Higher June 2022 Paper 6 Q19
19
(a) Write \(x^2 - 8x + 9\) in the form \((x - a)^2 - b\). [3]
(b) Use your answer from part (a) to solve.\[x^2 - 8x + 9 = 0\]
Give your answers in exact form.
You must show your working. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \((x - 4)^2 - 7\) final answer | 3 | B1 for \((x - 4)^2\) AND B2FT for \(-7\) or M1 for \(9 - (\textit{their } {-4})^2\) oe shown | No FT from \((x - 3)^2\) FT can be implied, check \(9 - (\textit{their } {-4})^2\) |
| If 0 or 1 scored, allow SC2 for final answer \((x - 4) - 7\) | |||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(4 + \sqrt{7}\), \(4 - \sqrt{7}\) final answer with working from (a) | 2FT | M1 for \((x - 4)^2 = \textit{their } 7\) FT from their (a) for solutions in exact form if working shown | Answers only score 0 Do not FT where \(b = 0\) e.g. \((x - 4)^2\) If their \(b\) is a perfect square, allow FT for \(a + \sqrt{b}\) and \(a - \sqrt{b}\) or simplified as two integers If \(b < 0\), a max of M1 |