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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-PM-PAR-0011 markL1 FoundationNon-calculatorConverting
x=3cos⁡tx=3\cos t, y=3sin⁡ty=3\sin t is a circle. Find its radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-0022 marksL1 FoundationNon-calculatorConverting
Find yy in terms of xx for x=t+1x=t+1, y=2t−3y=2t-3.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-G012 marksL1 FoundationNon-calculatorConverting
Find the Cartesian equation of x=2tx=2t, y=t2y=t^2. Give yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-Q011 markL1 FoundationNon-calculatorIntersections
x=cos⁡tx=\cos t, y=sin⁡ty=\sin t for 0≤t≤π0\le t\le\pi is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-X011 markL1 FoundationNon-calculatorConverting
A curve has x=t2x=t^2, y=t3y=t^3 (t>0t>0). Find yy when x=4x=4.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-X021 markL1 FoundationNon-calculatorConverting
Find the area enclosed by x=2cos⁡tx=2\cos t, y=2sin⁡ty=2\sin t, 0≤t≤2π0\le t\le2\pi.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-X031 markL1 FoundationNon-calculatorConverting
A curve has x=3tx=3t, y=6ty=\frac6t. Its Cartesian equation is xy=kxy=k. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-0042 marksL2 StandardNon-calculatorConverting
x=1+2cos⁡tx=1+2\cos t, y=3+2sin⁡ty=3+2\sin t. Find the yy-coordinate of the centre of this circle.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-X042 marksL2 StandardNon-calculatorIntersections
Find dydx\frac{dy}{dx} for x=t2x=t^2, y=2ty=2t at t=2t=2.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-X052 marksL2 StandardNon-calculatorConverting
A curve has x=cos⁡tx=\cos t, y=cos⁡2ty=\cos2t. Find yy when x=12x=\frac12.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-0033 marksL3 ExamNon-calculatorIntersections
The curve x=t2x=t^2, y=2ty=2t meets the line y=x−3y=x-3 at two points. Find their xx-coordinates.

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Salam Academy Original Practice · Proposed mark scheme
SA-PM-PAR-0053 marksL3 ExamNon-calculatorConverting
x=2sec⁡tx=2\sec t, y=3tan⁡ty=3\tan t satisfies x24−y2k=1\frac{x^2}4-\frac{y^2}k=1. Find kk.

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Salam Academy Original Practice · Proposed mark scheme