OCR MEI FP1 2011 January — Question 4 6 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Argand & Loci
TypeRegion shading with single inequality
DifficultyModerate -0.8 This is a straightforward loci question requiring students to shade an annular region between two circles centered at (3,2) with radii 2 and 3. It tests basic understanding of modulus inequalities and Argand diagram representation with no problem-solving or novel insight required—simpler than average even for Further Maths.
Spec4.02k Argand diagrams: geometric interpretation
4 Represent on an Argand diagram the region defined by \(2 < | z - ( 3 + 2 \mathrm { j } ) | \leqslant 3\).
Question 4:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Circle drawnB1 Circle
Centre \(3+2j\)B1 Centre \(3+2j\)
Radius \(= 2\) or \(3\), consistent with centreB1 Radius consistent with centre
Both circles correctB1 Both circles correct cao
Correct boundaries indicated, inner excluded, outer includedB1 (ft concentric circles)
Region between concentric circles indicated as solutionB1 [6] SC -1 if axes incorrect 
# Question 4:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Circle drawn | B1 | Circle |
| Centre $3+2j$ | B1 | Centre $3+2j$ |
| Radius $= 2$ or $3$, consistent with centre | B1 | Radius consistent with centre |
| Both circles correct | B1 | Both circles correct cao |
| Correct boundaries indicated, inner excluded, outer included | B1 | (ft concentric circles) |
| Region between concentric circles indicated as solution | B1 [6] | SC -1 if axes incorrect |

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4 Represent on an Argand diagram the region defined by $2 < | z - ( 3 + 2 \mathrm { j } ) | \leqslant 3$.

\hfill \mbox{\textit{OCR MEI FP1 2011 Q4 [6]}}
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Q1 5 Q2 7 Q3 7 Q4 6 Q5 5 Q6 6 Q7 12 Q8 12 Q9 12