UPDATED for the 2026-27 School Year. Below is every single AP Calculus AB FRQ from 2015-2026 sorted by topic.
At the end is the predicted FRQs for the upcoming 2027 exam. Good luck!
PRO TIP: Links open in FRQ Atlas — You find the FRQ and upload your working for free, instant AI grading based on scoring guidelines.
FRQ Types
Breakdown by question style. Most exams follow a predictable pattern of particle motion, rate/accumulation tables, and graph analysis.
Particle Motion
Often Q1 or Q2 (calculator active). Focus on the relationship between position, velocity, and acceleration, plus “total distance” vs “displacement”.
Rate & Accumulation Tables
Standard fare involving Riemann sums and the Fundamental Theorem of Calculus. Watch units carefully when integrating rates.
Graph Analysis
Usually a function g defined as an integral of a graph f. You must connect geometric area to function values and derivatives.
Differential Equations
Separation of variables and slope fields. Don’t forget the +C immediately after integrating both sides!
Implicit/Related Rates
Often involves geometric shapes changing size or curves defined implicitly. Chain rule is your best friend here.
Skills
Specific mathematical practices tested across all units. Justification is key in Calculus AB.
Implementing Mathematical Processes
93 questions. The core mechanics of solving.
1.D: Rules & Relationships
Identify procedure based on concept connections. (15)
1.E: Apply Rules/Procedures
Execute calculations accurately, with or without calculator. (66)
Connecting Representations
55 questions. Linking graphs, tables, and equations.
2.B: Identify Info
Pull data correctly from a graph or table. (27)
2.D: Characteristics & Properties
Relate function properties (like max/min) across forms. (16)
Justification
94 questions. The “Why” behind the math.
3.D: Apply Definitions/Theorems
Use IVT, MVT, or EVT to prove a conclusion. (29)
3.E: Provide Rationale
Explain your reasoning clearly in writing. (42)
3.F: Contextual Meaning
Interpret a derivative or integral value in real-world terms. (12)
Units
Drill down into the specific content areas. Units 4, 5, and 8 dominate the FRQ section.
Unit 1: Limits & Continuity
9 questions. Rarely a standalone FRQ, but critical for IVT/MVT existence theorems.
Unit 2: Differentiation: Definition
27 questions. Foundation of rates of change; heavily tested in table problems.
Unit 3: Differentiation: Composite/Implicit
16 questions. The mechanics of chain rule, essential for related rates and differential equations.
Unit 4: Contextual Differentiation
39 questions. Massive unit. Covers particle motion, related rates, and linear approximation.
Unit 5: Analytical Differentiation
40 questions. The most tested unit. Connecting f, f’, and f” graphs to find extrema and concavity.
Unit 6: Integration & Accumulation
29 questions. Area under curves, Riemann sums, and the Fundamental Theorem of Calculus.
Unit 7: Differential Equations
10 questions. Slope fields and separation of variables; specific but high-value problems.
Unit 8: Applications of Integration
33 questions. Volume (disk/washer/cross-section) and average value; almost guaranteed to be one full FRQ.
Unit 1: Limits and Continuity
- 2026 Q1 (free-response) — Bird arrival rates, accumulation, average value.
- 2026 Q6 (free-response) — Tabular values of f and f′, chain rule, accumulation.
- 2025 Q1 (free-response) — Invasive species, average value, accumulation.
- 2025 Q3 (free-response) — Reading rates, IVT, trapezoidal sums.
- 2022 Q4 (free-response) — Melting ice, IVT, Riemann sums.
- 2022 Q6 (free-response) — Particle motion, limits at infinity.
- 2021 Q6 (Differential Equation/Slope Field) — Slope field, separation of variables, limit.
- 2019 Q6 (free-response) — L’Hospital’s Rule, Squeeze Theorem, tangents.
- 2016 Q1 (free-response) — Water tank, accumulation, IVT.
Unit 2: Differentiation: Definition and Fundamental Properties
- 2026 Q1 (free-response) — Bird arrival rates, accumulation, average value.
- 2026 Q2 (free-response) — Areas and volumes, regions bounded by f and g.
- 2026 Q4 (free-response) — Graph of f′, extrema and concavity analysis.
- 2026 Q6 (free-response) — Tabular values of f and f′, chain rule, accumulation.
