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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-DF-0042 marksL1 FoundationCalculatorSecond derivatives
f(x)=x3−4xf(x)=x^3-4x. Find f′′(2)f''(2).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF-0052 marksL1 FoundationCalculatorGradients
Find the gradient of y=x3−3x2+2y=x^3-3x^2+2 at the point where x=−1x=-1.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0012 marksL1 FoundationNon-calculatorGradients
Find the gradient of y=2x3y=2x^3 at the point where x=−1x=-1.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0022 marksL1 FoundationNon-calculatorSecond derivatives
f(x)=x4f(x)=x^4. Find f′′(1)f''(1).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0031 markL1 FoundationNon-calculatorSecond derivatives
Given y=5x2−3xy=5x^2-3x, find d2ydx2\dfrac{d^2y}{dx^2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0042 marksL1 FoundationNon-calculatorGradients
Find the xx-coordinate of the point on y=x2−6xy=x^2-6x where the gradient is zero.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF-0063 marksL2 StandardCalculatorGradients
Find the xx-coordinates of the points on y=x3−3x2y=x^3-3x^2 where the gradient is 99.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0052 marksL2 StandardNon-calculatorSecond derivatives
f(x)=1xf(x)=\dfrac1x. Find f′′(1)f''(1).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0063 marksL2 StandardNon-calculatorGradients
The curve y=x3+kxy=x^3+kx has gradient 77 at x=1x=1. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0072 marksL2 StandardNon-calculatorGradients
f(x)=2xf(x)=2\sqrt x. Find f′(4)f'(4).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF2-0082 marksL2 StandardNon-calculatorGradients
The volume of water in a tank is V=t3+2tV=t^3+2t litres after tt minutes. Find the rate at which the volume is increasing when t=2t=2, in litres per minute.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-DF-0115 marksL4 ChallengingCalculatorGradients
A curve has equation y=ax2+bxy=ax^2+bx. Its gradient is 55 at x=1x=1 and 1111 at x=2x=2. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme