OCR FP1 2012 January — Question 6 6 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Argand & Loci
TypeIntersection of two loci
DifficultyModerate -0.3 This is a straightforward Further Maths question requiring students to sketch two standard loci: a circle centered at √3 + i with radius 2, and a half-line from the origin at angle π/6. While it's Further Maths content (making it harder than basic A-level), it's a direct application of standard locus definitions with no problem-solving or calculation required, making it slightly easier than average for FP1.
Spec4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines

6 Sketch, on a single Argand diagram, the loci given by \(| z - \sqrt { 3 } - \mathrm { i } | = 2\) and \(\arg z = \frac { 1 } { 6 } \pi\).

Question 6:
AnswerMarks Guidance
AnswerMarks Guidance
CircleB1
Centre \((\sqrt{3}, 1)\)B1
Passing through \(O\) and crosses \(y\)-axis againB1
Line, with correct slope shownB1
\(\frac{1}{2}\) line starting at \(O\)B1
Completely correct diagram for both lociB1 Ignore shading
[6]
## Question 6:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Circle | B1 | |
| Centre $(\sqrt{3}, 1)$ | B1 | |
| Passing through $O$ and crosses $y$-axis again | B1 | |
| Line, with correct slope shown | B1 | |
| $\frac{1}{2}$ line starting at $O$ | B1 | |
| Completely correct diagram for both loci | B1 | Ignore shading |
| **[6]** | | |

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6 Sketch, on a single Argand diagram, the loci given by $| z - \sqrt { 3 } - \mathrm { i } | = 2$ and $\arg z = \frac { 1 } { 6 } \pi$.

\hfill \mbox{\textit{OCR FP1 2012 Q6 [6]}}