June 2018 Paper 2 Q11
11 Expand and simplify fully \(\qquad (x + 2)(x + 3)(x + 4)\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 expands \((x + 2)(x + 3)\) first | ||
| \(x^2 + 3x + 2x + 6\) or \(x^2 + 5x + 6\) | M1 | oe must have a term in \(x^2\) allow one error but no omissions or extras implied by \(x^2 + 5x + k\) or \(ax^2 + 5x + 6\) |
| \(x^3 + 5x^2 + 6x + 4x^2 + 20x + 24\) | M1dep | oe eg \(x^3 + 3x^2 + 2x^2 + 6x + 4x^2 + 12x + 8x + 24\) allow one further error but no omissions or extras |
| \(x^3 + 9x^2 + 26x + 24\) | A1 | |
| Alternative method 2 expands \((x + 3)(x + 4)\) first | ||
| \(x^2 + 3x + 4x + 12\) or \(x^2 + 7x + 12\) | M1 | oe must have a term in \(x^2\) allow one error but no omissions or extras implied by \(x^2 + 7x + k\) or \(ax^2 + 7x + 12\) |
| \(x^3 + 7x^2 + 12x + 2x^2 + 14x + 24\) | M1dep | oe eg \(x^3 + 3x^2 + 4x^2 + 12x + 2x^2 + 6x + 8x + 24\) allow one further error but no omissions or extras |
| \(x^3 + 9x^2 + 26x + 24\) | A1 | |
| Alternative method 3 expands \((x + 2)(x + 4)\) first | ||
| \(x^2 + 4x + 2x + 8\) or \(x^2 + 6x + 8\) | M1 | oe must have a term in \(x^2\) allow one error but no omissions or extras implied by \(x^2 + 6x + k\) or \(ax^2 + 6x + 8\) |
| \(x^3 + 6x^2 + 8x + 3x^2 + 18x + 24\) | M1dep | oe eg \(x^3 + 4x^2 + 2x^2 + 8x + 3x^2 + 12x + 6x + 24\) allow one further error but no omissions or extras |
| \(x^3 + 9x^2 + 26x + 24\) | A1 | |
Additional guidance
| For M marks terms may be seen in a grid (+ signs not needed) | |
| Correct answer followed by further work | M2A0 |
| Ignore further simplification after 4 terms seen eg Alt 1 \(\ x^2 + 3x + 2x + 6 = x^2 + 6x + 6\) \((x^2 + 6x + 6)(x + 4) \rightarrow x^3 + 4x^2 + 6x^2 + 24x + 6x + 18\) (error) | M1 M1depA0 |
| Second M1 Must be the product of a two term bracket and a three or four term bracket | |
| Missing brackets may be recovered |