FP2 June 2005 Q1
1.
(a) Sketch the graph of \(y = |x - 2a|\), given that \(a \gt 0\). (2)
(b) Solve \(|x - 2a| \gt 2x + a\), where \(a \gt 0\). (3)
| Scheme | Marks |
|---|---|
| Shape, vertex on \(x\)-axis | B1 |
| At least \(2a\) seen on positive \(x\)-axis | B1 |
| (2) |
| Scheme | Marks |
|---|---|
| Attempting to solve \(-(x - 2a) = 2x + a\) anywhere | M1 |
| Completely correct method [e.g. solving \(-(x - 2a) \gt 2x + a\); if finding two “solutions” needs to be evidence for giving “correct” result] | dep M1 |
| \(x \lt \tfrac{1}{3}a\) | A1 |
| (3) | |
| (5 marks) |