AP Calculus AB · 24 questions from 4 exams
Past free-response questions
Practice released AP Calculus AB free-response questions from 2023 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 · Calculator required · 9 points Bird arrivals at a nesting area Use tabulated rates and a second arrival model to estimate bird counts and compare changes in arrival rates. Unit 6, Unit 8, Unit 4
- Question 2 · Calculator required · 9 points Regions bounded by two functions Evaluate integrals for plane regions and a solid with rectangular cross sections using two intersecting function graphs. Unit 8
- Question 3 · Calculator not allowed · 9 points A pie cooling on a table Evaluate a proposed slope field, use a tangent approximation and solve the cooling differential equation by separation. Unit 7, Unit 4, Unit 5
- Question 4 · Calculator not allowed · 9 points A function described by its derivative Use a derivative graph to find a composite derivative, intervals of concavity, inflection points and absolute extrema. Unit 5, Unit 2
- Question 5 · Calculator not allowed · 9 points A toy car changing velocity Find acceleration, compare speed changes and integrate a piecewise velocity model to find distance and average velocity. Unit 4, Unit 8
- Question 6 · Calculator not allowed · 9 points Function values, derivatives and accumulation Use a table to find a limit and a composition derivative, then evaluate derivatives and integrals of related functions. Unit 1, Unit 3, Unit 6
2025
- Question 1 · Calculator required · 9 points An invasive plant in a fruit grove Find average affected area, compare rates and analyze the long term behavior and maximum of a changing model. Unit 8, Unit 2, Unit 1, Unit 5
- Question 2 · Calculator required · 9 points Area and solids between two curves Use intersections to compute area and cross section volume, set up a rotation integral and compare tangent slopes. Unit 8, Unit 2
- Question 3 · Calculator not allowed · 9 points A student and teacher reading Use a reading rate table to estimate change and accumulated words and compare it with a teacher’s rate model. Unit 1, Unit 6, Unit 8
- Question 4 · Calculator not allowed · 9 points An accumulation function from a graph Use semicircular and linear pieces of a graph to analyze an integral function, its concavity and its absolute minimum. Unit 6, Unit 5
- Question 5 · Calculator not allowed · 9 points Two particles moving on a line Compare motion directions and speed changes, then use velocity to determine when two particles occupy the same position. Unit 4, Unit 8
- Question 6 · Calculator not allowed · 9 points Tangent lines on an implicit curve Differentiate a relation, approximate a point with a tangent line and analyze a vertical tangent and related rates. Unit 3, Unit 4, Unit 5
2024
- Question 1 · Calculator required · 9 points Coffee temperature over time Approximate the rate and average temperature of cooling coffee using tabulated values and an integral model. Unit 2, Unit 6, Unit 8
- Question 2 · Calculator required · 9 points Particle motion on a line Analyze a velocity model to find when a particle stops, its acceleration, position and total distance traveled. Unit 4, Unit 8
- Question 3 · Calculator not allowed · 9 points A differential equation for seawater depth Sketch a solution on a slope field, analyze a depth model and solve the equation using an initial condition. Unit 7, Unit 5
- Question 4 · Calculator not allowed · 9 points Accumulation from a function graph Use a graph and signed areas to evaluate accumulation functions and their derivatives at specified points. Unit 6
- Question 5 · Calculator not allowed · 9 points An implicit curve and related rates Use a tangent line, implicit derivatives and related rates to analyze a curve and a second changing relation. Unit 3, Unit 4, Unit 5
- Question 6 · Calculator not allowed · 9 points Areas and volumes between parabolas Set up integrals for a bounded area and volumes from cross sections and rotation about a horizontal line. Unit 8
2023
- Question 1 · Calculator required · 9 points Gasoline flowing into a tank Estimate the change and accumulation of a flow rate using a table and interpret an average rate in context. Unit 2, Unit 6, Unit 8
- Question 2 · Calculator required · 9 points A swimmer moving along a pool Use a velocity model to find changes in direction, speeding up, displacement and distance traveled by a swimmer. Unit 4, Unit 8
- Question 3 · Calculator not allowed · 9 points Milk warming in a pan Sketch a solution to a differential equation and use derivatives and separation of variables to study warming milk. Unit 7, Unit 4, Unit 5
- Question 4 · Calculator not allowed · 9 points Analyzing a derivative graph Read a graph of a derivative to determine extrema and concavity and use signed areas to evaluate the original function. Unit 5, Unit 6
- Question 5 · Calculator not allowed · 9 points Derivatives from a table Use tabulated function values and derivatives to differentiate a composition, a product and an inverse function. Unit 3, Unit 2
- Question 6 · Calculator not allowed · 9 points An implicitly defined curve Differentiate an implicit curve, locate horizontal or vertical tangents and relate the rates of its changing coordinates. Unit 3, Unit 5, Unit 4
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