AP Exam Prep · AP Precalculus

AP Precalculus FRQ Practice

The free-response section is 37.5% of your AP score, and its points come from showing your work and giving reasons. Practise with 4 original FRQs, one of each official type, in the exam's 6-point format. Write your answers, then check them against the scoring guide or get AI feedback.

Function Concepts (like question 1) · Unit 1 · 6 points · Graphing calculator allowed

A rational function and a table

The function r is given by r(x) = (2x² − 2x − 12) ÷ (x² − 9). The table gives selected values of a function g. Give exact answers or decimals correct to three decimal places.

Each part is worth 1 point. For “explain” parts, say how or why, not just what.

Source: values of g

Selected values of g
x	−1	0	2	5
g(x)	3	−2	0	1

(A(i))Find the value of r(g(2)), or explain why it doesn't exist.
(A(ii))Find every x-value in the table for which r(g(x)) = 0. Give a reason.
(B(i))Find the equation of every vertical asymptote of the graph of r. Give a reason.
(B(ii))The graph of r has a hole. Find its coordinates.
(C(i))Describe the end behaviour of r using limit notation.
(C(ii))Find the average rate of change of r over the interval 0 ≤ x ≤ 2.

AI scoring is a practice aid, not an official AP score. It follows our scoring guide, which is written by StudyCoach, not the College Board.

Task verbs: what each part is asking for

Most lost FRQ points come from answering a different question than the one asked. Match your answer to the verb.

Find / Determine: Give the value or expression asked for, with the work that leads to it. A bare answer often loses the point when the question says “show the work”.
Justify / Give a reason: Say why, using the function, graph or data: for example “the graph is concave down on this interval, so the rate of change is decreasing”.
Rewrite / Express: Give an equivalent expression in exactly the form requested, such as 2^{ax + b} or c + d·log₂(x).
Explain / Describe: Describe the behaviour (increasing, concave up, approaching an asymptote) and connect it to the context and its units.
Interpret: Say what a number means in the context, with units: “the temperature falls about 1.9 °C below the model’s prediction”.

Ready for the multiple-choice section? Take the full practice exam or a unit test.

FRQ practice FAQs

How is the AP Precalculus free-response section structured?

From May 2027, Section II has 4 questions in 70 minutes, worth 37.5% of the score. Part A (35 minutes, graphing calculator required) has question 1, Function Concepts, and question 2, Modeling a Non-Periodic Context. Part B (35 minutes, no calculator) has question 3, Modeling a Periodic Context, and question 4, Symbolic Manipulations. Each question is worth 6 points.

Are these past AP Precalculus FRQs?

No. These are original questions written by StudyCoach in the same format. Official sample free-response questions and scoring guidelines are published by the College Board on AP Central.

How is my FRQ scored here?

You can check each part yourself against our scoring guide and worked sample answer for free. With a free account you can also have one FRQ a day scored by AI, part by part; Premium scores every FRQ. AI scoring is a practice aid, not an official AP score.

How do I get full marks on an AP Precalculus FRQ?

Show the work that leads to each answer, give decimals to three places when a calculator is allowed, label each part, and when a part asks for a reason, refer to the function, graph or data. Write units in context questions.

Original StudyCoach questions and scoring guides, not College Board material. AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, StudyCoach.