AP Calculus AB Study Guide
Calculus AB covers limits, derivatives, and integrals at a pace equivalent to a first-semester college calculus course. The exam weights procedural fluency (can you compute it) about as heavily as conceptual understanding (do you know why it works and when to apply it) — FRQs consistently test the latter.
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AP Calculus AB Score CalculatorUnit Breakdown
Unit 1: Limits and Continuity
Estimating limits graphically/numerically, limit laws, and the formal definition of continuity.
Unit 2: Differentiation: Definition & Properties
The derivative as a limit, differentiation rules, and the relationship between differentiability and continuity.
Unit 3: Differentiation: Composite, Implicit, Inverse Functions
Chain rule, implicit differentiation, and derivatives of inverse functions.
Unit 4: Contextual Applications of Differentiation
Related rates, motion problems (position/velocity/acceleration), and linearization.
Unit 5: Analytical Applications of Differentiation
Extrema, concavity, the Mean Value Theorem, and optimization.
Unit 6: Integration and Accumulation of Change
Riemann sums, the Fundamental Theorem of Calculus, and antiderivatives.
Unit 7: Differential Equations
Slope fields, separable differential equations, and exponential growth/decay models.
Unit 8: Applications of Integration
Area between curves, volumes of solids (including disc/washer methods), and average value of a function.
Unit topics reflect College Board's published Course and Exam Description at a high level — always check the current CED for exact skill weighting, since College Board revises these periodically.
Common Mistakes to Avoid
- Computing a derivative or integral correctly but failing to answer the actual question asked (e.g. finding a critical point instead of classifying it as a max/min).
- Forgetting units and context in applied FRQs — a correct number without proper justification ("because f'(x) changes from positive to negative") loses points.
- Mixing up when to use the chain rule vs. product/quotient rule on composite functions.
- Not showing work on calculator-active questions — even with a correct final answer, FRQs require justification, not just a number.
What's Next
Once you've worked through these units, check the AP Calculus AB exam format and score curve to see how MCQ and FRQ points combine into your final score, or review 2027 exam dates and registration deadlines.