Cheat Sheet
Quadratics Cheat Sheet: Factorising and Solving
A one-page summary of everything needed to factorise and solve quadratic equations: the sum-and-product method, common factors, difference…
- Difficulty
- Level 3 · Challenge
- Time
- 15 min
Topic TestYear 10Level 3 · Challenge
Free Year 10 Quadratics Topic Test
Expanding binomials, factorising and solving quadratic equations in a 45-minute Year 10 test with marks and fully worked solutions.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 10
- Subject
- Mathematics
- Topic
- Quadratics
- Difficulty
- Level 3 · Challenge
- Estimated time
- 45 minutes
- Curriculum
- Australian Curriculum
- Questions
- 18
- Answers
- Included, with working
- Format
- PDF (A4) + print
Students will practise
- expanding binomial products
- collecting like terms
- working with negative terms
- factorising quadratic expressions
- finding factor pairs
- applying the null factor law
Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
What's next?
Completed: Year 10 Quadratics Topic Test
How to use this topic test
- 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 topic test for?
Year 10 students (typically ages 15–16) working on quadratics. It is pitched at level 3 · challenge.
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 45 minutes for 18 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 10 Simultaneous Equations Worksheet — Level 2.
Preview
Year 10 · Mathematics · Quadratics
Year 10 Quadratics Topic Test
Success Tutoring
Student name:
Date:
Score: /
Time allowed: 45 minutes. Total marks: 36. Show your working — marks are given for method as well as answers.
Part A — Expanding Brackets
1.Expand and simplify: (x − 8)(x − 7)[2 marks]
2.Expand and simplify: (x − 7)(x − 1)[2 marks]
3.Expand and simplify: (x + 1)(x − 8)[2 marks]
4.Expand and simplify: (x − 4)(x + 6)[2 marks]
5.Expand and simplify: (x − 2)(x + 4)[2 marks]
Part B — Factorising and Solving Quadratics
6.Factorise: x2 + x − 2[2 marks]
7.Factorise: x2 − 7x − 18[2 marks]
8.Factorise: x2 − 11x + 30[2 marks]
9.Factorise: x2 + 12x + 35[2 marks]
10.Factorise: x2 + 6x − 27[2 marks]
Part C — Factorising and Solving Quadratics
11.Solve: x2 + 8x + 15 = 0[2 marks]
12.Solve: x2 − 11x + 30 = 0[2 marks]
13.Solve: x2 − 3x − 10 = 0[2 marks]
14.Solve: x2 − 8x + 7 = 0[2 marks]
15.Solve: x2 − 3x − 4 = 0[2 marks]
Preview — the PDF contains the full resource and answer sheet.
More Year 10 quadratics resources
- Worksheet
Year 10 Factorising and Solving Quadratics Worksheet — Level 2
Factorise monic quadratics and solve quadratic equations by factorising. Expected-level practice for this year group. This Year 10…
- Difficulty
- Level 2 · Standard
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
- Worksheet
Year 10 Factorising and Solving Quadratics Worksheet — Level 2 (Set 2)
Factorise monic quadratics and solve quadratic equations by factorising. Expected-level practice for this year group. This Year 10…
- Difficulty
- Level 2 · Standard
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
- Worksheet
Year 10 Factorising and Solving Quadratics Worksheet — Level 3
Factorise monic quadratics and solve quadratic equations by factorising. A challenge set for students ready to stretch further. This Year…
- Difficulty
- Level 3 · Challenge
- Time
- 15 min
- Questions
- 10 questions
- Answers
- Answers included
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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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