| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Region shading with multiple inequalities |
| Difficulty | Moderate -0.3 This is a standard FP1 loci question requiring sketching a circle (center 3-4i, radius 5) and a perpendicular bisector (the line Re(z)=3). While it involves complex number geometry, these are textbook locus types with straightforward interpretations and no problem-solving insight required. Slightly easier than average A-level due to being routine application of definitions. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks |
|---|---|
| B1B1 2 | Circle centre \((3, -4)\), through origin |
| Answer | Marks |
|---|---|
| B1B1 2 | Vertical line, clearly \(x = 3\) |
| Answer | Marks |
|---|---|
| B1ft | Inside their circle |
| B1ft 2 | And to right of their line, if vertical |
## (i)
### (a)
| B1B1 2 | Circle centre $(3, -4)$, through origin
### (b)
| B1B1 2 | Vertical line, clearly $x = 3$
## (ii)
| B1ft | Inside their circle
| B1ft 2 | And to right of their line, if vertical
---\begin{enumerate}[label=(\roman*)]
\item Sketch on a single Argand diagram the loci given by
\begin{enumerate}[label=(\alph*)]
\item $|z - 3 + 4\text{i}| = 5$, [2]
\item $|z| = |z - 6|$. [2]
\end{enumerate}
\item Indicate, by shading, the region of the Argand diagram for which
$$|z - 3 + 4\text{i}| \leq 5 \quad \text{and} \quad |z| \geq |z - 6|.$$ [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2010 Q6 [6]}}