| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Circle equations in complex form |
| Difficulty | Moderate -0.3 Part (i) requires writing a circle equation in the form |z - a| = r from a diagram, which is straightforward recall of complex number loci. Part (ii) involves finding intersection points of a circle with an argument line, requiring geometric visualization but standard technique. This is slightly easier than average as it's mostly direct application of definitions with minimal problem-solving, though the complex number context makes it non-trivial. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (i) | z(cid:16)(2(cid:14)3i) (cid:32)2 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Form z(cid:16)(cid:68)(cid:32)k |
| All correct | Cartesian form of equation |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (ii) | (cid:83) |
| Answer | Marks |
|---|---|
| S | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1a |
| Answer | Marks |
|---|---|
| M | N |
Question 3:
3 | (i) | z(cid:16)(2(cid:14)3i) (cid:32)2 | M1
A1
[2] | 1.1
1.1 | Form z(cid:16)(cid:68)(cid:32)k
All correct | Cartesian form of equation
scores M0A0.
3 | (ii) | (cid:83)
Attempt at locus arg(z − 2i) = drawn soi.
4
E
P
S | M1
A1
I
C
[2] | 3.1a
1.1
M | N
Line at acute angle to real axis
EHalf-line from 2i
A0 if any other wrong point
marked.\begin{enumerate}[label=(\roman*)]
\item Write down, in complex form, the equation of the locus represented by the circle in the Argand diagram shown in Fig. 3. [2]
\includegraphics{figure_3}
\item On the copy of Fig. 3 in the Printed Answer Booklet mark with a cross any point(s) on the circle for which $\arg(z - 2i) = \frac{\pi}{4}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS Q3 [4]}}