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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2506 questions · page 46 of 126 · choose a topic above to narrow them down

SA-FP-TF-0012 marksL1 FoundationNon-calculatorIdentities

t=\frac12

, find

\cos x

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SA-FP-TF-0021 markL1 FoundationNon-calculatorIntegrals

With

t=\tan\frac x2

\frac{dx}{dt}=\frac{k}{1+t^2}

. Find

k

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SA-FP-TF-G011 markL1 FoundationNon-calculatorIdentities

t=\tan\frac x2=1

, find

\sin x

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SA-FP-TL-0021 markL1 FoundationNon-calculatorLimits

Find

\displaystyle\lim_{x\to0}\frac{\sin3x}{x}

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SA-FP-TL-G011 markL1 FoundationNon-calculatorTaylor series

In the Taylor series of

\ln x

about

x=1

, find the coefficient of

(x-1)

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SA-FP-VD-G012 marksL1 FoundationNon-calculatorPoint distances

Find the distance from the origin to the plane

2x+y+2z=9

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SA-FP-VI-G012 marksL1 FoundationCalculatorVolumes

The line

y=x

for

0\le x\le3

is rotated

2\pi

about the

x

-axis. Find the volume (to 3 s.f.).

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SA-FP-VP-G012 marksL1 FoundationNon-calculatorCross product

Find the

x

-component of

\begin{pmatrix}1\\2\\3\end{pmatrix}\times\begin{pmatrix}0\\1\\4\end{pmatrix}

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SA-IAL-M1-DY-0012 marksL1 FoundationCalculatorF = ma

A car of mass

1200

kg has a driving force of

3000

N and experiences a resistance of

600

N. Find its acceleration.

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SA-IAL-M1-DY-0102 marksL1 FoundationCalculatorImpulse

A ball of mass

0.2

kg hits a wall at

15\ \text{m s}^{-1}

and rebounds at

10\ \text{m s}^{-1}

. Find the magnitude of the impulse on the ball.

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SA-IAL-M1-DY1-0011 markL1 FoundationNon-calculatorF = ma

Find the resultant force needed to give a

2

kg particle an acceleration of

3

m s⁻².

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SA-IAL-M1-DY1-0021 markL1 FoundationNon-calculatorF = ma

A resultant force of

20

N gives a particle an acceleration of

4

m s⁻². Find its mass.

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SA-IAL-M1-DY2-0012 marksL1 FoundationCalculatorFriction

4

kg block rests on rough horizontal ground with

\mu=0.5

. Find the maximum possible friction force.

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SA-IAL-M1-DY3-0013 marksL1 FoundationNon-calculatorTowing

Particles of mass

2

kg and

3

kg lie on a smooth horizontal surface, joined by a light inextensible string. A horizontal force of

10

N pulls the

3

kg particle away from the

2

kg one. Find (i) the acceleration (ii) the tension.

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SA-IAL-M1-DY3-0032 marksL1 FoundationCalculatorPulleys

Particles of mass

4

kg and

6

kg hang on either side of a smooth pulley, connected by a light inextensible string. Find the acceleration.

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SA-IAL-M1-DY4-0011 markL1 FoundationNon-calculatorImpulse

Find the momentum of a

3

kg particle moving at

4

m s⁻¹.

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SA-IAL-M1-DY4-0022 marksL1 FoundationNon-calculatorImpulse

2

kg particle speeds up from

3

m s⁻¹ to

8

m s⁻¹ in the same direction. Find the impulse on it.

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SA-IAL-M1-DY4-0061 markL1 FoundationNon-calculatorImpulse

A constant force of

6

N acts on a particle for

3

s. Find the impulse.

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SA-IAL-M1-DY-G012 marksL1 FoundationCalculatorF = ma

A resultant force of

12

N acts on a particle of mass

3

kg. Find its acceleration.

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SA-IAL-M1-KM-0013 marksL1 FoundationCalculatorsuvat

A cyclist moving at

20\ \text{m s}^{-1}

brakes with constant deceleration

2.5\ \text{m s}^{-2}

until she stops. Find the distance she travels while braking.

Salam Academy Original Practice · Proposed mark scheme