| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core (Further Pure Core) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| 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 Maths question testing standard loci definitions: (a) is a filled circle centered at (1,2) with radius 4, and (b) is a half-line from (-i) at angle π/3. Both require direct application of memorized definitions with no problem-solving or multi-step reasoning, making it easier than average even for Further Maths. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | circle |
| Answer | Marks |
|---|---|
| inside shaded | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.2 |
| Answer | Marks |
|---|---|
| 1.1 | soi. Can be seen beside sketch as long as sketch not |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (b) | Half line |
| Answer | Marks |
|---|---|
| 3 | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.2 |
| Answer | Marks |
|---|---|
| 1.1 | Intention for a half line must be clear |
Question 6:
6 | (a) | circle
centre 1 + 2i, radius 4
inside shaded | M1
A1
A1
[3] | 1.2
1.1
1.1 | soi. Can be seen beside sketch as long as sketch not
contradicted. Circle must enter all four quadrants.
Line for circle must be solid. Candidates may shade the
region that is not required but should clearly indicate that
what they have shaded is not required.
6 | (b) | Half line
starting at −i
𝜋
at rad to real axis
3 | M1
A1
A1
[3] | 1.2
1.1
1.1 | Intention for a half line must be clear
Can be seen beside sketch as long as sketch not
contradicted.
Labelled acute angle made with any horizontal line.
√3
Accept 60°. Accept 𝑥-intercept at without angle drawn
3
if half line starts at −i. Condone incorrect 𝑥-intercept if
𝜋
correct angle shown. Do not accept − rad.
36 On separate Argand diagrams, sketch the set of points represented by each of the following.
\begin{enumerate}[label=(\alph*)]
\item $| z - 1 - 2 i | \leqslant 4$.
\item $\quad \arg ( z + \mathrm { i } ) = \frac { 1 } { 3 } \pi$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core 2024 Q6 [6]}}