- 2025 Q1 (free-response) — Invasive species, average value, MVT.
- 2025 Q2 (free-response) — Area region, volume rotation, tangents.
- 2025 Q3 (free-response) — Reading rates, table data, net change.
- 2025 Q5 (free-response) — Two particles, velocity, speed.
- 2024 Q1 (free-response) — Coffee temperature, table values, rate.
- 2024 Q4 (free-response) — Accumulation function, integral of graph.
- 2023 Q1 (Rate and Accumulation Table) — Gasoline flow, Riemann sum, MVT.
- 2023 Q5 (Analytical Derivatives and Integrals) — Table analysis, chain rule, FTC.
- 2022 Q4 (free-response) — Melting ice, IVT, related rates.
- 2021 Q1 (Rate/Accumulation Table) — Bacteria density, table derivative, Riemann sum.
- 2021 Q4 (Graph Analysis) — Accumulation function, concavity, L’Hospital’s.
- 2019 Q6 (free-response) — Tangent lines, L’Hospital’s, Squeeze Theorem.
- 2018 Q4 (free-response) — Tree height, MVT, related rates.
- 2018 Q5 (free-response) — Transcendental function, extrema, graph limits.
- 2017 Q2 (free-response) — Bananas display, accumulation, removal rate.
- 2017 Q3 (free-response) — Derivative graph, intervals of increase.
- 2017 Q5 (free-response) — Two particles, position, velocity.
- 2017 Q6 (free-response) — Table derivatives, MVT, composite functions.
- 2016 Q1 (free-response) — Water tank, accumulation, IVT.
- 2016 Q6 (free-response) — Table values, quotient rule, substitution.
- 2015 Q2 (free-response) — Area between curves, square cross-sections.
- 2015 Q3 (free-response) — Jogging velocity, Riemann sums, acceleration.
- 2015 Q6 (free-response) — Implicit curve, vertical tangents.
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- 2026 Q6 (free-response) — Tabular values of f and f′, chain rule, accumulation.
- 2025 Q5 (free-response) — Two particles, velocity, position.
- 2025 Q6 (free-response) — Implicit curves, vertical tangents, related rates.
- 2024 Q5 (free-response) — Implicit curve, related rates, particle.
- 2023 Q3 (Differential Equation and Slope Field) — Milk cooling, separation of variables.
- 2023 Q5 (Analytical Derivatives and Integrals) — Table functions, chain rule, product rule.
- 2023 Q6 (Implicit Differentiation and Related Rates) — Implicit curve, horizontal tangents, related rates.
- 2021 Q5 (Implicit Differentiation) — Implicit derivative, tangent line, extrema.
- 2021 Q6 (Differential Equation/Slope Field) — Slope field, medication, separation of variables.
- 2019 Q4 (free-response) — Draining barrel, related rates, differential equation.
- 2017 Q4 (free-response) — Potato cooling, separable differential equation.
- 2017 Q6 (free-response) — Table derivatives, MVT, composite functions.
- 2016 Q6 (free-response) — Table values, quotient rule, substitution.
- 2015 Q2 (free-response) — Area between curves, square cross-sections.
- 2015 Q4 (free-response) — Slope field, concavity, linear solution.
- 2015 Q6 (free-response) — Implicit curve, vertical tangents.
Unit 4: Contextual Applications of Differentiation
- 2026 Q3 (free-response) — Cooling pie differential equation, separation of variables.
- 2026 Q5 (free-response) — Piecewise velocity, toy car particle motion.
- 2025 Q2 (free-response) — Area region, volume rotation, tangents.
- 2025 Q5 (free-response) — Two particles, velocity, speed.
- 2025 Q6 (free-response) — Implicit curves, vertical tangents, related rates.
- 2024 Q1 (free-response) — Coffee temperature, table values, rate.
- 2024 Q2 (free-response) — Particle motion, velocity function, x-axis.
- 2024 Q5 (free-response) — Implicit curve, related rates, particle.
- 2023 Q1 (Rate and Accumulation Table) — Gasoline flow, Riemann sum, MVT.
- 2023 Q2 (Particle Motion) — Swimming velocity, direction change, displacement.
- 2023 Q3 (Differential Equation and Slope Field) — Milk cooling, separation of variables.
- 2023 Q4 (Graph Analysis) — Derivative graph, relative extrema, concavity.
