| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Region shading with multiple inequalities |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question requiring standard knowledge of loci in the complex plane. Part (i) asks for a circle with center (1,-1) and radius √2, while part (ii) requires shading an annulus. These are routine applications of the modulus-locus relationship with no problem-solving or novel insight required, making it slightly easier than average despite being Further Maths content. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Circle | B1 | |
| Centre \((1, -1)\) | B1 | |
| Passing through \((0, 0)\) | B1 | (3 marks) |
| (ii) Sketch a concentric circle | B1 | |
| Inside (i) and touching axes | B1 | |
| Shade between the circles | B1 | (3 marks) |
(i) Circle | B1 |
Centre $(1, -1)$ | B1 |
Passing through $(0, 0)$ | B1 | (3 marks)
(ii) Sketch a concentric circle | B1 |
Inside (i) and touching axes | B1 |
Shade between the circles | B1 | (3 marks)4 (i) Sketch, on an Argand diagram, the locus given by $| z - 1 + \mathrm { i } | = \sqrt { 2 }$.\\
(ii) Shade on your diagram the region given by $1 \leqslant | z - 1 + \mathrm { i } | \leqslant \sqrt { 2 }$.
\hfill \mbox{\textit{OCR FP1 2007 Q4 [6]}}