Year 11 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · CalculusYear 11 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −4x2 − 5
Answer: dy/dx = −8x
- d/dx(−4x2) = −8x
- The derivative of the constant −5 is 0
2.Differentiate y = 6x + 8
Answer: dy/dx = 6
- d/dx(6x) = 6
- The derivative of the constant 8 is 0
3.Differentiate y = −5x3 − x
Answer: dy/dx = −15x2 − 1
- d/dx(−5x3) = −15x2
- d/dx(−x) = −1
4.Differentiate y = −6x2 + 8x
Answer: dy/dx = −12x + 8
- d/dx(−6x2) = −12x
- d/dx(8x) = 8
5.Differentiate y = 6x3 + 9x2
Answer: dy/dx = 18x2 + 18x
- d/dx(6x3) = 18x2
- d/dx(9x2) = 18x
6.Differentiate y = −4x3 + 4x
Answer: dy/dx = −12x2 + 4
- d/dx(−4x3) = −12x2
- d/dx(4x) = 4
7.Differentiate y = −2x2 − 5
Answer: dy/dx = −4x
- d/dx(−2x2) = −4x
- The derivative of the constant −5 is 0
8.Differentiate y = −7x3 + 6
Answer: dy/dx = −21x2
- d/dx(−7x3) = −21x2
- The derivative of the constant 6 is 0
9.Differentiate y = 7x2 + 8x
Answer: dy/dx = 14x + 8
- d/dx(7x2) = 14x
- d/dx(8x) = 8
10.Differentiate y = 8x2 + 7x
Answer: dy/dx = 16x + 7
- d/dx(8x2) = 16x
- d/dx(7x) = 7
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.