| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core (Further Pure Core) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Circle equations in complex form |
| Difficulty | Standard +0.8 This Further Maths question requires understanding that arg(z - 4i) = π/4 represents a half-line from 4i, then finding where a circle centered at 6+4i is tangent to this line. Part (i) is straightforward recall, but part (ii) requires geometric insight to find the perpendicular distance from the center to the line, then express the circle equation in complex form—moderately challenging problem-solving beyond routine exercises. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines4.02p Set notation: for loci |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) | Im |
| Answer | Marks |
|---|---|
| Re | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| Answer | Marks |
|---|---|
| i | e |
| Answer | Marks |
|---|---|
| positive x axis | Allow 4i included or |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (ii) | z(cid:16)(6(cid:14)4i) (cid:32)3 2 |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | correct form |
Question 2:
2 | (i) | Im
e
p
4
S
Re | B1
B1
c
[2] | 1.1a
m
1.1
i | e
half line from 4i
(cid:83)
direction above the
4
positive x axis | Allow 4i included or
excluded
2 | (ii) | z(cid:16)(6(cid:14)4i) (cid:32)3 2 | M1
A1
M1
A1
[4] | 1.1
1.1
3.1a
1.1 | correct form
centre correct
Attempt to find distance from
centre to line
radius correct\begin{enumerate}[label=(\roman*)]
\item On an Argand diagram draw the locus of points which satisfy $\arg(z - 4i) = \frac{\pi}{4}$. [2]
\item Give, in complex form, the equation of the circle which has centre at $6 + 4i$ and touches the locus in part (i). [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core Q2 [6]}}