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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-POL-G011 markL1 FoundationNon-calculatorConverting
The point has polar coordinates (2,π3)\left(2,\frac\pi3\right). Find its xx-coordinate.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-Q011 markL1 FoundationNon-calculatorSketching
The polar curve r=3r=3 is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-X011 markL1 FoundationNon-calculatorConverting
Convert the polar point (2,π3)\left(2,\frac\pi3\right) to Cartesian form. Find xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-X031 markL1 FoundationNon-calculatorAreas
Find the area enclosed by r=3r=3, 0≤θ≤2π0\le\theta\le2\pi.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-X051 markL1 FoundationNon-calculatorSketching
Find the greatest value of rr on the curve r=1+cos⁡θr=1+\cos\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-0012 marksL2 StandardCalculatorAreas
Use 12∫r2 dθ\frac12\int r^2\,d\theta to find the area enclosed by r=3r=3 (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-0032 marksL2 StandardNon-calculatorConverting
The curve r=2cos⁡θr=2\cos\theta is a circle. Find its radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-X022 marksL2 StandardNon-calculatorConverting
r=2cos⁡θr=2\cos\theta is a circle. Find its radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-0023 marksL3 ExamCalculatorAreas
Find the area enclosed by the cardioid r=2(1+cos⁡θ)r=2(1+\cos\theta) (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-0043 marksL3 ExamCalculatorAreas
Find the area swept by r=θr=\theta from θ=0\theta=0 to θ=π\theta=\pi (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-X043 marksL3 ExamNon-calculatorAreas
Find the area bounded by r=2θr=2\theta for 0≤θ≤π0\le\theta\le\pi.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-POL-0054 marksL4 ChallengingNon-calculatorTangents
Find the value of θ\theta, in degrees with 0<θ<1800<\theta<180, where the tangent to r=1+cos⁡θr=1+\cos\theta is parallel to the initial line.

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Salam Academy Original Practice · Proposed mark scheme