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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-RA-0042 marksL1 FoundationCalculatorArc length
Use the arc length formula to find the length of y=2xy=2x from x=0x=0 to x=1x=1 (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-Q011 markL1 FoundationNon-calculatorArc length
The arc length of y=f(x)y=f(x) from aa to bb is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-X041 markL1 FoundationNon-calculatorArc length
Use the arc length formula to find the length of y=2xy=2x from x=0x=0 to x=1x=1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-0012 marksL2 StandardCalculatorReduction formulae
Using the same formula, find I2I_2 (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-G012 marksL2 StandardNon-calculatorReduction formulae
In=∫01xnexdxI_n=\int_0^1x^ne^xdx with In=e−nIn−1I_n=e-nI_{n-1} and I0=e−1I_0=e-1. Find I1I_1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-X012 marksL2 StandardNon-calculatorReduction formulae
In=∫01xnex dxI_n=\int_0^1x^ne^x\,dx satisfies In=e−nIn−1I_n=e-nI_{n-1}, and I0=e−1I_0=e-1. Find I1I_1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-X022 marksL2 StandardNon-calculatorReduction formulae
Using the same reduction formula, find I2I_2 exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-X052 marksL2 StandardNon-calculatorSurface area
The line y=3y=3, 0≤x≤20\le x\le2, is rotated 2π2\pi about the xx-axis. Use the surface area formula to find the curved surface area.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-0023 marksL3 ExamCalculatorReduction formulae
In=∫0π/2sin⁡nx dxI_n=\int_0^{\pi/2}\sin^nx\,dx satisfies In=n−1nIn−2I_n=\frac{n-1}nI_{n-2}, I0=π2I_0=\frac\pi2. Find I4I_4 (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-0033 marksL3 ExamNon-calculatorArc length
Find the length of y=23x3/2y=\frac23x^{3/2} from x=0x=0 to x=3x=3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-X033 marksL3 ExamNon-calculatorArc length
Find the length of the curve y=23x3/2y=\frac23x^{3/2} from x=0x=0 to x=3x=3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RA-0053 marksL4 ChallengingCalculatorSurface area
The line y=xy=x, 0≤x≤10\le x\le1, is rotated about the xx-axis. Find the curved surface area (to 3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme