Power, sum and difference rules

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   A balloon holds V(t) = 3t³ + 2t² + 10 cm³ at time t (example data). Bo finds how fast it fills at t = 2. What is V′(2), in cm³ per second?

   44
2. 2.

   A sand pile holds V(t) = 4t³ − 5t² + 30 cm³ at time t (example data). Esme finds how fast it fills at t = 3. What is V′(3), in cm³ per second?

   78
3. 3.

   A rain gauge holds V(t) = 2t³ + 6t² + 15 mL at time t (example data). Jun finds how fast it fills at t = 5. What is V′(5), in mL per hour?

   210
4. 4.

   f(x) = kx³ + 5x, and f′(1) = -7. Luz solves for the number k. What is k?

   -4
5. 5.

   f(x) = kx³ + 6x, and f′(2) = -18. Milo solves for the number k. What is k?

   -2
6. 6.

   f(x) = kx³ + 10x, and f′(-1) = 1. Noah solves for the number k. What is k?

   -3
7. 7.

   Pia differentiates f(x) = 3x^(2/3) − 4/x³ + 7 and writes the answer with roots. Which is f′(x)?

   • f′(x) = 2/∛x + 12/x⁴ + 7
   • f′(x) = 2/∛x − 12/x⁴
   • f′(x) = 2/∛x + 12/x⁴
   • f′(x) = 2/∛x + 12/x²
8. 8.

   Ren differentiates f(x) = 6x^(4/3) + 5/x² − 1 and writes the answer with roots. Which is f′(x)?

   • f′(x) = 8∛x − 10/x³ − 1
   • f′(x) = 8∛x + 10/x³
   • f′(x) = 8∛x − 10/x
   • f′(x) = 8∛x − 10/x³
9. 9.

   Tala differentiates f(x) = 4x^(3/2) − 2/x⁴ + 9 and writes the answer with roots. Which is f′(x)?

   • f′(x) = 6√x + 8/x⁵ + 9
   • f′(x) = 6√x − 8/x⁵
   • f′(x) = 6√x + 8/x³
   • f′(x) = 6√x + 8/x⁵
10. 10.

    Zee differentiates f(x) = 9x^(1/3) + 7/x − 4 and writes the answer with roots. Which is f′(x)?

    • f′(x) = 3/∛(x²) − 7
    • f′(x) = 3/∛(x²) + 7/x²
    • f′(x) = 3/∛(x²) − 7/x² − 4
    • f′(x) = 3/∛(x²) − 7/x²