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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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15 questions

SA-9709-P2-IN-0033 marksL1 FoundationCalculatorExact integrals
Find the exact value of ∫01e2x dx\displaystyle\int_0^1e^{2x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I33-0012 marksL1 FoundationCalculatorExact integrals
Find the exact value of ∫1e2x dx\displaystyle\int_1^e\frac2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I33-Q011 markL1 FoundationCalculatorLog results
∫f′(x)f(x) dx\displaystyle\int\frac{f'(x)}{f(x)}\,dx equals
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0062 marksL1 FoundationCalculatorLog results
Find ∫12x+1 dx\displaystyle\int\frac{1}{2x+1}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0043 marksL2 StandardCalculatorLog results
Find the exact value of ∫1323x−1 dx\displaystyle\int_1^3\frac{2}{3x-1}\,dx, giving your answer in the form kln⁡4k\ln4. State kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0053 marksL2 StandardCalculatorExact integrals
Find the exact value of ∫0π/6sin⁡2x dx\displaystyle\int_0^{\pi/6}\sin2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0113 marksL2 StandardCalculatorExact integrals
Find the exact area of the region bounded by the curve y=2xy=\dfrac2x, the xx-axis and the lines x=1x=1 and x=2x=2.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I33-0023 marksL2 StandardCalculatorExact integrals
Find the exact value of ∫0ln⁡2e2x dx\displaystyle\int_0^{\ln2}e^{2x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0073 marksL2 StandardCalculatorLog results
Find the exact value of ∫012xx2+1 dx\displaystyle\int_0^1\frac{2x}{x^2+1}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0124 marksL3 ExamCalculatorUnknown limits
Given that ∫0aex/2 dx=4\displaystyle\int_0^ae^{x/2}\,dx=4, find the exact value of aa.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0134 marksL3 ExamCalculatorUnknown limits
Given that ∫1k12x−1 dx=ln⁡3\displaystyle\int_1^k\frac{1}{2x-1}\,dx=\ln3, where k>1k>1, find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I33-0032 marksL3 ExamCalculatorLog results
(Paper 3) Find ∫3x2x3+1 dx\displaystyle\int\frac{3x^2}{x^3+1}\,dx, for x>−1x>-1.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0085 marksL3 ExamCalculatorLog results
Given that 5x+1(x−1)(x+2)=2x−1+3x+2\dfrac{5x+1}{(x-1)(x+2)}=\dfrac2{x-1}+\dfrac3{x+2}, find the exact value of ∫245x+1(x−1)(x+2) dx\displaystyle\int_2^4\frac{5x+1}{(x-1)(x+2)}\,dx, in the form ln⁡k\ln k.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0093 marksL3 ExamCalculatorLog results
By writing tan⁡x=sin⁡xcos⁡x\tan x=\dfrac{\sin x}{\cos x}, find the exact value of ∫0π/3tan⁡x dx\displaystyle\int_0^{\pi/3}\tan x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0193 marksL3 ExamCalculatorLog results
Find the exact value of ∫0ln⁡3ex1+ex dx\displaystyle\int_0^{\ln3}\frac{e^x}{1+e^x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme