Average and instantaneous rates of change

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   t = 0 gives 3; t = 2 gives 11; t = 5 gives 26; t = 8 gives 47. Ari reads the table shown. What is the average rate of change from t = 2 to t = 8, in m/s?

   6
2. 2.

   t = 0 gives 10; t = 1 gives 16; t = 4 gives 34; t = 6 gives 51. Bo reads the table shown. What is the average rate of change from t = 1 to t = 6, in L per minute?

   7
3. 3.

   t = 1 gives 4; t = 3 gives 9; t = 7 gives 25; t = 9 gives 29. Jun reads the table shown. What is the average rate of change from t = 3 to t = 9, in cm per day?

   10/3
4. 4.

   Kira studies f(x) = x² + 1. What is its average rate of change from x = 2 to x = 5?

   7
5. 5.

   Luz studies f(x) = x² − 3. What is its average rate of change from x = 1 to x = 4?

   5
6. 6.

   Milo studies f(x) = x² + 4. What is its average rate of change from x = 3 to x = 7?

   10
7. 7.

   h = 0.1 gives 4.1; h = 0.01 gives 4.01; h = 0.001 gives 4.001. Pia lists secant slopes as the second point slides toward x = 2, in the table shown. What is the instantaneous rate at x = 2?

   4
8. 8.

   h = 0.1 gives 3.2; h = 0.01 gives 3.02; h = 0.001 gives 3.002. Ren lists secant slopes as the second point slides toward x = 1, in the table shown. What is the instantaneous rate at x = 1?

   3
9. 9.

   h = 0.1 gives -1.7; h = 0.01 gives -1.97; h = 0.001 gives -1.997. Tala lists secant slopes as the second point slides toward x = 3, in the table shown. What is the instantaneous rate at x = 3?

   -2
10. 10.

    h = 0.1 gives 10.4; h = 0.01 gives 10.04; h = 0.001 gives 10.004. Zee lists secant slopes as the second point slides toward x = 5, in the table shown. What is the instantaneous rate at x = 5?

    10