| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a standard Further Maths locus question requiring students to recognize that the first equation represents a circle (center (2,3), radius 2) and the second represents a perpendicular bisector. Finding the intersection and shading a region is routine for FP2 students, involving straightforward geometric interpretation rather than complex algebraic manipulation or novel insight. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines4.02p Set notation: for loci |
2
\begin{enumerate}[label=(\alph*)]
\item Draw on the Argand diagram below:
\begin{enumerate}[label=(\roman*)]
\item the locus of points for which
$$| z - 2 - 3 \mathrm { i } | = 2$$
\item the locus of points for which
$$| z + 2 - \mathrm { i } | = | z - 2 |$$
\end{enumerate}\item Indicate on your diagram the points satisfying both
$$| z - 2 - 3 \mathrm { i } | = 2$$
and
$$| z + 2 - \mathrm { i } | \leqslant | z - 2 |$$
(l mark)\\
\includegraphics[max width=\textwidth, alt={}, center]{ff63460d-0fa1-437d-bc08-3e7ce809e32b-3_1404_1431_1043_319}
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2012 Q2 [7]}}