Practise

Question bank

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

TopicSkillDifficulty

14 questions

SA-9709-P3-D35-G013 marksL1 FoundationCalculatorTangents and normals

Find the equation of the tangent to

y=\ln x

at the point where

x=1

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D35-Q011 markL1 FoundationCalculatorExact answers

How many solutions does

e^{3x}=0

have?

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SA-9709-P2-DF-0083 marksL2 StandardCalculatorTangents and normals

Find the equation of the tangent to

y=e^{2x}

at the point where

x=0

. Give your answer in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D35-0013 marksL2 StandardCalculatorStationary points

Find the

x

-coordinate of the stationary point of

y=xe^{2x}

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SA-9709-P3-D35-0033 marksL2 StandardCalculatorTangents and normals

Find the equation of the normal to

y=e^x

at the point

(0,1)

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D35-0043 marksL2 StandardCalculatorStationary points

Find the exact value of

x

, for

0<x<\dfrac{\pi}{2}

, at which

y=\sin x+\cos x

has a stationary point.

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SA-9709-P3-DF-0144 marksL2 StandardCalculatorStationary points

Find the exact coordinates of the stationary point of

y=xe^{-x}

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SA-9709-P2-DF-0065 marksL3 ExamCalculatorStationary points

Find the exact coordinates of the stationary point of the curve

y=x\ln x

, for

x>0

, and state whether it is a maximum or a minimum.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0074 marksL3 ExamCalculatorStationary points

Find the

x

-coordinate of the stationary point of

y=e^x\cos x

for

0<x<\pi

. Give your answer exactly.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0094 marksL3 ExamCalculatorTangents and normals

Find the equation of the normal to

y=\ln(3x-2)

at the point where

x=1

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D35-0024 marksL3 ExamCalculatorExact answers

Find the exact coordinates of the stationary point of

y=x^2e^{-x}

for

x>0

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0074 marksL3 ExamCalculatorExact answers

Find the exact coordinates of the stationary point of

y=\dfrac{\ln x}{x}

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SA-9709-P3-DF-0154 marksL3 ExamCalculatorStationary points

Find the exact

x

-coordinate of the stationary point of

y=e^x\sin x

in the interval

0<x<\pi

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D35-0054 marksL4 ChallengingCalculatorExact answers

Find the exact

x

-coordinate of the stationary point of

y=\dfrac{\ln x}{x^2}

Salam Academy Original Practice · Proposed mark scheme