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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-FM-CS-Q011 markL1 FoundationNon-calculatorSolids
For a solid of revolution about the xx-axis, xˉ\bar x is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-X011 markL1 FoundationNon-calculatorSolids
Find the distance of the centre of mass of a solid hemisphere of radius 44 from its flat face.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-X021 markL1 FoundationNon-calculatorSolids
Find the distance of the centre of mass of a solid cone of height 88 from its base.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-0012 marksL2 StandardNon-calculatorSolids
A solid cone has height 1212 cm. How far is its centre of mass from its base?

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-0021 markL2 StandardNon-calculatorSolids
A solid hemisphere has radius 88 cm. How far is its centre of mass from the flat face?

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-G013 marksL2 StandardNon-calculatorLaminas by integration
Find xˉ\bar x for the uniform lamina under y=x2y=x^2, 0≤x≤20\le x\le2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-X032 marksL2 StandardNon-calculatorLaminas by integration
Find xˉ\bar x for the uniform lamina under y=xy=x, 0≤x≤30\le x\le3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-X042 marksL2 StandardNon-calculatorSolids
The region under y=xy=x, 0≤x≤40\le x\le4, is rotated about the xx-axis. Find xˉ\bar x for the solid.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-0033 marksL3 ExamNon-calculatorSolids
The region under y=xy=\sqrt x, 0≤x≤40\le x\le4 is rotated about the xx-axis. Find xˉ\bar x for the solid.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-X052 marksL3 ExamNon-calculatorLaminas by integration
Find yˉ\bar y for the uniform lamina under y=xy=x, 0≤x≤30\le x\le3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-X062 marksL3 ExamCalculatorToppling
A uniform block of width 22 m and height 66 m stands on a rough slope that is slowly tilted (no sliding). Find the angle in degrees at which it topples.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CS-0043 marksL4 ChallengingCalculatorToppling
A uniform solid cylinder of radius 33 cm and height 1010 cm stands on a rough plane. The plane is slowly tilted; friction is enough to stop sliding. Find the angle (degrees) at which it topples.

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Salam Academy Original Practice · Proposed mark scheme