| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a standard Further Maths loci question requiring sketching a circle centered at (3,-2) with radius 4 and a half-line from (1,0) at angle -π/4, then identifying their intersection. While it requires understanding of complex number geometry, it's a routine FP2 exercise with no novel problem-solving or calculation required beyond basic sketching skills. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(i) Circle; Correct centre; Enclosing the origin | B1, B1, B1 | (3 marks) |
| (ii) Half line; Correct starting point; Correct angle | B1, B1, B1 | (3 marks) |
| (b) Correct part of the line indicated | B1F | (1 mark) |
**(a)(i)** Circle; Correct centre; Enclosing the origin | B1, B1, B1 | (3 marks)
**(ii)** Half line; Correct starting point; Correct angle | B1, B1, B1 | (3 marks)
**(b)** Correct part of the line indicated | B1F | (1 mark)
**Total: 7 marks**
---4
\begin{enumerate}[label=(\alph*)]
\item On one Argand diagram, sketch the locus of points satisfying:
\begin{enumerate}[label=(\roman*)]
\item $| z - 3 + 2 \mathrm { i } | = 4$;
\item $\quad \arg ( z - 1 ) = - \frac { 1 } { 4 } \pi$.
\end{enumerate}\item Indicate on your sketch the set of points satisfying both
$$| z - 3 + 2 i | \leqslant 4$$
and
$$\arg ( z - 1 ) = - \frac { 1 } { 4 } \pi$$
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2006 Q4 [7]}}