AP Calculus AB Unit Tests
Pick a unit to drill it head-on. Each unit has 4 different test variations so you can keep retaking until you master it.
Unit 1: Limits and Continuity
Limits from graphs, tables, and algebra; squeeze theorem; asymptotes; continuity and the IVT.
12 questions · ~18 min
Unit 2: Differentiation: Definition and Fundamental Properties
The limit definition, differentiability, and the power, product, quotient, trig, exponential, and log rules.
12 questions · ~18 min
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
The chain rule, implicit differentiation, inverse and inverse trig derivatives, and higher-order derivatives.
12 questions · ~18 min
Unit 4: Contextual Applications of Differentiation
Derivatives in context, straight-line motion, related rates, local linearity, and L’Hospital’s rule.
12 questions · ~18 min
Unit 5: Analytical Applications of Differentiation
The MVT and EVT, increasing and decreasing intervals, extrema, concavity, curve sketching, and optimization.
12 questions · ~18 min
Unit 6: Integration and Accumulation of Change
Riemann and trapezoidal sums, accumulation functions, both parts of the FTC, antiderivatives, and u-substitution.
12 questions · ~18 min
Unit 7: Differential Equations
Modeling with differential equations, slope fields, separation of variables, and exponential growth and decay.
12 questions · ~18 min
Unit 8: Applications of Integration
Average value, motion and accumulation, area between curves, and volumes by cross sections, discs, and washers.
12 questions · ~18 min
How unit tests work
- Focused on a single AP unit, between a single-topic quiz and the full diagnostic.
- 4 variations per unit — pick a fresh variation any time you retake.
- Roughly 90 seconds per question — the same pacing as the AP exam.
- You'll get a unit-level score, recommended topics to review, and a question-by-question explanation.
About the AP Calculus AB exam
AP Calculus AB covers the core of a first-semester college calculus course: limits and continuity, differentiation, applications of derivatives, integration and accumulation of change, and differential equations. The course is built around three big ideas that recur throughout every unit: change (the derivative), limits, and the analysis of functions. Students learn to interpret calculus graphically, numerically, analytically, and verbally, and they are expected to justify their reasoning rather than simply produce answers. Roughly speaking, derivatives and their applications dominate the first half of the course, while integrals and the Fundamental Theorem of Calculus anchor the second half. Where students most often struggle is in moving beyond mechanical computation toward genuine conceptual understanding: knowing not just how to take a derivative but what it means in context, when a limit fails to exist, why a function is or is not differentiable, and how the definite integral represents accumulated change. Free-response questions reward careful setup, correct units, and explicit justification using theorems like the Mean Value Theorem or the Intermediate Value Theorem. Strong preparation blends conceptual review with extensive timed practice on released free-response questions, deliberate work on no-calculator algebra and trig fluency, and attention to calculator-active problem types such as numeric integration and finding intersection points. Students who can read a graph or table and translate it into a calculus statement, and who write organized justifications, consistently outperform those who memorize procedures. Mastering notation, units, and the language of justification is as important as the calculus itself.
Exam structure
Two equally weighted sections totaling 3 hours 15 minutes: Section I is 45 multiple-choice questions in 1 hour 45 minutes (30 no-calculator in 60 min, 15 calculator in 45 min), and Section II is 6 free-response questions in 1 hour 30 minutes (2 calculator in 30 min, 4 no-calculator in 60 min). Each section is 50% of the score.
Scoring
Raw multiple-choice and free-response points are combined into a weighted composite that College Board converts to a 1-5 AP score, with 3 generally considered passing.
Common mistakes
- Forgetting units or context in free-response answers (e.g., stating a rate without specifying meters per second)
- Treating the Fundamental Theorem of Calculus mechanically and dropping the chain rule when the upper limit is a function
- Confusing average value of a function with average rate of change
- Failing to explicitly justify conclusions using named theorems (MVT, IVT, candidates test) when a question asks for justification
- Algebra and trig errors on no-calculator sections, especially sign errors and mishandling of trig derivatives