FP2 January 2006 Q1
1. Find the set of values of \(x\) for which \[\frac{x^2}{x - 2} \gt 2x.\]
| Scheme | Marks |
|---|---|
| 2 is a ‘critical value’, e.g. used in solution, or \(x = 2\) seen as an asymptote | |
| \(x^2 = 2x^2 - 4x \Rightarrow x^2 - 4x = 0\) | |
| \(x = 0,\ \ x = 4\) M1: two other critical values | |
| \(x \lt 0\) | B1 |
| \(2 \lt x \lt 4\) M1: An inequality using the critical value 2 | M1 A1 |
| (6 marks) |
Notes
First M mark can be implied by the two correct values, but otherwise a Method must be seen.
\(\leqslant\) appearing: maximum 1 mark penalty (at first occurrence).
The printed marks column shows only B1, M1 A1 against a total of 6 marks; the other marks (for the critical value 2 and for \(x = 0, x = 4\)) are not printed against a line.