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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-P1-IN-0013 marksL1 FoundationCalculatorIndefinite
Find ∫(8x3−6x+5) dx\displaystyle\int(8x^3-6x+5)\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0011 markL1 FoundationCalculatorIndefinite
Find ∫6x2 dx\displaystyle\int6x^2\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0022 marksL1 FoundationCalculatorIndefinite
Find ∫(x3−4x+1) dx\displaystyle\int(x^3-4x+1)\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0041 markL1 FoundationCalculatorIndefinite
Which of these is NOT an integral of 2x2x?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-Q011 markL1 FoundationCalculatorIndefinite
An indefinite integral includes + c+\,c because
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-G014 marksL1 FoundationCalculatorFinding the curve
A curve has gradient dydx=6x2−4x\dfrac{dy}{dx}=6x^2-4x and passes through the point (1,5)(1,5). Find the equation of the curve.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-Q011 markL1 FoundationCalculatorIndefinite
∫x4 dx\displaystyle\int x^4\,dx is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0023 marksL2 StandardCalculatorRewriting
Find ∫(4x3+x)dx\displaystyle\int\left(\frac{4}{x^3}+\sqrt{x}\right)dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0054 marksL2 StandardCalculatorFinding the curve
A curve has gradient dydx=3x\dfrac{dy}{dx}=3\sqrt{x} and passes through (4,10)(4,10). Find the equation of the curve.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0032 marksL2 StandardCalculatorRewriting
Find ∫3x2 dx\displaystyle\int\frac{3}{x^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0053 marksL2 StandardCalculatorRewriting
Find ∫2x3−1x2 dx\displaystyle\int\frac{2x^3-1}{x^2}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0063 marksL2 StandardCalculatorFinding the curve
A curve has gradient dydx=4x−3\dfrac{dy}{dx}=4x-3 and passes through (2,5)(2,5). Find the equation of the curve.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN1-0074 marksL4 ChallengingCalculatorFinding the curve
A function satisfies f′′(x)=6xf''(x)=6x, f′(1)=5f'(1)=5 and f(1)=2f(1)=2. Find f(x)f(x).

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Salam Academy Original Practice · Proposed mark scheme