"AP Calculus AB practice exam" is searched by students from about March, when the course reaches integration and the exam in May stops being abstract, and by parents trying to find out whether the practice their child is doing is the real thing. The exam has a fixed shape, the College Board gives away more free official practice than most students know, and a practice exam only tells you something if it is sat and scored the way the real one is. This page has the format, the units and their weights, where the free material is, how to take and score a practice exam, and a 20-question set in the exam's format with answers that you can print.
Download the AP Calculus AB 20-question practice set with answers (PDF) (twelve no-calculator and four calculator multiple-choice questions, four free-response style questions, the answers with one-line solutions, and a scoring box; two pages, free).
The exam format, section by section
| Section | Questions | Time | Calculator | Points | Share of the score |
|---|---|---|---|---|---|
| I, Part A: multiple choice | 30 | 60 min | No | 30 × 1.2 = 36 | 50% (Parts A and B together) |
| I, Part B: multiple choice | 15 | 45 min | Graphing calculator | 15 × 1.2 = 18 | |
| II, Part A: free response | 2 | 30 min | Graphing calculator | 2 × 9 = 18 | 50% (Parts A and B together) |
| II, Part B: free response | 4 | 60 min | No | 4 × 9 = 36 | |
| Total | 45 + 6 | 3 h 15 min | 108 |
There is no penalty for a wrong answer, so every multiple-choice question gets an answer. Each free-response question is marked out of 9 by a reader with the College Board's scoring guidelines, and the points are for the set-up, the working and the justification, not only the final number: a right answer with nothing written around it scores 1 of 3 on that part. Since May 2025 the exam is hybrid: the multiple choice is in the Bluebook app, the free response is handwritten in a booklet. How the 108 becomes a 1 to 5 is in the AP Calculus AB score calculator.
The eight units and how much of the exam each carries
| Unit | What it covers | Share of the multiple choice |
|---|---|---|
| 1. Limits and continuity | Limits from graphs, tables and algebra; the squeeze theorem; continuity; asymptotes; the Intermediate Value Theorem | 10 to 12% |
| 2. Differentiation: definition and basic rules | The derivative as a limit; power, product and quotient rules; derivatives of trig, exponential and log functions | 10 to 12% |
| 3. Differentiation: composite, implicit and inverse functions | The chain rule; implicit differentiation; derivatives of inverse functions | 9 to 13% |
| 4. Contextual applications of differentiation | Rates of change in context; motion (position, velocity, acceleration); related rates; linear approximation; L'Hospital's rule | 10 to 15% |
| 5. Analytical applications of differentiation | The Mean Value Theorem; extreme values; intervals of increase and concavity; curve sketching; optimisation | 15 to 18% |
| 6. Integration and accumulation of change | Riemann sums; the definite integral; the Fundamental Theorem; antiderivatives; substitution | 17 to 20% |
| 7. Differential equations | Slope fields; separable equations; exponential growth and decay | 6 to 12% |
| 8. Applications of integration | Average value; motion from velocity; area between curves; volumes by cross-sections and discs and washers | 10 to 15% |
Units 5 and 6 are more than a third of the exam between them, and the free-response questions draw on them most: a question that gives a graph of f′ and asks about f, and a question that gives a rate and asks for the accumulated amount, appear almost every year.
Where the free official practice is
- Every released free-response question since 1998, with the scoring guidelines, the chief reader's report and sample student answers at each score, on AP Central (search "AP Calculus AB past exam questions"). This is the most valuable practice there is, because you can mark your answer against what the readers actually gave points for. Questions from 2017 onwards match the current units exactly; earlier ones are still right for the mathematics.
- The course and exam description (the CED, a free PDF) has sample multiple-choice questions by unit and sample free-response questions, with answers, in the exact style of the exam.
- AP Classroom, through your teacher: personal progress checks for each unit in the real format, and a full-length practice exam that the teacher can assign. If your teacher has not assigned it, ask; it exists for every student in an AP course.
- The AP Daily videos in AP Classroom, one per topic, by AP teachers, free.
- Older full released exams (1998, 2003, 2008, 2012 and earlier) exist and circulate from teachers and in review books. The format was different (more questions, the old unit list), so use them for the mathematics, not for timing.
Review books (Princeton Review, Barron's, 5 Steps to a 5) each have three to six practice exams in the format; they are useful from March for timed full runs once the official free-response set has been used.
How to sit a practice exam so the score means something
- Real conditions. 3 hours 15 minutes, in the real order, with the calculator allowed only in Part B of Section I and Part A of Section II, and the free response handwritten. A practice exam taken in pieces over a week measures something else.
- Score it the real way. Multiple-choice correct × 1.2, plus six free-response scores out of 9 marked with the official guidelines (be strict: a reader is), composite out of 108. Then the conversion table.
- Sort the wrong answers by unit, not by number. Three wrong in Unit 6 is a lesson; three wrong spread across units is carelessness, and the fix is different.
- Read the scoring guidelines for every free-response point you lost. Most lost points are not mathematics: the set-up not written, the justification missing, the units missing, rounding before the end. Those come back fastest.
- One full exam every two weeks from eight weeks out, and the gaps spent on the two weakest units. Earlier than that, practise by unit.
