Free AP Calculus AB Practice — Understand change and accumulation through connected ideas
Connect limits, derivatives, integrals, and differential equations. Practice interpreting a result and justifying your reasoning alongside the calculations.
- 44
- Quizzes
- 8
- Modules
- 8
- Full practice exams
- 6
- Timed mini-exams
- $0
- Cost, forever
Calculus becomes easier to organize when you connect its two central questions: how fast is a quantity changing, and how much change has accumulated? Derivatives answer the first locally; definite integrals answer the second over an interval. The methods are closely related, but their units and interpretations differ.
This course moves from functions and limits into differentiation, applications, integration, and differential equations. Use the focused quizzes to check a specific idea, then combine those ideas in mixed practice. Keep a line of explanation beside each calculation so that a correct formula does not replace a clear argument.
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Make the connections in Calculus AB
A derivative is the limit of average rates of change. Its sign describes whether the function increases or decreases locally, while its magnitude measures the rate. Before using a theorem, check its hypotheses: a conclusion about a continuous or differentiable function is not justified merely because a graph looks smooth.
A definite integral represents signed accumulation. An antiderivative provides a way to evaluate it, but an application also needs an initial value and an interpretation. If a rate is measured in liters per minute and time in minutes, its integral has units of liters. A negative rate can reduce a quantity without making the quantity itself negative.
AP Calculus AB score overview
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No recommendation
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Possibly qualified
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Qualified
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Well qualified
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Extremely well qualified
Checkpoints only. A result on this site is practice feedback, not an official score.
Lessons
5Practice by topic
8 modules. Drill a weak topic before you open a longer set.
Functions
3 quizzesLimits & Continuity
3 quizzesDifferentiation
4 quizzesApplications Of Differential Calculus
7 quizzesAntidifferentiation
2 quizzesDefinite Integrals
3 quizzesApplications of Integration
4 quizzesDifferential Equations
4 quizzesFull-length practice exams
8 longer sets. Take the parts back to back for a realistic session.
Timed mini-exams
Short timed sets for a daily session, after the topic quizzes feel familiar.
Tips before you practice
- Keep f, f′, and f″ distinct when reading a graph.
- Include the chain-rule factor when differentiating a composition.
- Check endpoints when finding an absolute extremum on a closed interval.
- Distinguish a signed integral from total distance or total area.
Frequently asked questions
A problem may ask for an interpretation, an equation of a tangent line, or a justified extremum. The derivative is often an intermediate result, not the requested conclusion.