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 112 of 137 · choose a topic above to narrow them down

SA-FM-C1-0043 marksL2 StandardNon-calculatorRestitution

Two identical spheres collide head-on, each at

4

m s

^{-1}

, with

e=\frac12

. Find the speed of each afterwards.

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SA-FM-C2-0012 marksL2 StandardCalculatorOblique wall

With

e=\frac13

in the last question, find the angle (degrees) between the rebound direction and the wall.

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SA-FM-C2-0022 marksL2 StandardCalculatorOblique wall

Find the rebound speed in the same situation (3 s.f.).

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SA-FM-CL-0012 marksL2 StandardNon-calculatorParticles

Masses

2

3

5

kg at

(0,0)

(4,0)

(2,6)

. Find

\bar x

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SA-FM-CL-0023 marksL2 StandardNon-calculatorComposite laminas

An L-shape is made from a

4\times2

rectangle occupying

0\le x\le4

0\le y\le2

and a

2\times2

square occupying

0\le x\le2

2\le y\le4

. Find

\bar x

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SA-FM-CL-0041 markL2 StandardNon-calculatorComposite laminas

A uniform triangular lamina has height

9

cm above its base. How far above the base is its centre of mass?

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SA-FM-CS-0012 marksL2 StandardNon-calculatorSolids

A solid cone has height

12

cm. How far is its centre of mass from its base?

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SA-FM-CS-0021 markL2 StandardNon-calculatorSolids

A solid hemisphere has radius

8

cm. How far is its centre of mass from the flat face?

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SA-FM-CS-G013 marksL2 StandardNon-calculatorLaminas by integration

Find

\bar x

for the uniform lamina under

y=x^2

0\le x\le2

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SA-FM-EL-0012 marksL2 StandardCalculatorHooke's law

2

kg particle hangs in equilibrium on an elastic string of natural length

1.5

m and modulus

49

N. Find the extension in metres (

g=9.8

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SA-FM-EL-0032 marksL2 StandardCalculatorEnergy problems

The spring in the last question launches a

0.2

kg ball along a smooth table. Find its speed in m s

^{-1}

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SA-FM-EL-0042 marksL2 StandardCalculatorHooke's law

A string of natural length

0.8

m stretches to

1

m when a

0.5

kg mass hangs from it. Find the modulus

\lambda

(

g=9.8

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SA-FM-FK-0012 marksL2 StandardCalculatorVectors

For the same particle, find the speed at

t=1

(3 s.f.).

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SA-FM-FK-0021 markL2 StandardNon-calculatorVectors

For the same particle, find the

\mathbf j

-component of acceleration.

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SA-FM-RB-0012 marksL2 StandardNon-calculatorConditions

The same rod has a

40

N load at

3

m from

A

. Find the reaction at

B

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SA-FM-VF-G013 marksL2 StandardNon-calculatorF(t), F(v)

2

kg particle starts from rest under force

F=6t

N. Find its speed at

t=2

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SA-FP-CE-0021 markL2 StandardNon-calculatorEccentricity

For the same ellipse, find the positive directrix

x=k

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SA-FP-CE-0032 marksL2 StandardNon-calculatorParametric forms

Find the positive gradient of the asymptotes of

\frac{x^2}{16}-\frac{y^2}9=1

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SA-FP-CE-G012 marksL2 StandardNon-calculatorEccentricity

Find the eccentricity of

\frac{x^2}{25}+\frac{y^2}9=1

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SA-FP-CP-0032 marksL2 StandardNon-calculatorTangents

Find the gradient of the tangent to

y^2=4ax

at the point with parameter

t=2

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