AP PRECALCULUS Study Guide 2026
Everything you need to pass the AP PRECALCULUS 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 PRECALCULUS Exam Format at a Glance
📚 AP PRECALCULUS Topics to Study (6)
✍️ Sample AP PRECALCULUS Questions & Answers
1. For which values of x in [0, 2π) is cos x > 1/2?
cos x = 1/2 at x = π/3 and x = 5π/3. Cosine is above 1/2 near x = 0, so the solution is [0, π/3) together with (5π/3, 2π).
2. Where is the hole in the graph of f(x) = (x² + x − 6)/(x² − 4)?
Factoring gives f(x) = (x + 3)(x − 2)/((x − 2)(x + 2)). The factor (x − 2) cancels, so the hole is at x = 2. The simplified function (x + 3)/(x + 2) gives y = 5/4 there.
3. Let f(x) = 2x + 3 and g(x) = x². What is the value of (f ∘ g)(2)?
(f ∘ g)(2) = f(g(2)) = f(4) = 2(4) + 3 = 11. The inner function g is applied first.
4. What is the domain of f(x) = ln(5 − 2x)?
The argument of a logarithm must be strictly positive, so 5 − 2x > 0, which gives x < 5/2.
5. Which function is the inverse of h(x) = eˣ + 1?
Set y = eˣ + 1, subtract 1 to get y − 1 = eˣ, then take ln: x = ln(y − 1). Swapping variables gives h⁻¹(x) = ln(x − 1).
6. What is the value of arcsin(sin(5π/6))?
sin(5π/6) = 1/2, and arcsin returns the angle in [−π/2, π/2] whose sine is 1/2, which is π/6.
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How this page was made: written with AI tools and published by Nathan Beja, founder of Practice Test Geeks, who is responsible for its content. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy
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 — Score release, passing score, test dates · verified Nov 2026
- apcentral.collegeboard.org — Test delivery, exam dates, exam format, fees, late registration · verified Nov 2026