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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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12 questions

SA-FP-DM-G012 marksL1 FoundationNon-calculatorPowers
Find the real number (cos⁡π6+isin⁡π6)6\left(\cos\frac\pi6+i\sin\frac\pi6\right)^6.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-Q011 markL1 FoundationNon-calculatorRoots
How many distinct solutions does z6=−64z^6=-64 have?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-X011 markL1 FoundationNon-calculatorPowers
Find the real part of (cos⁡π6+isin⁡π6)6\left(\cos\frac\pi6+i\sin\frac\pi6\right)^6.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-X021 markL1 FoundationNon-calculatorPowers
Find ∣(1+i)8∣|(1+i)^8|.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-X041 markL1 FoundationNon-calculatorRoots
How many distinct complex cube roots does 8i8i have?

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-0012 marksL2 StandardNon-calculatorPowers
Find (1+i)8(1+i)^8.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-0022 marksL2 StandardNon-calculatorTrig identities
cos⁡3θ=acos⁡3θ+bcos⁡θ\cos3\theta=a\cos^3\theta+b\cos\theta. Find aa.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-0041 markL2 StandardNon-calculatorRoots
Find the sum of all the roots of z7=1z^7=1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-X032 marksL2 StandardNon-calculatorPowers
Find the real part of (1+i)8(1+i)^8.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-X051 markL2 StandardNon-calculatorRoots
Find the sum of the five fifth roots of unity.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-0033 marksL3 ExamNon-calculatorRoots
Solve z3=8iz^3=8i. Give the arguments of the roots in degrees, in the range −180<θ≤180-180<\theta\le180.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DM-0053 marksL4 ChallengingNon-calculatorRoots
ω\omega is a complex cube root of unity (ω≠1\omega\neq1). Find (1+ω)(1+ω2)(1+\omega)(1+\omega^2).

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Salam Academy Original Practice · Proposed mark scheme