Question 4 - A-Level Maths

OCR Further Pure Core 1 Specimen — Question 4 3 marks

Exam Board	OCR
Module	Further Pure Core 1 (Further Pure Core 1)
Session	Specimen
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Complex Numbers Argand & Loci
Type	Region shading with multiple inequalities
Difficulty	Standard +0.3 This question requires understanding of modulus inequalities and their geometric interpretation (circle and perpendicular bisector), then shading the intersection. While it involves Further Maths content, it's a straightforward application of standard loci with no complex algebraic manipulation or proof required.
Spec	4.02k Argand diagrams: geometric interpretation 4.02o Loci in Argand diagram: circles, half-lines

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

Show mark scheme Show mark scheme source

Question 4:

Answer	Marks
4	Im

Re

1.5i

Re

2 The shaded region

Answer	Marks
is the required locus	B1

B1

Answer	Marks
[3]	1.1

1.1

Answer	Marks
i	Circle centre 0, radius 2

Line parallel to x axis… Through 1.5i

Correct shading with continuous arc and

dashed line

n

e

Answer	Marks
m	Must state which region is the

required locus

4

Question 4:
4 | Im
Re
1.5i
Re
2
The shaded region
is the required locus | B1
B1
B1
[3] | 1.1
1.1
1.1
i | Circle centre 0, radius 2
Line parallel to x axis… Through 1.5i
Correct shading with continuous arc and
dashed line
n
e
m | Must state which region is the
required locus
4

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4 Draw the region in an Argand diagram for which $| z | \leq 2$ and $| z | > | z - 3 i |$.

\hfill \mbox{\textit{OCR Further Pure Core 1  Q4 [3]}}

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