Higher November 2024 Paper 5 Q18
18 Solve.
\(\dfrac{x^2 - 5}{x - 4} = 4x\)
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{1}{3}\) and 5 with correct working | 6 | Correct working requires at least B3 and M1 | |
| B3 for \(3x^2 - 16x + 5\) [= 0] oe or M2 for \(x^2 - 5 = 4x^2 - 16x\) or better or M1 for \(x^2 - 5 = 4x(x - 4)\) | For B3 accept negative version, accept \(3x^2 - 16x = -5\) | ||
| M2 for \((3x - 1)(x - 5)\) [= 0] or M1 for \(3x(x - 5) - 1(x - 5)\) or for \(x(3x - 1) - 5(3x - 1)\) or for \((3x + a)(x + b)\) where \(ab = 5\) or \(3b + a = -16\) | M2 and M1 FT their 3-term quadratic M2 alt method correct substitution into formula or correct complete square M1 condone 1 error in substitution into formula For complete square, correct FT \((x + a)^2\) | ||
| If 0 or 1 scored instead award SC2 for correct answers | |||