--- title: "AP Calculus AB/BC Calculator FRQ Practice" description: "61 Calculator-Required FRQs written in the AP format, each scored part by part." canonical: "https://fiveable.me/ap-calc/frqs/calculator" type: "frq-type-practice" subject: "AP Calculus AB/BC" --- # AP Calculus AB/BC Calculator FRQ Practice ## What the Calculator FRQ asks Calculator-required FRQs are questions 1 and 2 on the AP Calculus AB and BC exams, in Part A of the FRQ section. Each has four parts built around a context, a function, a graph, or a table, and a graphing calculator is required. - **30 min**: for the 2 questions in Part A - **9 points**: across parts A to D - **50%**: of your score, for all six FRQs | Part | What it asks | Points | | --- | --- | --- | | A: Set up | Often a value, rate, or average from the given model, with the setup shown | 2 | | B: Apply | A derivative or integral applied to the context, with the expression before the result | 2 | | C: Build | Often an equation, integral expression, or approximation to write | 2 | | D: Conclude | A final value, often backed by a reason or a named theorem | 3 | ## How Calculator FRQ practice works 1. **Read the full question.** The setup, any graph or table, and parts A to D, laid out the way the exam shows them. 2. **Write on a 15-minute timer.** About the time each question gets on exam day. Pause it or turn it off, and your response saves as you go. 3. **Submit for a score out of 9.** Your response is scored against the scoring guidelines written for that question. Your first score is included. ## All 61 questions ### Unit 1: Limits and Continuity (8) - [Removable discontinuities and instantaneous rates of change](/ap-calc/frq-practice?id=698a19b01ee6abd3ecdb113a&type=frqs-graphing-calculator-required) - [Limits, continuity, and instantaneous rate of change](/ap-calc/frq-practice?id=698a203f1ee6abd3ecdb115b&type=frqs-graphing-calculator-required) - [Limits, continuity, and instantaneous rates of change](/ap-calc/frq-practice?id=698a234a1ee6abd3ecdb117c&type=frqs-graphing-calculator-required) - [Signal strength limits and instantaneous rate of change](/ap-calc/frq-practice?id=6abd46588b61320773e102ac&type=frqs-graphing-calculator-required) - [Battery charge limits and long-term behavior](/ap-calc/frq-practice?id=6abd49688b61320773e102e3&type=frqs-graphing-calculator-required) - [Squeeze theorem and limits of oscillating functions](/ap-calc/frq-practice?id=6abd5f41e8256b118b725591&type=frqs-graphing-calculator-required) - [Water temperature changes with depth in a lake](/ap-calc/frq-practice?id=6abdb79db4835a941b5eecf8&type=frqs-graphing-calculator-required) - [Water filtration rates and long-term behavior](/ap-calc/frq-practice?id=6abd5e40e8256b118b725579&type=frqs-graphing-calculator-required) ### Unit 2: Differentiation: Definition and Fundamental Properties (8) - [Cyclist distance and instantaneous speed over time](/ap-calc/frq-practice?id=6abbf8e746338eae3928138c&type=frqs-graphing-calculator-required) - [Temperature change and rates of change over time](/ap-calc/frq-practice?id=6abbfa0647b67df7f91d9a5e&type=frqs-graphing-calculator-required) - [Reagent concentration and instantaneous reaction rates](/ap-calc/frq-practice?id=6abc294eb06c70d863424b74&type=frqs-graphing-calculator-required) - [Piecewise drone height and rates of change](/ap-calc/frq-practice?id=6abdb7c89804fe051c0ac999&type=frqs-graphing-calculator-required) - [Derivative slopes, corners, and vertical tangents](/ap-calc/frq-practice?id=6abdd3968285c25b84bea5ec&type=frqs-graphing-calculator-required) - [Greenhouse temperature change over time](/ap-calc/frq-practice?id=6abea24f6f406bdeb371d354&type=frqs-graphing-calculator-required) - [Derivative