- 2023 Q6 (Implicit Differentiation and Related Rates) — Implicit curve, horizontal tangents, related rates.
- 2022 Q1 (free-response) — Toll plaza, vehicle rate, optimization.
- 2022 Q2 (free-response) — Area between curves, volume, related rates.
- 2022 Q4 (free-response) — Melting ice, IVT, related rates.
- 2022 Q5 (free-response) — Slope field, concavity, separation variables.
- 2022 Q6 (free-response) — Particle motion, speed, limits.
- 2021 Q1 (Rate/Accumulation Table) — Bacteria density, table derivative, Riemann sum.
- 2021 Q2 (Particle Motion) — Particle motion, velocity, total distance.
- 2021 Q4 (Graph Analysis) — Accumulation function, concavity, L’Hospital’s.
- 2021 Q5 (Implicit Differentiation) — Implicit derivative, tangent line, extrema.
- 2021 Q6 (Differential Equation/Slope Field) — Slope field, medication, separation of variables.
- 2019 Q1 (free-response) — Fish population, entering rate, leaving rate.
- 2019 Q3 (free-response) — Graph function, integrals, area properties.
- 2019 Q4 (free-response) — Draining barrel, related rates, differential equation.
- 2019 Q6 (free-response) — Tangent lines, L’Hospital’s, Squeeze Theorem.
- 2018 Q2 (free-response) — Particle motion, velocity, total distance.
- 2018 Q4 (free-response) — Tree height, MVT, related rates.
- 2018 Q5 (free-response) — Transcendental function, extrema, graph limits.
- 2018 Q6 (free-response) — Differential equation, slope field, approximation.
- 2017 Q1 (free-response) — Tank volume, Riemann sums, pumping rate.
- 2017 Q2 (free-response) — Bananas display, accumulation, removal rate.
- 2017 Q4 (free-response) — Potato cooling, separable differential equation.
- 2017 Q5 (free-response) — Two particles, position, velocity.
- 2016 Q2 (free-response) — Particle motion, speed, total distance.
- 2016 Q4 (free-response) — Slope field, tangent approximation, separable DE.
- 2016 Q5 (free-response) — Funnel volume, average radius, related rates.
- 2015 Q3 (free-response) — Jogging velocity, Riemann sums, acceleration.
Unit 5: Analytical Applications of Differentiation
- 2026 Q3 (free-response) — Cooling pie differential equation, separation of variables.
- 2026 Q4 (free-response) — Graph of f′, extrema and concavity analysis.
- 2025 Q1 (free-response) — Invasive species, average value, accumulation.
- 2025 Q4 (free-response) — Accumulation function, inflection points, minima.
- 2025 Q6 (free-response) — Implicit curves, vertical tangents, related rates.
- 2024 Q1 (free-response) — Coffee temperature, table values, rate.
- 2024 Q3 (free-response) — Seawater depth, differential equation, slope field.
- 2024 Q4 (free-response) — Accumulation function, integral of graph.
- 2024 Q5 (free-response) — Implicit curve, related rates, particle.
- 2023 Q1 (Rate and Accumulation Table) — Gasoline flow, Riemann sum, MVT.
- 2023 Q3 (Differential Equation and Slope Field) — Milk cooling, separation of variables.
- 2023 Q4 (Graph Analysis) — Derivative graph, relative extrema, concavity.
- 2023 Q5 (Analytical Derivatives and Integrals) — Table functions, chain rule, product rule.
- 2023 Q6 (Implicit Differentiation and Related Rates) — Implicit curve, horizontal tangents, related rates.
- 2022 Q1 (free-response) — Toll plaza, vehicle rate, optimization.
- 2022 Q2 (free-response) — Area between curves, volume, related rates.
- 2022 Q3 (free-response) — Derivative graph, inflection points, extrema.
- 2022 Q5 (free-response) — Slope field, concavity, separation variables.
- 2021 Q3 (Area/Volume) — Spinning toy, area, optimization parameter.
- 2021 Q4 (Graph Analysis) — Accumulation function, concavity, L’Hospital’s.
- 2021 Q5 (Implicit Differentiation) — Implicit derivative, tangent line, extrema.
- 2021 Q6 (Differential Equation/Slope Field) — Slope field, medication, separation of variables.
