calculator, so practice without one. The Desmos calculator in Bluebook is only available in the calculator parts. At least two free-response questions use a real-world context. Multiple choice gives you about 2.4 minutes per question, and free response about 15 minutes per question.

AP Calculus BC units

Units 9 and 10 are BC only, and together they are worth up to 35%. Series alone matches integration as the biggest unit. Check your derivatives and integrals with the Derivative, Integral, Taylor Series, Polar Coordinates and Differential Equations calculators.

AP Calculus BC practice test questions with answers

We wrote these for this page. Each tests a BC-only topic. Do them without a calculator.

1. Series: interval of convergence

Question: Find the interval of convergence of the series whose nth term is (x − 1)ⁿ ÷ (n · 2ⁿ), for n ≥ 1.

The ratio test gives a limit of |x − 1| ÷ 2. The series converges when that limit is below one, so for x between −1 and 3. Now test each endpoint separately. Putting x = 3 in gives terms of 1/n: that is the harmonic series, and it diverges. Putting x = −1 in gives (−1)ⁿ/n, and the alternating series test shows that one converges. The interval is −1 ≤ x < 3. Skipping the endpoint checks is the most common lost point.

2. Parametric curves

Question: A curve is defined by x = t² + 1 and y = t³ − 12t. Find dy/dx when t = 1, and the values of t that give a horizontal tangent.

Divide dy/dt by dx/dt. A horizontal tangent needs dy/dt = 0 while dx/dt is not zero: 3t² − 12 = 0 gives t = 2 and t = −2, and dx/dt = 2t isn't zero at either.

3. Polar area: a rose curve

Question: Find the total area enclosed by all four petals of the rose r = 4 sin 2θ.

Over 0 to 2π, sin² 2θ integrates to π, so A = 8π, which is about 25.1. Each petal has area 2π. Remember the ½ and the square: polar area is ½∫r² dθ, not ∫r dθ. Integrating over 0 to 2π here traces every petal once.

Definite integrals sit under every area question. Try one from our Calculus course, then press Mark.

4. Euler's method

Question: dy/dx = x + y with y(0) = 1. Use Euler's method with two steps of 0.5 to estimate y(1).

Each step adds step size × slope. At (0, 1) the slope is 1, so y(0.5) ≈ 1 + 0.5(1) = 1.5. At (0.5, 1.5) the slope is 2, so y(1) ≈ 1.5 + 0.5(2) = 2.5. Show each step on its own line, because scoring guidelines reward the method as well as the answer.

AP Calculus BC scores and the AB subscore

In 2026, 46% of AP Calculus BC students scored 5, 22% scored 4, 14% scored 3, 14% scored 2 and 4% scored 1, so 82% scored 3 or higher. You also get a Calculus AB subscore from 1 to 5, based on the AB topics, which make up about 60% of the exam. College Board recommends that colleges treat it like an AP Calculus AB score, but each college sets its own credit policy.

• Exam: Monday, May 10, 2027, in the morning session, at 8 a.m. local time in the lower 48 states, Hawaii and Washington, D.C.
• Ordering deadline: November 13, 2026, through your school's AP coordinator.
• Fee: $99 in the US, US territories and Canada, $129 elsewhere, plus $40 for exams ordered from November 14 to March 12.
• Scores: released in July 2027.

Use the daily papers as short timed practice tests

1. Open today's AP Calculus AB paper and work to the suggested time, 35 to 45 minutes, without a calculator where you can.
2. On the AP Calculus BC paper, answer the series, polar and volume questions and skip the rest.
3. Write the method as well as the answer: name the test you use for a series and check its conditions.
4. Mark it and note the AP unit behind each lost mark.

Common AP Calculus BC mistakes

• Not testing endpoints of an interval of convergence.
• Leaving out the ½ or the square in polar area.
• Dividing dy/dt by dx/dt the wrong way up for a parametric derivative.
• Naming a series test without checking its conditions, such as the terms decreasing to 0 for the alternating series test.
• Dropping the constant of integration in integration by parts or when solving a differential equation.

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United States · APAP Calculus AB Practice Test: Free Questions, 2027 GuideFree AP Calculus AB practice test questions with worked answers, plus the 2027 exam format, calculator rules, all 8 units, scores and a short daily paper.