Exam prep · AP Calculus AB

AP Calculus AB flashcards: rules, theorems and the setups they unlock

Calculus rewards instant recall of a short list of rules and theorems so that your working memory is free for the setup. Flashcards cover that list in a week; the rest of your time goes to released problems. Start with the free derivatives and integrals deck below.

Updated 2026-10-27. Decks are shared by Quizcard and its users; study them on the page or copy them into a free account.

AP Calculus AB at a glance

What the AP Calculus AB tests

• Unit 1: Limits and continuity. 10 to 12% of the exam. Study guide →
• Unit 2: Differentiation: definition and fundamental properties. 10 to 12%. Study guide → Watch the lesson →
• Unit 3: Differentiation: composite, implicit and inverse functions. 9 to 13%. Study guide →
• Unit 4: Contextual applications of differentiation. Related rates, motion, linearization, L’Hospital. 10 to 15%. Study guide →
• Unit 5: Analytical applications of differentiation. Mean Value Theorem, extrema, concavity, optimization. 15 to 18%. Study guide → Watch the lesson →
• Unit 6: Integration and accumulation of change. Riemann sums, the Fundamental Theorem, u-substitution. 17 to 20%. Study guide → Watch the lesson →
• Unit 7: Differential equations. Slope fields, separation of variables, exponential models. 6 to 12%. Study guide → Watch the lesson →
• Unit 8: Applications of integration. Average value, motion, area between curves, volumes. 10 to 15%. Study guide →

AP Calculus AB unit study guides

Each guide is the unit on one page: a mindmap, the ideas in order, a worked exam-style question, the mistake students make most, then the flashcards and quiz for it.

• Unit 1: Limits and continuityStudy guide and mindmap
• Unit 2: Differentiation: definition and fundamental propertiesStudy guide, mindmap and video lesson
• Unit 3: Differentiation: composite, implicit and inverse functionsStudy guide and mindmap
• Unit 4: Contextual applications of differentiationStudy guide and mindmap
• Unit 5: Analytical applications of differentiationStudy guide, mindmap and video lesson
• Unit 6: Integration and accumulation of changeStudy guide, mindmap and video lesson
• Unit 7: Differential equationsStudy guide, mindmap and video lesson
• Unit 8: Applications of integrationStudy guide and mindmap

Free AP Calculus AB flashcard decks

• Calculus: Derivatives and Integrals30 cards · University · Applications · Derivative rules · Integrals · Limits
• Algebra and Geometry: Essential Formulas30 cards · High school · Algebra · Geometry
• AP Calculus AB: Limits, Continuity and Derivative Rules34 cards · High school · Continuity and Discontinuities · Definition of the Derivative · Derivative Rules · Derivatives of Trig Functions

Missing a topic? Upload the chapter from your prep book and Quizcard builds the deck for you, grouped by topic, with figures kept from PDFs. How it works.

Test yourself: free AP Calculus AB practice quizzes

• Algebra and Geometry: Essential Formulas quiz18 multiple-choice questions with explanations · no account needed
• AP Calculus AB: Limits, Continuity and Derivative Rules quiz15 multiple-choice questions with explanations · no account needed

Each quiz scores you at the end and explains every answer. Redo it any time; the questions reshuffle.

AP Calculus AB video lessons

One unit per video: the ideas, a worked exam-style question and the mistake students make most. Study the flashcards and take the quiz above after watching.

Sample cards from “Calculus: Derivatives and Integrals”

What is linear approximation?

Answer: f(x) ≈ f(a) + f'(a)(x − a) near x = a.

Explanation

The tangent line as an estimate; differentials dy = f'(x)dx.

Geometric series sum

Answer: ∑ arⁿ (n from 0) = a / (1 − r) when |r| < 1

Explanation

Diverges when |r| ≥ 1.

Taylor series of eˣ, sin x, cos x at 0

Answer: eˣ = ∑ xⁿ/n!; sin x = ∑ (−1)ⁿ x²ⁿ⁺¹/(2n+1)!; cos x = ∑ (−1)ⁿ x²ⁿ/(2n)!

Explanation

All converge for every real x.

Ratio test

Answer: Let L = lim |aₙ₊₁ / aₙ|: converges absolutely if L < 1, diverges if L > 1, inconclusive if L = 1.

Explanation

Best for factorials and exponentials.

What is the nth-term test for divergence?

Answer: If lim aₙ ≠ 0, the series ∑aₙ diverges.

Explanation

Does not prove convergence when the limit is 0 (harmonic series).

What is an improper integral and when does it converge?

Answer: An integral with an infinite limit or an unbounded integrand; it converges if the limit of the proper integrals exists and is finite.

Explanation

∫₁^∞ 1/xᵖ dx converges when p > 1.

Showing 6 of 30 cards. Study the whole deck or copy it into your account.

A flashcard study plan for the AP Calculus AB

1. Week 1: derivative rules and the derivatives of the standard functions, one card each, until flipping the deck takes under five minutes.
2. Week 2: theorems with their hypotheses (IVT, EVT, MVT, Fundamental Theorem). Front: the theorem name. Back: what it needs and what it gives.
3. Week 3: integration techniques and the accumulation interpretation. Card the “units of the integral” reasoning the free-response questions ask for.
4. Week 4: upload your textbook chapters or notes and generate decks; card every released free-response rubric point you missed.
5. Weeks 5 to 6: two released exams under time, then only the “missed” deck in the last five days.

How to write AP Calculus AB cards that work

• Card the justification sentences, not just answers: “f has a relative maximum at x = 2 because f′ changes from positive to negative there.”
• One card per setup: related rates (what to differentiate), optimization (what to minimise and over what domain), volumes (which cross-section).
• Keep a separate no-calculator deck of exact values: trig at special angles, e and ln facts, derivatives of inverse trig functions.
• Mark cards you miss twice and study only those in the final week.

Questions

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Official information: College Board: AP Calculus AB. Formats and weights change; check the official page before test day.