rates of coating thickness ratios and products](/ap-calc/frq-practice?id=6abea2cd6f406bdeb371d35f&type=frqs-graphing-calculator-required) - [Average rates of change and derivatives of piecewise functions](/ap-calc/frq-practice?id=6abd5db935456b9ebca3bc9b&type=frqs-graphing-calculator-required) ### Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (5) - [Drone altitude and sensor readings via inverse functions](/ap-calc/frq-practice?id=6abc2b6a5283f15921474fc9&type=frqs-graphing-calculator-required) - [Exponential temperature gradients and inverse functions](/ap-calc/frq-practice?id=6abc43c240de6d4b00d16b86&type=frqs-graphing-calculator-required) - [Bacterial growth and nutrient concentration changes](/ap-calc/frq-practice?id=6abd608ed3b48568a0755fcf&type=frqs-graphing-calculator-required) - [Algae photosynthesis rates and light intensity at depth](/ap-calc/frq-practice?id=6abd6123d3b48568a0755fdd&type=frqs-graphing-calculator-required) - [Inverse functions and reactor pressure rates](/ap-calc/frq-practice?id=6abd782156ad68758a2fafa3&type=frqs-graphing-calculator-required) ### Unit 4: Contextual Applications of Differentiation (1) - [Battery charge accumulation and charging rates](/ap-calc/frq-practice?id=6abc36405abe8b114ccd511d&type=frqs-graphing-calculator-required) ### Unit 5: Analytical Applications of Differentiation (1) - [Drone altitude, rates of change, extrema](/ap-calc/frq-practice?id=6abbf95913eea5a2c0c8b894&type=frqs-graphing-calculator-required) ### Unit 6: Integration and Accumulation of Change (1) - [Museum visitor entry rates and accumulation](/ap-calc/frq-practice?id=6abc36bc319dce86ab4cf869&type=frqs-graphing-calculator-required) ### Unit 7: Differential Equations (9) - [Bacterial population growth with logistic differential equation](/ap-calc/frq-practice?id=698a146d1ee6abd3ecdb111b&type=frqs-graphing-calculator-required) - [Logistic population growth and differential equations](/ap-calc/frq-practice?id=698a17df1ee6abd3ecdb112c&type=frqs-graphing-calculator-required) - [Logistic population growth and differential equations](/ap-calc/frq-practice?id=698a19681ee6abd3ecdb1137&type=frqs-graphing-calculator-required) - [Saltwater decay and numerical approximations](/ap-calc/frq-practice?id=6abc2809e6aaeca7dab51226&type=frqs-graphing-calculator-required) - [Medication concentration and drug removal rates](/ap-calc/frq-practice?id=6abc28aae6aaeca7dab51238&type=frqs-graphing-calculator-required) - [Tree growth approaching maximum height](/ap-calc/frq-practice?id=6abc2bbde6aaeca7dab5128a&type=frqs-graphing-calculator-required) - [Fungus growth modeled by a differential equation](/ap-calc/frq-practice?id=6abc319f35160d76812561c8&type=frqs-graphing-calculator-required) - [Exponential decay of undissolved mineral mass](/ap-calc/frq-practice?id=6abd5cf89dc406979aff6e43&type=frqs-graphing-calculator-required) - [Differential equations modeling algae growth in ponds](/ap-calc/frq-practice?id=6abd662c0724d2f430f0fc65&type=frqs-graphing-calculator-required) ### Unit 8: Applications of Integration (11) - [Average function value and particle position calculations](/ap-calc/frq-practice?id=697808a4ae052c99bd7d7dc9&type=frqs-graphing-calculator-required) - [Boat velocity modeling and bounded region area](/ap-calc/frq-practice?id=698a150b1ee6abd3ecdb111f&type=frqs-graphing-calculator-required) - [Pollutant flow rates and accumulated mass](/ap-calc/frq-practice?id=698a166d1ee6abd3ecdb1124&type=frqs-graphing-calculator-required) - [Water accumulation rate and basin volume](/ap-calc/frq-practice?id=698a18631ee6abd3ecdb112f&type=frqs-graphing-calculator-required) - [Kayak velocity modeling and region area calculation](/ap-calc/frq-practice?id=698a190a1ee6abd3ecdb1135&type=frqs-graphing-calculator-required) - [Water tank accumulation with sinusoidal inflow and linear leakage](/ap-calc/frq-practice?id=698a1a871ee6abd3ecdb113f&type=frqs-graphing-calculator-required) - [Water accumulation rates and tank volume](/ap-calc/frq-practice?id=698a24301ee6abd3ecdb1185&type=frqs-graphing-calculator-required) - [Areas and volumes of solids of revolution](/ap-calc/frq-practice?id=6abc2d44221f7013aed531be&type=frqs-graphing-calculator-required) - [Area and volume between exponential and sinusoidal curves](/ap-calc/frq-practice?id=6abc46559e06eccb58b226d0&type=frqs-graphing-calculator-required) - [Area, solids of revolution, cross-sectional volume](/ap-calc/frq-practice?id=6abc46fc9e06eccb58b226e1&type=frqs-graphing-calculator-required) - [Medication concentration over time and effective dosage levels](/ap-calc/frq-practice?id=6abdb9439c2bf9cc2a15b839&type=frqs-graphing-calculator-required) ### Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC only) (9) - [Parametric particle motion and arc length calculations](/ap-calc/frq-practice?id=698a14451ee6abd3ecdb111a&type=frqs-graphing-calculator-required) - [Parametric motion and polar curves](/ap-calc/frq-practice?id=698a1b031ee6abd3ecdb1142&type=frqs-graphing-calculator-required) - [Parametric particle motion and polar curves](/ap-calc/frq-practice?id=698a1e721ee6abd3ecdb1151&type=frqs-graphing-calculator-required) - [Parametric motion, derivatives, and arc length](/ap-calc/frq-practice?id=698a1f031ee6abd3ecdb1152&type=frqs-graphing-calculator-required) - [Parametric particle motion and velocity in the plane](/ap-calc/frq-practice?id=6abc43bbf09afbe5316ae2ce&type=frqs-graphing-calculator-required) - [Rover motion along a parametric path](/ap-calc/frq-practice?id=6abd6141169b9647486819a1&type=frqs-graphing-calculator-required) - [Polar area, curve rates, and sector boundaries](/ap-calc/frq-practice?id=6abd73f59f4c7fd25df2b50f&type=frqs-graphing-calculator-required) - [Polar curves, radial motion, tangent slope, enclosed area](/ap-calc/frq-practice?id=6abd77952bdfe443bbfd3948&type=frqs-graphing-calculator-required) - [Parametric motion, speed, and distance traveled](/ap-calc/frq-practice?id=6abea5fd4574a487779dbff9&type=frqs-graphing-calculator-required) ### Unit 10: Infinite Sequences and Series (BC only) (8) - [Taylor polynomial approximation of logarithmic function](/ap-calc/frq-practice?id=698a12f21ee6abd3ecdb1115&type=frqs-graphing-calculator-required) - [Polynomial approximations and series convergence](/ap-calc/frq-practice?id=6abc33f2c3959b560e336f0d&type=frqs-graphing-calculator-required) - [Diffraction amplitude and Taylor series approximation](/ap-calc/frq-practice?id=6abd717f802a99adca27f48f&type=frqs-graphing-calculator-required) - [Maclaurin series convergence and approximation error](/ap-calc/frq-practice?id=6abc3299c3959b560e336eeb&type=frqs-graphing-calculator-required) - [Taylor polynomial approximation and Maclaurin series convergence](/ap-calc/frq-practice?id=6abc34a4c3959b560e336f22&type=frqs-graphing-calculator-required) - [Taylor polynomial approximation and Lagrange error bounds](/ap-calc/frq-practice?id=6abe9efc7a53bfd41a61b726&type=frqs-graphing-calculator-required) - [Taylor polynomial approximations and Lagrange error bounds](/ap-calc/frq-practice?id=6abd75a7c12fa149444dd0fc&type=frqs-graphing-calculator-required) - [Maclaurin series and alternating error bounds](/ap-calc/frq-practice?id=6abd5ce9e44a1bc151665ef7&type=frqs-graphing-calculator-required) ## Sample question **Removable discontinuities and instantaneous rates of change** The following functions are defined for this question: k(x) = (x² - 4)/(x - 2) p(x) = (x² - 