| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | November |
| 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 standard Further Maths FP1 loci question requiring routine knowledge: (i) is a circle with center (1,-2) and radius 3, (ii) is the perpendicular bisector of points -1 and 2. Part (b) requires shading the intersection region. While this is Further Maths content, it's a textbook exercise testing basic understanding of complex number loci with no problem-solving or novel insight required, making it easier than average overall. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | (i) |
| Centre 1−2i, Radius 3 | B1 | |
| B1 | 1.1 | |
| 2.2a | Be generous over circles drawn freehand |
| Answer | Marks |
|---|---|
| (ii) | Straight vertical line |
| Answer | Marks |
|---|---|
| 2 | B1 |
| B1 | 1.1 |
| 2.2a | Can be seen by x = ½ being labelled on the axis and |
| Answer | Marks |
|---|---|
| (b) | Inside circle |
| Answer | Marks |
|---|---|
| 2 | B1 |
| B1 | 1.1 |
| 2.2a | Or their line if it is vertical. |
Question 1:
1 | (a) | (i) | Circle
Centre 1−2i, Radius 3 | B1
B1 | 1.1
2.2a | Be generous over circles drawn freehand
If the axes are scaled then a mark at (1, -2) will do.
For radius, an indication that the radius is 3 will do
(e.g. passing through (4, -2) etc if marked will do.)
[2]
(ii) | Straight vertical line
1
x=
2 | B1
B1 | 1.1
2.2a | Can be seen by x = ½ being labelled on the axis and
vertical line through it
[2]
(b) | Inside circle
1
And to the left of x=
2 | B1
B1 | 1.1
2.2a | Or their line if it is vertical.
[2]\begin{enumerate}[label=(\alph*)]
\item Sketch on a single Argand diagram the loci given by
\begin{enumerate}[label=(\roman*)]
\item $|z - 1 + 2\mathrm{i}| = 3$, [2]
\item $|z + 1| = |z - 2|$. [2]
\end{enumerate}
\item Indicate, by shading, the region of the Argand diagram for which $|z - 1 + 2\mathrm{i}| \leqslant 3$ and $|z + 1| \leqslant |z - 2|$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q1 [6]}}