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S3 Maths: Factorising Quadratic Expressions (Paper 1 (basics))
Tutor Prep Guide · Taking out common factors, difference of two squares, perfect squares and cross multiplication, factorising quadratic trinomials over the integers and checking the result
S3 Maths: Factorising Quadratic Expressions (Paper 1 (basics))
Paper 1 (basics): ten questions on factorising quadratic expressions, with answers and one line notes.
Direct answers Level: S3 maths; format: factorisation questions using common factors, difference of squares, perfect squares and cross multiplication.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Factorising Quadratic Expressions |
| Level | S3 |
02 Questions (10 items)
- FoundationFactorise 6x squared plus 9x.
- FoundationFactorise x squared minus 25.
- FoundationFactorise x squared plus 10x plus 25.
- IntermediateFactorise x squared plus 7x plus 12.
- IntermediateFactorise x squared minus 9x plus 20.
- IntermediateFactorise 4x squared minus 9.
- ChallengeFactorise x squared minus x minus 12.
- ChallengeFactorise 2x squared plus 7x plus 3.
- ChallengeFactorise 8x cubed minus 2x completely.
- Error redoError clinic: a student writes x squared plus 9 as (x + 3) squared. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3x(2x + 3) | The common factor of both terms is 3x, leaving 2x + 3 inside the bracket. |
| 2 | (x + 5)(x – 5) | This is a difference of two squares with a equal to x and b equal to 5. |
| 3 | (x + 5) squared | The first and last terms are x squared and 5 squared, and the middle term is twice x times 5, so it is a perfect square. |
| 4 | (x + 3)(x + 4) | Find two numbers whose product is 12 and sum is 7, namely 3 and 4. |
| 5 | (x – 4)(x – 5) | The numbers multiply to 20 and add to minus 9, so both are negative, namely minus 4 and minus 5. |
| 6 | (2x + 3)(2x – 3) | 4x squared is (2x) squared and 9 is 3 squared, so the pattern of a difference of squares applies. |
| 7 | (x – 4)(x + 3) | The numbers multiply to minus 12 and add to minus 1, so they are minus 4 and 3, one negative and one positive. |
| 8 | (2x + 1)(x + 3) | Expanding gives 2x squared plus 6x plus x plus 3, and the middle terms add to 7x as required. |
| 9 | 2x(2x + 1)(2x – 1) | Take out the common factor 2x to get 4x squared minus 1, then apply the difference of squares. |
| 10 | x squared plus 9 does not factorise over the integers | Expanding (x + 3) squared gives x squared plus 6x plus 9, which has a middle term and so differs from x squared plus 9. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Take out any common factor first, then count the terms: two terms point to a difference of squares, three terms to a perfect square or cross multiplication. Always expand the answer to check the middle term.Tutor Registration →
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