The Ultimate Guide to AP Calculus AB/BC + Study Resource
What to Know, How to Prepare & Free Study Resources
AP Calculus is often considered the gold standard of high school math. A strong score on AB or BC can earn you credit for one or two semesters of college calculus, putting you ahead in STEM fields from engineering to economics to computer science.
AB or BC? AP Calculus AB covers roughly one semester of college calculus (Calculus I). AP Calculus BC covers two semesters (Calculus I + II) and includes everything in AB plus additional topics like parametric equations, polar curves, and series. BC isn't necessarily "harder" — it just covers more material. Both exams test conceptual understanding, not just computation.
Here's everything you need to know.
What Does AP Calculus Cover?
Calculus AB — 8 Units:
| Unit | Topics | Exam Weight |
|---|---|---|
| 1: Limits & Continuity | Limit definition, properties, squeeze theorem, continuity, IVT | 10–12% |
| 2: Differentiation: Definition & Fundamental Properties | Derivative definition, basic rules, product/quotient/chain rule | 10–12% |
| 3: Differentiation: Composite, Implicit & Inverse | Chain rule applications, implicit differentiation, inverse functions | 9–13% |
| 4: Contextual Applications of Differentiation | Related rates, linearization, L'Hôpital's Rule, motion problems | 10–15% |
| 5: Analytical Applications of Differentiation | Mean Value Theorem, extrema, concavity, optimization, curve sketching | 15–18% |
| 6: Integration & Accumulation of Change | Riemann sums, FTC, definite/indefinite integrals, u-substitution | 17–20% |
| 7: Differential Equations | Slope fields, separation of variables, exponential growth/decay | 6–12% |
| 8: Applications of Integration | Area between curves, volumes of revolution (disk/washer), cross-sections | 10–15% |
Calculus BC includes all AB units plus:
| Unit | Topics |
|---|---|
| 9: Parametric, Polar & Vector-Valued Functions | Parametric derivatives, polar area, vector motion |
| 10: Infinite Sequences & Series | Convergence tests, Taylor/Maclaurin series, power series, error bounds |
Units 5 and 6 carry the most weight in AB. Analytical applications of derivatives and integration together make up roughly a third of the exam.
The Exam Format
Both AP Calculus AB and BC exams are 3 hours and 15 minutes long with identical structure:
Section I — Multiple Choice (50% of score)
- Part A: 30 questions in 60 minutes — no calculator
- Part B: 15 questions in 45 minutes — calculator required
- Total: 45 questions in 105 minutes
Section II — Free Response (50% of score)
- Part A: 2 questions in 30 minutes — calculator required
- Part B: 4 questions in 60 minutes — no calculator
- Total: 6 questions in 90 minutes
FRQs test your ability to set up and solve problems, justify your answers, and interpret results in context. Showing your work is critical — even a correct answer with no supporting work may not earn full credit.
BC Subscore: If you take BC, you'll also receive an AB subscore based on the portions of the exam that cover AB-only content.
Study Tips That Actually Work for AP Calculus
1. Understand the Fundamental Theorem of Calculus — Deeply
The FTC connects differentiation and integration, and it's the conceptual backbone of the entire course. Make sure you can explain both parts, apply them to accumulation functions, and use them in novel contexts. FRQs frequently test FTC understanding.
2. Show Every Step on FRQs
Calculus FRQs award points for setup, method, and answer separately. Even if your final answer is wrong, you can earn most of the points for correct setup and process. Never skip steps, and always write the integral or derivative expression before evaluating.
3. Practice Without a Calculator
Half the exam is no-calculator. Make sure you can differentiate and integrate by hand fluently. Practice computing limits, derivatives (including chain rule and implicit), and integrals (u-substitution, basic antiderivatives) without technology.
4. Memorize Key Derivative and Integral Rules
You need these to be automatic: power rule, product rule, quotient rule, chain rule, trig derivatives, inverse trig derivatives, exponential and logarithmic derivatives, and their corresponding antiderivatives. Speed matters when you have 2 minutes per MC question.
5. Connect Graphs of f, f', and f''
The exam frequently gives you the graph of a derivative and asks about the original function (or vice versa). Practice identifying where f is increasing/decreasing from f', where f has extrema, and where f is concave up/down from f''. This is tested on both MC and FRQ.
6. For BC: Start Series Early
Infinite series (Unit 10) is the topic BC students struggle with most, and it often appears on 2–3 FRQs. Learn the convergence tests (ratio, comparison, integral, alternating series), Taylor series construction, and error bounds well before exam season.
Get Your Free AP Calculus Vocabulary Guide
We created a comprehensive AP Calculus AB/BC Vocabulary & Key Concepts Guide for the exam, and it's completely free.
Here's what's inside:
- 70+ essential terms covering all AB units plus BC-only topics
- Clear definitions with mathematical notation and formulas
- Key theorems and rules (FTC, MVT, IVT, L'Hôpital's) explained in plain language
- BC-only topics clearly marked so AB students know what to skip
- Exam format breakdown with calculator vs. no-calculator strategies
- Unit weight guide to focus your study time
From limits to L'Hôpital's Rule to Taylor series — every concept the AP Calculus exam tests is covered.
🎀 [Download the Free AP Calculus AB/BC Vocabulary Guide]
AP Exam Master is available online and as an iOS and Android app.