AP Calculus practice problems, unit by unit
Free AP Calculus practice problems for all ten units: Units 1 to 8 for AB and BC, and Units 9 and 10 for BC. Each question has a hint and a worked solution you reveal one step at a time, and each unit ends with a free-response question with a points-based scoring guide.
On this page
Practice by unit
- Unit 1: Limits and continuityLimits from graphs, tables and algebra, limits at infinity, continuity and the intermediate value theorem. 8 questions and a free-response question.
- Unit 2: Differentiation: definition and fundamental propertiesThe derivative as a limit, the power, product and quotient rules, and derivatives of sin, cos, e<sup>x</sup> and ln x. 8 questions and a free-response question.
- Unit 3: Differentiation: composite, implicit and inverse functionsThe chain rule, implicit differentiation, derivatives of inverse functions and inverse trigonometric functions. 8 questions and a free-response question.
- Unit 4: Contextual applications of differentiationRates of change in context, motion along a line, related rates, linear approximation and L'Hôpital's rule. 8 questions and a free-response question.
- Unit 5: Analytical applications of differentiationThe mean value theorem, increasing and decreasing intervals, the first and second derivative tests, concavity and optimisation. 8 questions and a free-response question.
- Unit 6: Integration and accumulation of changeRiemann sums and the trapezoidal rule, definite integrals, the fundamental theorem of calculus, and techniques of integration. 8 questions and a free-response question.
- Unit 7: Differential equationsSlope fields, separable differential equations, exponential models, and (for BC) Euler's method and logistic growth. 8 questions and a free-response question.
- Unit 8: Applications of integrationAverage value, displacement and distance, areas between curves, and volumes with cross-sections, discs and washers. 8 questions and a free-response question.
- Unit 9: Parametric equations, polar coordinates and vector-valued functions (BC)BC only. Derivatives and arc length of parametric curves, motion with vectors, and slopes and areas in polar coordinates. 8 questions and a free-response question.
- Unit 10: Infinite sequences and series (BC)BC only. Convergence tests, geometric and alternating series, Taylor and Maclaurin polynomials, and radius of convergence. 8 questions and a free-response question.
Ready for a full test? Take the free AP Calculus mock exam: every unit, timed, marked as you go.
How it works
- Try first. Type your answer or pick an option, and it is marked straight away.
- Stuck? Open the hint before the solution. Then reveal the worked solution one step at a time, and stop as soon as you can finish it yourself.
- Mark your free-response answers with the scoring guide, point by point, the way exam readers do.
- Track your progress. Each unit above shows how many questions you have done, saved on this device.
- Share it with your tutor. Every unit page has a button that sends your score on WhatsApp. Tutors: send a unit link as homework, and ask for the score back.
The AP Calculus exam format
| Section | Questions | Time | Score |
|---|---|---|---|
| Section I: multiple choice | 42 questions | 1 hour 40 minutes | 50% |
| Part A | 29 questions, no calculator | 62 minutes | |
| Part B | 13 questions, graphing calculator required | 38 minutes | |
| Section II: free response | 6 questions | 1 hour 30 minutes | 50% |
| Part A | 2 questions, graphing calculator required | 30 minutes | |
| Part B | 4 questions, no calculator | 60 minutes |
This is the format from the May 2027 exam onwards. The exam is hybrid digital: multiple-choice answers go into the Bluebook app, and free-response answers are handwritten in a paper booklet. Before 2027 the multiple-choice section had 45 questions in 1 hour 45 minutes. The free-response section has not changed, so every past FRQ on this page is exactly the kind of question you will meet.
Frequently asked questions
Are these AP Calculus questions from real exams?
No. They are original questions written by our tutors in the style of the AP Calculus exam, so we can give full worked solutions. For real exam questions, use the official AP Calculus past papers, which we link to with their scoring guidelines.
Do I need an account?
No. Everything is free and there is no sign-up. Your progress is saved in your own browser on this device, and you can reset it on any unit page.
How should I use these alongside past papers?
Use the unit practice while you learn each topic, then move to timed past papers once you have covered most of the course. When a past paper question goes wrong, come back to that unit's questions.
Do these questions cover AB or BC?
Both. Units 1 to 8 are on both exams. Units 9 (parametric, polar and vector functions) and 10 (series) are BC only, and some questions in other units, such as Euler's method, are marked BC only.
How do I enter an answer like 1/6?
Type it as a fraction, 1/6, or as a decimal, 0.1667. Both are marked correctly.