AP Calculus Formula Review: What You Must Know Cold

By Mobin Akhter · Updated July 10, 2026 · CalcRef study guides

Here is the fact that should organize your entire AP Calculus review: the exam does not give you a formula sheet. Unlike AP Physics or AP Statistics, Calculus AB and BC hand you nothing but the questions. Every derivative rule, antiderivative, identity, and (for BC) series fact you plan to use must come from memory. That makes formula review not a finishing touch but a core pillar of preparation — and it rewards students who organize it deliberately instead of hoping familiarity carries them through.

How the exam actually uses formulas

AP problems rarely say "state the quotient rule." Instead, formulas appear as the entry ticket to a larger task: you can't do the related-rates problem without the chain rule, can't evaluate the definite integral without knowing the antiderivative of sec²x, can't answer the series question without the conditions of the alternating series test. A shaky formula doesn't cost you one point — it blocks the whole problem. That is why "mostly knowing" a formula is functionally the same as not knowing it.

The calculator policy sharpens this further. Substantial portions of both the multiple-choice and free-response sections are no-calculator, so even computational fluency (unit circle values, common antiderivatives) has to live in your head.

The AB core: formula families to master

• Limits and continuity: limit laws, the definition of continuity at a point, the squeeze theorem, and the special limits lim sin x / x = 1 and lim (1−cos x)/x = 0 as x→0. Know when L'Hôpital's rule legitimately applies (0/0 or ∞/∞ only).
• Derivative rules: power, product, quotient, chain — plus the full table of trig, inverse trig, exponential, and logarithmic derivatives. These must be automatic; see our derivative rules guide for the structure behind them.
• Applications of derivatives: the Mean Value Theorem statement and hypotheses, first- and second-derivative tests, and the linear approximation formula.
• Integrals and the FTC: both parts of the Fundamental Theorem of Calculus, standard antiderivatives (including ∫1/x dx = ln|x| + C with the absolute value), and average value of a function.
• Applications of integrals: area between curves, volumes by disks/washers and by known cross-sections, and accumulation-of-change setups.

The BC additions

• Techniques of integration: integration by parts and partial fractions setups.
• Sequences and series: geometric series sum and its convergence condition, the p-series criterion, the ratio test, and the conditions for the alternating series test with its error bound. Choosing among tests is its own skill — covered in our convergence test guide.
• Taylor and Maclaurin series: the general Taylor term and the standard Maclaurin expansions for eˣ, sin x, cos x, and 1/(1−x), with their intervals of convergence.
• Parametric, polar, and vectors: parametric derivatives and arc length, polar area A = ½∫r² dθ, and vector-valued velocity/acceleration relationships.

Trig identities: the quiet prerequisite

A surprising number of AP integration problems hinge on precalculus identities: the Pythagorean identities for simplifying, double-angle formulas for integrating sin²x and cos²x, and instant unit-circle values at the standard angles in both degrees and radians. Students routinely rate these "already known" and then stall on them mid-problem. Put them in the review rotation like everything else.

Organizing the review: a topic-by-topic plan

1. Inventory first. Quiz yourself once over every topic, blank-page style, and let the misses — not your feelings — define the weak list. Self-assessment by intuition consistently overrates the topics you saw most recently.
2. Drill by topic, in curriculum order. Limits before derivatives, derivatives before integrals: later formulas lean on earlier ones, so repairs propagate forward.
3. Mix in the final stretch. The exam interleaves everything, so your last week of formula practice should too. Mixed-topic rounds train the "which tool is this?" reflex that single-topic drilling never touches. Our memorization guide covers the full spacing-and-interleaving system.
4. Track results over time. A topic isn't done when you get it right once; it's done when it stays right across sessions spaced days apart.

Frequently asked

Is there a formula sheet on the AP Calculus exam?

No. Neither AB nor BC provides one. Every formula you use must be memorized — which is why formula review deserves dedicated time, not leftover time.

How early should formula review start?

Ideally the week each topic is taught, with light ongoing maintenance. Spaced review needs a runway; starting in the final month means fighting the forgetting curve instead of riding it.

AB vs. BC — how different is the formula load?

BC contains all of AB plus techniques of integration, the series/convergence toolkit, Taylor/Maclaurin expansions, and parametric/polar/vector formulas. If you're in BC, budget roughly a third of your formula time for the BC-only material.