Fiveable
♾️AP Calculus AB/BC
​

♾️AP Calculus AB/BC

FRQs – No graphing calculator
​
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.

Practice FRQ 1 of 41/4
No Calculator

2. Let fff be the function defined by f(x)=x2−4x−2f(x)=\dfrac{x^2-4}{x-2}f(x)=x−2x2−4​ for x≠2x≠ 2x=2. Let ggg be the function defined by g(x)=3x2+1x2−1g(x)=\dfrac{3x^2+1}{x^2-1}g(x)=x2−13x2+1​ for x≠±1x≠ ± 1x=±1. No graphing calculator is allowed for this question.

A.

Approximate f′(2)f'(2)f′(2) by using the average rate of change of fff over the interval 1.9≤x≤2.11.9≤ x≤ 2.11.9≤x≤2.1. Show the work that leads to your answer.

B.

Write an expression in correct limit notation that represents the statement “The values of f(x)f(x)f(x) can be made arbitrarily close to 4 by taking xxx sufficiently close to 2, but not equal to 2.” Then find the value of the limit.

C.

Find lim⁡x→∞g(x)\lim_{x\to\infty} g(x)limx→∞​g(x). Then interpret the meaning of the limit in terms of the end behavior of the graph of ggg.

D.

A new function FFF is defined by F(2)=4F(2)=4F(2)=4 and F(x)=f(x)F(x)=f(x)F(x)=f(x) for x≠2x≠ 2x=2. Find the intervals on which FFF is continuous. Justify your answer. The function f(x)=x2−4x−2f(x)=\dfrac{x^2-4}{x-2}f(x)=x−2x2−4​ is defined for x≠2x≠ 2x=2, and the function FFF is defined by assigning the value F(2)=4F(2)=4F(2)=4 while keeping F(x)=f(x)F(x)=f(x)F(x)=f(x) for all other xxx.

Pep

essential ap study content awaits..

Features
Testimonials
Testimonials
start studying →
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.