# AP Calculus BC: Units, Exam Format, Study Guide and Free Practice > A free AP Calculus BC study guide: all 10 units and their exam weights, the 2027 exam format and date, the AB subscore, sample questions and practice. Source: https://practicecalculus.com/ap-calculus/bc Updated: 2026-11-06 ## At a glance - **Exam date:** Monday, May 10, 2027 - **Exam length:** 3 hours 10 minutes - **Questions:** 42 multiple choice and 6 free response - **Format:** Hybrid digital: answer in the Bluebook app, write free-response work on paper - **Calculator:** Graphing calculator for some parts only - **College equivalent:** A first-semester college calculus course and the single-variable course after it - **Units:** 10: the 8 AB units plus parametric and polar curves, and series - **Scores:** A BC score plus an AB subscore, both from 1 to 5 - **Practice here:** [Calculus 1](/learn/calculus-1) and [Calculus 2](/learn/calculus-2) ## Key takeaways - AP Calculus BC covers everything in AB plus parametric, polar and vector-valued functions and infinite series, matching about two semesters of college calculus. - The 2027 exam is on Monday, May 10, lasts 3 hours 10 minutes and has 42 multiple-choice and 6 free-response questions. - Infinite sequences and series carry the most weight of any BC unit, at 15 to 20 percent, tied with integration and accumulation. - Every BC student also gets an AB subscore, so the AB topics still matter a great deal. **AP Calculus BC** is College Board's faster calculus course. It includes all of [AP Calculus AB](/ap-calculus/ab) plus parametric and polar curves and infinite series, and it matches about two semesters of college calculus. This guide covers all 10 units, how much each one counts, how the exam and the AB subscore work, and where to practice every topic with instant feedback. ## The 2027 AP Calculus BC exam The exam is on **Monday, May 10, 2027**. It is a hybrid digital exam: you answer multiple-choice questions and read the free-response questions in the Bluebook app, then write your free-response work by hand in a paper booklet. | Section | Questions | Time | Calculator | Share of score | | --- | --- | --- | --- | --- | | Multiple choice, Part A | 29 | 1 hr 40 min for both parts | No | 35% | | Multiple choice, Part B | 13 | (shared with Part A) | Graphing calculator for some | 15% | | Free response, Part A | 2 | 30 min | Graphing calculator for some | 16.7% | | Free response, Part B | 4 | 60 min | No | 33.3% | In total that is **3 hours 10 minutes**: 42 multiple-choice and 6 free-response questions. You get two scores from 1 to 5: your **BC score** and an **AB subscore**, which comes from the part of the exam that covers AB topics. Colleges can use the subscore like an AB exam score. ## AP Calculus BC units and what to practice BC has 10 units. Units 1 to 8 share their names with AB but add BC topics such as integration by parts, partial fractions, improper integrals, Euler's method, logistic growth and arc length. Units 9 and 10 are only in BC. | Unit | Exam weight | Practice | Read | | --- | --- | --- | --- | | 1. Limits and Continuity | 5–10% | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [Squeeze Theorem](/theorems/squeeze-theorem) | | 2. Differentiation: Definition and Fundamental Properties | 5–10% | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative), [product and quotient rules](/blog/product-and-quotient-rules) | | 3. Differentiation: Composite, Implicit, and Inverse Functions | 5–10% | [Inverse trig derivatives](/learn/calculus-1/derivative-rules/inverse-trig-derivatives) | [Chain rule](/rules/chain-rule), [inverse function rule](/rules/inverse-function-rule) | | 4. Contextual Applications of Differentiation | 5–10% | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates), [L'Hôpital's rule](/rules/lhopitals-rule) | | 5. Analytical Applications of Differentiation | 10–15% | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Mean Value Theorem](/theorems/mean-value-theorem), [curve sketching](/blog/curve-sketching-with-derivatives) | | 6. Integration and Accumulation of Change | 15–20% | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Fundamental Theorem of Calculus](/theorems/fundamental-theorem-of-calculus-part-2), [improper integrals](/blog/improper-integrals) | | 7. Differential Equations | 5–10% | [Euler's method](/learn/calculus-2/improper-integrals-and-applications/eulers-method) | [Logistic growth](/learn/calculus-2/improper-integrals-and-applications/logistic-growth) | | 8. Applications of Integration | 5–10% | [Volumes with cross-sections](/learn/calculus-1/applications-of-integrals/volumes-cross-sections) | [Volumes of revolution](/blog/volumes-of-revolution), [area between curves](/blog/area-between-curves) | | 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions | 10–15% | [Parametric motion](/learn/calculus-2/power-series-parametric-polar/parametric-motion) | [Slopes of polar curves](/learn/calculus-2/power-series-parametric-polar/polar-slopes) | | 10. Infinite Sequences and Series | 15–20% | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests), [Taylor series](/blog/taylor-series) | Units 6 and 10 can each be up to a fifth of the exam. Series in particular is new to most students and builds slowly: geometric series first, then convergence tests, then power series, Taylor polynomials and error bounds. Give it several weeks. ## What the BC free-response questions look like Free response is half of the score. BC students meet the same question types as AB, often with a BC twist, plus questions only BC asks: - **A particle in the plane.** Given $x'(t)$ and $y'(t)$, find the velocity vector, the speed, the total distance traveled and the slope $\dfrac{dy}{dx}$ at a point. - **A polar curve.** Find the area inside a region with $\frac{1}{2}\int r^2\,d\theta$, and decide whether the point is moving toward or away from the origin. - **A Taylor polynomial.** Write the first terms of a series, find its interval of convergence, and bound the error with the [alternating series](/rules/alternating-series-test) or Lagrange error bound. - **A differential equation.** Use [Euler's method](/learn/calculus-2/improper-integrals-and-applications/eulers-method) for an estimate, then decide whether it is too high or too low from the concavity. As with AB, every claim needs a reason. Name the test or theorem, check its conditions, and connect the answer to the question in a short sentence. ## Example problems at the AP Calculus BC level **1. Integration by parts (Unit 6).** Evaluate $\int x e^x\,dx$ with $u = x$ and $dv = e^x\,dx$: $$\int x e^x\,dx = x e^x - \int e^x\,dx = (x - 1)e^x + C$$ **2. A parametric slope (Unit 9).** For $x = t^2$ and $y = t^3 - 3t$, find $\dfrac{dy}{dx}$ at $t = 2$. $$\frac{dy}{dx} = \frac{3t^2 - 3}{2t} = \frac{12 - 3}{4} = \frac{9}{4}$$ **3. A geometric series (Unit 10).** Find the sum. $$\sum_{n=0}^{\infty} 3\left(\frac{1}{4}\right)^n = \frac{3}{1 - \frac{1}{4}} = 4$$ ## How to prepare for AP Calculus BC - **Do not neglect the AB topics.** They are most of the exam and the whole AB subscore. Keep practicing derivatives, integrals and accumulation alongside the new BC units. - **Start series early.** Work through [sequences](/learn/calculus-2/sequences-and-series/sequences), [geometric series](/learn/calculus-2/sequences-and-series/geometric-series) and the [ratio test](/rules/ratio-test) well before spring, so there is time for power series and Taylor polynomials. - **Practice a little every day.** Every lesson here gives new numbers each time, so you can repeat a topic until it feels automatic. - **Keep the formulas close.** The [calculus formula sheet](/formulas) has every derivative, integral and series on one page. No formula sheet is provided on the exam. - **Take timed practice exams** in the final weeks using [practice exams](/practice), and review every mistake. Not sure BC is right for you? Read our comparison of [AP Calculus AB vs BC](/blog/ap-calculus-ab-vs-bc) or the [AP Calculus AB guide](/ap-calculus/ab). > AP and Advanced Placement are registered trademarks of College Board, which is not affiliated with PracticeCalculus and does not endorse this guide. Exam details come from College Board's AP Calculus BC pages; check them for any changes. ## Frequently asked questions ### What is on the AP Calculus BC exam? All 8 AB units, from limits to applications of integration, with some extra BC topics inside them such as integration by parts, Euler's method and logistic growth, plus two BC-only units: parametric, polar and vector-valued functions, and infinite sequences and series. ### When is the 2027 AP Calculus BC exam? College Board lists the 2027 AP Calculus BC exam for Monday, May 10, 2027. Your AP coordinator confirms the exact time and room. ### What is the AB subscore? Every BC exam also reports an AB subscore from 1 to 5, based on the part of the exam that covers AB topics. Colleges can use it like an AB exam score, for example to give credit for Calculus 1 when the BC score alone does not earn credit for Calculus 2. ### Can I take both AP Calculus AB and BC? Not in the same year. College Board does not allow students to take both exams in one year, and the AB subscore on the BC exam already covers the AB material. ### Is AP Calculus BC harder than AB? The ideas are not much harder, but there are more of them in the same school year, so the pace is faster. Series is usually the unit students find most new, so start practicing it early.