4)/(x² - 5x + 6) The function k is defined for x ≠ 2. The function p is defined for x ≠ 2, 3. Figure 1 shows the graphs of these functions. A graphing calculator may be used to help analyze the behavior of these functions near their points of discontinuity and as x → ∞. Figures: Type: shaded_region Caption: Figure 1. Graphs of y = k(x) and y = p(x) with discontinuities highlighted (hole at x = 2 for both; vertical asymptote at x = 3 for p). URL: https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-calc/7aac88d9-af2d-47e4-ae00-da6ff3f064d9_fig1.jpg Placement: after-background Part A (2 points): Prompt: Use correct limit notation to represent lim_(x → 2)k(x). Then find the value of the limit. Show the work that leads to your answer. Verb: find Topic: 1.6 Determining Limits Using Algebraic Manipulation Part B (2 points): Prompt: Let x approach 2 through the values 1.9, 1.99, 2.01, and 2.1. (i) Use a calculator to approximate the average rate of change of k on the interval [1.9, 2.1]. (ii) Use a calculator to approximate the average rate of change of k on the interval [1.99, 2.01]. (iii) Define g by g(x) = k(x) for x ≠ 2 and g(2) = 4. Based on your results in parts (i) and (ii), estimate g′(2). Justify your reasoning. Verb: approximate Topic: 2.1 Defining Average and Instantaneous Rates of Change at a Point Part C (2 points): Prompt: Write a limit expression that describes the end behavior of p(x) as x → ∞. Then evaluate the limit using limit theorems. Verb: write Topic: 1.15 Connecting Limits at Infinity and Horizontal Asymptotes Part D (3 points): Prompt: Define a new function q by q(x) = p(x), x ≠ 2; a, x = 2 Find the value of the constant a such that q is continuous at x = 2. Justify your answer using the definition of continuity at a point. Context: Continuity of a piecewise-defined function at x = 2 is enforced by matching the function value to the two-sided limit. Verb: find Topic: 1.13 Removing Discontinuities Image URLs (1): - https://kcbwzropdukwhmmvdylp.supabase.co/storage/v1/object/public/frq_stimulus/ap-calc/7aac88d9-af2d-47e4-ae00-da6ff3f064d9_fig1.jpg ## Questions **How many responses can I get scored?** You can read every question without a plan. Your first scored response is included. A plan unlocks unlimited scoring. **Can I use a calculator while I practice?** Yes. Calculator-required questions open a graphing calculator from the question panel. Write the integral or equation you evaluated, then the result to three decimal places. **How do I type math in my answer?** Type it in plain text, use the superscript button for exponents, and pick symbols like ∫ and √ from the special characters menu. You can also switch to handwrite and add a photo of your work. **Are these for Calculus AB or BC?** Both. The AB and BC exams use the same FRQ format, and some of these questions cover BC-only topics like series and parametric equations. **How are the 9 points split?** Across parts A to D, most often 2, 2, 2, and 3. The split changes by question, and on the exam each part is scored on its own. ## Related - [Calculator FRQ exam guide](/ap-calc/ap-calculus-ab-bc-exams/ap-calc-frq/study-guide/ap-calc-frq) - [AP Calculus AB/BC No-Calculator FRQ practice](/ap-calc/frqs/no-calculator) - [AP Calculus AB/BC FRQs](/ap-calc/frqs) - Any question by id: the `get_frq` tool on the [Fiveable MCP server](/mcp/docs) ## About This Document Canonical Fiveable pages are available as Markdown at the same path plus `.md`. - [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns - [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing - [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`) - [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)