Practise

Question bank

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

12 questions

SA-FP-MAC-0011 markL1 FoundationNon-calculatorStandard series

State the coefficient of

x^3

in the Maclaurin series of

\sin x

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SA-FP-MAC-G012 marksL1 FoundationNon-calculatorStandard series

Find the coefficient of

x^2

in the Maclaurin series of

e^{3x}

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SA-FP-MAC-Q011 markL1 FoundationNon-calculatorDeriving

The

x^n

coefficient in a Maclaurin series is

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SA-FP-MAC-X011 markL1 FoundationNon-calculatorStandard series

Find the coefficient of

x^3

in the Maclaurin series of

e^x

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SA-FP-MAC-X021 markL1 FoundationNon-calculatorStandard series

Find the coefficient of

x^2

in the Maclaurin series of

\cos x

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SA-FP-MAC-X031 markL1 FoundationNon-calculatorStandard series

Find the coefficient of

x^3

in the series for

\ln(1+x)

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SA-FP-MAC-X051 markL1 FoundationNon-calculatorApplications

Use

e^x\approx1+x+\frac{x^2}2

to estimate

e^{0.1}

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SA-FP-MAC-0022 marksL2 StandardNon-calculatorDeriving

Find the coefficient of

x^3

in the series for

\ln(1+x)

by differentiation (

f'''(0)/3!

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SA-FP-MAC-0042 marksL2 StandardNon-calculatorApplications

Use

\cos x\approx1-\frac{x^2}2

to estimate

\cos0.2

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SA-FP-MAC-X042 marksL2 StandardNon-calculatorApplications

Find the coefficient of

x^2

in the Maclaurin series of

e^{2x}

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SA-FP-MAC-0033 marksL3 ExamNon-calculatorStandard series

Find the coefficient of

x^3

in the series for

e^x\sin x

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SA-FP-MAC-0053 marksL4 ChallengingNon-calculatorApplications

Use series to find

\displaystyle\lim_{x\to0}\frac{x-\sin x}{x^3}

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