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AP Calculus AB/BC Calculator FRQ Practice

61 calculator-required FRQs written in the AP format for Calculus AB and BC. Pick one, read the full question, and write your response.

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Your first scored response is included. A plan unlocks unlimited scoring.

New to the Calculator FRQ? Read the exam guide

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61 questions

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Removable discontinuities and instantaneous rates of change

Unit 1: Limits and Continuity

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The following functions are defined for this question: k(x)=x2−4x−2k(x)=\frac{x^2-4}{x-2} p(x)=x2−4x2−5x+6p(x)=\frac{x^2-4}{x^2-5x+6}

The function kk is defined for x≠2x≠ 2. The function pp is defined for x≠2,3x≠ 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→∞x\to\infty.

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).

Figure 1
A.

Use correct limit notation to represent lim⁡x→2k(x)\lim_{x\to 2}k(x). Then find the value of the limit. Show the work that leads to your answer.

B.

Let xx 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 kk on the interval [1.9,2.1][1.9,2.1].

(ii) Use a calculator to approximate the average rate of change of kk on the interval [1.99,2.01][1.99,2.01].

(iii) Define gg by g(x)=k(x)g(x)=k(x) for x≠2x\ne2 and g(2)=4g(2)=4. Based on your results in parts (i) and (ii), estimate g′(2)g'(2). Justify your reasoning.

C.

Write a limit expression that describes the end behavior of p(x)p(x) as x→∞x\to\infty. Then evaluate the limit using limit theorems.

D.

Define a new function qq by Continuity of a piecewise-defined function at x=2x=2 is enforced by matching the function value to the two-sided limit.

q(x)={p(x),x≠2a,x=2q(x)=\begin{cases}p(x),& x≠ 2\\ a,& x=2\end{cases}

Find the value of the constant aa such that qq is continuous at x=2x=2. Justify your answer using the definition of continuity at a point.

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
read the exam guide

  1. Part A: Set up

    Often a value, rate, or average from the given model, with the setup shown

    2 pts

  2. Part B: Apply

    A derivative or integral applied to the context, with the expression before the result

    2 pts

  3. Part C: Build

    Often an equation, integral expression, or approximation to write

    2 pts

  4. Part D: Conclude

    A final value, often backed by a reason or a named theorem

    3 pts

How Calculator FRQ practice works

Each question follows the exam’s format, from the full prompt to a score on every part.

  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.

Feedback on every part

A summary at the top tells you what to work on next. Below it, each part shows whether you earned the point and what the scoring guidelines were looking for.

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Detailed Feedback

Part A(A1): 1/1 point

The student correctly sets up the difference quotient (W(2.1) - W(1.9)) / (2.1 - 1.9), which matches the required form. This earns A1.

Part A(A2): 0/1 point

The student's final answer of 1.225 is incorrect. The correct value is approximately 1.222. The student made a rounding error when computing W(2.1) ≈ 3.455 (correct is ≈ 3.4548) and W(1.9) ≈ 3.210 (correct is ≈ 3.2103), leading to a slightly off numerator. The answer 1.225 does not match the required 1.222 to three decimal places, so A2 is not earned.

Part B(B1): 1/1 point

The student explicitly references the interval [1.9, 2.1] from Part A, which contains t = 2, and sets up the difference quotient (W(2.1) - W(1.9)) / (2.1 - 1.9). This is a valid setup for estimating W'(2), earning B1.

Detailed feedback on a practice Calculator FRQ

Questions about the Calculator FRQ

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.

More AP Calculus AB/BC practice

No-Calculator FRQ practice

No-calculator FRQs with the full setup and all four parts.

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AP Calculus AB/BC FRQs

Every FRQ type for AP Calculus AB/BC, with practice for each.

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AP Calculus AB/BC study guides

Unit-by-unit review for the whole course.

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Write your first Calculator FRQ

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Teaching AP Calculus AB/BC? Assign these Calculator FRQs to your class