| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Topic | Complex Numbers Argand & Loci |
| Type | Area calculations in complex plane |
| Difficulty | Standard +0.3 This is a straightforward Further Maths complex numbers question involving standard loci (circle and argument sector). Part (a) is routine plotting, part (b) requires identifying the intersection of two regions (standard technique), and part (c) involves calculating a circular sector area minus a triangle—all standard procedures with no novel insight required. Slightly easier than average due to the geometric simplicity and clear structure. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
\begin{enumerate}[label=(\alph*)]
\item Show on an Argand diagram the locus of points given by
$$|z - 10 - 12i| = 8$$ [2]
Set $A$ is defined by
$$A = \left\{z : 0 \leq \arg(z - 10 - 10i) \leq \frac{\pi}{2}\right\} \cap \{z : |z - 10 - 12i| < 8\}$$
\item Shade the region defined by $A$ on your Argand diagram. [2]
\item Determine the area of the region defined by $A$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q3 [8]}}