AP Precalculus practice test: free questions, exam format and 2027 date

The daily AP Precalculus paper has 8 original questions worth 25 to 35 marks. It is practice for the exponential, logarithmic and trigonometric parts of the course: logs, geometric sequences, composite and transformed functions, polynomials and trig equations. It has no rational functions, sinusoidal modeling or polar graphs, and its binomial expansion, partial fractions and proof questions go beyond AP Precalculus.

AP Precalculus exam format for 2027

Each free-response question is worth 6 points, and they come in a fixed order: function concepts, modeling a non-periodic context, modeling a periodic context, then symbolic manipulations. Set your calculator to radian mode. It is a hybrid digital exam: multiple choice in the Bluebook app, free-response answers handwritten, and the Desmos calculator only appears in the calculator parts. Multiple choice gives you about 2.5 minutes per question.

AP Precalculus units

Your class may teach Unit 4, but the exam doesn't test it. College Board recommends introductory algebra and geometry first. Learn the graphs in our Graphing Functions course, and check working with the Logarithm, Polynomial Division, Sequences and Series, Trigonometry and Polar Coordinates calculators.

Precalculus practice test questions with answers

We wrote these for this page, in AP style. Use a calculator only for question 4.

1. Rational functions: holes and asymptotes

Question: For f(x) = (x² − 4) ÷ (x² − x − 2), find any holes and the vertical and horizontal asymptotes.

Factor top and bottom: (x − 2)(x + 2) ÷ ((x − 2)(x + 1)). The factor x − 2 cancels, so there is a hole at x = 2, at y = 4/3. The factor x + 1 stays in the denominator, so there is a vertical asymptote at x = −1. The leading terms are both x², so as x grows large f(x) approaches y = 1, the horizontal asymptote.

2. Exponential models

Question: A bacteria culture starts at 200 cells and triples every 5 hours. Write a model and find when it reaches 5,400 cells.

So t/5 = 3 and t = 15 hours. When the numbers aren't a neat power, take logs: t = 5 log₃(N ÷ 200). Equal time steps multiply the population by the same factor, which is what makes it exponential and links it to a geometric sequence.

3. Composition

Question: If f(x) = 2x − 3 and g(x) = x², find f(g(3)) and g(f(3)).

Work from the inside out. g(3) = 9, so f(g(3)) = 2(9) − 3 = 15. f(3) = 3, so g(f(3)) = 3² = 9. The order matters: composition is usually not the same both ways round.

4. Sinusoidal models

Question: A Ferris wheel seat rises from 2 m above the ground to 30 m and back every 40 seconds, starting at the bottom. Write a model for its height h after t seconds, and find h when t = 25.

The midline is halfway, (2 + 30) ÷ 2 = 16 m, and the amplitude is 30 − 16 = 14 m. Starting at the bottom means a negative cosine, and a period of 40 s means the angle is 2πt ÷ 40 = πt ÷ 20.

Here x is time in seconds and y is height in meters. The seat is 25.9 m up after 25 seconds, just past the top and on its way down. Your calculator must be in radian mode for this.

Trig expressions come up in the symbolic manipulation question too. Try one from our Trigonometry course, then press Mark.

5. Polar coordinates

Question: Convert the polar point (r, θ) = (4, π/3) to rectangular coordinates.

Use x = r cos θ and y = r sin θ: x = 4 cos(π/3) = 4 × ½ = 2, and y = 4 sin(π/3) = 4 × (√3 ÷ 2) = 2√3. The point is (2, 2√3), about (2, 3.46). Check it in the Polar Coordinates Calculator.

AP Precalculus scores, date and deadlines

In 2026, 29% of AP Precalculus students scored 5, 29% scored 4, 24% scored 3, 11% scored 2 and 7% scored 1, so 82% scored 3 or higher. Each college sets its own policy for credit or placement.

• Exam: Tuesday, May 11, 2027, in the morning session, at 8 a.m. local time in the lower 48 states, Hawaii and Washington, D.C.
• Ordering deadline: November 13, 2026, through your school's AP coordinator. Your school may set an earlier date.
• Fee: $99 in the US, US territories and Canada, $129 elsewhere, plus $40 for exams ordered from November 14 to March 12.
• Scores: released in July 2027.

Use the daily paper as a short timed practice test

1. Open today's AP Precalculus paper and work to the suggested time, 35 to 45 minutes.
2. Answer the exponential, logarithm, function and trig questions; treat binomial expansion, partial fractions and proof as extra.
3. Write each step: free-response points reward the method and a reason for each conclusion.
4. Practice rational functions, sinusoidal models and polar graphs separately, because the paper doesn't include them.

Common precalculus mistakes

• Calling a cancelled factor an asymptote: it makes a hole, not an asymptote.
• Calculator in degree mode on a radians question.
• Composing in the wrong order: f(g(x)) means g first.
• Confusing amplitude and midline in a sinusoidal model.
• Treating percent growth as linear: a fixed factor per time step is exponential.

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