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

FRQs – No graphing calculator
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Unit 1: Limits and Continuity
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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.

Practice FRQ 1 of 41/4

2. Let f be the function defined by

f(x)={x2−9x−3,x≠37,x=3f(x) = \begin{cases} \dfrac{x^2-9}{x-3}, & x ≠ 3 \\ 7, & x = 3 \end{cases}f(x)=⎩⎨⎧​x−3x2−9​,7,​x=3x=3​

and let p be the rational function defined by p(x)=2x2+1x2−4p(x) = \dfrac{2x^2+1}{x^2-4}p(x)=x2−42x2+1​.

A.

Approximate f′(3)f'(3)f′(3) using the average rate of change of f over the interval 3.1≤x≤3.23.1 ≤ x ≤ 3.23.1≤x≤3.2. Show the work that leads to your answer.

B.

Write the limit lim⁡x→3f(x)\lim_{x\to 3} f(x)limx→3​f(x) using correct analytic notation and find its value. Show the algebraic work that leads to your answer.

C.

Is f continuous at x=3x = 3x=3? Justify your answer using the definition of continuity at a point.

D.

The function g, defined by g(x)=∫0xp(t) dtg(x) = \int_0^x p(t)\,dtg(x)=∫0x​p(t)dt, is defined for all x in the interval 0≤x<20 ≤ x < 20≤x<2. Find lim⁡x→2−g(x)\lim_{x\to 2^-} g(x)limx→2−​g(x) and interpret the result in terms of the behavior of p. Justify your answer.

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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 carefullybefore 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.