Motion, Forces and Energy Core Foundation Calculation 3 marks
Question 1 · Speed
A cyclist travels 1.8 km in 4.0 minutes. Calculate the average speed in m/s.
Paper style: Theory
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Worked answer
Convert 1.8 km to 1800 m and 4.0 min to 240 s. Average speed = 1800 / 240 = 7.5 m/s.
Original marking points
- ✓converts distance to 1800 m
- ✓converts time to 240 s
- ✓7.5 m/s
Motion, Forces and Energy Supplement Standard Graph and data 3 marks
Question 2 · Acceleration
The speed of a car increases uniformly from 6.0 m/s at 2.0 s to 24.0 m/s at 8.0 s. Calculate the acceleration represented by this section of the speed-time graph.
Paper style: Theory
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Worked answer
Acceleration is the gradient: (24.0 - 6.0) / (8.0 - 2.0) = 18.0 / 6.0 = 3.0 m/s².
Original marking points
- ✓uses change in speed divided by change in time
- ✓correct substitution
- ✓3.0 m/s²
Motion, Forces and Energy Core Standard Practical 4 marks
Question 3 · Density
Describe how to determine the density of an irregular metal object that sinks in water.
Paper style: Practical skills
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Worked answer
Measure the mass using a balance. Measure initial water volume in a measuring cylinder, fully submerge the object without trapped bubbles, and record the final volume. Object volume is the increase in water volume. Density = mass / volume.
Original marking points
- ✓measures mass with a balance
- ✓uses displacement to determine volume
- ✓object fully submerged with no trapped air
- ✓calculates mass divided by volume
Motion, Forces and Energy Core Standard Calculation 3 marks
Question 4 · Moments
A 30 N force acts 0.40 m from a pivot. What force acting 0.60 m on the opposite side produces equilibrium?
Paper style: Theory
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Worked answer
Clockwise moment = 30 × 0.40 = 12 N m. For equilibrium, F × 0.60 = 12, so F = 20 N.
Original marking points
- ✓calculates 12 N m
- ✓uses equal clockwise and anticlockwise moments
- ✓20 N
Motion, Forces and Energy Supplement Challenge Calculation 4 marks
Question 5 · Momentum
A 0.20 kg trolley moving at 3.0 m/s collides with a stationary 0.30 kg trolley. They join together. Calculate their common speed.
Paper style: Theory
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Worked answer
Initial momentum = 0.20 × 3.0 = 0.60 kg m/s. Combined mass = 0.50 kg. By conservation of momentum, common speed = 0.60 / 0.50 = 1.2 m/s.
Original marking points
- ✓calculates initial momentum
- ✓uses combined mass 0.50 kg
- ✓applies conservation of momentum
- ✓1.2 m/s
Motion, Forces and Energy Supplement Standard Calculation 3 marks
Question 6 · Efficiency
A pump receives 750 J and transfers 510 J usefully to gravitational potential energy. Calculate its efficiency.
Paper style: Theory
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Worked answer
Efficiency = useful output / total input × 100% = 510 / 750 × 100% = 68%.
Original marking points
- ✓uses useful output divided by total input
- ✓correct substitution
- ✓68%
Thermal Physics Core Foundation Calculation 2 marks
Question 7 · Kelvin scale
Convert -18 °C to kelvin.
Paper style: Theory
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Worked answer
T = θ + 273 = -18 + 273 = 255 K.
Original marking points
Thermal Physics Core Standard Explanation 3 marks
Question 8 · Gas pressure
A fixed mass of gas is heated in a rigid sealed container. Explain why its pressure increases.
Paper style: Theory
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Worked answer
The particles gain kinetic energy and move faster. They collide with the container walls more frequently and with a greater change of momentum, increasing the force on the walls. The wall area is unchanged, so pressure increases.
Original marking points
- ✓particles move faster or gain kinetic energy
- ✓wall collisions become more frequent and/or produce greater force
- ✓greater force per unit area means greater pressure
Thermal Physics Supplement Standard Calculation 3 marks
Question 9 · Gas law
A gas occupies 80 cm³ at 120 kPa. Its temperature is kept constant while the pressure increases to 200 kPa. Calculate the new volume.
Paper style: Theory
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Worked answer
p1V1 = p2V2. V2 = 120 × 80 / 200 = 48 cm³.
