| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Region shading with multiple inequalities |
| Difficulty | Moderate -0.3 This is a standard FP2 loci question requiring routine techniques: recognizing |z - a| = r as a circle and arg(z - a) = θ as a half-line, then sketching both. While Further Maths content, it's a textbook exercise with no problem-solving or novel insight required—just direct application of memorized loci forms. The 8 marks reflect drawing accuracy rather than conceptual difficulty, making it slightly easier than average overall. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
\begin{enumerate}[label=(\alph*)]
\item Draw on the same Argand diagram:
\begin{enumerate}[label=(\roman*)]
\item the locus of points for which
$$|z - 2 - 5i| = 5$$ [3 marks]
\item the locus of points for which
$$\arg(z + 2i) = \frac{\pi}{4}$$ [3 marks]
\end{enumerate}
\item Indicate on your diagram the set of points satisfying both
$$|z - 2 - 5i| \leqslant 5$$
and
$$\arg(z + 2i) = \frac{\pi}{4}$$ [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2011 Q1 [8]}}