Foundation June 2022 Paper 1 Q25
25.
(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]
\(x^2-10x+21=0\). [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 |
|---|---|---|
| (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 |
| (ii) \(x=3,\ x=7\) | B1 | STRICT FT from ‘their \((x\ \ldots\ a)(x\ \ldots\ b)\)’ where \(a\) and \(b\) are constants; |
| (6) |