A2 June 2024 Paper 1 Q6
6 On separate Argand diagrams, sketch the set of points represented by each of the following.
(a) \(|z - 1 - 2\mathrm{i}| \leqslant 4\). [3]
(b) \(\arg(z + \mathrm{i}) = \frac{1}{3}\pi\). [3]
| Scheme | Marks | AO |
|---|---|---|
| circle | M1 | 1.2 |
| centre \(1 + 2\mathrm{i}\), radius 4 | A1 | 1.1 |
| inside shaded | A1 | 1.1 |
| [3] |
Notes
A1: soi. Can be seen beside sketch as long as sketch not contradicted. Circle must enter all four quadrants.
A1: Line for circle must be solid. Candidates may shade the region that is not required but should clearly indicate that what they have shaded is not required.
| Scheme | Marks | AO |
|---|---|---|
| Half line | M1 | 1.2 |
| starting at \(-\mathrm{i}\) | A1 | 1.1 |
| at \(\frac{\pi}{3}\) rad to real axis | A1 | 1.1 |
| [3] |
Notes
M1: Intention for a half line must be clear
A1: Can be seen beside sketch as long as sketch not contradicted.
A1: Labelled acute angle made with any horizontal line. Accept \(60^\circ\). Accept \(x\)-intercept at \(\frac{\sqrt{3}}{3}\) without angle drawn if half line starts at \(-\mathrm{i}\). Condone incorrect \(x\)-intercept if correct angle shown. Do not accept \(-\frac{\pi}{3}\) rad.