Where can I find AP Calculus AB practice questions?

Start with the sample prompt types on this page, then move into the official AP Calculus AB past-exams page for the strongest calibration.

Are Calc AB sample questions enough to study from?

They are useful for pattern recognition, but you should follow them with real timed practice and official prompts.

What should I do after reviewing Calc AB examples?

Pick one question type or weak skill and do a short timed set immediately so the example turns into active practice.

AP Calculus AB

AP Calculus AB Practice Questions, Examples, and FRQ Samples

10 MCQs and 3 FRQs on the topics that show up most. Answers and explanations included.

days until your Calc AB exam

Mon, May 11 · Morning session

Pick an answer to reveal the explanation.

Question 1 of 10 · Unit 1: Limits

Easy

What is lim(x→2) (x² − 4)/(x − 2)?

Question 2 of 10 · Unit 2: Derivatives

Medium

If f(x) = sin(3x²), then f'(x) = ?

Question 3 of 10 · Unit 2: Derivatives

Medium

Let h(x) = x² · eˣ. What is h'(x)?

Question 4 of 10 · Unit 4: Contextual Applications

Hard

A spherical balloon is being inflated so its radius increases at 2 cm/s. The volume is V = (4/3)πr³.

How fast is the volume increasing when the radius is 5 cm?

Question 5 of 10 · Unit 5: Analytical Applications

Medium

If f is continuous on [1, 5] and differentiable on (1, 5) with f(1) = 3 and f(5) = 11, the Mean Value Theorem guarantees some c in (1, 5) where f'(c) equals which value?

Question 6 of 10 · Unit 6: Integration

Medium

The table gives selected values of a continuous function f on [0, 12]. f(0)=2, f(3)=5, f(6)=8, f(9)=6, f(12)=3.

Use a left Riemann sum with four equal subintervals to approximate ∫₀¹² f(x) dx.

Question 7 of 10 · Unit 6: Integration

Hard

If g(x) = ∫₂ˣ √(1 + t³) dt, then g'(x) = ?

Question 8 of 10 · Unit 7: Differential Equations

Medium

Which function is a solution to dy/dx = 2xy with y(0) = 3?

Question 9 of 10 · Unit 8: Applications of Integration

Medium

A particle moves along a line with velocity v(t) = t² − 4t for 0 ≤ t ≤ 6. What is the total distance traveled from t = 0 to t = 6?

Question 10 of 10 · Unit 8: Applications of Integration

Medium

Find the area of the region enclosed by y = x and y = x² between x = 0 and x = 1.

4 moves that pick up easy Calc AB points

Small writing habits that turn a partial-credit FRQ into a full-credit one. Apply them as you work through the questions above.

1
Show the setup before the answer
FRQ graders reward a correctly written integral, derivative, or equation even if the final number is wrong. Writing just the answer is how students lose partial credit they actually earned.
Write ∫₀⁶ |v(t)| dt = 24 - not just '24'.
2
State units on every applied answer
If the problem is in gallons, seconds, or dollars, the answer must carry the unit. Missing units is the most common one-point loss on AP Calc FRQs.
3
Interpret, don't just calculate
When a prompt says 'interpret in the context,' write one sentence explaining what the number means - e.g. 'the cost of producing the 51st widget.' Numeric answers alone don't earn the interpretation point.
4
Justify with a theorem, not a guess
For 'justify' parts, cite the specific theorem: Mean Value, Extreme Value, IVT, FTC, or the sign of a derivative. Vague answers like 'because it's continuous' don't earn the justification point.

Calc AB practice - common questions

Write your response to any FRQ on this page and we'll score it against the College Board rubric in seconds. You get a breakdown of which points you earned, which you missed, and exactly what to add to pick them up.

Yes. Every MCQ and FRQ on this page is built around the task shapes the College Board keeps returning to. If a topic isn't on the exam, it isn't on this page.

Guessing wastes study time. The fastest shortcut is to hand us one FRQ - we flag the units and skills it reveals as weak (e.g. related rates, particle motion, or FTC) so your next study block targets the gap instead of covering everything equally.

The past-exams page collects the released free-response sets. Pair them with the questions on this page for a full calibration: released prompts show you the exact difficulty, these show you the recurring patterns.

Open official Calc AB FRQs

Most colleges accept a 4 or 5. Some accept a 3. Composite thresholds move year to year, but roughly: 39+ for a 3, and about 68+ for a 5. Use the calculator to see where your current practice puts you.

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Score the 5. Keep the credit.

Write one Calc AB FRQ. Get it graded in seconds. Know exactly which points you'd lose before exam day.

Keep exploring

AP Calculus AB Subject Guide

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Calc AB Exam Format

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Calc AB Study Guide

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Calc AB Scoring Guide

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