Practise questions | Salam Academy

SA-9709-P4-MO3-0023 marksL2 StandardCalculatorDirections

Particle

A

(

1

kg) at

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

and particle

B

(

2

kg) at

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

move towards each other. After the collision

A

rebounds at

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

. Find the velocity of

B

after the collision, taking

A

's original direction as positive.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL-0024 marksL2 StandardCalculatorLifts

A lift of mass

500

kg carries a passenger of mass

70

kg and accelerates upwards at

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

. Find the tension in the lift cable and the force of the floor on the passenger.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL-0034 marksL2 StandardCalculatorSlopes

A block of mass

5

kg slides down a plane inclined at

30^\circ

. Find its acceleration if the plane is smooth, and if it is rough with

\mu=0.2

(3 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL-0064 marksL2 StandardCalculatorConnected particles

A

4

kg block on a smooth horizontal table is connected by a string over a smooth pulley at the edge to a

1

kg mass hanging freely. Find the acceleration and the tension.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL1-0023 marksL2 StandardCalculatorF = ma

A car of mass

900

kg accelerates uniformly from rest to

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

in

10

s. The resistance to motion is

400

N. Find the driving force.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL1-0063 marksL2 StandardCalculatorF = ma

A car of mass

1500

kg travelling at

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

brakes with a constant force and stops in

50

m. Find the braking force.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL2-0034 marksL2 StandardCalculatorSlopes

A block of mass

6

kg slides down a rough plane inclined at

25^\circ

. The coefficient of friction is

0.3

. Find its acceleration, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL2-0044 marksL2 StandardCalculatorSlopes and suvat

A particle is released from rest on a smooth plane inclined at

30^\circ

and slides

10

m down the plane. Find its speed and the time taken.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL3-0035 marksL2 StandardCalculatorConnected particles

A

5

kg block on a rough horizontal table, with

\mu=0.2

, is connected by a light string over a smooth pulley at the edge to a

3

kg particle hanging freely. Find the acceleration and the tension.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-NL4-0043 marksL2 StandardCalculatorLifts

A person of mass

60

kg stands on scales in a lift. The scales read

720

N. Find the size of the lift's acceleration and say whether it is upwards or downwards (give the acceleration as positive if upwards).

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DR-0024 marksL2 StandardCalculatorCoding

For

12

values of

x

,

\Sigma(x-50)=36

and

\Sigma(x-50)^2=420

. Find the mean and the standard deviation of

x

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DR-0122 marksL2 StandardCalculatorHistograms

Marks are whole numbers. The class

10

–

19

contains

25

students. Find the frequency density for this class.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DR1-0023 marksL2 StandardCalculatorDisplays

A stem-and-leaf diagram (key

2\,|\,3

means

23

) has the rows

1\,|\,2\ 5\ 7

,

\ 2\,|\,0\ 3\ 3\ 8

,

\ 3\,|\,1\ 4\ 6\ 9

. Find the median and the interquartile range.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DR1-0032 marksL2 StandardCalculatorDisplays

A data set has

Q_1=20

and

Q_3=32

. An outlier is defined as a value more than

1.5\times

IQR above

Q_3

or below

Q_1

. Find the value above which a data point is an outlier.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DR2-0022 marksL2 StandardCalculatorHistograms

A histogram has bars over

0\le x<10

with frequency density

1.5

,

10\le x<15

with density

4

, and

15\le x<30

with density

2

. Find the total frequency.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DR4-0022 marksL2 StandardCalculatorCoding

The coded values

y=\dfrac{x-50}{10}

have mean

2.4

and standard deviation

0.8

. Find the mean and standard deviation of

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV-0043 marksL2 StandardCalculatorBinomial

X\sim B(8,0.25)

. Find

P(X\le2)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV-0092 marksL2 StandardCalculatorGeometric

X\sim\text{Geo}(0.3)

. Find

P(X>3)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV2-0023 marksL2 StandardCalculatorE(X) and Var(X)

For the same

X

(values

1,2,3

with probabilities

0.5,\ 0.3,\ 0.2

,

E(X)=1.7

), find

\text{Var}(X)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV3-0063 marksL2 StandardCalculatorBinomial

A multiple-choice test has

8

questions, each with

4

options. A student guesses every answer at random. Find the probability that exactly

3

answers are correct (3 s.f.).

Salam Academy Original Practice · Proposed mark scheme

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