Free-response practice
Calculus AB free-response questions
Free-response questions (FRQs) are the part of the AP® Calculus AB 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.
12 questions · 2 types
Free response with a graphing calculator (Part A)
A multi-part problem, usually set in a real-world context, where you need a graphing calculator for things like definite integrals, derivatives at a point and solving equations. You show your setup, give decimal answers to three places, and explain or justify your conclusions.
On the exam: 2 questions in Part A of the free-response section (30 minutes, graphing calculator required). The whole free-response section is 6 questions in 90 minutes and counts for 50% of the score. AB and BC use the same format; on BC, one of these is usually a parametric, polar or vector question. Plan on about 15 minutes for one.
Units 4, 5, 6 and 8
Water in a storage tank
9 points · about 15 minutes · calculator allowed
Units 4, 5 and 8
Particle motion with a calculator
9 points · about 15 minutes · calculator allowed
Unit 8
Area and volume of a region
9 points · about 15 minutes · calculator allowed
Units 4, 6 and 8
Grain pile: accumulation and related rates
9 points · about 15 minutes · calculator allowed
Free response without a calculator (Part B)
A multi-part problem you solve by hand, often from a graph, a table, an equation or a differential equation. You show your work, use exact values, and justify answers with calculus reasons such as a sign change in a derivative or the conditions of a theorem.
On the exam: 4 questions in Part B of the free-response section (60 minutes, no calculator). The whole free-response section is 6 questions in 90 minutes and counts for 50% of the score. AB and BC use the same format; on BC, Part B usually includes a series question and a question on BC-only topics. Plan on about 15 minutes for one.
Units 2, 4, 5, 6 and 8
Cooling soup: data table
9 points · about 15 minutes
Units 2, 5 and 6
Analyzing f from the graph of f′
9 points · about 15 minutes
Units 1 and 2
Limits, continuity and differentiability
9 points · about 15 minutes
Units 3, 4 and 7
Slope field and separable differential equation
9 points · about 15 minutes
Units 4, 6 and 8
Two particles on a line
9 points · about 15 minutes
Units 3, 4 and 5
Implicitly defined curve
9 points · about 15 minutes
Units 4, 5 and 6
Accumulation function from the graph of f
9 points · about 15 minutes
Units 2, 3, 4 and 5
Table of function and derivative values
9 points · about 15 minutes