Practise questions | Salam Academy

SA-PROOF2-0031 markL2 StandardNon-calculatorClassic proofs

In proving

\sqrt3

irrational, assume

\sqrt3=\dfrac ab

in lowest terms, so

a^2=3b^2

and

a=3c

. Substituting gives

9c^2=3b^2

, so

b^2=kc^2

. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-PROOF2-0041 markL2 StandardCalculatorThe assumption

To prove "if

n^2

is odd then

n

is odd" by contradiction, assume

n^2

is odd and

n

is even,

n=2k

. Which line gives the contradiction?

Salam Academy Original Practice · Proposed mark scheme

SA-PX-AC-0022 marksL2 StandardCalculatorCyclotrons

A proton moving at

1.0\times10^7

m s⁻¹ enters a

0.50

T magnetic field at right angles. Calculate the radius of its path in m. (

m_p=1.67\times10^{-27}

kg)

Salam Academy Original Practice · Proposed mark scheme

SA-PX-AC-0032 marksL2 StandardCalculatorCyclotrons

Calculate the frequency, in MHz, of the alternating supply in a cyclotron accelerating protons in a field of

1.0

T.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-AC-0051 markL2 StandardCalculatorDetectors

An electron's track in a detector has radius

0.10

m in a

0.010

T field. Calculate its momentum in units of

10^{-22}

kg m s⁻¹.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-DC-0021 markL2 StandardCalculatorModulation

An FM broadcast has frequency deviation

75

kHz and maximum signal frequency

15

kHz. Calculate its bandwidth in kHz.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-DC-0041 markL2 StandardCalculatorMedia

Eight telephone channels, each

64

kbit s⁻¹, share a link by time-division multiplexing. Calculate the minimum link bit rate in kbit s⁻¹.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-DL-0052 marksL2 StandardCalculatorCounters

A

1600

Hz clock drives a 4-bit binary counter. Calculate the frequency of the most significant output bit in Hz.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EA-0022 marksL2 StandardCalculatorDecibels

Calculate the intensity, in units of

10^{-4}

W m⁻², of an

80

dB sound.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EA-0031 markL2 StandardCalculatorDecibels

Two identical machines each produce an intensity level of

80

dB at a point. Calculate the total intensity level when both run.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EC-0051 markL2 StandardCalculatorECG traces

An ECG signal of

1.0

mV is amplified to

1.0

V. Calculate the voltage gain.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EL-0022 marksL2 StandardCalculatorCathode rays

Electrons are accelerated from rest through

1000

V. Using

\frac em=1.76\times10^{11}

C kg⁻¹, calculate their speed in units of

10^7

m s⁻¹.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EL-0032 marksL2 StandardCalculatorSpecific charge

With the electric field switched off, electrons at

2.0\times10^7

m s⁻¹ move in a circle of radius

0.114

m in a field of

1.0\times10^{-3}

T. Calculate

\frac em

in units of

10^{11}

C kg⁻¹.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EL-0042 marksL2 StandardCalculatorMillikan

An oil drop of mass

3.26\times10^{-15}

kg is held stationary between plates

10

mm apart with a p.d. of

1000

V. Calculate its charge in units of

10^{-19}

C.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EN-0032 marksL2 StandardCalculatorProcesses

Air (

\gamma=1.4

) at

1.0\times10^5

Pa is compressed adiabatically to half its volume. Calculate the final pressure in units of

10^5

Pa.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EN-0051 markL2 StandardCalculatorEfficiency

A heat pump delivers

3000

J of heat to a house for every

1000

J of work. Calculate its coefficient of performance.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EY-0022 marksL2 StandardCalculatorDefects

A short-sighted person has a far point of

2.0

m. Calculate the power of the lens needed to see distant objects clearly.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-NR-0032 marksL2 StandardCalculatorNuclear radius

A

5.0

MeV α particle is fired directly at a gold nucleus (

Z=79

). Using

\frac{e^2}{4\pi\varepsilon_0}=1.44

MeV fm, calculate the distance of closest approach in fm.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-OA-0042 marksL2 StandardCalculatorAmplifiers

A summing amplifier has

R_f=R_1=R_2=10

kΩ. Inputs are

1.0

V and

2.0

V. Calculate the output.

Salam Academy Original Practice · Proposed mark scheme

SA-PX-OA-0051 markL2 StandardCalculatorAmplifiers

An inverting amplifier with gain

-50

and supply

\pm12

V has an input of

0.40

V. State the output voltage.

Salam Academy Original Practice · Proposed mark scheme

Question bank