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

The daily AP Calculus AB paper has 8 original questions worth 25 to 35 marks. It fits AB well: derivatives from first principles, the chain, product and quotient rules, tangents, rates of change, stationary points, integration, area and differential equations. Two of its topics, parametric equations and integration by parts, are BC only, so skip those questions. Limits only come up through first principles, and continuity not at all, so practice Unit 1 separately.

AP Calculus AB exam format for 2027

More than two thirds of the score comes from parts with no calculator, and the Desmos calculator in Bluebook only appears in the calculator parts. Free-response questions mix procedural and conceptual tasks, and at least two use a real-world context. You get about 2.4 minutes per multiple-choice question and about 15 minutes per free-response question.

AP Calculus AB units

Derivatives fill Units 2 to 5, up to 60% of the score, so they come first in practice. Learn or refresh them in our Calculus course, and check working with the Limit, Derivative, Integral, Rate of Change and Differential Equations calculators.

AP Calculus AB practice test questions with answers

We wrote these five for this page, one from each of the biggest areas. Do them without a calculator.

1. Limits

Question: Find the limit of (x² − 2x − 8) ÷ (x − 4) as x approaches 4.

Substituting gives 0/0, which tells you to simplify, not that the limit doesn't exist. Factor the top: (x − 4)(x + 2) ÷ (x − 4) = x + 2 for x ≠ 4. As x approaches 4, that approaches 6. The graph has a hole at (4, 6), but the limit is still 6.

2. The chain rule and a tangent line

Question: Find the equation of the tangent line to f(x) = (2x + 1)⁴ at x = 0.

So f(0) = 1 and the slope is f′(0) = 8. The tangent line is y = 8x + 1. Leaving out the × 2 from the inside function is the classic chain rule slip.

Try a differentiation question from our Calculus course, then press Mark.

3. Related rates

Question: The radius of a spherical balloon grows at 0.5 cm/s. How fast is its volume increasing when the radius is 10 cm?

The volume grows at 200π cm³/s, about 628 cm³/s. Differentiate with respect to time first, and only then put in r = 10. Substituting before differentiating turns r into a constant and gives zero.

4. Optimization

Question: A rectangular pen is built against a long wall, with 240 m of fencing for the other three sides. What dimensions give the largest area?

Let x be each side at right angles to the wall. The side parallel to the wall is 240 − 2x, so the area is A(x) = x(240 − 2x) = 240x − 2x². Then A′(x) = 240 − 4x, which is zero at x = 60. A″(x) = −4 is negative, so this is a maximum. The pen is 60 m by 120 m, with area 7,200 m².

Here x is the side length in meters and y is the area in square meters. The curve rises, peaks at x = 60 and falls back to zero at x = 120. Always justify a maximum, with the second derivative or a sign chart, because the scoring guidelines ask for it.

5. The Fundamental Theorem of Calculus

Question: Evaluate the integral of 3√x from x = 1 to x = 4.

The answer is 14. Rewrite roots as powers before you integrate, and remember 4^3/2 = (√4)³ = 8.

AP Calculus AB scores, date and deadlines

In 2026, 20% of AP Calculus AB students scored 5, 28% scored 4, 17% scored 3, 24% scored 2 and 11% scored 1, so 65% scored 3 or higher. College Board calls a 5 extremely well qualified, a 4 very well qualified and a 3 qualified, and 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. Calculus BC is at the same time.
• 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 paper as a short timed practice test

1. Open today's AP Calculus AB paper and work to the suggested time, 35 to 45 minutes.
2. Do it without a calculator, to match most of the real exam.
3. Write each step and justify every conclusion, such as why a point is a maximum.
4. Mark it and note the AP unit behind each lost mark.

Common AP Calculus AB mistakes

• Missing the inside derivative in the chain rule.
• Substituting values before differentiating in related rates.
• Stating a maximum or minimum without justification.
• Treating 0/0 as "no limit" instead of simplifying.
• Forgetting + C on an indefinite integral, or the initial condition in a differential equation.
• Giving a decimal too early in a calculator question: keep full accuracy until the final answer.

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United States · APAP Calculus BC Practice Test: Free Questions, 2027 GuideFree AP Calculus BC practice test questions on series, parametric, polar and Euler's method, plus the 2027 exam format, units, AB subscore and scores.