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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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12 questions

SA-IAL-P1-IN2-0013 marksL1 FoundationNon-calculatorFinding the curve
dydx=2x\dfrac{dy}{dx}=2x, and the curve passes through (1,4)(1,4). Find yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0033 marksL1 FoundationNon-calculatorFinding the curve
dydx=4x−1\dfrac{dy}{dx}=4x-1, and the curve passes through (2,5)(2,5). Find the constant of integration cc in y=2x2−x+cy=2x^2-x+c.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0071 markL1 FoundationCalculatorApplying it
The curves y=x2+cy=x^2+c, for different values of cc, are
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN-0044 marksL2 StandardCalculatorFinding the curve
f′(x)=6x−4f'(x)=6x-4, and the curve y=f(x)y=f(x) passes through (1,5)(1,5). Find f(x)f(x).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0023 marksL2 StandardNon-calculatorApplying it
f′(x)=3x2f'(x)=3x^2 and f(0)=−2f(0)=-2. Find f(2)f(2).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0044 marksL2 StandardNon-calculatorFinding the curve
f′(x)=6xf'(x)=6\sqrt x and f(1)=1f(1)=1. Find f(x)f(x).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0054 marksL2 StandardNon-calculatorFinding the curve
dydx=2−1x2\dfrac{dy}{dx}=2-\dfrac1{x^2}, and the curve passes through (1,4)(1,4). Find yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0063 marksL2 StandardNon-calculatorApplying it
A particle moves so that dsdt=3t2+2\dfrac{ds}{dt}=3t^2+2, where ss metres is its displacement at time tt seconds, and s=0s=0 when t=0t=0. Find ss when t=2t=2.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN-0055 marksL3 ExamCalculatorFinding the curve
dydx=3x12−2\dfrac{dy}{dx}=3x^{\frac12}-2, and the curve passes through (4,10)(4,10). Find yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN-0065 marksL3 ExamCalculatorApplying it
f′(x)=4x2+1f'(x)=\dfrac4{x^2}+1, and the curve y=f(x)y=f(x) passes through (2,3)(2,3). Find f(4)f(4).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN-0074 marksL3 ExamCalculatorApplying it
The gradient of a curve is 2x+k2x+k. The curve passes through (0,1)(0,1) and (2,3)(2,3). Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN-0096 marksL4 ChallengingCalculatorFinding the curve
f′(x)=x2−42xf'(x)=\dfrac{x^2-4}{2\sqrt x} for x>0x>0, and the curve y=f(x)y=f(x) passes through (4,0)(4,0). Find f(x)f(x).

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Salam Academy Original Practice · Proposed mark scheme