Worksheet

Average and instantaneous rates of change

Grade 12 Math Worksheet

NameDate

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 coffee's temperature over the first 10 minutes is -3 °C per minute. Pia explains it. What does it mean?

    • on average it cooled 3 °C each minute
    • its value at the end was 3
    • it changed by 3 in total over the first 10 minutes

  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
    • it changed by 2 in total over 5 minutes
    • on average it lost 2 L each minute

  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?

    • on average it moved 6 m each second
    • it changed by 6 in total over the first 8 seconds
    • its value at the end was 6
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Average and instantaneous rates of change

Answer Key - Grade 12 Math Worksheet

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?

    3

  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?

    -5

  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?

    -7

  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?

    6

  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?

    4

  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?

    0.03

  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

  8. The average rate of change of a coffee's temperature over the first 10 minutes is -3 °C per minute. Pia explains it. What does it mean?

    • on average it cooled 3 °C each minute
    • its value at the end was 3
    • it changed by 3 in total over the first 10 minutes

  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
    • it changed by 2 in total over 5 minutes
    • on average it lost 2 L each minute

  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?

    • on average it moved 6 m each second
    • it changed by 6 in total over the first 8 seconds
    • its value at the end was 6