Study Guide
The Quadratic Formula and the Discriminant
A senior study guide to solving any quadratic equation with the quadratic formula and using the discriminant to predict how many real…
- Difficulty
- Level 2 · Standard
- Time
- 25 min
WorksheetYear 12Level 3 · Challenge
Free Year 12 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 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
- Quadratics
- Difficulty
- Level 3 · Challenge
- Estimated time
- 15 minutes
- Curriculum
- New Zealand Curriculum
- Questions
- 10
- Answers
- Included, with working
- Format
- PDF (A4) + print
Students will practise
- factorising quadratic expressions
- solving quadratic equations by factorising
- applying the null factor law
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 Factorising and Solving Quadratics Worksheet — Level 3
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 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 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 Simultaneous Equations Worksheet — Level 3.
Preview
Year 12 · Mathematics · Quadratics
Year 12 Factorising and Solving Quadratics Worksheet — Level 3
Success Tutoring
Student name:
Date:
Score: /
Factorise, then use the null factor law.
1.Solve: 2x2 + 14x + 12 = 0
2.Solve: 3x2 + 3x − 6 = 0
3.Solve: 2x2 − 9x − 18 = 0
4.Solve: 2x2 − 11x + 5 = 0
5.Solve: 3x2 − 17x + 10 = 0
6.Solve: 3x2 − 11x − 20 = 0
7.Solve: 3x2 − 13x + 12 = 0
8.Solve: 2x2 + 11x − 63 = 0
9.Solve: 2x2 + 16x + 14 = 0
10.Solve: 2x2 − 12x + 18 = 0
Preview — the PDF contains the full resource and answer sheet.
More Year 12 quadratics resources
Quadratics in other year levels
- Year 11 Factorising and Solving Quadratics Worksheet — Level 2
Worksheet · Year 11 · Quadratics · Level 2 · Standard
- Year 11 Factorising and Solving Quadratics Worksheet — Level 2 (Set 2)
Worksheet · Year 11 · Quadratics · Level 2 · Standard
- Year 10 Factorising and Solving Quadratics Worksheet — Level 1
Worksheet · Year 10 · Quadratics · Level 1 · Easier
Was this resource helpful?
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.