Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

15 questions

SA-9709-P3-D32-0022 marksL1 FoundationCalculatorProduct rule

Differentiate

x\sin x

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D32-Q011 markL1 FoundationCalculatorQuotient rule

For

y=\dfrac uv

\dfrac{dy}{dx}

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SA-9709-P3-DF-0042 marksL1 FoundationCalculatorProduct rule

Find

\dfrac{dy}{dx}

when

y=x\ln x

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SA-9709-P3-DF-Q021 markL1 FoundationCalculatorProduct rule

For

y=uv

\dfrac{dy}{dx}

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SA-9709-P2-DF-0013 marksL2 StandardCalculatorProduct rule

Differentiate

y=x^2e^{2x}

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0023 marksL2 StandardCalculatorQuotient rule

Differentiate

y=\dfrac{\sin3x}{x}

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0053 marksL2 StandardCalculatorQuotient rule

Differentiate

y=\dfrac{2x+1}{x-3}

, giving your answer as a single fraction.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D32-0012 marksL2 StandardCalculatorProduct rule

Differentiate

x^3\ln x

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D32-0032 marksL2 StandardCalculatorQuotient rule

Differentiate

\dfrac{e^x}{x}

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D32-0043 marksL2 StandardCalculatorQuotient rule

Differentiate

\dfrac{x^2}{x+1}

with respect to

x

, giving your answer as a single fraction.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D32-0051 markL2 StandardCalculatorQuotient rule

Applying the quotient rule to

\dfrac{\sin x}{\cos x}

gives

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SA-9709-P3-DF-0033 marksL2 StandardCalculatorProduct rule

Find

\dfrac{dy}{dx}

when

y=x^2e^{3x}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0062 marksL2 StandardCalculatorQuotient rule

Find

\dfrac{dy}{dx}

when

y=\dfrac{\sin x}{x}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0182 marksL2 StandardCalculatorQuotient rule

Given that

\dfrac{d}{dx}(\sec x)=\sec x\tan x

, differentiate

\sec2x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0194 marksL3 ExamCalculatorSimplifying

Find the

x

-coordinate of the stationary point of

y=\dfrac{e^{2x}}{x+1}

x\neq-1

Salam Academy Original Practice · Proposed mark scheme