Free-response practice
Precalculus free-response questions
Free-response questions (FRQs) are the part of the AP® Precalculus exam where you write your own answers. Here they're grouped the way the exam uses them. Write your answer, then score it yourself with the rubric and a model answer, or sign in for free AI scoring.
16 questions · 4 types
Function concepts
You work with functions given as a table, a graph described in words, or an equation: composition, inverses, zeros, end behavior and asymptotes, and picking the function type that fits a table. You'll use a graphing calculator.
On the exam: Question 1 of 4. Part A of the free-response section: 2 questions in 35 minutes, graphing calculator required. Plan on about 18 minutes for one.
Units 1 and 2
A table function and a cubic
6 points · about 18 minutes · calculator allowed
Units 1 and 2
A piecewise-linear graph and a rational function
6 points · about 18 minutes · calculator allowed
Unit 2
An exponential function and a log-like table
6 points · about 18 minutes · calculator allowed
Units 1 and 2
A rational function with a hole
6 points · about 18 minutes · calculator allowed
Modeling a non-periodic context
A real-world situation is modeled by a polynomial, piecewise, exponential or logarithmic function. You set up and solve equations for the model's constants, find and use average rates of change with units, and explain an assumption or limit of the model. You'll use a graphing calculator.
On the exam: Question 2 of 4. Part A of the free-response section: 2 questions in 35 minutes, graphing calculator required. Plan on about 18 minutes for one.
Units 1 and 2
A cooling cup of tea
6 points · about 18 minutes · calculator allowed
Units 1 and 2
Podcast listeners
6 points · about 18 minutes · calculator allowed
Unit 1
A fish population
6 points · about 18 minutes · calculator allowed
Units 1 and 2
Medicine in the bloodstream
6 points · about 18 minutes · calculator allowed
Modeling a periodic context
A repeating real-world situation is modeled by a sinusoidal function. You find coordinates of key points on its graph, write the function's equation, and describe how the function, its concavity and its rate of change behave on an interval. No calculator.
On the exam: Question 3 of 4. Part B of the free-response section: 2 questions in 35 minutes, no calculator allowed. Plan on about 18 minutes for one.
Unit 3
A Ferris wheel ride
6 points · about 18 minutes
Unit 3
Tides at a harbor
6 points · about 18 minutes
Unit 3
A paddle wheel
6 points · about 18 minutes
Unit 3
A buoy on the waves
6 points · about 18 minutes
Symbolic manipulations
You solve exponential, logarithmic and trigonometric equations by hand and rewrite log, exponential and trig expressions in equivalent forms, giving exact answers and showing your work. No calculator.
On the exam: Question 4 of 4. Part B of the free-response section: 2 questions in 35 minutes, no calculator allowed. Plan on about 18 minutes for one.
Units 2 and 3
Logs, sine and a quadratic in 2ˣ
6 points · about 18 minutes
Units 2 and 3
Natural logs, arccosine and secant
6 points · about 18 minutes
Units 2 and 3
Different bases and a quadratic in sine
6 points · about 18 minutes
Units 2 and 3
A log quotient, arctangent and a double angle
6 points · about 18 minutes