--- title: "Every AP Calculus BC FRQ Sorted By Unit" description: "Prepare for the AP Calculus BC exam with our complete list of FRQs from 2015-2025, sorted by unit. Includes topic predictions for 2026." featured_image: "https://nerd-notes.com/wp-content/uploads/2026/02/calculus-3d-fabric-nerd-notes-1.png" url: "https://nerd-notes.com/every-ap-calculus-bc-frq-sorted-by-unit/" date_modified: "2026-03-17T23:09:20+00:00" --- # Every AP Calculus BC FRQ Sorted By Unit ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/every-ap-calculus-bc-frq-sorted-by-unit/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/every-ap-calculus-bc-frq-sorted-by-unit/ UPDATED FOR 2026. Below is every single AP Calculus BC FRQ from 2015-2025 sorted by topic. At the end is the **predicted** FRQs for the upcoming 2026 exam. Good luck! PRO TIP: Links open in [FRQ Atlas](https://nerd-notes.com/frq/) — You find the FRQ and upload your working for **free**, instant AI grading based on scoring guidelines. ## FRQ Types Breakdown of common question formats and strategies. Free-Response Standard multi-part problems. **Tip:** Show every step of your algebraic manipulation; bald answers get zero points. **Frequency:** 55 questions Calculator Active Requires a graphing calculator for integration or finding roots. **Tip:** Write the setup integral before plugging it into your calculator. **Frequency:** 3 questions Calculator Inactive Pure analytical work. **Tip:** Leave answers in unsimplified exact forms (e.g., ln(3) + 4) to save time and avoid arithmetic errors. **Frequency:** 4 questions Table and Related Rates Data interpretation from tables. **Tip:** Watch units carefully and use the specific values given in the table for approximations. **Frequency:** 2 questions Graph Analysis Extracting data from function or derivative graphs. **Tip:** Clearly label coordinates and reference the specific graph (e.g., “graph of f'”) in your justification. **Frequency:** 4 questions ## Skills Key mathematical practices tested. Implementing Processes **Frequency:** 80 questions 1.E: Apply Rules Execute procedures like integration or differentiation accurately. **Count:** 60 1.D: Identify Rules Recognize which theorem or rule applies to a relationship. **Count:** 16 1.C: Classify Rules Select procedures based on expression type. **Count:** 4 Connecting Representations **Frequency:** 43 questions 2.B: Identify Info Pull data correctly from graphs, tables, or equations. **Count:** 19 2.D: Relate Properties Link function features across different forms. **Count:** 14 2.E: Describe Relationships Explain connections between functions and derivatives. **Count:** 6 Justification **Frequency:** 79 questions 3.E: Provide Rationale Explain “why” clearly using mathematical reasoning. **Count:** 36 3.D: Apply Theorems Use definitions like MVT or IVT appropriately. **Count:** 32 3.F: Explain Meaning Interpret mathematical results in the problem’s context. **Count:** 9 ## Units Frequency of topics by unit. Unit 6: Integration & Accumulation The heavyweight champion. Mastering accumulation functions and the Fundamental Theorem is non-negotiable. **Frequency:** 29 questions Unit 5: Analytical Differentiation Connecting analytical derivatives to graph behavior (MVT, extrema) is a staple of almost every exam. **Frequency:** 28 questions Unit 4: Contextual Differentiation Expect real-world rate problems (tanks, particles) that require translating word problems into calculus. **Frequency:** 21 questions Unit 8: Applications of Integration Area and volume are consistent, but look out for average value and motion problems here too. **Frequency:** 20 questions Unit 2: Differentiation Definition Fundamental properties often appear as parts of larger problems rather than standalone questions. **Frequency:** 14 questions Unit 10: Infinite Sequences & Series The dreaded BC exclusive. Taylor series and error bounds are guaranteed to show up in Q6. **Frequency:** 14 questions Unit 9: Parametric, Polar, Vector Another BC exclusive. Usually a dedicated FRQ involving particle motion or polar area. **Frequency:** 12 questions Unit 1: Limits and Continuity Often tested via L’Hospital’s Rule or IVT within other contexts rather than isolation. **Frequency:** 7 questions Unit 7: Differential Equations Slope fields and separation of variables are classic, reliable points if you know the procedure. **Frequency:** 6 questions Unit 3: Composite/Implicit/Inverse Implicit differentiation often hides inside related rates or differential equation problems. **Frequency:** 5 questions ### Unit 1: Limits and Continuity - **[2025 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=3)** (*Free-Response*) — Invasive species, average value, rate of change, limits at infinity. - **[2025 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=6)** (*Free-Response*) — Reading rates, estimation, IVT, trapezoidal sums. - **[2022 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=8)** (*Table and Related Rates*) — Melting cone, tabular data, approximation, related rates. - **[2022 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=9)** (*Area and Volume*) — Rational functions, improper integral, bounded region area. - **[2019 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=6)** (*Analytical / Improper Integral*) — Parameter family, tangent slopes, partial fractions, improper integral. - **[2017 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=6)** (*Function Analysis and Series*) — Rational function, slope extrema, improper integral, series convergence. - **[2016 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=2)** (*free-response*) — Water tank, rate function, removal table, net change. ### Unit 2: Differentiation: Definition and Fundamental Properties - **[2025 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=3)** (*Free-Response*) — Invasive species, average value, rate of change, limits at infinity. - **[2025 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=6)** (*Free-Response*) — Reading