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
Extra practice for Year 12 Integration (Polynomials) Worksheet — Level 2: the same skill with fresh questions.
WorksheetYear 12Level 2 · Standard
Free Year 12 Integration (Polynomials) Worksheet — Level 2 — Practice Set 2
Practice Set 2 for Year 12 Integration (Polynomials) Worksheet — Level 2: the same skill and level with a fresh set of questions and a full answer sheet.
More practice: Set 1 · Practice Set 3 · Practice Set 4 — same skill, fresh questions, full answers.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 12
- Subject
- Maths
- 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
- integrating polynomials
- adding the constant of integration
- integrating term by term
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 Integration (Polynomials) Worksheet — Level 2 — Practice Set 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 and a harder version are 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 3.
Preview
Success TutoringWorksheetsYear 12 · Mathematics · CalculusYear 12 Integration (Polynomials) Worksheet — Level 2 — Practice Set 2
Name
Date
Score /
Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.
1.Find ∫ (15x4 + 3x2 + 3) dx
2.Find ∫ (8x3 − 6x2 + 1) dx
3.Find ∫ (8x3 + 3x2 + 4) dx
4.Find ∫ (10x4 − 4x3 − 1) dx
5.Find ∫ (−5x4 − 8x3 + 6x) dx
6.Find ∫ (−5x4 − 6x2 + 6x) dx
7.Find ∫ (−10x4 − 6x2 − 2x) dx
8.Find ∫ (20x4 − 6x2 − 2) dx
9.Find ∫ (−10x4 − 3x2 + 3) dx
10.Find ∫ (16x3 + 6x2 + 4x) dx
Preview — the PDF contains the full resource and answer sheet.
More Year 12 calculus resources
- Study Guide
Differentiation: Product, Quotient and Chain Rules
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- Difficulty
- Level 3 · Challenge
- Time
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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
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- Time
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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…
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- Time
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- Questions
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- Answers included
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Year 12 Differentiation (Power Rule) Worksheet — Level 3
Differentiate polynomial functions using the power rule. A challenge set for students ready to stretch further. This Year 12 worksheet has…
- Difficulty
- Level 3 · Challenge
- Time
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- 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
- Worksheet
Year 12 Integration (Polynomials) Worksheet — Level 2
Find indefinite integrals of polynomials and evaluate simple definite integrals. Expected-level practice for this year group. This Year 12…
- Difficulty
- Level 2 · Standard
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
- Worksheet
Year 12 Integration (Polynomials) Worksheet — Level 3
Find indefinite integrals of polynomials and evaluate simple definite integrals. A challenge set for students ready to stretch further.…
- Difficulty
- Level 3 · Challenge
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
Calculus in other year levels
- Differentiating Exponential, Logarithmic and Trigonometric Functions
Worksheet · Year 13 · Calculus · Level 3 · Challenge
- Motion in a Straight Line: Displacement, Velocity and Acceleration
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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