OCR MEI FP1 2006 June — Question 4 8 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2006
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Argand & Loci
TypeRegion shading with multiple inequalities
DifficultyModerate -0.8 This is a straightforward Further Pure 1 question testing basic loci in the complex plane. Parts (i) and (ii) require recognizing and sketching circles (filled disk and annulus), while part (iii) requires sketching a half-line from a point. These are standard textbook exercises requiring only direct application of definitions with no problem-solving or novel insight needed.
Spec4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines

Indicate, on separate Argand diagrams,
  1. the set of points \(z\) for which \(|z-(3-\mathrm{j})| \leqslant 3\), [3]
  2. the set of points \(z\) for which \(1 < |z-(3-\mathrm{j})| \leqslant 3\), [2]
  3. the set of points \(z\) for which \(\arg(z-(3-\mathrm{j})) = \frac{1}{4}\pi\). [3]

Indicate, on separate Argand diagrams,
\begin{enumerate}[label=(\roman*)]
\item the set of points $z$ for which $|z-(3-\mathrm{j})| \leqslant 3$, [3]

\item the set of points $z$ for which $1 < |z-(3-\mathrm{j})| \leqslant 3$, [2]

\item the set of points $z$ for which $\arg(z-(3-\mathrm{j})) = \frac{1}{4}\pi$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI FP1 2006 Q4 [8]}}