Year 10 Factorising and Solving Quadratics Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 quadratics worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · QuadraticsYear 10 Factorising and Solving Quadratics Worksheet — Level 1 — Practice Set 3 — Answers
Factorise each quadratic.
1.Factorise: x2 − 10x + 21
Answer: (x − 7)(x − 3)
- Find two numbers that multiply to 21 and add to −10: −7 and −3
2.Factorise: x2 − 13x + 40
Answer: (x − 5)(x − 8)
- Find two numbers that multiply to 40 and add to −13: −5 and −8
3.Factorise: x2 − 6x − 16
Answer: (x − 8)(x + 2)
- Find two numbers that multiply to −16 and add to −6: −8 and 2
4.Factorise: x2 + 5x − 36
Answer: (x + 9)(x − 4)
- Find two numbers that multiply to −36 and add to 5: 9 and −4
5.Factorise: x2 + 6x − 27
Answer: (x − 3)(x + 9)
- Find two numbers that multiply to −27 and add to 6: −3 and 9
6.Factorise: x2 − 4x − 45
Answer: (x − 9)(x + 5)
- Find two numbers that multiply to −45 and add to −4: −9 and 5
7.Factorise: x2 − 9x + 20
Answer: (x − 5)(x − 4)
- Find two numbers that multiply to 20 and add to −9: −5 and −4
8.Factorise: x2 − 4
Answer: (x − 2)(x + 2)
- Find two numbers that multiply to −4 and add to 0: −2 and 2
9.Factorise: x2 − 6x + 8
Answer: (x − 2)(x − 4)
- Find two numbers that multiply to 8 and add to −6: −2 and −4
10.Factorise: x2 − x − 56
Answer: (x + 7)(x − 8)
- Find two numbers that multiply to −56 and add to −1: 7 and −8
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.