| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a standard Further Maths FP2 loci question requiring identification of a circle (center (4,-2), radius 2) and perpendicular bisector, then shading the intersection region. While it involves multiple steps and geometric interpretation, these are routine techniques for FP2 students with no novel problem-solving required, making it slightly easier than average. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
2
\begin{enumerate}[label=(\alph*)]
\item Sketch on one diagram:
\begin{enumerate}[label=(\roman*)]
\item the locus of points satisfying $| z - 4 + 2 \mathrm { i } | = 2$;
\item the locus of points satisfying $| z | = | z - 3 - 2 \mathrm { i } |$.
\end{enumerate}\item Shade on your sketch the region in which\\
both
$$| z - 4 + 2 i | \leqslant 2$$
and
$$| z | \leqslant | z - 3 - 2 \mathrm { i } |$$
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2007 Q2 [8]}}