OCR Further Pure Core AS Specimen — Question 4 4 marks

Exam BoardOCR
ModuleFurther Pure Core AS (Further Pure Core AS)
SessionSpecimen
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Argand & Loci
TypeRegion shading with multiple inequalities
DifficultyStandard +0.3 This is a straightforward Further Maths loci question requiring students to identify and shade the intersection of a disc (circle with interior) and a half-plane. While it involves two conditions, both are standard loci types with no algebraic manipulation needed—just geometric interpretation and careful shading. Slightly easier than average due to its routine nature.
Spec4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines

4 Draw the region of the Argand diagram for which \(| z - 3 - 4 i | \leq 5\) and \(| z | \leq | z - 2 |\).

Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
A circle with centre \(3+4i\)M1 Accept the correct minor arc alone
passing through originA1
A line parallel to \(y\)-axis through \(1\)B1 Accept the correct line segment alone
Correct shading and continuous lines; the shaded region is the required locusB1 Must state which region is the required locus
## Question 4:

| Answer | Marks | Guidance |
|--------|-------|----------|
| A circle with centre $3+4i$ | M1 | Accept the correct minor arc alone |
| passing through origin | A1 | |
| A line parallel to $y$-axis through $1$ | B1 | Accept the correct line segment alone |
| Correct shading and continuous lines; the shaded region is the required locus | B1 | Must state which region is the required locus |

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4 Draw the region of the Argand diagram for which $| z - 3 - 4 i | \leq 5$ and $| z | \leq | z - 2 |$.

\hfill \mbox{\textit{OCR Further Pure Core AS  Q4 [4]}}