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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-VI-G012 marksL1 FoundationCalculatorVolumes
The line y=xy=x for 0≤x≤30\le x\le3 is rotated 2π2\pi about the xx-axis. Find the volume (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-Q011 markL1 FoundationNon-calculatorImproper integrals
Which integral diverges?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-X012 marksL1 FoundationNon-calculatorVolumes
The region under y=xy=\sqrt x, 0≤x≤40\le x\le4, is rotated 2π2\pi about the xx-axis. Find the volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-X022 marksL1 FoundationNon-calculatorMean value
Find the mean value of x2x^2 on [0,3][0,3].

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-X032 marksL1 FoundationNon-calculatorImproper integrals
Evaluate ∫1∞1x2 dx\int_1^\infty\frac1{x^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-X051 markL1 FoundationNon-calculatorImproper integrals
∫1∞1x dx\int_1^\infty\frac1x\,dx
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-0012 marksL2 StandardNon-calculatorImproper integrals
Evaluate ∫1∞dxx2\displaystyle\int_1^\infty\frac{dx}{x^2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-0022 marksL2 StandardNon-calculatorImproper integrals
Evaluate ∫01dxx\displaystyle\int_0^1\frac{dx}{\sqrt x}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-0032 marksL2 StandardNon-calculatorMean value
Find the mean value of x2x^2 over 0≤x≤30\le x\le3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-0042 marksL2 StandardCalculatorVolumes
y=xy=\sqrt x, 0≤x≤40\le x\le4, is rotated about the xx-axis. Find the volume (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-X042 marksL2 StandardNon-calculatorImproper integrals
Evaluate ∫0∞e−2x dx\int_0^\infty e^{-2x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-VI-0053 marksL3 ExamCalculatorVolumes
The curve y=x2y=x^2, 0≤y≤20\le y\le2, is rotated about the yy-axis. Find the volume (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme