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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

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

  1. A scooter is s(t) meters from home at t seconds. s(0) = 2 and s(4) = 14. Ari wants the average velocity from t = 0 to 4. What is it, in m/s?

  2. A robot backs up; it is s(t) meters from its charger. s(2) = 30 and s(6) = 10. Bo wants the average velocity from t = 2 to 6. What is it, in m/s?

  3. A ball rolls back; it is s(t) meters up a ramp. s(1) = 40 and s(5) = 12. Esme wants the average velocity from t = 1 to 5. What is it, in m/s?

  4. A drone is s(t) meters high at t seconds. s(3) = 5 and s(7) = 29. Jun wants the average velocity from t = 3 to 7. What is it, in m/s?

  5. For f, the values at 2 − 0.1 and 2 + 0.1 are 3.61 and 4.41. Kira estimates the rate at 2 with the secant across both. What is the estimate?

  6. For g, the values at 1 − 0.01 and 1 + 0.01 are 2.9997 and 3.0003. Luz estimates the rate at 1 with the secant across both. What is the estimate?

  7. For the tank volume V, the values at 4 − 0.2 and 4 + 0.2 are 10.24 and 13.44. Milo estimates the rate at 4 with the secant across both. What is the estimate?

  8. The average rate of change of a sunflower's height over June is 4 cm per week. Ren explains it. What does it mean?

    • on average it grew 4 cm each week
    • it changed by 4 in total over June
    • its value at the end was 4

  9. The average rate of change of the water in a draining tub over 5 minutes is -2 L per minute. Tala explains it. What does it mean?

    • its value at the end was 2
    • on average it lost 2 L each minute
    • it changed by 2 in total over 5 minutes

  10. The average rate of change of a cart's position over the first 8 seconds is 6 m/s. Zee explains it. What does it mean?

    • it changed by 6 in total over the first 8 seconds
    • its value at the end was 6
    • on average it moved 6 m each second
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12th grade Average and instantaneous rates of change worksheet – printable
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About this worksheet

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

What your child will learn

  • 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)

Words to know

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.

Common mistakes

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.

Questions parents ask

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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