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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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13 questions

SA-9709-P3-I35-0081 markL1 FoundationCalculatorChanging limits
With u=x2+1u=x^2+1, the limits x=0x=0 and x=2x=2 become
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-G013 marksL1 FoundationCalculatorRecognising
Use the substitution u=x2+1u=x^2+1 to find ∫2x(x2+1)4 dx\displaystyle\int2x(x^2+1)^4\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-Q011 markL1 FoundationCalculatorRecognising
The best substitution for ∫x(x2−3)7 dx\displaystyle\int x(x^2-3)^7\,dx is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0013 marksL2 StandardCalculatorSubstitution
Use the substitution u=x2+4u=x^2+4 to find ∫xx2+4 dx\displaystyle\int x\sqrt{x^2+4}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0024 marksL2 StandardCalculatorChanging limits
Use the substitution u=x2+1u=x^2+1 to find the exact value of ∫01x(x2+1)2 dx\displaystyle\int_0^1\frac{x}{(x^2+1)^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0032 marksL2 StandardCalculatorRecognising
Find ∫cos⁡x esin⁡x dx\displaystyle\int\cos x\,e^{\sin x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0043 marksL2 StandardCalculatorChanging limits
Use the substitution u=sin⁡xu=\sin x to find the exact value of ∫0π/2cos⁡xsin⁡2x dx\displaystyle\int_0^{\pi/2}\cos x\sin^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0104 marksL2 StandardCalculatorChanging limits
Use the substitution u=x2+1u=x^2+1 to find ∫01x(x2+1)3 dx\displaystyle\int_0^1x(x^2+1)^3\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0073 marksL3 ExamCalculatorRecognising
Use the substitution u=1+exu=1+e^x to find ∫ex(1+ex)2 dx\displaystyle\int\frac{e^x}{(1+e^x)^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0124 marksL3 ExamCalculatorSubstitution
Use the substitution u=cos⁡xu=\cos x to find ∫0π/2sin⁡xcos⁡3x dx\displaystyle\int_0^{\pi/2}\sin x\cos^3x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0065 marksL4 ChallengingCalculatorSubstitution
Use the substitution u=x+1u=x+1 to find the exact value of ∫03xx+1 dx\displaystyle\int_0^3\frac{x}{\sqrt{x+1}}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0115 marksL4 ChallengingCalculatorChanging limits
Use the substitution u=1+xu=1+\sqrt x to find the exact value of ∫141x (1+x) dx\displaystyle\int_1^4\frac{1}{\sqrt x\,(1+\sqrt x)}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I35-0055 marksL5 ExtensionCalculatorSubstitution
Use the substitution u=2x−1u=2x-1 to find the exact value of ∫1/21x(2x−1)5 dx\displaystyle\int_{1/2}^{1}x(2x-1)^5\,dx.

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Salam Academy Original Practice · Proposed mark scheme