| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Region shading with multiple inequalities |
| Difficulty | Moderate -0.8 This is a straightforward Further Pure 1 question testing basic loci in the complex plane. Parts (i) and (ii) require recognizing and sketching circles (filled disk and annulus), while part (iii) requires sketching a half-line from a point. These are standard textbook exercises requiring only direct application of definitions with no problem-solving or novel insight needed. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
Indicate, on separate Argand diagrams,
\begin{enumerate}[label=(\roman*)]
\item the set of points $z$ for which $|z-(3-\mathrm{j})| \leqslant 3$, [3]
\item the set of points $z$ for which $1 < |z-(3-\mathrm{j})| \leqslant 3$, [2]
\item the set of points $z$ for which $\arg(z-(3-\mathrm{j})) = \frac{1}{4}\pi$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2006 Q4 [8]}}