| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a straightforward Further Maths FP1 question requiring students to sketch two standard loci (a circle and a half-line) and identify their intersection. While it's Further Maths content, it involves direct application of definitions with no problem-solving or novel insight required—just careful sketching and observation. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks | Guidance |
|---|---|---|
| Sketch of Argand diagram with point \(3+4j\) | B1 | Circle must not touch either axis. B1 max if no labelling or scales. Award even if centre incorrect |
| Circle, radius 2 | B1 [2] | — |
| Answer | Marks | Guidance |
|---|---|---|
| Half-line starting from \((4, 0)\), vertically upwards | B1, B1 [2] | — |
| Answer | Marks | Guidance |
|---|---|---|
| Points where line crosses circle clearly indicated | B1 [1] | Identifying 2 points where their line cuts the circle |
## Question 5:
### Part (i)
Sketch of Argand diagram with point $3+4j$ | B1 | Circle must not touch either axis. B1 max if no labelling or scales. Award even if centre incorrect
Circle, radius 2 | B1 **[2]** | —
### Part (ii)
Half-line starting from $(4, 0)$, vertically upwards | B1, B1 **[2]** | —
### Part (iii)
Points where line crosses circle clearly indicated | B1 **[1]** | Identifying 2 points where their line cuts the circle
---5 (i) Sketch the locus $| z - ( 3 + 4 j ) | = 2$ on an Argand diagram.\\
(ii) On the same diagram, sketch the locus $\arg ( z - 4 ) = \frac { 1 } { 2 } \pi$.\\
(iii) Indicate clearly on your sketch the points which satisfy both
$$| z - ( 3 + 4 j ) | = 2 \quad \text { and } \quad \arg ( z - 4 ) = \frac { 1 } { 2 } \pi$$
\hfill \mbox{\textit{OCR MEI FP1 2005 Q5 [5]}}