Functions studied deeply — polynomial, rational, exponential, trig, and beyond — as preparation for calculus.
Study guide last reviewed September 25, 2026 · see what changed
Format reflects the current published structure — always confirm against AP Central before test day, since formats occasionally change.
| Section | Details | Time | Weight |
|---|---|---|---|
| Section I – Multiple Choice | 42 questions (29 no-calculator, 13 calculator) | 1 hr 45 min | 62.5% |
| Section II – Free Response | 4 questions (2 calculator, 2 no-calculator) | 1 hr 10 min | 37.5% |
Straight answers about the AP Precalculus exam — format, credit, dates, and this site.
Section I – Multiple Choice: 42 questions (29 no-calculator, 13 calculator) (1 hr 45 min, 62.5% of the total score); Section II – Free Response: 4 questions (2 calculator, 2 no-calculator) (1 hr 10 min, 37.5% of the total score). See the Exam Format tab above for the full breakdown, and always double-check the current year's format on AP Central before test day.
It's multiple-choice questions and written free-response or essay questions.
Partly — this exam has both a calculator-allowed portion and a no-calculator portion. Check the Exam Format tab above for exactly which section allows one.
It depends entirely on the college — most award credit for a 3 or higher, but many selective schools require a 4 or a 5, and some don't grant credit at all for certain scores. Always check your target college's own AP credit policy page rather than assuming a 3 will count everywhere.
AP exams are administered during the College Board's annual testing window in the first two full weeks of May, with the exact date and time for each subject set by the College Board and announced the preceding fall. Check AP Central or your school's AP coordinator for this year's exact date.
Yes. The unit-by-unit study guide, worked examples, practice quiz, and full-length timed practice exam on this page are all free, with no login, signup, or paywall.
Unit-by-unit breakdown of what the course actually covers, in teaching order.
End behavior determined by a polynomial's degree and leading coefficient, finding and interpreting zeros (real and complex, including multiplicity's effect on whether the graph crosses or touches the x-axis), and rational function analysis including vertical asymptotes (where the denominator is zero), horizontal asymptotes (comparing degrees), and holes (common factors that cancel).
Exponential growth/decay models (A = A0(1+r)^t) and the natural exponential base e, logarithms as the inverse of exponentials with their key properties (product, quotient, power rules), and solving exponential/logarithmic equations, including applications like compound interest and radioactive decay/half-life.
The unit circle as the foundation for all trig values, the six trig functions and their graphs (amplitude, period, phase shift, midline), fundamental trig identities (Pythagorean, sum/difference, double angle), and representing and converting between rectangular and polar coordinates, including graphing basic polar curves.
Parametric equations describing motion or curves using a third variable (parameter), an introduction to vectors (magnitude, direction, addition, scalar multiplication) and their applications to physics-style problems, and basic matrix operations (addition, multiplication) and their use in representing linear transformations and systems of equations.
Concrete, fully worked examples — this is what separates a page reviewers see as genuinely useful from one that just lists topics.
Analyze f(x) = (x² − 4)/(x² − x − 6).
Step 1: Factor both: numerator (x−2)(x+2); denominator (x−3)(x+2).
Step 2: The (x+2) factor cancels, so there's a hole at x = −2, not an asymptote — evaluating the reduced form there gives y = (−2−2)/(−2−3) = 0.8, so the hole sits at (−2, 0.8).
Step 3: The remaining (x−3) in the denominator gives a vertical asymptote at x = 3, and since the degrees match, the horizontal asymptote is y = 1 (ratio of leading coefficients).
Solve 32x−1 = 20 for x.
Step 1: Take ln of both sides: (2x−1)ln 3 = ln 20.
Step 2: 2x − 1 = ln 20 / ln 3 ≈ 2.7268.
Step 3: x ≈ 1.863. Keep the log ratio in exact form as long as possible — rounding early is the most common way to lose the final answer point.
Convert the rectangular point (3, 4) to polar coordinates.
r = √(3² + 4²) = √25 = 5. θ = arctan(4/3) ≈ 53.13° — check the quadrant before trusting arctan directly; here both coordinates are positive so Quadrant I is correct as-is.
Identify the curve x(t) = 3cos t, y(t) = 3sin t, and find dy/dx at t = π/4.
Since x²+y² = 9cos²t + 9sin²t = 9, this traces a circle of radius 3 centered at the origin.
dy/dx = (dy/dt)/(dx/dt) = (3cos t)/(−3sin t) = −cot t. At t = π/4: dy/dx = −1.
The errors that cost the most points across the whole exam, not just one unit.
Unofficial practice questions written for this study guide — not official AP content and not from College Board. Use them to self-check, then use the real past free-response questions below for authentic exam practice.
Unofficial practice, timed to feel like the real thing. Section I pulls from this page's full multiple-choice bank; Section II gives you free-response prompts to write out and self-score against a rubric. Bank size is still growing toward full exam length — timing is paced per-question, not pulled from this subject's official duration.