Review AP Calculus AB and BC with unit study guides, targeted practice questions, and FRQ practice across limits, derivatives, integrals, and series. Use these AP Calculus resources to build fluency with graphs, tables, equations, accumulation, and rate-of-change reasoning.
AP Calculus AB/BC is a college-level math course built around derivatives and integrals, asking you to reason about how things change and accumulate using graphical, numerical, and algebraic thinking.
Get the big picture: what AP Calculus AB/BC covers, how it is scored, and how the units connect.
read the overviewAnswer a quick mix of questions to see which units need the most review.
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browse all 9 unitsAP Calculus AB/BC, often searched simply as AP Calc, is a college-level course built around two big ideas: how things change through derivatives, and how things accumulate through integrals. You start with limits and continuity, then move through differentiation, integration, differential equations, and real-world applications like motion, optimization, and related rates. Throughout, you work with graphical, numerical, and algebraic representations and learn to justify your reasoning, not just compute answers.
AB covers differential and integral calculus across Units 1 through 8, equivalent to a first-semester college course. BC adds parametric, polar, and vector-valued functions, advanced integration techniques, and infinite series across Units 9 and 10, equivalent to a full year. Because each unit builds on the last, keeping up week to week matters more than any single cram session. Understanding why the math works is what carries you through the harder applications.
Evaluate limits and confirm continuity using graphs, tables, and algebraic methods
Apply the power, product, quotient, and chain rules plus implicit and inverse differentiation
Solve related rates, optimization, and motion problems in real contexts
Use the Fundamental Theorem of Calculus to evaluate definite integrals and accumulation functions
Model and solve differential equations and compute areas and volumes
For BC, analyze parametric and polar curves and test infinite series for convergence
The course is organized into 9 units. The percentages below are the College Board exam weights, so you can see which units carry the most multiple-choice points. Open each unit for its study guide, topic pages, key terms, and practice questions.
AP Calculus Unit 1, Limits and Continuity, makes up 10-12% of the AP exam and builds the single idea everything else in calculus rests on.
AP Calculus Unit 2, Fundamentals of Differentiation, is where you formally define the derivative as a limit of a difference quotient and learn the core rules for computing it, including the Power Rule, Product Rule, Quotient Rule, and the derivatives of sin x, cos x, e^x, and ln x.
AP Calculus Unit 3 is about one rule and everything it unlocks.
AP Calculus Unit 4, Contextual Applications of Differentiation, is where derivatives stop being abstract slope machines and start answering real questions, like how fast a ladder slides down a wall or what a population's growth rate means.
AP Calculus Unit 5, Analytical Applications of Differentiation, is where derivatives stop being a computation and start being evidence.
AP Calculus Unit 6, Integration and Accumulation of Change, is where the second half of calculus begins.
AP Calculus Unit 7 covers differential equations, which are equations that relate a function to its own derivative, like dy/dx = ky.
AP Calculus Unit 8, Applications of Integration, is where the definite integral stops being an abstract area calculation and starts answering real geometric questions, like the average value of a function, how far a particle travels, the area trapped between two curves, and the volume of a 3D solid.
AP Calculus BC Unit 9 extends everything you know about derivatives and integrals to curves that can't be written as y = f(x), using parametric equations, vector-valued functions, and polar coordinates.
These trends come from real Fiveable practice data, so you can see what students are reviewing, which topics need extra attention, and how written practice can improve over time.
Miss rate is based on high-volume AP Calculus AB/BC multiple-choice practice.
Average MCQ accuracy by student practice volume across 2,534 AP Calculus AB/BC students.
Among AP Calculus AB/BC FRQ responses that students retried on Fiveable, average scores rose from 41% on the first attempt to 61% on the latest attempt.
practice AP Calculus AB/BC FRQs →These guides collect important exam skills, big ideas, essay tasks, and other subject-specific resources.
15 guides
Work through the material unit by unit and practice problems by hand every day, since reading examples feels productive but only solving builds the skill. Calculus is cumulative, so review earlier units as you go to keep limits and derivative rules sharp. Do problems on both calculator and no-calculator sections, because the exam tests both. Pull free-response questions from past exams to see exactly how reasoning is expected, and practice writing organized work that earns partial credit. Target your weak spots, whether that is related rates, integration techniques, or series, instead of redoing what you already know.
Build the foundation in Units 1 through 3: limits, continuity, and core derivative rules
Practice contextual and analytical derivative applications from Units 4 and 5, including related rates and optimization
Drill integration in Unit 6 with Riemann sums, the Fundamental Theorem, and substitution
Work differential equations and integration applications in Units 7 and 8, including volumes
For BC, add parametric, polar, and series work from Units 9 and 10
Take timed mixed multiple-choice sets and full FRQ practice, then review every mistake
Use the question types below to plan written-response practice and connect exam guides to timed FRQs.
| Question | Focus | Details | % of Score |
|---|---|---|---|
| FRQs 1-2 | Part A (Calculator) | 30 min | 16% |
| FRQs 3-6 | Part B (No Calculator) | 60 min | 32% |
AP Calculus AB/BC covers limits, derivatives, integrals, applications of those ideas, and BC-only topics like series and advanced accumulation methods.
Review the main concept first, then work practice problems right away so the formulas and reasoning stick. Topic guides help most when you pair them with active problem-solving.
Use Fiveable's AP Calculus FRQ practice for AP-style free-response questions with AI-supported scoring on setup, notation, calculator use, and mathematical reasoning.
Start by unit if you are following class material, and switch to skill-based review closer to the exam. That makes it easier to connect related ideas like derivatives, integrals, and their applications.