OCR Further Pure Core 1 2019 June — Question 2 3 marks

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2019
SessionJune
Marks3
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 two standard regions: a half-plane (from |z| ≤ |z-4|, which is the perpendicular bisector inequality) and a disc (centered at 3+2i with radius 2). While it requires understanding of complex number geometry, the techniques are standard and the intersection is simple to visualize and shade.
Spec4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines

2 Indicate by shading on an Argand diagram the region \(\{ z : | z | \leqslant | z - 4 | \} \cap \{ z : | z - 3 - 2 i | \leqslant 2 \}\).

Question 2:
AnswerMarks
2B1
B1
B1
AnswerMarks
[3]2.2a
2.2a
AnswerMarks
1.1Correct circle
Centre 3+2i radius 2
Correct line
Re(z) = 2
AnswerMarks
Correct shading.“correct” requires
clear indication of
centre and touching x-
axis
Alternatively,
candidates may shade
the region that is not
required, but should
indicate clearly that
what they have shaded
is not required.
Question 2:
2 | B1
B1
B1
[3] | 2.2a
2.2a
1.1 | Correct circle
Centre 3+2i radius 2
Correct line
Re(z) = 2
Correct shading. | “correct” requires
clear indication of
centre and touching x-
axis
Alternatively,
candidates may shade
the region that is not
required, but should
indicate clearly that
what they have shaded
is not required.
2 Indicate by shading on an Argand diagram the region\\
$\{ z : | z | \leqslant | z - 4 | \} \cap \{ z : | z - 3 - 2 i | \leqslant 2 \}$.

\hfill \mbox{\textit{OCR Further Pure Core 1 2019 Q2 [3]}}