A 20-question practice set in the exam's format
The printable has all twenty with the answer choices and the answers. Here are the questions, so you can see the level: Part A (no calculator), Part B (calculator) and four free-response style questions.
Part A, no calculator.
- lim (x → 3) of (x² − 9)/(x − 3)
- lim (x → ∞) of (5x² − 3x)/(2x² + 7)
- If f(x) = x³ − 4x, f′(2) = ?
- d/dx [sin 3x]
- d/dx [ln(x² + 1)]
- If y = e^(2x), d²y/dx² = ?
- f(x) = x³ − 3x² has a local minimum at x = ?
- The integral from 0 to 2 of (3x² + 2x) dx
- The integral of cos 2x dx
- If F(x) is the integral from 1 to x of √(t³ + 1) dt, F′(2) = ?
- The average value of f(x) = x² on [0, 3]
- If x² + y² = 25, dy/dx at (3, 4)
Part B, calculator allowed.
- A particle moves on a line with velocity v(t) = t² − 4t + 3, t ≥ 0. When is it at rest, and what is its acceleration at t = 1?
- dy/dx = 2y and y(0) = 3. Find y.
- The area between y = x and y = x² from x = 0 to x = 1
- The radius of a circle grows at 2 cm/s. How fast is the area growing when r = 5 cm?
Free-response style.
- f(x) = x² on [1, 3]. (a) State what the Mean Value Theorem guarantees for f on this interval. (b) Find the c it guarantees.
- The region under y = √x from x = 0 to x = 4 is rotated about the x-axis. (a) Write the integral for the volume. (b) Evaluate it.
- (a) Estimate the integral from 0 to 4 of x² dx with a left Riemann sum of four equal subintervals. (b) Is it an under- or over-estimate? Justify in one sentence.
- (a) Write the equation of the line tangent to y = x³ at x = 1. (b) Use it to approximate y at x = 1.1, and say whether the approximation is below or above the true value, with a reason.
The answers
| No. | Answer | Why |
|---|---|---|
| 1 | 6 | (x − 3)(x + 3)/(x − 3) = x + 3 |
| 2 | 5/2 | Ratio of leading coefficients |
| 3 | 8 | f′(x) = 3x² − 4 |
| 4 | 3 cos 3x | Chain rule |
| 5 | 2x/(x² + 1) | Chain rule on ln |
| 6 | 4e^(2x) | Differentiate twice |
| 7 | x = 2 | f′ = 3x(x − 2); f″ = 6x − 6 > 0 at 2 |
| 8 | 12 | [x³ + x²] from 0 to 2 |
| 9 | (1/2) sin 2x + C | Reverse chain rule |
| 10 | 3 | Fundamental Theorem: √(8 + 1) |
| 11 | 3 | (1/3) × 9 |
| 12 | −3/4 | 2x + 2y·y′ = 0, so y′ = −x/y |
| 13 | At rest at t = 1 and t = 3; a(1) = −2 | v = (t − 1)(t − 3); a = 2t − 4 |
| 14 | y = 3e^(2x) | Separable; C = 3 |
| 15 | 1/6 | ∫(x − x²) = 1/2 − 1/3 |
| 16 | 20π cm²/s | dA/dt = 2πr·dr/dt |
| 17 | (a) f′(c) = (9 − 1)/(3 − 1) = 4 for some c in (1, 3); (b) c = 2 | f is continuous and differentiable, so the theorem applies |
| 18 | (a) π × the integral from 0 to 4 of x dx; (b) 8π | Disc method, radius √x |
| 19 | (a) 14; (b) under-estimate | x² is increasing, so each left rectangle is below the curve (true value 64/3) |
| 20 | (a) y = 3x − 2; (b) 1.3, below the true 1.331 | y″ > 0 at x = 1, concave up, tangent below the curve |
Score it as the exam would: a weak Part A is derivative and integral rules, which drill quickly; a weak free-response section is the set-up and the justification, which is where most 4s become 5s and takes six weeks of one marked question a day.
What the scores say
In May 2025, 286,722 students took AP Calculus AB. The College Board's distribution: 20.3% scored a 5, 28.9% a 4, 15.0% a 3, 22.8% a 2 and 13.0% a 1; 64.2% scored 3 or higher, and the mean was 3.21. Half the students who sit it get a 4 or a 5, which is unusual among AP exams, and the reason is that the exam rewards exactly what practice exams teach: the rules automatic, the set-up written, the justification in words.
Where to get help
A 1-on-1 online class for AP Calculus AB with a tutor who holds a master's in mathematics and has taught AB and BC since 2018: the unit the class is on a week ahead, and from January a released free-response question in every lesson, marked to the College Board's scoring guidelines, with timed practice exams every two weeks from March and the composite worked out properly. Before school (7 am Eastern is 4:30 pm for the tutor), after school or weekends, US time; the recording and notes after every class; US$10 to $13 an hour, billed monthly. The free 30-minute first class is a real lesson on the unit you are on. The AB and BC decision is in AP Calculus AB vs BC, and where calculus sits in the US sequence in what grade do you take calculus.
Download the AP Calculus AB 20-question practice set with answers (PDF)
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