Original marking points
- ✓uses p1V1 = p2V2
- ✓correct rearrangement and substitution
- ✓48 cm³
Thermal Physics Supplement Challenge Calculation 4 marks
Question 10 · Specific heat capacity
A 0.40 kg metal block receives 9.6 kJ of energy and its temperature rises by 30 °C. Calculate its specific heat capacity.
Paper style: Theory
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Worked answer
Convert 9.6 kJ to 9600 J. c = ΔE / (mΔθ) = 9600 / (0.40 × 30) = 800 J/(kg °C).
Original marking points
- ✓converts 9.6 kJ to 9600 J
- ✓uses c = ΔE/(mΔθ)
- ✓correct substitution
- ✓800 J/(kg °C)
Thermal Physics Core Standard Explanation 3 marks
Question 11 · Evaporation
Explain why evaporation can cool the liquid that remains.
Paper style: Theory
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Worked answer
The more energetic particles escape from the surface. The particles left behind have a lower average kinetic energy, so the liquid's temperature falls.
Original marking points
- ✓more energetic particles escape
- ✓average kinetic energy of remaining particles decreases
- ✓temperature decreases
Thermal Physics Supplement Standard Explanation 4 marks
Question 12 · Thermal expansion
Equal initial volumes of a solid, liquid and gas are heated through the same temperature rise at constant pressure. State the expansion order and explain it using particles.
Paper style: Theory
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Worked answer
The solid expands least, then the liquid, and the gas expands most. Solid particles are closely packed and constrained, liquid particles are less rigidly arranged, and gas particles are widely separated and move freely, so their average separation can increase most.
Original marking points
- ✓correct order: solid, liquid, gas
- ✓solid particles constrained and closely packed
- ✓liquid less rigidly arranged
- ✓gas widely separated/free to move
Waves Core Foundation Calculation 3 marks
Question 13 · Wave speed
A wave has frequency 12 Hz and wavelength 0.75 m. Calculate its speed.
Paper style: Theory
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Worked answer
v = fλ = 12 × 0.75 = 9.0 m/s.
Original marking points
- ✓uses v = fλ
- ✓correct substitution
- ✓9.0 m/s
Waves Core Foundation Recall 2 marks
Question 14 · Reflection
A ray strikes a plane mirror at an angle of 34° to the normal. State the angle of reflection and the law used.
Paper style: Theory
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Worked answer
The angle of reflection is 34°. The angle of incidence equals the angle of reflection.
Original marking points
- ✓34°
- ✓states i = r or equivalent law
Waves Supplement Standard Calculation 3 marks
Question 15 · Refraction
Light travels from air into glass. The angle of incidence is 50° and the angle of refraction is 30°. Calculate the refractive index of the glass.
Paper style: Theory
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Worked answer
n = sin i / sin r = sin 50° / sin 30° = 1.53.
Original marking points
- ✓uses n = sin i / sin r
- ✓correct angle substitution
- ✓1.53 or suitable rounding
Waves Supplement Standard Calculation 3 marks
Question 16 · Critical angle
A transparent material has refractive index 1.60. Calculate its critical angle.
Paper style: Theory
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Worked answer
n = 1 / sin c, so sin c = 1 / 1.60. c = sin⁻¹(0.625) = 38.7°, approximately 39°.
Original marking points
- ✓uses n = 1/sin c
- ✓correct inverse-sine method
- ✓about 39°
Waves Core Standard Explanation 3 marks
Question 17 · Electromagnetic spectrum
Choose a region of the electromagnetic spectrum used for satellite communication and explain one reason it is suitable.
Paper style: Theory
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Worked answer
Microwaves are suitable because they can pass through the atmosphere and carry information. A complete response must name the region and link a relevant property to the application.
Original marking points
- ✓microwaves
- ✓relevant property such as atmospheric transmission
- ✓links the property to communication
Waves Core Standard Calculation 4 marks
Question 18 · Sound
A student stands 170 m from a cliff and hears an echo 1.0 s after making a sharp sound. Calculate the speed of sound and explain why the distance used is not 170 m.
Paper style: Practical skills
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Worked answer
The sound travels to the cliff and back, so total distance = 340 m. Speed = 340 / 1.0 = 340 m/s.
Original marking points
- ✓states the sound travels there and back
- ✓uses total distance 340 m
- ✓uses speed = distance/time
- ✓340 m/s
Electricity and Magnetism Core Foundation Calculation 3 marks
Question 19 · Resistance
A resistor has a potential difference of 6.0 V and a current of 0.25 A. Calculate its resistance.
