AP CALC BC Study Guide 2026
Everything you need to pass the AP CALC BC exam in one place: the exam format, every topic to study, real practice questions with explanations, flashcards, and full-length practice tests. Free, no sign-up needed.
AP CALC BC exam key facts
📋 AP CALC BC Exam Format at a Glance
📚 AP CALC BC Topics to Study (6)
✍️ Sample AP CALC BC Questions & Answers
1. What is lim(x→3) (x² − 9)/(x − 3)?
Factor the numerator as (x − 3)(x + 3) and cancel (x − 3). The limit is then lim(x→3) (x + 3) = 6.
2. A function f is continuous on [1, 4] with f(1) = −3 and f(4) = 5. Which statement must be true?
0 lies between f(1) = −3 and f(4) = 5, so the Intermediate Value Theorem guarantees at least one c in (1, 4) with f(c) = 0.
3. A particle moves along a line with position s(t) = t³ − 9t² + 15t for t ≥ 0. At which time is the particle speeding up?
v(t) = 3(t − 1)(t − 5) and a(t) = 6t − 18. At t = 2, v = −9 and a = −6 have the same sign, so the speed is increasing.
4. Which of the following series converges?
By the integral test, ∫₂^∞ dx/(x(ln x)²) = 1/ln 2 is finite, so the series converges. The other three series diverge.
5. What is lim(x→0) sin(5x)/(2x)?
Rewrite as (5/2)·[sin(5x)/(5x)]. Since sin(u)/u → 1 as u → 0, the limit is 5/2.
6. A farmer has 200 feet of fencing to enclose a rectangular pen along a straight river. No fence is needed along the river, so only three sides are fenced. What is the maximum possible area of the pen?
With width x and length y along the river, 2x + y = 200, so A = x(200 − 2x). A′ = 200 − 4x = 0 gives x = 50, y = 100, and A = 5,000 ft².
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Sources & references
Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy
- apcentral.collegeboard.org — Test delivery, registration deadline · verified Nov 2026
- apstudents.collegeboard.org — Retake policy, score release, passing score, test dates, exam dates · verified Nov 2026