AP Calculus AB: Units, Exam Format, Study Guide and Free Practice

AP Calculus AB is College Board's course in differential and integral calculus. It matches a first-semester college calculus course, and a good score on the May exam can earn you college credit. This guide covers all 8 units, how much each one counts, how the exam works, and where to practice every topic with instant feedback.

The 2027 AP Calculus AB exam

The exam is on Monday, May 10, 2027. It is a hybrid digital exam: you answer multiple-choice questions and read the free-response questions in the Bluebook app, then write your free-response work by hand in a paper booklet.

In total that is 3 hours 10 minutes: 42 multiple-choice questions and 6 free-response questions. About two thirds of the score comes from parts where calculators are not allowed, so fast, accurate hand skills matter most.

AP Calculus AB units and what to practice

College Board splits the course into 8 units. Each row shows the unit's share of the exam, a lesson where you can practice it, and pages that explain the ideas.

Units 5 and 6 together are up to 40% of the exam, so give them the most practice time. Unit 6 also feeds almost every free-response question, because accumulation, the Fundamental Theorem and Riemann or trapezoid sums from tables show up again and again.

What the free-response questions look like

Free response is half of the score, and it rewards clear reasoning as much as correct numbers. Most years include questions like these:

• Rate in, rate out. Water flows into and out of a tank at given rates. Find the amount at a given time with an integral, and decide when it is greatest.
• Data in a table. Estimate a derivative from nearby values, approximate an integral with a trapezoid sum, and explain what it means in context.
• The graph of f'. Read where f increases, has extrema or changes concavity, and evaluate an accumulation function from areas.
• Motion on a line. Use velocity to find position, total distance and when the particle changes direction.
• A differential equation. Sketch a slope field, write a tangent line approximation and solve with separation of variables.

Always state the theorem or reason you use, such as "since f' changes from positive to negative at x = 3, f has a relative maximum there". Answers without justification lose points even when the number is right.

Example problems at the AP Calculus AB level

1. A limit (Unit 1). Find \displaystyle\lim_{x \to 3} \frac{x^2 - 9}{x - 3}.

2. The chain rule (Unit 3). Differentiate y = \sin(x^2).

3. An accumulation function (Unit 6). If g(x) = \int_0^x (3t^2 - 4)\,dt, then by the Fundamental Theorem of Calculus

How to prepare for AP Calculus AB

• Practice a little every day. Short daily sessions build the hand skills you need for the no-calculator parts. Every lesson here gives new numbers each time, so you can repeat a topic until it feels automatic.
• Learn the justifications. Know when to cite the Intermediate Value Theorem, the Mean Value Theorem and the Extreme Value Theorem, and practice writing one clear sentence for each.
• Keep the formulas close. The calculus formula sheet has every derivative and integral on one page. No formula sheet is provided on the exam.
• Take timed practice exams in the final weeks using practice exams, then review every mistake.
• Avoid the classic slips. Our list of common calculus mistakes covers the errors that cost the most points.

Thinking about the faster course instead? See the AP Calculus BC guide and our comparison of AP Calculus AB vs BC.

AP and Advanced Placement are registered trademarks of College Board, which is not affiliated with PracticeCalculus and does not endorse this guide. Exam details come from College Board's AP Calculus AB pages; check them for any changes.