Paper style: Theory
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Worked answer
R = V/I = 6.0 / 0.25 = 24 Ω.
Original marking points
- ✓uses R = V/I
- ✓correct substitution
- ✓24 Ω
Electricity and Magnetism Supplement Standard Calculation 3 marks
Question 20 · Electric current
A charge of 180 C passes a point in a circuit in 2.0 minutes. Calculate the current.
Paper style: Theory
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Worked answer
Convert 2.0 min to 120 s. I = Q/t = 180 / 120 = 1.5 A.
Original marking points
- ✓converts time to 120 s
- ✓uses I = Q/t
- ✓1.5 A
Electricity and Magnetism Supplement Standard Graph and data 3 marks
Question 21 · Diodes and LEDs
Describe the current-voltage characteristic of a diode in the forward and reverse directions.
Paper style: Theory
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Worked answer
In the forward direction, little current flows at first and then current rises rapidly after sufficient forward potential difference. In the reverse direction, current is approximately zero over the range considered.
Original marking points
- ✓little forward current initially
- ✓rapid forward-current rise
- ✓approximately zero reverse current
Electricity and Magnetism Core Standard Calculation 3 marks
Question 22 · Series circuits
Three resistors of 4.0 Ω, 7.0 Ω and 9.0 Ω are connected in series to a 10 V supply. Calculate the circuit current.
Paper style: Theory
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Worked answer
Total resistance = 4.0 + 7.0 + 9.0 = 20 Ω. Current = V/R = 10 / 20 = 0.50 A.
Original marking points
- ✓total resistance 20 Ω
- ✓uses I = V/R
- ✓0.50 A
Electricity and Magnetism Core Standard Calculation 3 marks
Question 23 · Transformers
A transformer has 1200 turns on the primary coil and 80 turns on the secondary coil. The primary voltage is 240 V. Calculate the secondary voltage.
Paper style: Theory
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Worked answer
Vp/Vs = Np/Ns. Vs = 240 × 80 / 1200 = 16 V.
Original marking points
- ✓uses transformer turns-voltage ratio
- ✓correct rearrangement and substitution
- ✓16 V
Electricity and Magnetism Supplement Challenge Explanation 4 marks
Question 24 · Power transmission
Explain why transmitting the same electrical power at a higher voltage reduces energy dissipation in cables.
Paper style: Theory
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Worked answer
For the same power, a higher voltage gives a lower current because P = IV. Cable heating is P_loss = I²R. The lower current therefore produces much less heating, so less energy is dissipated in the cables.
Original marking points
- ✓same power with higher voltage gives lower current
- ✓uses or states P = IV
- ✓heating loss depends on I²R
- ✓lower current reduces cable energy dissipation
Nuclear Physics Core Foundation Calculation 2 marks
Question 25 · Nuclide notation
A nucleus is written as ²⁷₁₃Al. State the numbers of protons and neutrons.
Paper style: Theory
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Worked answer
Protons = 13. Neutrons = 27 - 13 = 14.
Original marking points
Nuclear Physics Core Standard Calculation 3 marks
Question 26 · Half-life
A sample contains 6400 undecayed nuclei. Its half-life is 3.0 hours. How many remain undecayed after 9.0 hours?
Paper style: Theory
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Worked answer
9.0 hours is three half-lives. 6400 → 3200 → 1600 → 800. Therefore 800 nuclei remain.
Original marking points
- ✓identifies three half-lives
- ✓correct halving sequence
- ✓800
Nuclear Physics Supplement Challenge Calculation 4 marks
Question 27 · Background radiation
A detector records 920 counts per minute from a source plus background. The background count is 120 counts per minute. After one half-life, what total count rate should the detector record?
Paper style: Practical skills
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Worked answer
Initial source count = 920 - 120 = 800 counts/min. After one half-life the source count is 400 counts/min. Add background: total = 400 + 120 = 520 counts/min.
Original marking points
- ✓subtracts background to obtain 800
- ✓halves source count to 400
- ✓adds background again
- ✓520 counts/min
Nuclear Physics Supplement Standard Calculation 3 marks
Question 28 · Alpha decay
Radium-226 undergoes alpha decay. Complete the daughter nucleon number and proton number.
Paper style: Theory
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Worked answer
An alpha particle has nucleon number 4 and proton number 2. The daughter therefore has nucleon number 222 and proton number 86.
