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S3 Maths: Factorising Quadratic Expressions (Paper 2 (intermediate))
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 2 (intermediate))
Paper 2 (intermediate): 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 3x squared minus 6x.
- FoundationFactorise x squared minus 16.
- FoundationFactorise x squared plus 8x plus 16.
- IntermediateFactorise x squared minus 5x minus 24.
- IntermediateFactorise 6x squared plus 11x plus 4.
- IntermediateFactorise 9x squared minus 16.
- ChallengeFactorise 2x squared minus 5x minus 3.
- ChallengeFactorise 12x squared minus 7x plus 1.
- ChallengeFactorise 5x squared plus 13x minus 6.
- Error redoError clinic: a student writes x squared minus 7x plus 12 as (x + 3)(x + 4). What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3x(x – 2) | The common factor is 3x, leaving x minus 2 inside the bracket. |
| 2 | (x + 4)(x – 4) | 16 is 4 squared, so the difference of squares gives the two brackets at once. |
| 3 | (x + 4) squared | 16 is 4 squared and the middle term 8x is twice x times 4, so it is a perfect square. |
| 4 | (x – 8)(x + 3) | The numbers multiply to minus 24 and add to minus 5, namely minus 8 and 3. |
| 5 | (2x + 1)(3x + 4) | Expanding gives 6x squared plus 8x plus 3x plus 4, and the middle terms add to 11x. |
| 6 | (3x + 4)(3x – 4) | 9x squared is (3x) squared and 16 is 4 squared, so this is a difference of squares. |
| 7 | (2x + 1)(x – 3) | Expanding gives 2x squared minus 6x plus x minus 3, and the middle terms add to minus 5x. |
| 8 | (3x – 1)(4x – 1) | Expanding gives 12x squared minus 3x minus 4x plus 1, and the middle terms add to minus 7x. |
| 9 | (5x – 2)(x + 3) | Expanding gives 5x squared plus 15x minus 2x minus 6, and the middle terms add to 13x. |
| 10 | (x – 3)(x – 4) | The constant 12 needs numbers of the same sign while the middle term minus 7 needs a negative sum, so both numbers are negative. |
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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