rates, estimation, IVT, trapezoidal sums. - **[2024 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=3)** (*Calculator Active*) — Coffee temp table, derivative approximation, Riemann sum, rate change. - **[2022 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=8)** (*Table and Related Rates*) — Melting cone, tabular data, approximation, related rates. - **[2021 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=3)** (*free-response*) — Bacterial density table, derivative estimation, Riemann sums. - **[2021 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=8)** (*free-response*) — Integral-defined function, concavity, piecewise graph, MVT. - **[2019 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=4)** (*Graph Analysis*) — Piecewise graph, accumulation function extrema, limit evaluation. - **[2019 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=6)** (*Analytical / Improper Integral*) — Parameter family, tangent slopes, partial fractions, improper integral. - **[2018 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=3)** (*free-response*) — Plankton density, boat parametric velocity, total distance. - **[2018 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=5)** (*free-response*) — Tree growth table, derivative estimation, MVT, related rates. - **[2017 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=4)** (*Graph Analysis*) — Derivative graph, function values, extrema, second derivative. - **[2017 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=6)** (*Function Analysis and Series*) — Rational function, slope extrema, improper integral, series convergence. - **[2016 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=2)** (*free-response*) — Water tank, rate function, removal table, net change. - **[2015 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=4)** (*free-response*) — Velocity table, acceleration, average velocity, distance. ### Unit 3: Differentiation: Composite, Implicit, and Inverse Functions - **[2025 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=8)** (*Free-Response*) — Implicit higher-order derivatives, Taylor polynomials, Lagrange error. - **[2023 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=3)** (*free-response*) — Gasoline pumping rate, Riemann sum, MVT, flow average. - **[2023 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=7)** (*free-response*) — Milk cooling, slope field, tangent approximation, concavity error. - **[2016 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=5)** (*free-response*) — Differential equation, second derivative, extrema categorization, limit. - **[2015 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=5)** (*free-response*) — Slope fields, second derivatives, concavity, extrema tests. ### Unit 4: Contextual Applications of Differentiation - **[2025 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=4)** (*Free-Response*) — Polar curves, radius rate, area, coordinate optimization. - **[2023 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=3)** (*free-response*) — Gasoline pumping rate, Riemann sum, MVT, flow average. - **[2023 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=7)** (*free-response*) — Milk cooling, slope field, tangent approximation, concavity error. - **[2023 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=8)** (*free-response*) — Derivative graph, extrema, concavity, L’Hospital’s Rule. - **[2022 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=8)** (*Table and Related Rates*) — Melting cone, tabular data, approximation, related rates. - **[2021 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=3)** (*free-response*) — Bacterial density table, derivative estimation, Riemann sums. - **[2021 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=8)** (*free-response*) — Integral-defined function, concavity, piecewise graph, MVT. - **[2019 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=2)** (*Rate In/Rate Out*) — Fish entering/leaving lake, net change, rate extrema. - **[2019 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=4)** (*Graph Analysis*) — Piecewise graph, accumulation function extrema, limit evaluation. - **[2019 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=5)** (*Related Rates / Differential Equations*) — Draining barrel, related rates, height differential equation. - **[2018 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=2)** (*free-response*) — Escalator line rates, accumulation, time solution, optimization. - **[2018 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=3)** (*free-response*) — Plankton density, boat parametric velocity, total distance. - **[2018 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=5)** (*free-response*) — Tree growth table, derivative estimation, MVT, related rates. - **[2018 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=6)** (*free-response*) — Polar curves, area, tangent slope, particle rate. - **[2017 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=2)** (*Rate and Accumulation*) — Tank volume, Riemann sums, cross-section model, related rates. - **[2017 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=5)** (*Differential Equations*) — Potato cooling, linear approx, concavity, separation of variables. - **[2016 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=5)** (*free-response*) — Differential equation, second derivative, extrema categorization, limit. - **[2016 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=6)** (*free-response*) — Funnel dimensions, average value, volume, related rates. - **[2015 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=2)** (*free-response*) — Drainpipe rainwater flow, total flow, extrema, overflow. - **[2015 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=4)** (*free-response*) — Velocity table, acceleration, average velocity, distance. - **[2015 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=6)** (*free-response*) — Rational function, tangent line, critical points, partial fractions. ### Unit 5: Analytical Applications of Differentiation - **[2025 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=3)** (*Free-Response*) — Invasive species, average value, rate of change, limits at infinity. - **[2025 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=7)** (*Free-Response*) — Integral-defined function, inflection points, absolute extrema. - **[2024 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=3)** (*Calculator Active*) — Coffee temp table, derivative approximation, Riemann sum, rate change. - **[2024 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=7)** (*Calculator Inactive*) — Seawater depth, slope field, separation of variables. - **[2024 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=8)** (*Calculator Inactive*) — Integral-defined function g, graph area, critical points. - **[2023 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=3)** (*free-response*) — Gasoline pumping rate, Riemann sum, MVT, flow average. - **[2023 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=7)** (*free-response*) — Milk cooling, slope field, tangent approximation, concavity error. - **[2023 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=8)** (*free-response*) — Derivative graph, extrema, concavity, L’Hospital’s Rule. - **[2022 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=3)** (*Rate and Accumulation*) — Toll plaza vehicle rate, integrals, optimization. - **[2022 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=7)** (*Graph Analysis*) — Derivative graph, inflection points, extrema, function values. - **[2021 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=4)** (*free-response*) — Planar particle motion, velocity vector, speed, distance. - **[2021 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=7)** (*free-response*) — Function family, area, radius maximization, volume. - **[2021 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=8)** (*free-response*) — Integral-defined function, concavity, piecewise graph, MVT. - **[2019 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=2)** (*Rate In/Rate Out*) — Fish entering/leaving lake, net change, rate extrema. - **[2019 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=4)** (*Graph Analysis*) — Piecewise graph, accumulation function extrema, limit evaluation. - **[2019 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=5)** (*Related Rates / Differential Equations*) — Draining barrel, related rates, height differential equation. - **[2018 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=2)** (*free-response*) — Escalator line rates, accumulation, time solution, optimization. - **[2018 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=4)** (*free-response*) — Derivative graph, function values, concavity, inflection points. - **[2018 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=5)** (*free-response*) — Tree growth table, derivative estimation, MVT, related rates. - **[2017 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=3)** (*Polar Coordinates*) — Polar curves, area, dividing ray equation, distance. - **[2017 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=4)** (*Graph Analysis*) — Derivative graph, function values, extrema, second derivative. - **[2017 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=5)** (*Differential Equations*) — Potato cooling, linear approx, concavity, separation of variables. - **[2017 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=6)** (*Function Analysis and Series*) — Rational function, slope extrema, improper integral, series convergence. - **[2016 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=4)** (*free-response*) — Integral-defined function g, piecewise linear f, properties. - **[2016 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=5)** (*free-response*) — Differential equation, second derivative, extrema categorization, limit. - **[2015 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=2)** (*free-response*) — Drainpipe rainwater flow, total flow, extrema, overflow. - **[2015 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=5)** (*free-response*) — Slope fields, second derivatives, concavity, extrema tests. - **[2015 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=6)** (*free-response*) — Rational function, tangent line, critical points, partial fractions. ### Unit 6: Integration and Accumulation of Change - **[2025 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=3)** (*Free-Response*) — Invasive species, average value, rate of change, limits at infinity. - **[2025 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=6)** (*Free-Response*) — Reading rates, estimation, IVT, trapezoidal sums. - **[2025 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=7)** (*Free-Response*) — Integral-defined function, inflection points, absolute extrema. - **[2024 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=3)** (*Calculator Active*) — Coffee temp table, derivative approximation, Riemann sum, rate change. - **[2024 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=8)** (*Calculator Inactive*) — Integral-defined function g, graph area, critical points. - **[2024 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=9)** (*Calculator Inactive*) — Function properties, integral derivative, arc length, Euler’s method. - **[2023 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=3)** (*free-response*) — Gasoline pumping rate, Riemann sum, MVT, flow average. - **[2023 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=8)** (*free-response*) — Derivative graph, extrema, concavity, L’Hospital’s Rule. - **[2023 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=9)** (*free-response*) — Area between curves, improper integral, integration by parts. - **[2022 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=3)** (*Rate and Accumulation*) — Toll plaza vehicle rate, integrals, optimization. - **[2022 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=4)** (*Parametric Motion*) — Parametric motion, slope, speed, acceleration, distance. - **[2022 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=7)** (*Graph Analysis*) — Derivative graph, inflection points, extrema, function values. - **[2022 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=8)** (*Table and Related Rates*) — Melting cone, tabular data, approximation, related rates. - **[2022 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=9)** (*Area and Volume*) — Rational functions, improper integral, bounded region area. - **[2021 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=3)** (*free-response*) — Bacterial density table, derivative estimation, Riemann sums. - **[2021 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=7)** (*free-response*) — Function family, area, radius maximization, volume. - **[2021 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=8)** (*free-response*) — Integral-defined function, concavity, piecewise graph, MVT. - **[2019 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=4)** (*Graph Analysis*) — Piecewise graph, accumulation function extrema, limit evaluation. - **[2019 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=6)** (*Analytical / Improper Integral*) — Parameter family, tangent slopes, partial fractions, improper integral. - **[2018 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=4)** (*free-response*) — Derivative graph, function values, concavity, inflection points. - **[2018 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=5)** (*free-response*) — Tree growth table, derivative estimation, MVT, related rates. - **[2017 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=2)** (*Rate and Accumulation*) — Tank volume, Riemann sums, cross-section model, related rates. - **[2017 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=4)** (*Graph Analysis*) — Derivative graph, function values, extrema, second derivative. - **[2017 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=6)** (*Function Analysis and Series*) — Rational function, slope extrema, improper integral, series convergence. - **[2016 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=2)** (*free-response*) — Water tank, rate function, removal table, net change. - **[2016 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=3)** (*free-response*) — Particle motion, parametric equations, component graph. - **[2016 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=4)** (*free-response*) — Integral-defined function g, piecewise linear f, properties. - **[2015 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=4)** (*free-response*) — Velocity table, acceleration, average velocity, distance. - **[2015 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=6)** (*free-response*) — Rational function, tangent line, critical points, partial fractions. ### Unit 7: Differential Equations - **[2024 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=7)** (*Calculator Inactive*) — Seawater depth, slope field, separation of variables. - **[2023 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=7)** (*free-response*) — Milk cooling, slope field, tangent approximation, concavity error. - **[2021 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=9)** (*free-response*) — Differential equation, Taylor polynomial, Euler’s method. - **[2019 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=5)** (*Related Rates / Differential Equations*) — Draining barrel, related rates, height differential equation. - **[2017 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=5)** (*Differential Equations*) — Potato cooling, linear approx, concavity, separation of variables. - **[2015 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=5)** (*free-response*) — Slope fields, second derivatives, concavity, extrema tests. ### Unit 8: Applications of Integration - **[2025 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=3)** (*Free-Response*) — Invasive species, average value, rate of change, limits at infinity. - **[2025 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=6)** (*Free-Response*) — Reading rates, estimation, IVT, trapezoidal sums. - **[2024 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=3)** (*Calculator Active*) — Coffee temp table, derivative approximation, Riemann sum, rate change. - **[2023 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=3)** (*free-response*) — Gasoline pumping rate, Riemann sum, MVT, flow average. - **[2023 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=9)** (*free-response*) — Area between curves, improper integral, integration by parts. - **[2022 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=3)** (*Rate and Accumulation*) — Toll plaza vehicle rate, integrals, optimization. - **[2022 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=9)** (*Area and Volume*) — Rational functions, improper integral, bounded region area. - **[2021 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=3)** (*free-response*) — Bacterial density table, derivative estimation, Riemann sums. - **[2021 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=7)** (*free-response*) — Function family, area, radius maximization, volume. - **[2019 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=2)** (*Rate In/Rate Out*) — Fish entering/leaving lake, net change, rate extrema. - **[2019 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=3)** (*Polar Coordinates*) — Polar region, area, average distance, circle limits. - **[2018 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=2)** (*free-response*) — Escalator line rates, accumulation, time solution, optimization. - **[2018 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=3)** (*free-response*) — Plankton density, boat parametric velocity, total distance. - **[2018 Q4](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=5)** (*free-response*) — Tree growth table, derivative estimation, MVT, related rates. - **[2017 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=2)** (*Rate and Accumulation*) — Tank volume, Riemann sums, cross-section model, related rates. - **[2017 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=3)** (*Polar Coordinates*) — Polar curves, area, dividing ray equation, distance. - **[2016 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=2)** (*free-response*) — Water tank, rate function, removal table, net change. - **[2016 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=6)** (*free-response*) — Funnel dimensions, average value, volume, related rates. - **[2015 Q1](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=2)** (*free-response*) — Drainpipe rainwater flow, total flow, extrema, overflow. - **[2015 Q3](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=4)** (*free-response*) — Velocity table, acceleration, average velocity, distance. ### Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions - **[2025 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=4)** (*Free-Response*) — Polar curves, radius rate, area, coordinate optimization. - **[2024 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=4)** (*Calculator Active*) — Parametric motion, speed, distance, position vector. - **[2024 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=9)** (*Calculator Inactive*) — Function properties, integral derivative, arc length, Euler’s method. - **[2023 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=4)** (*free-response*) — Parametric motion, acceleration, speed, total distance. - **[2022 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=4)** (*Parametric Motion*) — Parametric motion, slope, speed, acceleration, distance. - **[2021 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=4)** (*free-response*) — Planar particle motion, velocity vector, speed, distance. - **[2019 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=3)** (*Polar Coordinates*) — Polar region, area, average distance, circle limits. - **[2018 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=3)** (*free-response*) — Plankton density, boat parametric velocity, total distance. - **[2018 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=6)** (*free-response*) — Polar curves, area, tangent slope, particle rate. - **[2017 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=3)** (*Polar Coordinates*) — Polar curves, area, dividing ray equation, distance. - **[2016 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=3)** (*free-response*) — Particle motion, parametric equations, component graph. - **[2015 Q2](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=3)** (*free-response*) — Velocity vector, position, tangent slope, speed. ### Unit 10: Infinite Sequences and Series - **[2025 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=8)** (*Free-Response*) — Implicit higher-order derivatives, Taylor polynomials, Lagrange error. - **[2025 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2025&pg=9)** (*Free-Response*) — Taylor series convergence, derivative series, geometric series. - **[2024 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2024&pg=10)** (*Calculator Inactive*) — Maclaurin series, alternating error, derivative series. - **[2023 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=9)** (*free-response*) — Area between curves, improper integral, integration by parts. - **[2023 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2023&pg=10)** (*free-response*) — Higher-order derivative, Taylor polynomial, Lagrange error. - **[2022 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2022&pg=10)** (*Power Series*) — Power series, interval of convergence, error bound. - **[2021 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=9)** (*free-response*) — Differential equation, Taylor polynomial, Euler’s method. - **[2021 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2021&pg=10)** (*free-response*) — Maclaurin series, Integral Test, Ratio Test, error. - **[2019 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2019&pg=7)** (*Series*) — Taylor polynomials, Maclaurin manipulation, error bounds. - **[2018 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2018&pg=7)** (*free-response*) — Logarithmic Maclaurin series, interval convergence, alternating error. - **[2017 Q5](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=6)** (*Function Analysis and Series*) — Rational function, slope extrema, improper integral, series convergence. - **[2017 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2017&pg=7)** (*Taylor Series*) — Maclaurin construction, convergence analysis, alternating error. - **[2016 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2016&pg=7)** (*free-response*) — Taylor series construction, convergence interval, error estimation. - **[2015 Q6](https://nerd-notes.com/frq/?subject=calculus-bc&yr=2015&pg=7)** (*free-response*) — Maclaurin radius, derivative series, related Taylor polynomial. ### 2026 FRQ Topics Prediction We used [Phy AI](https://nerd-notes.com/ai) + the frequency of topics above to make an educated guess on what you might see on the upcoming 2026 AP Calculus BC Exam FRQ: - **Unit 6: Integration and Accumulation** — 29 appearances. Expect at least one major problem involving a function defined by an integral graph, requiring you to find values, derivatives, and extrema from geometric areas. - **Unit 10: Infinite Sequences and Series** — 14 appearances. A dedicated Series FRQ (usually Q6) is virtually guaranteed; prepare specifically for finding intervals of convergence (Ratio Test) and estimating error (Alternating Series or Lagrange). - **Unit 9: Parametric/Polar/Vector** — 12 appearances. You will likely see one full FRQ on either particle motion (parametric vectors) or finding the area bounded by polar curves. - **Unit 5: Analytical Differentiation** — 28 appearances. Look for “justify your answer” questions involving the Mean Value Theorem or Intermediate Value Theorem applied to table data or analytical functions. 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