AP Precalculus past papers and free-response questions
College Board publishes the AP Precalculus free-response questions every year, with scoring guidelines, sample student responses and a chief reader report. The first exam was in 2024, and this page collects every year since, 2024 to 2026. Each paper has the same four question types: function concepts, a non-periodic model, a periodic model and symbolic manipulations.
On this page
AP Precalculus free-response questions by year
Each file opens from College Board's official site. Preview shows it here, Open in new tab gives you the full screen, and Download saves a copy to print.
2026
- Free-response questionsPreviewOpen in new tabDownload
- Scoring guidelinesPreviewOpen in new tabDownload
- Sample responses and chief reader reportCollege Board usually adds these in the autumn after the exam
2025
- Free-response questionsPreviewOpen in new tabDownload
- Scoring guidelinesPreviewOpen in new tabDownload
- Chief reader reportPreviewOpen in new tabDownload
- Scoring statisticsPreviewOpen in new tabDownload
- Score distributionsPreviewOpen in new tabDownload
- Sample student responsesQ1Q2Q3Q4
2024
- Free-response questionsPreviewOpen in new tabDownload
- Scoring guidelinesPreviewOpen in new tabDownload
- Chief reader reportPreviewOpen in new tabDownload
- Scoring statisticsPreviewOpen in new tabDownload
- Score distributionsPreviewOpen in new tabDownload
- Sample responses and chief reader reportCollege Board usually adds these in the autumn after the exam
Source: AP Precalculus past exam questions on AP Central. All papers are © College Board.
What each AP Precalculus free-response question tests
Use this index to find past questions on the topics you need to practise. The descriptions are our own summaries.
2026
| Q1 | A graphed function and a logarithmic function: composition and inverses (function concepts) |
|---|---|
| Q2 | A car's value falling over time: exponential model (non-periodic modelling) |
| Q3 | A rotating waterwheel: sinusoidal model of height (periodic modelling) |
| Q4 | Rewriting exponential, logarithmic and trigonometric expressions (symbolic manipulations) |
2025
| Q1 | A decreasing function from a table and a cubic: function concepts |
|---|---|
| Q2 | Plays of a song on a streaming service: building and using a model (non-periodic modelling) |
| Q3 | A vibrating guitar string: sinusoidal model (periodic modelling) |
| Q4 | Rewriting exponential, logarithmic and trigonometric expressions (symbolic manipulations) |
2024
| Q1 | A graphed function composed with an exponential function: function concepts |
|---|---|
| Q2 | Daily sales of a new video game: building and using a model (non-periodic modelling) |
| Q3 | A rolling car tyre: sinusoidal model of a point's height (periodic modelling) |
| Q4 | Rewriting exponential, logarithmic and trigonometric expressions (symbolic manipulations) |
AP Precalculus exam format
| Section | Questions | Time | Score |
|---|---|---|---|
| Section I: multiple choice | 42 questions | 1 hour 45 minutes | 62.5% |
| Part A | 29 questions, no calculator | 65 minutes | |
| Part B | 13 questions, graphing calculator required | 40 minutes | |
| Section II: free response | 4 questions | 1 hour 10 minutes | 37.5% |
| Part A | 2 questions, graphing calculator required | 35 minutes | |
| Part B | 2 questions, no calculator | 35 minutes |
This is the format from the May 2027 exam onwards; before, the multiple-choice section had 40 questions in 2 hours and free response took 1 hour. The course content has not changed. The four free-response questions keep the same types: function concepts, modelling a non-periodic context, modelling a periodic context, and symbolic manipulations, so every past paper on this page is still exactly on target.
How to use past free-response questions
- Start with the newest papers. They match the current exam most closely.
- Do one question at a time, timed. Use the timings in the exam format above, with no notes open.
- Mark yourself strictly with the scoring guidelines, point by point, before reading anything else.
- Compare with the sample responses to see exactly what earned or lost each point.
- Read the chief reader report for the mistakes most students made that year, and keep a list of your own.
- Go back to weak topics using the topic index, then redo the question a week later.
Tips specific to AP Precalculus:
- Show the expression you use on calculator questions before the decimal answer, and give three decimal places.
- For modelling questions, state the type of model (linear, quadratic, exponential, sinusoidal) and why it fits the context.
- On the periodic question, find the period, amplitude and midline from the context first; then the sinusoidal function follows.
- Practise the symbolic question without a calculator: log and exponent rules, and the Pythagorean and double-angle identities.
Free AP Precalculus practice questions
Ten original multiple-choice questions written by our tutors in the style of the exam. Choose an answer to see if you are right and why.
Answered 0 of 10 · 0 correct
1. If f(x) = 2x, what is f(5)?
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C. 25 = 32.
2. What is log2 8?
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B. 23 = 8, so log2 8 = 3.
3. What is the period of y = sin(4x)?
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B. The period is 2π/4 = π/2, about 1.571.
4. A value of 100 grows by 5% a year. What is it after 2 years?
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C. 100 × 1.052 = 110.25.
5. What is the average rate of change of f(x) = x2 from x = 1 to x = 3?
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C. (9 − 1)/(3 − 1) = 4.
6. If f(x) = 3x + 2, what is f−1(11)?
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A. Solve 3x + 2 = 11: x = 3.
7. Solve 3 · 2x = 48.
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B. 2x = 16, so x = 4.
8. What is the amplitude of y = 5cos(2x) + 1?
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C. The amplitude is the coefficient of the cosine: 5. The +1 moves the midline.
9. The polar point (r, θ) = (2, π/2) is which rectangular point?
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B. x = 2cos(π/2) = 0 and y = 2sin(π/2) = 2.
10. Where is the vertical asymptote of y = (x + 1)/(x − 3)?
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C. The denominator is zero at x = 3, where the numerator is not zero.
Frequently asked questions
Are AP Precalculus past papers free?
Yes. College Board publishes the AP Precalculus free-response questions, scoring guidelines and sample responses free on AP Central. This page links to those official files so you can preview, open or download them.
Why are there no older AP Precalculus papers before 2023?
College Board currently makes the most recent years public on AP Central and removed older years from public access. Teachers can find many older released questions in AP Classroom.
Can I get full AP Precalculus past exams with the multiple-choice section?
College Board does not publish full past multiple-choice sections publicly; complete practice exams are released to teachers through AP Classroom. The free-response questions, which are half of your score, are public, and this page has 10 original multiple-choice questions to practise with.
How is the AP Precalculus free-response section scored?
Each free-response question is worth 6 points, so the section is out of 24.