A2 October 2021 Paper 1 Q1
1
(a) Sketch on a single Argand diagram the loci given by
(i) \(|z - 1 + 2\mathrm{i}| = 3\), [2]
(ii) \(|z + 1| = |z - 2|\). [2]
(b) Indicate, by shading, the region of the Argand diagram for which \(|z - 1 + 2\mathrm{i}| \leqslant 3\) and \(|z + 1| \leqslant |z - 2|\). [2]
| Scheme | Marks | AO |
|---|---|---|
| (i) Circle Centre \(1 - 2\mathrm{i}\), Radius 3 | B1 B1 | 1.1 2.2a |
| [2] | ||
| (ii) Straight vertical line | B1 | 1.1 |
| \(x = \dfrac{1}{2}\) | B1 | 2.2a |
| [2] |
Notes
(a)(i)
Be generous over circles drawn freehand
If the axes are scaled then a mark at \((1, -2)\) will do.
For radius, an indication that the radius is 3 will do (e.g. passing through \((4, -2)\) etc if marked will do.)
(a)(ii)
B1: Can be seen by \(x = \frac{1}{2}\) being labelled on the axis and vertical line through it
| Scheme | Marks | AO |
|---|---|---|
| Inside circle | B1 | 1.1 |
| And to the left of \(x = \dfrac{1}{2}\) | B1 | 2.2a |
| [2] |
Notes
B1: Or their line if it is vertical.