AP CALC AB Study Guide 2026
Everything you need to pass the AP CALC AB 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 AB Exam Format at a Glance
📚 AP CALC AB Topics to Study (6)
✍️ Sample AP CALC AB Questions & Answers
1. What is the value of ∫ from 0 to 2 of (3x² − 2x) dx?
An antiderivative is x³ − x². Evaluating from 0 to 2 gives (8 − 4) − 0 = 4.
2. Which function is the solution to dy/dx = −x/y with initial condition y(0) = 2?
Separating gives y dy = −x dx, so y²/2 = −x²/2 + C and y² + x² = 4. Since y(0) = 2 is positive, y = √(4 − x²).
3. If f(x) = x² sin x, what is f′(π)?
By the product rule, f′(x) = 2x sin x + x² cos x. At x = π this is 2π(0) + π²(−1) = −π².
4. What is the absolute maximum value of f(x) = x³ − 6x² + 9x + 1 on the closed interval [0, 5]?
f'(x) = 3(x − 1)(x − 3), so the critical points are x = 1 and x = 3. Evaluating gives f(0) = 1, f(1) = 5, f(3) = 1, f(5) = 21, so the maximum is 21.
5. Which function is the solution to dy/dx = y − 4 with y(0) = 1?
Separating gives dy/(y − 4) = dx, so y − 4 = Ce^x. Using y(0) = 1 gives C = −3, so y = 4 − 3e^x.
6. The base of a solid is the region in the first quadrant bounded by y = 1 − x² and the coordinate axes. Cross-sections perpendicular to the x-axis are squares. What is the volume of the solid?
Each square has side 1 − x², so V = ∫₀¹ (1 − x²)² dx = ∫₀¹ (1 − 2x² + x⁴) dx = 1 − 2/3 + 1/5 = 8/15.
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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
- apstudents.collegeboard.org — Test delivery, eligibility, exam dates, retake policy, score release, test dates · verified Nov 2026