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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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14 questions

SA-9709-P3-CX-0043 marksL1 FoundationCalculatorPolynomial roots
Solve the equation z2−4z+13=0z^2-4z+13=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0012 marksL1 FoundationCalculatorPolynomial roots
Solve z2+6z+13=0z^2+6z+13=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0022 marksL1 FoundationCalculatorPolynomial roots
Solve z2−2z+5=0z^2-2z+5=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0081 markL1 FoundationCalculatorPolynomial roots
A polynomial with real coefficients has 3−2i3-2i as a root. Which number must also be a root?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0091 markL1 FoundationCalculatorPolynomial roots
The quadratic with roots 1±4i1\pm4i is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0101 markL1 FoundationCalculatorSquare roots
How many square roots does a non-zero complex number have?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0033 marksL2 StandardCalculatorPolynomial roots
2−i2-i is a root of z2+bz+c=0z^2+bz+c=0, where bb and cc are real. Find bb and cc.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0055 marksL3 ExamCalculatorPolynomial roots
Given that 1+2i1+2i is a root of z3−z2+3z+5=0z^3-z^2+3z+5=0, find the other two roots.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0064 marksL3 ExamCalculatorSquare roots
Find the two square roots of 5+12i5+12i, in the form x+iyx+iy.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0044 marksL3 ExamCalculatorPolynomial roots
Given that 3i3i is a root of z3−2z2+9z−18=0z^3-2z^2+9z-18=0, find the other two roots.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0054 marksL3 ExamCalculatorSquare roots
Find the two square roots of −3−4i-3-4i, in the form x+iyx+iy.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0064 marksL3 ExamCalculatorSquare roots
Find the two square roots of 8i8i, in the form x+iyx+iy.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0157 marksL5 ExtensionCalculatorSquare roots
Solve the equation z2−(3+i)z+(4+3i)=0z^2-(3+i)z+(4+3i)=0, giving your answers in the form x+iyx+iy.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX4-0076 marksL5 ExtensionCalculatorPolynomial roots
Given that 2i2i is a root of z4−4z3+9z2−16z+20=0z^4-4z^3+9z^2-16z+20=0, find all the roots.

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Salam Academy Original Practice · Proposed mark scheme