| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Single locus sketching |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring standard techniques: calculating modulus/argument of a given complex number, then sketching a circle (constant modulus from a point) and a half-line (constant argument from a point). While FP1 content is inherently more advanced than core A-level, these are routine locus types with no problem-solving insight required, making it slightly easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
2 The complex number $3 + 4 \mathrm { i }$ is denoted by $a$.\\
(i) Find $| a |$ and $\arg a$.\\
(ii) Sketch on a single Argand diagram the loci given by
\begin{enumerate}[label=(\alph*)]
\item $| z - a | = | a |$,
\item $\arg ( z - 3 ) = \arg a$.
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2008 Q2 [7]}}