Practise

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

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2730 questions · page 113 of 137 · choose a topic above to narrow them down

SA-FP-CT-0012 marksL2 StandardNon-calculatorTransformations

Under

w=\frac1z

, the circle

|z|=2

maps to

|w|=r

. Find

r

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SA-FP-CT-0022 marksL2 StandardNon-calculatorLoci

The locus

|z-2|=|z+2i|

is the line

y=mx

. Find

m

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SA-FP-DE1-0042 marksL2 StandardNon-calculatorIntegrating factor

For

x\frac{dy}{dx}+3y=x^2

, which is the integrating factor?

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SA-FP-DE2-0012 marksL2 StandardNon-calculatorComplementary function

The general solution of

y''+4y=0

A\cos\omega x+B\sin\omega x

. Find

\omega

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SA-FP-DE2-0021 markL2 StandardNon-calculatorComplementary function

Find the repeated root of the auxiliary equation for

y''+2y'+y=0

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SA-FP-DE2-0032 marksL2 StandardNon-calculatorParticular integral

Find the constant particular integral of

y''-3y'+2y=4

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SA-FP-DM-0012 marksL2 StandardNon-calculatorPowers

Find

(1+i)^8

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SA-FP-DM-0022 marksL2 StandardNon-calculatorTrig identities

\cos3\theta=a\cos^3\theta+b\cos\theta

. Find

a

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SA-FP-DM-0041 markL2 StandardNon-calculatorRoots

Find the sum of all the roots of

z^7=1

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SA-FP-EIG-0022 marksL2 StandardNon-calculatorEigenvectors

\begin{pmatrix}1\\k\end{pmatrix}

is an eigenvector of

\begin{pmatrix}4&1\\2&3\end{pmatrix}

with eigenvalue

2

. Find

k

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SA-FP-EIG-G012 marksL2 StandardNon-calculatorEigenvalues

Find the eigenvalues of

\begin{pmatrix}4&1\\2&3\end{pmatrix}

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SA-FP-GR-0021 markL2 StandardNon-calculatorOrders

Find the order of

2

(\mathbb Z_{10},+_{10})

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SA-FP-GR-0032 marksL2 StandardNon-calculatorSubgroups

A group has order

12

. How many different orders are possible for its subgroups (including trivial and whole group)?

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SA-FP-GR-0042 marksL2 StandardNon-calculatorOrders

How many generators does the cyclic group

(\mathbb Z_8,+_8)

have?

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SA-FP-GR-G012 marksL2 StandardNon-calculatorOrders

Find the order of

3

in the group

\{1,2,3,4,5,6\}

under multiplication mod

7

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SA-FP-HYP-0012 marksL2 StandardNon-calculatorDefinitions

Find the exact value of

\sinh(\ln2)

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SA-FP-HYP-0022 marksL2 StandardNon-calculatorIdentities

Given

\sinh x=\frac34

, find

\tanh x

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SA-FP-HYP-0042 marksL2 StandardNon-calculatorInverses and equations

Find the exact value of

e^{\operatorname{arsinh}(3/4)}

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SA-FP-IC-0012 marksL2 StandardNon-calculatorDifferentiating

Find

\frac{d}{dx}\arctan(2x)

x=0

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SA-FP-IC-0022 marksL2 StandardCalculatorDifferentiating

Find the gradient of

y=\operatorname{arcosh}x

x=2

(to 3 s.f.).

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