AP exams, 10 units
AP Calculus BC exam guide
All ten AP Calculus BC units with published exam weightings, including parametric and polar functions and infinite series.
Follows the fall 2020 course and exam description, from 3 May 2021
Overview
What AP Calculus BC covers.
AP Calculus BC covers everything in AP Calculus AB and adds two further units: parametric equations, polar coordinates, and vector-valued functions, and infinite sequences and series. It also extends several AB units with additional techniques such as integration by parts, partial fractions, improper integrals, Euler's method, and the logistic model.
The published weightings shift substantially from AB. The eight shared units are individually lighter because the two additional units together carry close to thirty percent of the multiple-choice section, with infinite series alone weighted comparably to integration. Students who treat series as an afterthought consistently underperform relative to their calculus ability.
Arcade Academy is an independent study workspace. Use the official Course and Exam Description as the authoritative content list and the official exam page for current format details, and use the unit pages below to organize problem practice and timed free-response work.
At a glance
- Total time
- 3 hours 10 minutes
- Section I
- 42 multiple-choice questions in 1 hour 40 minutes, 50% of the exam score
- Section I detail
- Part A is 29 questions in 62 minutes with no calculator; Part B is 13 questions in 38 minutes with a graphing calculator required
- Section II
- 6 free-response questions in 1 hour 30 minutes, 50% of the exam score
- Section II detail
- Part A is 2 questions in 30 minutes with a graphing calculator required; Part B is 4 questions in 60 minutes with no calculator
- Format update
- The multiple-choice count and section timing changed beginning with the May 2027 exam; confirm the current numbers on the official exam page
- Delivery
- Hybrid digital: multiple-choice questions are answered and free-response prompts are read in College Board's Bluebook app, and free-response answers are handwritten in a paper booklet
- AB subscore
- College Board reports an AB subscore alongside the BC score, based on the portion of the exam covering AB content
- Score scale
- 1 to 5
- Governing body
- College Board
- Who takes it
- High school students taking a full-year calculus course covering first- and second-semester college content, typically headed toward a quantitative major.
Scoring
The multiple-choice and free-response sections each contribute half of a composite score, which College Board converts to the reported 1 to 5 scale using cut points set for that year's exam. BC students also receive an AB subscore, and colleges decide independently how to apply either score for credit or placement.
Exam structure
Units
AP Calculus BC covers 10 units. Open one for its topics, published weighting, and section-specific study tips.
Unit 1: Limits and Continuity
4–7%Unit 1 develops the limit and defines continuity in terms of it, working algebraically, graphically, and numerically. The squeeze…
6 topics
Unit 2: Differentiation: Definition and Fundamental Properties
4–7%Unit 2 defines the derivative through difference quotients and establishes the basic differentiation rules. Differentiability and…
6 topics
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
4–7%Unit 3 covers the chain rule, implicit differentiation, and derivatives of inverse functions including the inverse trigonometric…
6 topics
Unit 4: Contextual Applications of Differentiation
6–9%Unit 4 applies derivatives in context: motion along a line, related rates, linear approximation, and L'Hospital's rule. BC…
5 topics
Unit 5: Analytical Applications of Differentiation
8–11%Unit 5 covers the Mean Value and Extreme Value Theorems, the first and second derivative tests, concavity, curve sketching, and…
6 topics
Unit 6: Integration and Accumulation of Change
17–20%Unit 6 carries the largest published weighting among the shared units. Riemann sums lead to the definite integral, the…
6 topics
Unit 7: Differential Equations
6–9%Unit 7 covers slope fields, separable equations with initial conditions, and exponential models, and BC adds Euler's method for…
5 topics
Unit 8: Applications of Integration
6–9%Unit 8 uses definite integrals to compute average value, accumulated change, area between curves, volumes by cross sections and…
6 topics
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
11–12%Unit 9 is the first of the two BC-only units. It extends calculus to curves described parametrically, to vector-valued functions…
6 topics
Unit 10: Infinite Sequences and Series
17–18%Unit 10 carries a weighting comparable to integration and is the material most unique to BC. It covers convergence tests for…
6 topics
Study strategies
How to work through this exam.
These strategies follow from the exam's own structure. Adapt them to the time you actually have each week.
- Front-load the two BC-only units, since parametric and polar functions plus infinite series together carry close to thirty percent of the multiple-choice section.
- Practice justification in rubric language, because on the free-response section reasoning earns points independently of the final answer.
- Split practice between calculator and no-calculator conditions to match the four separately timed parts of the exam.
- Maintain a convergence-test decision tree and rehearse it until test selection is fast and confident.
- Rotate through the recurring free-response formats: accumulation from a rate, a table problem, particle motion in the plane, an area or volume setup, and a series problem.
- Take at least one full timed exam to build stamina, since the exam runs over three hours across four timed parts.
Common questions
AP Calculus BC questions students ask.
How is the AP Calculus BC Exam structured?
The exam runs 3 hours 10 minutes. Section I is 42 multiple-choice questions in 1 hour 40 minutes for 50% of the score, split into a 29-question no-calculator part and a 13-question calculator part. Section II is 6 free-response questions in 1 hour 30 minutes for the other 50%, split into a 2-question calculator part and a 4-question no-calculator part. Confirm current numbers on the official exam page, since the format changed beginning with the May 2027 exam.
Which BC topics do students find most challenging?
College Board does not rank difficulty. Students most often report that infinite series demands the most practice, particularly test selection and error bounds, and that polar area setups are a frequent source of lost points. Your own practice data should guide your plan.
How is BC scored, and what is the AB subscore?
The two sections contribute equally to a composite score converted to the reported 1 to 5 scale using cut points set each year. BC students also receive an AB subscore based on the portion of the exam covering AB content, which some colleges use for placement when the BC score alone does not qualify.
How much extra material does BC cover beyond AB?
BC adds two full units, parametric, polar, and vector-valued functions and infinite sequences and series, and extends several shared units with techniques such as integration by parts, partial fractions, improper integrals, Euler's method, and the logistic model.
When do students typically start series review?
A common approach is to begin series practice as soon as the unit starts and keep a small amount of series work in every study session afterward, rather than saving it for a final review block. Its published weighting is comparable to integration, so late starts are hard to recover from.
Is Arcade Academy affiliated with College Board?
No. AP® is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this site. Arcade Academy is an independent educational resource.
Before you build the schedule
Exam structures change. Confirm the current format, eligibility, and policies with College Board before you commit to a study plan.
Official exam information opens in a new tabGuide structure last checked against official sources on August 30, 2026.
Markdown version of this guide for citation, offline reading, and language models.
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