Original marking points
- ✓subtracts 4 from nucleon number
- ✓subtracts 2 from proton number
- ✓daughter is ²²²₈₆Rn if the element is required
Nuclear Physics Supplement Standard Calculation 3 marks
Question 29 · Fission
Complete the number of neutrons x in: ²³⁵₉₂U + ¹₀n → ¹⁴⁰₅₄Xe + ⁹³₃₈Sr + x(¹₀n).
Paper style: Theory
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Worked answer
Conserve nucleon number: 235 + 1 = 140 + 93 + x, so 236 = 233 + x and x = 3. Proton numbers already balance: 54 + 38 = 92.
Original marking points
- ✓sets up nucleon-number conservation
- ✓obtains x = 3
- ✓checks or recognises proton-number conservation
Nuclear Physics Supplement Standard Explanation 3 marks
Question 30 · Fusion
Explain why very high temperature is needed for nuclear fusion.
Paper style: Theory
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Worked answer
The light nuclei are positively charged and repel one another. A very high temperature gives them enough kinetic energy to approach very closely so that the strong nuclear force can bind them and fusion can occur.
Original marking points
- ✓positive nuclei repel
- ✓high temperature gives high kinetic energy
- ✓nuclei approach closely enough for the strong nuclear force/fusion
Space Physics Core Standard Calculation 3 marks
Question 31 · Light travel time
A spacecraft is 2.4 × 10¹¹ m from Earth. Calculate the time taken for a radio signal travelling at 3.0 × 10⁸ m/s to reach Earth.
Paper style: Theory
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Worked answer
t = s/v = (2.4 × 10¹¹) / (3.0 × 10⁸) = 8.0 × 10² s = 800 s.
Original marking points
- ✓uses t = s/v
- ✓handles standard form correctly
- ✓800 s
Space Physics Supplement Challenge Calculation 4 marks
Question 32 · Orbital speed
A satellite moves in an approximately circular orbit of radius 7.0 × 10⁶ m with period 5.8 × 10³ s. Calculate its average orbital speed.
Paper style: Theory
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Worked answer
v = 2πr/T = 2π(7.0 × 10⁶)/(5.8 × 10³) = 7.6 × 10³ m/s to two significant figures.
Original marking points
- ✓uses v = 2πr/T
- ✓correct standard-form substitution
- ✓correct calculation
- ✓approximately 7.6 × 10³ m/s
Space Physics Core Standard Explanation 4 marks
Question 33 · Redshift
Explain how redshift observations support the Big Bang Theory.
Paper style: Theory
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Worked answer
Spectral lines from distant galaxies are observed at longer wavelengths. This redshift shows that the galaxies are receding. Recession of many distant galaxies is evidence that the Universe is expanding, supporting the idea that matter was closer together in the past.
Original marking points
- ✓observed wavelength is longer
- ✓galaxies are receding
- ✓evidence of expansion
- ✓links expansion backward to matter being closer together/Big Bang
Space Physics Supplement Standard Calculation 2 marks
Question 34 · Light-years
A star is 12 light-years from Earth. Use 1 light-year = 9.5 × 10¹⁵ m to calculate the distance in metres.
Paper style: Theory
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Worked answer
Distance = 12 × 9.5 × 10¹⁵ = 1.14 × 10¹⁷ m.
Original marking points
- ✓multiplies by 9.5 × 10¹⁵
- ✓1.14 × 10¹⁷ m
Space Physics Supplement Challenge Calculation 3 marks
Question 35 · Hubble constant
A galaxy is 6.0 × 10²³ m from Earth. Use H₀ = 2.2 × 10⁻¹⁸ s⁻¹ to calculate its recession speed.
Paper style: Theory
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Worked answer
H₀ = v/d, so v = H₀d = (2.2 × 10⁻¹⁸)(6.0 × 10²³) = 1.32 × 10⁶ m/s.
Original marking points
- ✓rearranges to v = H₀d
- ✓correct standard-form substitution
- ✓1.32 × 10⁶ m/s
Space Physics Supplement Standard Recall 5 marks
Question 36 · Stellar evolution
State the stages after the main-sequence stage for (a) a star with mass similar to the Sun and (b) a much more massive star.
Paper style: Theory
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Worked answer
Sun-like branch: red giant → planetary nebula → white dwarf. Massive branch: red supergiant → supernova → neutron star or black hole.
Original marking points
- ✓red giant
- ✓planetary nebula then white dwarf
- ✓red supergiant
- ✓supernova
- ✓neutron star or black hole
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