Study Guide
Differentiation Basics: The Power Rule
Introduces the derivative as a gradient function and sets out the power rule for differentiating polynomials, including negative and…
- Difficulty
- Level 3 · Challenge
- Time
- 20 min
WorksheetYear 12Level 2 · Standard
Free Year 12 Differentiation (Power Rule) Worksheet — Level 2
Differentiate polynomial functions using the power rule. Expected-level practice for this year group. This Year 12 worksheet has 10 questions and comes with a full answer sheet showing the working for every question.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 12
- Subject
- Mathematics
- Topic
- Calculus
- Difficulty
- Level 2 · Standard
- Estimated time
- 15 minutes
- Curriculum
- New Zealand Curriculum
- Questions
- 10
- Answers
- Included, with working
- Format
- PDF (A4) + print
Students will practise
- differentiating polynomials with the power rule
- differentiating term by term
- handling constant terms
Curriculum: New Zealand Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
What's next?
Completed: Year 12 Differentiation (Power Rule) Worksheet — Level 2
How to use this worksheet
- Print the PDF or complete it on screen. Write the student's name and date at the top.
- Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
- Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
- Record the score, celebrate what went well, then follow the "What's next" suggestion.
Common questions
Who is this worksheet for?
Year 12 students (typically ages 16–17) working on calculus. It is pitched at level 2 · standard; an easier version is linked above.
Are the answers included?
Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.
How long does it take?
About 15 minutes for 10 questions. Short, regular sessions work best: two or three a week beats one long one.
Do I need to sign up to download?
No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.
What should we do next?
Try Year 12 Integration (Polynomials) Worksheet — Level 1.
Preview
Year 12 · Mathematics · Calculus
Year 12 Differentiation (Power Rule) Worksheet — Level 2
Success Tutoring
Student name:
Date:
Score: /
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −4x5 − 2x3 + 8
2.Differentiate y = −7x5 + 6x3 − 7x2
3.Differentiate y = 5x5 + 3x4 − 4
4.Differentiate y = −x5 + 9x4 − 4x2
5.Differentiate y = 4x4 + 5x2 + 9x
6.Differentiate y = −x4 + 7x2 − 4
7.Differentiate y = −3x5 − 5x4 + 9x3
8.Differentiate y = 9x5 − 4x4 − 5x2
9.Differentiate y = 3x5 + 5x2 + x
10.Differentiate y = x4 − x3 − 3x2
Preview — the PDF contains the full resource and answer sheet.
More Year 12 calculus resources
- Study Guide
Differentiation: Product, Quotient and Chain Rules
A senior study guide to the three rules that let you differentiate products, quotients and composite functions. Each worked example names…
- Difficulty
- Level 3 · Challenge
- Time
- 30 min
- Worksheet
Year 12 Differentiation (Power Rule) Worksheet — Level 1
Differentiate polynomial functions using the power rule. Builds confidence with the core skill before adding complexity. This Year 12…
- Difficulty
- Level 1 · Easier
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
- Worksheet
Year 12 Integration (Polynomials) Worksheet — Level 1
Find indefinite integrals of polynomials and evaluate simple definite integrals. Builds confidence with the core skill before adding…
- Difficulty
- Level 1 · Easier
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
Calculus in other year levels
- Year 13 Differentiation (Power Rule) Worksheet — Level 3
Worksheet · Year 13 · Calculus · Level 3 · Challenge
- Year 13 Differentiation (Power Rule) Worksheet — Level 3 (Set 2)
Worksheet · Year 13 · Calculus · Level 3 · Challenge
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About this resource
- Created by
- Success Tutoring Maths Team
- Reviewed by
- Success Tutoring
- Last reviewed
- 1 October 2026
- How it was made
- Generated by checked procedures
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