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Practise

Question bank

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

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13 questions

SA-9709-P3-CX-0111 markL1 FoundationCalculatorLoci
The locus arg⁡(z−1−i)=π4\arg(z-1-i)=\dfrac\pi4 is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0012 marksL1 FoundationCalculatorLoci
The locus ∣z−1+2i∣=3|z-1+2i|=3 is a circle. State the coordinates of its centre and its radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0022 marksL1 FoundationCalculatorLoci
The locus ∣z+3∣=∣z−1∣|z+3|=|z-1| is a straight line. Its equation is x=cx=c. Find cc.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0061 markL1 FoundationCalculatorLoci
The locus ∣z−a∣=∣z−b∣|z-a|=|z-b| is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0093 marksL2 StandardCalculatorRegions
The complex number zz satisfies ∣z−3−4i∣=2|z-3-4i|=2. Find the greatest and least possible values of ∣z∣|z|.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0032 marksL2 StandardCalculatorLoci
The locus arg⁡(z−2)=π3\arg(z-2)=\dfrac\pi3 is part of a straight line. Find the gradient of this line, giving an exact value.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0042 marksL2 StandardCalculatorRegions
For points satisfying ∣z−2i∣≤1|z-2i|\le1, find the greatest and least values of ∣z∣|z|.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0071 markL2 StandardCalculatorRegions
Where does the point z=4+iz=4+i lie relative to the region ∣z−1−i∣<3|z-1-i|<3?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0104 marksL3 ExamCalculatorLoci
The locus ∣z−2∣=∣z+4i∣|z-2|=|z+4i| is a straight line in the Argand diagram. Find its Cartesian equation in the form y=mx+cy=mx+c.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0053 marksL3 ExamCalculatorRegions
The region RR is given by ∣z∣≤3|z|\le3 and Re⁡z≥1\operatorname{Re}z\ge1. Find the greatest value of arg⁡z\arg z for points in RR, in radians correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0083 marksL3 ExamCalculatorRegions
zz lies on the circle ∣z−2−2i∣=2|z-2-2i|=2. Find the exact least value of ∣z∣|z|.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX5-0093 marksL3 ExamCalculatorRegions
Find the complex number zz on the circle ∣z−6−8i∣=5|z-6-8i|=5 that is closest to the origin.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0163 marksL4 ChallengingCalculatorRegions
The complex number zz lies on the circle ∣z−4i∣=2|z-4i|=2. Find the least possible value of arg⁡z\arg z, giving an exact answer.

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Salam Academy Original Practice · Proposed mark scheme