- 2019 Q1 (free-response) — Fish population, entering rate, leaving rate.
- 2019 Q2 (free-response) — Velocity table, MVT, trapezoidal sum.
- 2019 Q3 (free-response) — Graph function, integrals, area properties.
- 2019 Q4 (free-response) — Draining barrel, related rates, differential equation.
- 2018 Q1 (free-response) — Escalator line, accumulation, optimization.
- 2018 Q3 (free-response) — Derivative graph, integration, function behavior.
- 2018 Q4 (free-response) — Tree height, MVT, related rates.
- 2018 Q5 (free-response) — Transcendental function, extrema, graph limits.
- 2017 Q2 (free-response) — Bananas display, accumulation, removal rate.
- 2017 Q3 (free-response) — Derivative graph, intervals of increase.
- 2017 Q4 (free-response) — Potato cooling, separable differential equation.
- 2017 Q6 (free-response) — Table derivatives, MVT, composite functions.
- 2016 Q2 (free-response) — Particle motion, speed, total distance.
- 2016 Q3 (free-response) — Integral function, extrema, inflection points.
- 2015 Q1 (free-response) — Rainwater flow, total flow, overflow.
- 2015 Q4 (free-response) — Slope field, concavity, linear solution.
- 2015 Q5 (free-response) — Derivative graph, extrema, inflection points.
- 2015 Q6 (free-response) — Implicit curve, vertical tangents.
Unit 6: Integration and Accumulation of Change
- 2026 Q1 (free-response) — Bird arrival rates, accumulation, average value.
- 2026 Q2 (free-response) — Areas and volumes, regions bounded by f and g.
- 2026 Q5 (free-response) — Piecewise velocity, toy car particle motion.
- 2026 Q6 (free-response) — Tabular values of f and f′, chain rule, accumulation.
- 2025 Q1 (free-response) — Invasive species, average value, accumulation.
- 2025 Q3 (free-response) — Reading rates, IVT, trapezoidal sums.
- 2025 Q4 (free-response) — Accumulation function, inflection points, minima.
- 2024 Q1 (free-response) — Coffee temperature, table values, rate.
- 2024 Q4 (free-response) — Accumulation function, integral of graph.
- 2023 Q1 (Rate and Accumulation Table) — Gasoline flow, Riemann sum, MVT.
- 2023 Q5 (Analytical Derivatives and Integrals) — Table functions, chain rule, product rule.
- 2022 Q3 (free-response) — Derivative graph, inflection points, extrema.
- 2022 Q4 (free-response) — Melting ice, IVT, related rates.
- 2021 Q1 (Rate/Accumulation Table) — Bacteria density, table derivative, Riemann sum.
- 2021 Q2 (Particle Motion) — Particle motion, velocity, total distance.
- 2021 Q3 (Area/Volume) — Spinning toy, area, optimization parameter.
- 2021 Q4 (Graph Analysis) — Accumulation function, concavity, L’Hospital’s.
- 2019 Q2 (free-response) — Velocity table, MVT, trapezoidal sum.
- 2019 Q3 (free-response) — Graph function, integrals, area properties.
- 2018 Q1 (free-response) — Escalator line, accumulation, optimization.
- 2018 Q3 (free-response) — Derivative graph, integration, function behavior.
- 2018 Q4 (free-response) — Tree height, MVT, related rates.
- 2017 Q1 (free-response) — Tank volume, Riemann sums, pumping rate.
- 2017 Q3 (free-response) — Derivative graph, intervals of increase.
- 2016 Q1 (free-response) — Water tank, accumulation, IVT.
- 2016 Q3 (free-response) — Integral function, extrema, inflection points.
- 2016 Q6 (free-response) — Table values, quotient rule, substitution.
- 2015 Q3 (free-response) — Jogging velocity, Riemann sums, acceleration.
- 2015 Q5 (free-response) — Derivative graph, extrema, inflection points.
Unit 7: Differential Equations
- 2026 Q3 (free-response) — Cooling pie differential equation, separation of variables.
- 2024 Q3 (free-response) — Seawater depth, differential equation, slope field.
- 2023 Q3 (Differential Equation and Slope Field) — Milk cooling, separation of variables.
- 2022 Q5 (free-response) — Slope field, concavity, separation variables.
- 2021 Q6 (Differential Equation/Slope Field) — Slope field, medication, separation of variables.
- 2019 Q4 (free-response) — Draining barrel, related rates, differential equation.
- 2018 Q6 (free-response) — Differential equation, slope field, approximation.
- 2017 Q4 (free-response) — Potato cooling, separable differential equation.
- 2016 Q4 (free-response) — Slope field, tangent approximation, separable DE.
- 2015 Q4 (free-response) — Slope field, concavity, linear solution.
Unit 8: Applications of Integration
- 2026 Q1 (free-response) — Bird arrival rates, accumulation, average value.
- 2026 Q2 (free-response) — Areas and volumes, regions bounded by f and g.
- 2026 Q5 (free-response) — Piecewise velocity, toy car particle motion.
- 2025 Q1 (free-response) — Invasive species, average value, accumulation.
- 2025 Q2 (free-response) — Area region, volume rotation, tangents.
- 2025 Q3 (free-response) — Reading rates, IVT, trapezoidal sums.
- 2025 Q5 (free-response) — Two particles, velocity, speed.
- 2024 Q1 (free-response) — Coffee temperature, table values, rate.
- 2024 Q2 (free-response) — Particle motion, velocity function, x-axis.
- 2024 Q6 (free-response) — Area between curves, volume rotation.
- 2023 Q1 (Rate and Accumulation Table) — Gasoline flow, Riemann sum, MVT.
- 2023 Q2 (Particle Motion) — Swimming velocity, direction change, displacement.
- 2022 Q1 (free-response) — Toll plaza, vehicle rate, optimization.
- 2022 Q2 (free-response) — Area between curves, volume, related rates.
- 2022 Q6 (free-response) — Particle motion, speed, limits.
- 2021 Q1 (Rate/Accumulation Table) — Bacteria density, table derivative, Riemann sum.
- 2021 Q2 (Particle Motion) — Particle motion, velocity, total distance.
- 2021 Q3 (Area/Volume) — Spinning toy, area, optimization parameter.
- 2019 Q1 (free-response) — Fish population, entering rate, leaving rate.
- 2019 Q2 (free-response) — Velocity table, MVT, trapezoidal sum.
- 2019 Q5 (free-response) — Area enclosed, cross-sections, volume.
- 2018 Q1 (free-response) — Escalator line, accumulation, optimization.
- 2018 Q2 (free-response) — Particle motion, velocity, total distance.
- 2018 Q4 (free-response) — Tree height, MVT, related rates.
- 2017 Q1 (free-response) — Tank volume, Riemann sums, pumping rate.
- 2017 Q2 (free-response) — Bananas display, accumulation, removal rate.
- 2017 Q5 (free-response) — Two particles, position, velocity.
- 2016 Q1 (free-response) — Water tank, accumulation, IVT.
- 2016 Q2 (free-response) — Particle motion, speed, total distance.
- 2016 Q5 (free-response) — Funnel volume, average radius, related rates.
- 2015 Q1 (free-response) — Rainwater flow, total flow, overflow.
- 2015 Q2 (free-response) — Area between curves, square cross-sections.
- 2015 Q3 (free-response) — Jogging velocity, Riemann sums, acceleration.
2027 FRQ Topics Prediction
We used Phy AI + the frequency of topics above to make an educated guess on what you might see on the upcoming 2027 AP Calculus AB Exam FRQ:
- Unit 5: Analytical Applications of Differentiation — 40 appearances. The 2026 exam ran the classic f′-graph analysis (Q4). Prepare to connect f, f′, and f″ to find extrema, concavity, and justify with sign charts.
- Unit 4: Contextual Applications of Differentiation — 39 appearances. 2026 tested particle motion with a piecewise velocity (Q5). Expect a particle motion or related-rates problem with interpretation in context.
- Unit 8: Applications of Integration — 33 appearances. 2026 Q2 was the standard area/volume question. Area between curves plus disk/washer or cross-section volumes remain near-guaranteed.
- Unit 6: Integration and Accumulation of Change — 29 appearances. Threaded through four 2026 questions. Riemann sums from tables and Fundamental Theorem accumulation reasoning are core.
- Unit 7: Differential Equations — 10 appearances. The 2026 cooling-pie question delivered the annual separation-of-variables problem — slope fields and the +C discipline remain a safe bet every year.
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