AP Precalculus · 12 questions from 3 exams
Past free-response questions
Every free-response question College Board has released for AP Precalculus from 2024 to 2026. Each one opens College Board's own question beside a space to write your answer, part by part, and then College Board's scoring guidelines so you can score it yourself.
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2026
- Question 1 · Function Concepts · 6 points Graphed increasing function and a logarithmic function Using a graph of f and a natural log function g, evaluate a composition, find where f hits a value, solve a log equation, write a one-sided limit of g near its asymptote, and decide whether f is invertible using points on the graph. Unit 2
- Question 2 · Modeling a Non-Periodic Context · 6 points Exponential model for a car's falling value Fit an exponential decay model to two data points, use the secant line's slope to estimate a value and explain why the estimate sits above the model, then use the owner's plan to donate the car to set a domain limit. Unit 2, Unit 1
- Question 3 · Modeling a Periodic Context · 6 points Sinusoidal height of a point on a waterwheel Give coordinates for five labeled points on the graph of a waterwheel point's height, find the constants of a sine model, and describe the sign, direction, concavity and rate of change of the function between two of the points. Unit 3
- Question 4 · Symbolic Manipulations · 6 points Solving and rewriting log, exponential and trig expressions Without a calculator, solve an exponential equation and a log equation, combine a product of powers of 7 into one power and rewrite a trig product using sine alone, then find where a squared tangent equals 1 on an interval. Unit 2, Unit 3
2025
- Question 1 · Function Concepts · 6 points Table of values and a cubic function Using a table for f and a cubic g, evaluate a composition and an inverse value, find the zeros and end behavior of g, then pick the function type that best fits the table and justify it from how the outputs change. Unit 2, Unit 1
- Question 2 · Modeling a Non-Periodic Context · 6 points Quadratic model for total plays of a song Set up and solve a system for a quadratic model through three data points, use an average rate of change to estimate a value and explain why it underestimates the model, then use the vertex and the context to bound the model's domain. Unit 1
- Question 3 · Modeling a Periodic Context · 6 points Sinusoidal motion of a vibrating guitar string Give coordinates for five labeled points on the graph of a string's displacement, find the constants of a sine model, and describe the sign, direction, concavity and rate of change of the function between two of the points. Unit 3
- Question 4 · Symbolic Manipulations · 6 points Solving and rewriting log, exponential and trig expressions Without a calculator, solve a log equation and a squared cosine equation on an interval, rewrite a log sum as one log and a trig expression in terms of tangent alone, then find the zeros of an exponential expression that factors like a quadratic. Unit 2, Unit 3
2024
- Question 1 · Function Concepts · 6 points Composing a graphed function with an exponential Using a graph of f and an exponential g, evaluate a composition, find inputs that give a set output, solve an exponential equation, state the limit that describes where g heads, and decide whether f is invertible with a reason from the graph. Unit 2
- Question 2 · Modeling a Non-Periodic Context · 6 points Logarithmic model for daily video game sales Fit a logarithmic sales model to two data points, use an average rate of change to estimate a middle value and explain why that estimate falls below the model, then explain why the model gets worse once real sales start dropping. Unit 2, Unit 1
- Question 3 · Modeling a Periodic Context · 6 points Sinusoidal height of a point on a rolling tire Give coordinates for five labeled points on the graph of a tire point's height, find the constants of a sine model, and describe the sign, direction and changing rate of change of the function between two of the points. Unit 3
- Question 4 · Symbolic Manipulations · 6 points Solving and rewriting log, exponential and trig expressions Without a calculator, solve an exponential equation and an inverse sine equation, combine a sum of logs into one log and simplify a trig expression to a tangent, then find where an inverse cosine of a tangent equals zero. Unit 2, Unit 3
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