Higher June 2022 Paper 1 Q7
7.
(a) Expand and simplify \((4x + 5)(2x - 1)\). [3]
(b)
(i) Factorise \(x^2 - 10x + 21\). [2]
(ii) Use your answer to part (b)(i) to write down the solutions of the equation \(x^2 - 10x + 21 = 0\). [1]
| Scheme | Marks | Comments |
|---|---|---|
| \(8x^2 - 4x + 10x - 5\) | B2 | B1 for any two terms correct; \(nx^2 + 6x + m\) implies two terms correct if not from wrong working |
| \(8x^2 + 6x - 5\) | B1 | Implies previous B2; FT for equivalent level of difficulty, providing a quadratic expression with 4 terms to consider and like terms in \(x\) to collect with opposite signs mark final answer except ignore ‘=0’ |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) \((x - 3)(x - 7)\) oe | B2 | If not B2, award B1 for \((x \ldots 3)(x \ldots 7)\) or for \(x(x - 7) - 3(x - 7)\) oe; ignore ‘= 0’ If no marks, award SC1 for factors \(x - 3\) and \(x - 7\) stated but not as a product |
| (b)(ii) \(x = 3,\ x = 7\) | B1 | STRICT FT from ‘their \((x \ldots a)(x \ldots b)\)’ where \(a\) and \(b\) are constants; |
| (6) |