Year 10 Factorising and Solving Quadratics Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 10 quadratics worksheet.
Year 10 · Mathematics · Quadratics
Year 10 Factorising and Solving Quadratics Worksheet — Level 2 — Answers
Success Tutoring
Factorise, then use the null factor law.
1.Solve: x2 + 10x + 9 = 0
Answer: x = −1 or x = −9
- Factorise: (x + 1)(x + 9) = 0
- Null factor law: x + 1 = 0 or x + 9 = 0
- x = −1 or x = −9
2.Solve: x2 − 5x + 4 = 0
Answer: x = 1 or x = 4
- Factorise: (x − 1)(x − 4) = 0
- Null factor law: x − 1 = 0 or x − 4 = 0
- x = 1 or x = 4
3.Solve: x2 + 6x − 7 = 0
Answer: x = −7 or x = 1
- Factorise: (x + 7)(x − 1) = 0
- Null factor law: x + 7 = 0 or x − 1 = 0
- x = −7 or x = 1
4.Solve: x2 − 9x + 18 = 0
Answer: x = 6 or x = 3
- Factorise: (x − 6)(x − 3) = 0
- Null factor law: x − 6 = 0 or x − 3 = 0
- x = 6 or x = 3
5.Solve: x2 + 7x + 6 = 0
Answer: x = −1 or x = −6
- Factorise: (x + 1)(x + 6) = 0
- Null factor law: x + 1 = 0 or x + 6 = 0
- x = −1 or x = −6
6.Solve: x2 + 7x − 8 = 0
Answer: x = 1 or x = −8
- Factorise: (x − 1)(x + 8) = 0
- Null factor law: x − 1 = 0 or x + 8 = 0
- x = 1 or x = −8
7.Solve: x2 + x − 20 = 0
Answer: x = 4 or x = −5
- Factorise: (x − 4)(x + 5) = 0
- Null factor law: x − 4 = 0 or x + 5 = 0
- x = 4 or x = −5
8.Solve: x2 − 3x − 4 = 0
Answer: x = −1 or x = 4
- Factorise: (x + 1)(x − 4) = 0
- Null factor law: x + 1 = 0 or x − 4 = 0
- x = −1 or x = 4
9.Solve: x2 + x − 2 = 0
Answer: x = 1 or x = −2
- Factorise: (x − 1)(x + 2) = 0
- Null factor law: x − 1 = 0 or x + 2 = 0
- x = 1 or x = −2
10.Solve: x2 − 7x + 10 = 0
Answer: x = 5 or x = 2
- Factorise: (x − 5)(x − 2) = 0
- Null factor law: x − 5 = 0 or x − 2 = 0
- x = 5 or x = 2
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.