Year 12 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · CalculusYear 12 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −5x + 9
Answer: dy/dx = −5
- d/dx(−5x) = −5
- The derivative of the constant 9 is 0
2.Differentiate y = x2 + 3
Answer: dy/dx = 2x
- d/dx(x2) = 2x
- The derivative of the constant 3 is 0
3.Differentiate y = 7x3 + 7x2
Answer: dy/dx = 21x2 + 14x
- d/dx(7x3) = 21x2
- d/dx(7x2) = 14x
4.Differentiate y = −5x + 7
Answer: dy/dx = −5
- d/dx(−5x) = −5
- The derivative of the constant 7 is 0
5.Differentiate y = −6x2 − 7
Answer: dy/dx = −12x
- d/dx(−6x2) = −12x
- The derivative of the constant −7 is 0
6.Differentiate y = −7x3 + 6x2
Answer: dy/dx = −21x2 + 12x
- d/dx(−7x3) = −21x2
- d/dx(6x2) = 12x
7.Differentiate y = 8x3 − 7x2
Answer: dy/dx = 24x2 − 14x
- d/dx(8x3) = 24x2
- d/dx(−7x2) = −14x
8.Differentiate y = −5x2 + 8
Answer: dy/dx = −10x
- d/dx(−5x2) = −10x
- The derivative of the constant 8 is 0
9.Differentiate y = 3x3 − 7
Answer: dy/dx = 9x2
- d/dx(3x3) = 9x2
- The derivative of the constant −7 is 0
10.Differentiate y = 5x3 − 4
Answer: dy/dx = 15x2
- d/dx(5x3) = 15x2
- The derivative of the constant −4 is 0
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.