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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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14 questions

SA-9709-P2-IN-Q021 markL1 FoundationCalculatorSquares
To integrate sin⁡2x\sin^2x, first rewrite it as
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I32-0031 markL1 FoundationCalculatorSquares
Find ∫(1+tan⁡2x)dx\displaystyle\int\left(1+\tan^2x\right)dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-Q021 markL1 FoundationCalculatorSquares
To integrate cos⁡2x\cos^2x, first write it as
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0063 marksL2 StandardCalculatorSquares
Find ∫sin⁡2x dx\displaystyle\int\sin^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0083 marksL2 StandardCalculatorSquares
Find ∫tan⁡2x dx\displaystyle\int\tan^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0103 marksL2 StandardCalculatorDouble angles
Find the exact value of ∫0π/24sin⁡xcos⁡x dx\displaystyle\int_0^{\pi/2}4\sin x\cos x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I32-0013 marksL2 StandardCalculatorSquares
Find ∫cos⁡2x dx\displaystyle\int\cos^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I32-0022 marksL2 StandardCalculatorDouble angles
Find ∫2sin⁡3xcos⁡3x dx\displaystyle\int2\sin3x\cos3x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I32-0043 marksL2 StandardCalculatorExact values
Find the exact value of ∫0πcos⁡2x dx\displaystyle\int_0^{\pi}\cos^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0034 marksL2 StandardCalculatorExact values
Find the exact value of ∫0π/2sin⁡2x dx\displaystyle\int_0^{\pi/2}\sin^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0074 marksL3 ExamCalculatorExact values
Find the exact value of ∫0π/4cos⁡2x dx\displaystyle\int_0^{\pi/4}\cos^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0094 marksL3 ExamCalculatorDouble angles
By expanding the bracket, find ∫(sin⁡x+cos⁡x)2 dx\displaystyle\int(\sin x+\cos x)^2\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0054 marksL3 ExamCalculatorExact values
Find the exact value of ∫0π/4cos⁡22x dx\displaystyle\int_0^{\pi/4}\cos^22x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I32-0054 marksL4 ChallengingCalculatorDouble angles
By using sin⁡2x=2sin⁡xcos⁡x\sin2x=2\sin x\cos x and then a double-angle formula, find ∫8sin⁡2xcos⁡2x dx\displaystyle\int8\sin^2x\cos^2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme