Grade 12 · Math · Calculus

12th grade Average and instantaneous rates of change worksheet

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Average and instantaneous rates of change

Grade 12 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

Ari finds that f(x) = x² has average rate of change 7 from x = 1 to x = b. What is b?
Bo finds that f(x) = x² has average rate of change 11 from x = 2 to x = b. What is b?
Jun finds that f(x) = x² has average rate of change 10 from x = 3 to x = b. What is b?
A ball thrown down falls s(t) = 4.9t² + 3t m after t seconds. Kira shrinks [2, 2 + h] to find the velocity at t = 2. What is it, in m/s?
A cart's position is s(t) = 3t² + 2t m after t seconds. Luz shrinks [3, 3 + h] to find the velocity at t = 3. What is it, in m/s?
A sled's position is s(t) = 2t² − 2t m after t seconds. Noah shrinks [5, 5 + h] to find the velocity at t = 5. What is it, in m/s?
Pia studies f(x) = 12/x. What is its average rate of change from x = 2 to x = 6?
Ren studies f(x) = 6/x. What is its average rate of change from x = 1 to x = 3?
Tala studies f(x) = 20/x. What is its average rate of change from x = 4 to x = 10?
Zee studies f(x) = 8/x. What is its average rate of change from x = 2 to x = 4?

Average and instantaneous rates of change. Every version has 10 questions, and the answer key prints on the second page.

I can find an average rate of change from a table or formula, with units.
I can estimate an instantaneous rate from shrinking secants.
I can find a velocity at a moment as a limit of average velocities, and say what a rate means.

Standard: none (beyond CCSS)

average rate of change: Change in output ÷ change in input: a secant's slope.

instantaneous rate: Where the secant slopes head as the interval shrinks.

average velocity: Change in position ÷ change in time; its sign gives the direction.

Gave the change instead of the rate. A rate is the change divided by the change in time or x.

Divided the run by the change. The output's change goes on top: rise over run.

Divided by the end x instead of the change in x.

What is the most common mistake with average and instantaneous rates of change?

Gave the change instead of the rate. A rate is the change divided by the change in time or x.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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