Grade 12 · Math · Calculus

12th grade Power, sum and difference rules worksheet

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Power, sum and difference rules

Grade 12 Math Worksheet - Challenge Me

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

A tank holds V(t) = 2t³ − 3t² + 50 liters at time t (example data). Ari finds how fast it fills at t = 4. What is V′(4), in L per minute?
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?
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?
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?
f(x) = kx³ + 2x, and f′(2) = 50. Kira solves for the number k. What is k?
f(x) = kx³ + 5x, and f′(1) = -7. Luz solves for the number k. What is k?
f(x) = kx³ + 6x, and f′(2) = -18. Milo solves for the number k. What is k?
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
- f′(x) = 8∛x + 10/x³
- f′(x) = 8∛x − 10/x³ − 1
- f′(x) = 8∛x − 10/x
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.
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 − 4
- f′(x) = 3/∛(x²) + 7/x²
- f′(x) = 3/∛(x²) − 7/x²

The power, sum and difference rules. Every version has 10 questions, and the answer key prints on the second page.

I can use the power rule for whole, negative and fraction powers.
I can differentiate a polynomial term by term and drop the constant.
I can rewrite roots and fractions as powers, and use f′ to find a rate or an unknown coefficient.

Standard: none (beyond CCSS)

power rule: The derivative of xⁿ is nxⁿ⁻¹.

term by term: The derivative of a sum is the sum of the derivatives.

negative power: x⁻ⁿ means 1/xⁿ.

Brought the power down but did not lower it by 1. The power rule turns xⁿ into nxⁿ⁻¹.

Lowered the power but did not bring it down as a factor. xⁿ becomes n times xⁿ⁻¹.

Kept the constant term. A constant has slope 0, so it drops out.

What is the most common mistake with power, sum and difference rules?

Brought the power down but did not lower it by 1. The power rule turns xⁿ into nxⁿ⁻¹.

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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