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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2730 questions · page 68 of 137 · choose a topic above to narrow them down

SA-PX-VI-0021 markL1 FoundationCalculatorStokes’ law

A ball of volume

4.0\times10^{-6}

m³ is fully submerged in water (

\rho=1000

kg m⁻³). Calculate the upthrust in N. (

g=9.81

N kg⁻¹)

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SA-PX-VI-0041 markL1 FoundationCalculatorViscosity

In laminar flow

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SA-PX-VI-0051 markL1 FoundationCalculatorViscosity

As a liquid such as oil is heated, its viscosity

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SA-ST-CS-0011 markL1 FoundationNon-calculatorStatistic

How many degrees of freedom does the die test have?

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SA-ST-CS-0031 markL1 FoundationNon-calculatorContingency

Find the degrees of freedom for a

3\times4

contingency table.

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SA-ST-EX-0011 markL1 FoundationNon-calculatorMean and memory

Find the variance of

X\sim\text{Exp}(4)

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SA-ST-NP-0011 markL1 FoundationNon-calculatorWilcoxon

For a Wilcoxon signed-rank test with

n=8

, find

P+Q

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SA-ST-PG-0011 markL1 FoundationNon-calculatorDefinition

For

G(t)=\frac14(1+2t+t^2)

, find

P(X=1)

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SA-ST-PG-G012 marksL1 FoundationNon-calculatorDefinition

G(t)=k(1+2t+t^2)

is a PGF. Find

k

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SA-ST-SA-0011 markL1 FoundationNon-calculatorMethods

For a systematic sample of 20 from a list of 400, what is the interval

k

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SA-ST-SA-0031 markL1 FoundationNon-calculatorKey terms

A list of every member of the population from which a sample is drawn is called

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SA-ST-SA-G012 marksL1 FoundationNon-calculatorMethods

A school has 360 boys and 240 girls. How many boys should be in a stratified sample of 50?

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SA-ST-TD-G011 markL1 FoundationNon-calculatorIntervals

How many degrees of freedom are used for a

t

-interval from a sample of 12?

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SA-VM-0012 marksL1 FoundationCalculatorMagnitude & direction

A particle moves with velocity

(3\mathbf i+4\mathbf j)\ \text{m s}^{-1}

. Find the angle between its direction of motion and

\mathbf i

, in degrees to 1 decimal place.

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SA-VM-0032 marksL1 FoundationCalculatorPosition

A particle starts at the point with position vector

(2\mathbf i+\mathbf j)

m and moves with constant velocity

(3\mathbf i-2\mathbf j)\ \text{m s}^{-1}

. Its position after

4

s is

(p\mathbf i+q\mathbf j)

m. Find

p

and

q

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SA-VM1-0011 markL1 FoundationNon-calculatorMagnitude & direction

Find the magnitude of

(-8\mathbf i+6\mathbf j)

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SA-VM1-0032 marksL1 FoundationNon-calculatorVector forces

Forces

(3\mathbf i+\mathbf j)

(-\mathbf i+4\mathbf j)

N and

(2\mathbf i-2\mathbf j)

N act on a particle. The resultant is

(p\mathbf i+q\mathbf j)

N. Find

p

and

q

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SA-VM2-0012 marksL1 FoundationNon-calculatorPosition

A particle starts at

(4\mathbf i-\mathbf j)

m and moves with constant velocity

(2\mathbf i+3\mathbf j)

m s⁻¹. Its position after

5

s is

(p\mathbf i+q\mathbf j)

m. Find

p

and

q

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SA-VM2-0021 markL1 FoundationNon-calculatorVelocity & acceleration

A particle has velocity

(5\mathbf i-12\mathbf j)

m s⁻¹. Find its speed.

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SA-VM-G011 markL1 FoundationCalculatorMagnitude & direction

Find the magnitude of

5\mathbf i-12\mathbf j

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