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WorksheetYear 12Level 2 · Standard

Free 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 worksheet has 10 questions and comes with a full answer sheet showing the working for every question.

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Year
Year 12
Subject
Mathematics
Topic
Calculus
Difficulty
Level 2 · Standard
Estimated time
15 minutes
Curriculum
Australian 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: Australian 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

  1. 1Year 12 Integration (Polynomials) Worksheet — Level 3

How to use this worksheet

  1. Print the PDF or complete it on screen. Write the student's name and date at the top.
  2. Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
  3. Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
  4. 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 17–18) working on calculus. It is pitched at level 2 · standard; a harder 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 3.

Preview

Year 12 · Mathematics · Calculus

Year 12 Integration (Polynomials) Worksheet — Level 2

Success Tutoring

Student name:

Date:

Score: /

Use the rule ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C.

1.Find ∫ (−4x3 + 2x − 3) dx
2.Find ∫ (15x4 − 6x2 − 1) dx
3.Find ∫ (−10x4 + 12x3 − 3) dx
4.Find ∫ (4x3 + 12x2 + 1) dx
5.Find ∫ (12x3 − 3x2 + 8x) dx
6.Find ∫ (5x4 − 4x − 1) dx
7.Find ∫ (−8x3 + 4x − 1) dx
8.Find ∫ (10x4 + 9x2 − 1) dx
9.Find ∫ (−10x4 + 3x2 + 2) dx
10.Find ∫ (10x4 + 8x3 − 4x) dx
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Preview — the PDF contains the full resource and answer sheet.

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Calculus in other year levels

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

Free to print and share for personal, classroom and homeschool use. Please don't resell. Spotted an error? Let us know.