Salam Academy
Sign inCreate account
Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

Sign in to check answers. Your attempts build your mastery and error book.

12 questions

SA-FP-CT-G011 markL1 FoundationNon-calculatorTransformations
Under w=2z+3iw=2z+3i, the circle ∣z∣=1|z|=1 maps to a circle. Find its radius.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-Q011 markL1 FoundationNon-calculatorLoci
The locus ∣z−1∣=∣z−5∣|z-1|=|z-5| is
Choose one option

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-X011 markL1 FoundationNon-calculatorLoci
Find the radius of the locus ∣z−3−4i∣=5|z-3-4i|=5.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-X021 markL1 FoundationNon-calculatorLoci
Find the real part of the centre of the circle ∣z−3−4i∣=5|z-3-4i|=5.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-X041 markL1 FoundationNon-calculatorLoci
The locus arg⁡z=π4\arg z=\frac\pi4 is a half-line from the origin. Find its gradient.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-0012 marksL2 StandardNon-calculatorTransformations
Under w=1zw=\frac1z, the circle ∣z∣=2|z|=2 maps to ∣w∣=r|w|=r. Find rr.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-0022 marksL2 StandardNon-calculatorLoci
The locus ∣z−2∣=∣z+2i∣|z-2|=|z+2i| is the line y=mxy=mx. Find mm.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-X031 markL2 StandardNon-calculatorLoci
The locus ∣z−2∣=∣z+2∣|z-2|=|z+2| is
Choose one option

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-X052 marksL2 StandardNon-calculatorTransformations
Under w=z+2iw=z+2i, the circle ∣z∣=1|z|=1 maps to a circle. Find the imaginary part of its centre.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-0033 marksL3 ExamNon-calculatorLoci
The locus ∣z−3∣=2∣z∣|z-3|=2|z| is a circle. Find its radius.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-0043 marksL3 ExamNon-calculatorTransformations
Under w=1zw=\frac1z, the line Re⁡z=1\operatorname{Re}z=1 maps to a circle. Find its radius.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FP-CT-0053 marksL4 ChallengingNon-calculatorTransformations
Under w=iz+1w=iz+1, the circle ∣z−2∣=3|z-2|=3 maps to ∣w−c∣=3|w-c|=3. Find the imaginary part of cc.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme