Foundation November 2022 Paper 3 Q21
21 Solve.
\[x^2 - 4x - 165 = 0\]You must show your working.\(x =\) .................... or \(x =\) .................... [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| –11 15 with correct working | 3 | M2 for \((x + 11)(x - 15)\) or M1 for \((x + a)(x + b)\) where either \(ab = -165\) or \(a + b = -4\) OR M2 for 2 correct trials with any number or M1 for 1 correct trial with any number If 0 scored, SC1 for –11 and 15 with no working or insufficient working | “correct working” requires M2 M2 and M1 may be implied by grids and other forms such as \(x(x - 15) + 11(x - 15)\) Must see substitutions e.g. \(5^2 - 4 \times 5 - 165\) Use of formula M2 for \(\dfrac{[--]4 \pm \sqrt{([-]4)^2 - 4 \times [1] \times -165}}{2\,[\times 1]}\) or better e.g. \(\dfrac{4 \pm \sqrt{676}}{2}\) M1 for formula with at most two errors Do not award if wrong working |