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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-TL-0021 markL1 FoundationNon-calculatorLimits
Find lim⁡x→0sin⁡3xx\displaystyle\lim_{x\to0}\frac{\sin3x}{x}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-G011 markL1 FoundationNon-calculatorTaylor series
In the Taylor series of ln⁡x\ln x about x=1x=1, find the coefficient of (x−1)(x-1).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-Q011 markL1 FoundationNon-calculatorLimits
L'Hôpital's rule can be applied directly to
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-X011 markL1 FoundationNon-calculatorLimits
Find lim⁡x→0sin⁡xx\lim_{x\to0}\frac{\sin x}x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-0012 marksL2 StandardNon-calculatorLimits
Find lim⁡x→01−cos⁡xx2\displaystyle\lim_{x\to0}\frac{1-\cos x}{x^2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-0032 marksL2 StandardCalculatorTaylor series
Find the coefficient of (x−2)2(x-2)^2 in the Taylor series of exe^x about x=2x=2 (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-X022 marksL2 StandardNon-calculatorLimits
Find lim⁡x→01−cos⁡xx2\lim_{x\to0}\frac{1-\cos x}{x^2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-X032 marksL2 StandardNon-calculatorLimits
Find lim⁡x→0e2x−1x\lim_{x\to0}\frac{e^{2x}-1}x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-X042 marksL2 StandardNon-calculatorTaylor series
Find the coefficient of (x−1)2(x-1)^2 in the Taylor series of ln⁡x\ln x about x=1x=1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-0043 marksL3 ExamNon-calculatorLeibniz
Use Leibniz's theorem to find d3dx3(x2ex)\frac{d^3}{dx^3}(x^2e^x) at x=0x=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-X052 marksL3 ExamNon-calculatorLeibniz
Use Leibniz's theorem to find d3dx3(xex)\frac{d^3}{dx^3}\left(xe^x\right) at x=0x=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TL-0054 marksL4 ChallengingNon-calculatorLeibniz
y′=x+yy'=x+y, y(0)=1y(0)=1. Find the coefficient of x3x^3 in the series solution.

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Salam Academy Original Practice · Proposed mark scheme