Guide to the AP Calculus BC Exam (2025)

The AP® Calculus BC Exam is a college-level test given every May after the completion of AP Calculus BC. It covers all of AP Calculus AB plus additional advanced topics, making it one of the most challenging AP math exams. A high score can earn you college credit equivalent to a full year of college calculus.

This guide walks you through everything you need to know — exam format, content, formulas, scoring, strategies, and FAQs.

Guide to AP Calculus BC Exam Overview

AP Calculus BC is equivalent to a full-year college course in calculus (Calculus I & II). The exam tests both conceptual understanding and procedural fluency across derivatives, integrals, sequences, and series.

• Exam Length: 3 hours, 15 minutes

• Format: Multiple Choice + Free Response

• Calculator Policy: Certain sections allow graphing calculators; others prohibit them.

AP Calculus BC Exam Sections & Question Types

Section	Time	Number of Questions	% of Exam	Calculator?
Multiple Choice Part A	60 minutes	30	33.3%	No
Multiple Choice Part B	45 minutes	15	16.7%	Yes
Free Response Part A	30 minutes	2	16.7%	Yes
Free Response Part B	60 minutes	4	33.3%	No

Total: 105 questions in 3 hours, 15 minutes.

What’s on the AP Calculus BC Exam?

The exam includes all AP Calculus AB topics plus extra BC topics.

AB Topics (also on BC)

• Limits and Continuity

• Derivatives (rules, applications, motion, optimization, related rates)

• Integrals (definite/indefinite, substitution, applications like area & volume)

• Differential Equations (slope fields, separable DEs)

• Fundamental Theorem of Calculus

BC-Only Topics

• Parametric, Polar, and Vector Functions

• Sequences and Series (convergence/divergence, Taylor & Maclaurin series, power series)

• Advanced Integration Techniques (integration by parts, partial fractions)

• Arc Length & Surface Area (parametric/polar curves)

Calculator Policy

• Permitted Graphing Calculators: TI-84, TI-Nspire CX, Casio fx-9860, etc. (check College Board list).

• Calculator Sections: MC Part B & FRQ Part A.

• Non-Calculator Sections: MC Part A & FRQ Part B — expect algebra-heavy, symbolic manipulation questions here.

Key Formulas & Theorems

You’ll get a formula sheet on exam day, but know how to apply:

Limits & Derivatives

• Limit definition of derivative:

• Chain Rule, Product Rule, Quotient Rule

Integrals

• Fundamental Theorem of Calculus:

• Substitution, integration by parts:

Series

• Geometric Series: converges if |r| < 1.

• Taylor Series for e^x, sin⁡x, cos⁡x, ln⁡(1+x)

• Convergence Tests: Ratio Test, Alternating Series Test, Comparison Test.

Polar & Parametric

• Area (polar):

• Arc Length (parametric):

How Is the AP Calculus BC Exam Scored?

AP scores are reported on a scale of 1–5. Here’s the May 2025 score distribution:

Score	Meaning	% of Test Takers
5	Extremely qualified	44%
4	Well qualified	22%
3	Qualified	13%
2	Possibly qualified	15%
1	No recommendation	6%

👉 Nearly 60% of students score a 4 or 5, making Calc BC one of the more successful AP exams for well-prepared students.

Common Mistakes to Avoid

1. Not Practicing Without a Calculator – Non-calc sections require strong algebra skills.

2. Misusing Series Tests – Always check conditions (e.g., ratio test only works for positive terms).

3. Forgetting Differential Equation Methods – Don’t skip slope fields and separable DEs.

4. Ignoring Units/Context – FRQs often require interpreting answers with context (e.g., “rate of change in population”).

Best Prep Resources

• College Board FRQs & Practice Exams – Essential practice.

• Khan Academy AP Calculus – Free lessons and problems.

• Paul’s Online Math Notes – Great for proofs, derivations, and extra practice.

• Books: Barron’s (hard practice), Princeton Review (strategy-focused).

Strategies for Exam Day

• Multiple Choice: Skip tough questions and return later.

• FRQs: Show all work — partial credit matters!

• Calculator Use: Don’t over-rely — know when to solve analytically.

• Time Management: Practice pacing — FRQs often require multi-step solutions.

Who Should Take AP Calculus BC?

• Strong fit for students planning majors in STEM, engineering, computer science, economics, or data science.

• Often preferred by selective colleges since it shows mastery of higher-level math.

• Can earn credit for Calculus I & II at many universities.

AP Calculus BC Exam FAQ

Q: How is AP Calculus BC different from AB?

A: BC covers all AB topics plus advanced material (series, polar, parametric). BC is considered more rigorous.

Q: If I take BC, do I also get an AB score?

A: Yes! College Board automatically gives you an AB subscore.

Q: Do I need to memorize every formula?

A: No — you get a formula sheet, but you must know when and how to use each formula.

Q: What’s the hardest part of the exam?

A: Most students find series convergence tests and polar/parametric integrals the toughest.

Q: How should I study the week before the exam?

A: Focus on past FRQs, review series tests, and do mixed timed practice to build speed.

Final Thoughts

Based on the information found in our Guide to the AP Calculus BC exam, we know it rewards students who practice consistently and focus on both procedural fluency and conceptual understanding. Master the foundations of AB material, then carefully review BC-only units like sequences, series, and polar functions. With enough practice, earning a 4 or 5 is very achievable.