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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-P1-IN-0063 marksL1 FoundationCalculatorDefinite
Evaluate ∫13(3x2−2x) dx\displaystyle\int_1^3(3x^2-2x)\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0012 marksL1 FoundationCalculatorDefinite
Evaluate ∫14(2x+1) dx\displaystyle\int_1^4(2x+1)\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-G012 marksL1 FoundationCalculatorDefinite
Evaluate ∫023x2 dx\displaystyle\int_0^2 3x^2\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-Q011 markL1 FoundationCalculatorDefinite
If ∫13f(x) dx=5\displaystyle\int_1^3f(x)\,dx=5, then ∫31f(x) dx\displaystyle\int_3^1f(x)\,dx is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0022 marksL2 StandardCalculatorDefinite
Evaluate ∫126x2 dx\displaystyle\int_1^2\frac{6}{x^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0033 marksL2 StandardCalculatorDefinite
Evaluate ∫01(2x+1)3 dx\displaystyle\int_0^1(2x+1)^3\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0043 marksL2 StandardCalculatorDefinite
Evaluate ∫191x dx\displaystyle\int_1^9\frac{1}{\sqrt x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0074 marksL3 ExamCalculatorDefinite
Evaluate ∫042x+1 dx\displaystyle\int_0^4\sqrt{2x+1}\,dx, giving an exact answer.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0133 marksL3 ExamCalculatorImproper
Evaluate the improper integral ∫1∞4x3 dx\displaystyle\int_1^\infty\frac{4}{x^3}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0143 marksL3 ExamCalculatorImproper
Evaluate the improper integral ∫041x dx\displaystyle\int_0^4\frac{1}{\sqrt{x}}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0053 marksL3 ExamCalculatorUnknown limits
Given that ∫1k2x dx=15\displaystyle\int_1^k2x\,dx=15, where k>1k>1, find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0063 marksL3 ExamCalculatorImproper
Evaluate ∫1∞2x2 dx\displaystyle\int_1^\infty\frac{2}{x^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0083 marksL3 ExamCalculatorImproper
Evaluate ∫08x−23 dx\displaystyle\int_0^8x^{-\frac23}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN3-0073 marksL4 ChallengingCalculatorUnknown limits
Find the positive value of aa for which ∫0a(x−1) dx=0\displaystyle\int_0^a(x-1)\,dx=0.

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Salam Academy Original Practice · Proposed mark scheme