Practise questions | Salam Academy

SA-FP-VI-0042 marksL2 StandardCalculatorVolumes

y=\sqrt x

,

0\le x\le4

, is rotated about the

x

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

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SA-FP-VP-0012 marksL2 StandardNon-calculatorPlanes

The plane through

(1,2,3)

with normal

\begin{pmatrix}2\\-1\\1\end{pmatrix}

is

2x-y+z=d

. Find

d

.

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SA-FP-VP-0023 marksL2 StandardNon-calculatorIntersections

Find the

x

-coordinate where

\mathbf r=\begin{pmatrix}1\\0\\2\end{pmatrix}+t\begin{pmatrix}1\\1\\1\end{pmatrix}

meets

x+2y+z=11

.

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SA-IAL-M1-DY-0034 marksL2 StandardCalculatorFriction

A box of mass

5

kg is pulled along rough horizontal ground by a horizontal force of

30

N. The coefficient of friction is

0.4

. Find the acceleration.

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SA-IAL-M1-DY1-0062 marksL2 StandardNon-calculatorF = ma

A car of mass

1000

kg experiences a resistance of

400

N. Find the driving force needed for an acceleration of

1.5

m s⁻².

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SA-IAL-M1-DY2-0022 marksL2 StandardCalculatorFriction

A

6

kg block rests on rough horizontal ground (

\mu=0.3

). A horizontal force of

10

N acts on it. Find the friction force.

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SA-IAL-M1-DY2-0042 marksL2 StandardCalculatorFriction

A puck slides across rough horizontal ice with

\mu=0.2

and no other horizontal forces. Find its deceleration.

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SA-IAL-M1-DY2-0053 marksL2 StandardCalculatorFriction

A

5

kg block is pulled by a horizontal

30

N force across rough ground and accelerates at

2

m s⁻². Find

\mu

, to 3 significant figures.

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SA-IAL-M1-DY3-0023 marksL2 StandardNon-calculatorTowing

A

1000

kg car tows an

800

kg caravan with a light horizontal tow bar. The driving force is

2700

N and resistances are ignored. Find (i) the acceleration (ii) the tension in the tow bar.

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SA-IAL-M1-DY3-0042 marksL2 StandardCalculatorPulleys

For the

4

kg and

6

kg particles over a smooth pulley (acceleration

1.96

m s⁻²), find the tension in the string.

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SA-IAL-M1-DY4-0032 marksL2 StandardNon-calculatorImpulse

A ball of mass

0.5

kg hits the floor at

6

m s⁻¹ and rebounds at

4

m s⁻¹. Find the magnitude of the impulse from the floor.

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SA-IAL-M1-KM-0044 marksL2 StandardCalculatorFalling

A stone is dropped from rest from a height of

20

m. Find, to 3 significant figures, (i) the time it takes to reach the ground and (ii) its speed when it hits the ground.

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SA-IAL-M1-KM-0063 marksL2 StandardCalculatorv–t graphs

A car starts from rest and accelerates uniformly to

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

in

4

s. It travels at

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

for

10

s, then decelerates uniformly to rest in

6

s. Find the total distance travelled.

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SA-IAL-M1-ST-0043 marksL2 StandardCalculatorRough ground

A box of mass

4

kg rests on rough horizontal ground. A horizontal force of

15

N is applied and the box is on the point of slipping. Find the coefficient of friction, to 3 significant figures.

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SA-IAL-M1-ST-0052 marksL2 StandardCalculatorRough slopes

A block rests on a rough plane inclined at angle

\alpha

, where

\tan\alpha=\tfrac34

. It is on the point of slipping down. Find the coefficient of friction.

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SA-IAL-M1-ST2-0021 markL2 StandardCalculatorRough ground

A

5

kg box rests on rough ground with

\mu=0.5

. A horizontal force of

20

N acts on it. What happens?

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SA-IAL-P1-AL-0022 marksL2 StandardCalculatorIndices

Write

\dfrac{x^2\sqrt x}{x^{-1}}

as a single power of

x

.

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SA-IAL-P1-AL-0063 marksL2 StandardCalculatorDiscriminant

The equation

x^2+kx+9=0

, where

k>0

, has equal roots. Find

k

.

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SA-IAL-P1-AL-0073 marksL2 StandardCalculatorDiscriminant

The equation

2x^2+4x+k=0

has two distinct real roots. This is true exactly when

k<c

. Find

c

.

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SA-IAL-P1-AL-0132 marksL2 StandardCalculatorTransformations

The curve

y=f(x)

has a maximum point at

(2,5)

. Write down the coordinates of the maximum point of

y=f(x+3)

.

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