Fiveable
♾️AP Calculus AB/BC
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♾️AP Calculus AB/BC

FRQs – Graphing calculator required
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Unit 1: Limits and Continuity
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Guided Practice

FRQs – Graphing calculator required
​
Unit 1: Limits and Continuity
​
FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Why are some FRQs missing?

For this first release, we focused on FRQs that:

  • We already have stimulus materials for (i.e. history/English)
  • Don't require stimulus materials at all
  • Use stimulus that can be generated with AI (like science data sets)

We also skipped FRQs that require audio playback or speaking responses for now.

Our goal is to eventually have practice available for every FRQ type across all AP subjects. We're actively working to add more!

Practice FRQ 1 of 81/8
1. A ramp is being designed so that its height above the ground is modeled for x≥0x ≥ 0x≥0 by the function HHH, where H(x)=x2−4x−2H(x)=\frac{x^2-4}{x-2}H(x)=x−2x2−4​ for x≠2x ≠ 2x=2. The value of H(2)H(2)H(2) is not defined by this expression. A table of selected values of H(x)H(x)H(x) near x=2x=2x=2 is shown. Let m(x)=H(x)−H(2.5)x−2.5m(x)=\frac{H(x)-H(2.5)}{x-2.5}m(x)=x−2.5H(x)−H(2.5)​ for x≠2.5x ≠ 2.5x=2.5.

Selected values of $$H(x)$$ near $$x=2$$

1.93.900
1.993.990
1.9993.999
2.0014.001
2.014.010
2.14.100
A. Use the table to estimate lim⁡x→2H(x)\lim_{x\to 2} H(x)limx→2​H(x). Write your answer using correct limit notation.
B. Find lim⁡x→2H(x)\lim_{x\to 2} H(x)limx→2​H(x) by rewriting H(x)H(x)H(x) as an equivalent expression for x≠2x≠ 2x=2. Show your work.
C. Write a limit expression that represents the instantaneous rate of change of HHH at x=2.5x=2.5x=2.5 in terms of average rates of change over intervals containing x=2.5x=2.5x=2.5. Then evaluate the limit.
D. A new function KKK is defined by K(x)=x2−4x−2K(x)=\frac{x^2-4}{x-2}K(x)=x−2x2−4​ for x≠2x≠ 2x=2 and K(2)=cK(2)=cK(2)=c, where ccc is a constant. Find the value of ccc such that KKK is continuous at x=2x=2x=2. Justify your answer using the definition of continuity at a point. The function KKK matches the ramp model HHH for all x≠2x≠ 2x=2, but the height at x=2x=2x=2 is defined separately as K(2)=cK(2)=cK(2)=c (in feet).
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FRQ Directions
Free Response Question Practice

This practice environment simulates the AP AP Calculus AB/BC Free Response Questions section. Here are some guidelines:

  • Read each question carefully before responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
  • Use the timer to practice time management. You can pause, restart, or hide the timer as needed.
  • Mark for Review if you want to come back to a question later.
  • Your responses are saved automatically as you type. You can also use the drawing tool for questions that require diagrams or graphs.
  • Use the toolbar for formatting options like bold, italic, subscript, and superscript.
  • Navigate between questions using the Previous and Next buttons at the bottom of the screen.

Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.