May/June 2025 Paper 21 Worked Answers (IGCSE Physics 0625 Extended)
40 questions · 40 marks · 45 minutes
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Worked answers for 40 questions
- Acceleration is the gradient of a speed-time graph. A straight sloping line has a constant gradient, so the acceleration is constant. A curved line has a gradient that keeps changing, so the acceleration is changing. A horizontal line means zero acceleration.Method:Link acceleration to the gradient of a speed-time graph; a curve has a changing gradient so changing acceleration.Examiner tips
- Constant gradient means constant acceleration; a curve means the acceleration is changing.
- The net vertical force is 120 - 60 = 60 kN upward. The net horizontal force is 60 - 40 = 20 kN forward. These are perpendicular, so the resultant magnitude is the square root of (60 squared + 20 squared) = square root of (3600 + 400) = square root of 4000, which is about 63 kN.Method:Compute net vertical (60 kN) and net horizontal (20 kN), then resultant = square root of (60^2 + 20^2) = 63 kN.Examiner tips
- Resolve into perpendicular directions first, then use Pythagoras for the resultant.
- Identical dimensions mean the two blocks have equal volumes. A force meter measures weight, and the readings are different, so the blocks have different weights. Equal volume but different weight means the metals have different densities.Method:Equal dimensions give equal volume; different meter readings give different weight.Examiner tips
- A force meter reads weight; identical dimensions fix the volume.
- Density = mass divided by volume. A balance measures the mass of the necklace. Its volume, since the shape is irregular, is found from the rise in water level in a measuring cylinder. No thermometer or stopwatch is needed.Method:Mass from a balance, volume from displacement in a measuring cylinder, then density = mass/volume.Examiner tips
- For an irregular solid, volume comes from water displacement in a measuring cylinder.
- The spring constant = change in force divided by change in extension. The extra load is 8.0 - 3.0 = 5.0 N. The extra extension is 30 - 20 = 10 cm. So the spring constant = 5.0 / 10 = 0.50 N/cm.Method:Extra force 5.0 N, extra extension 10 cm, spring constant = 5.0/10 = 0.50 N/cm.Examiner tips
- Always work with the change in load and the change in length for the spring constant.
- A block is in equilibrium when the resultant force on it is zero. Two equal forces acting in opposite directions cancel out, giving zero resultant force, so the block is in equilibrium.Method:Identify the case where the two forces cancel to give zero resultant force.Examiner tips
- Equilibrium requires the vector sum of all forces to be zero.
- Force equals the change of momentum divided by the time taken, not multiplied by time, so the statement in "Force equals change of momentum multiplied by time" is the incorrect one. Impulse does equal change of momentum, momentum is mass multiplied by velocity, and momentum is conserved in a closed system, so those statements are all correct.Method:Recall force = change of momentum / time; the statement multiplying by time is the incorrect one.Examiner tips
- Force is the rate of change of momentum: change of momentum divided by time.
- From F = ma, the acceleration a = F divided by m. With the force F kept constant, reducing the mass m increases the acceleration. Temperature, the ball being hollow, and the density do not affect the acceleration if the mass and force are unchanged.Method:Use a = F/m with F constant; smaller m gives larger a.Examiner tips
- For a fixed force, acceleration depends only on the mass.
- Pressure = force divided by area. The weight (force) is the same for both carts. Wide wheels have a larger contact area with the ground, so they exert a lower pressure. Lower pressure means the wheels sink less into soft ground.Method:Same weight, wider wheels give larger area, so lower pressure and less sinking.Examiner tips
- For a fixed force, a larger area always means a smaller pressure.
- In a gas the particles are much farther apart than in a liquid, so the separation is greater. A hot gas also has more thermal energy than a cool liquid, so its particles move faster on average. Hence greater separation and faster motion.Method:Gas has greater particle separation than liquid; a hot gas has faster particles than a cool liquid.Examiner tips
- Gas particles are widely spaced; higher temperature means faster particles.
- At constant temperature, pressure multiplied by volume is constant: p1 V1 = p2 V2. So 300 x 2.0 = p2 x 5.0, giving 600 = 5.0 p2, so p2 = 600 / 5.0 = 120 kPa.Method:Apply p1 V1 = p2 V2 with the given values to find p2 = 120 kPa.Examiner tips
- For a fixed mass of gas at constant temperature, p x V stays constant.
- Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 degree C. A greater specific heat capacity for P means more energy is needed to raise 1 kg of P by 1 degree C than for the same mass of Q. Specific heat capacity is about temperature change, not melting.Method:Apply the definition: larger specific heat capacity means more energy per kg per degree C.Examiner tips
- Specific heat capacity is per kilogram, per degree Celsius, for a temperature change.
- Water is made of molecules. During evaporation, the most energetic individual water molecules at the surface escape into the air. They leave one at a time as separate molecules, not as atoms, protons or droplets.Method:State that evaporation releases individual water molecules from the surface.Examiner tips
- Evaporation is the escape of individual molecules from the liquid surface.
- Heating the gas gives the particles more kinetic energy, so they move faster. Faster particles hit the container walls harder and more frequently. More frequent and harder collisions per unit area mean a greater force per unit area, which is a higher pressure.Method:Heating raises particle speed, so collisions with the walls are more frequent and harder, raising pressure.Examiner tips
- Gas pressure is explained by the rate and force of particle collisions with the walls.
- Copper is a much better thermal conductor than wood. The copper rod conducts thermal energy away from the warm hand quickly towards the cold ice, so the hand loses heat fast and the rod feels colder. Wood is a poor conductor, so little heat flows and it feels less cold.Method:Copper conducts heat away from the hand quickly, so it feels colder than the poorly conducting wood.Examiner tips
- Good conductors carry heat away from the hand quickly, so they feel colder.
- A dull black surface is the best absorber of infrared radiation and also the best emitter. So compared with a white surface at the same temperature, the black surface has both a higher rate of absorption and a higher rate of emission. Good absorbers are always good emitters.Method:Black surfaces both absorb and emit infrared better than white surfaces at the same temperature.Examiner tips
- A good absorber of radiation is also a good emitter.
- In a transverse wave the particles vibrate at right angles to the direction the wave travels. The wave moves horizontally, so the water surface and the floating cork move up and down about a fixed point. The cork is not carried along with the wave.Method:Apply the definition of a transverse wave: the cork vibrates up and down as the wave moves horizontally.Examiner tips
- Transverse means vibration perpendicular to the direction of wave travel.
- When the object is inside the focal length of a converging lens, the lens acts as a magnifying glass. The image formed is virtual, upright and enlarged, and it is on the same side of the lens as the object.Method:Use the magnifying-glass case for a converging lens: virtual, upright, enlarged image.Examiner tips
- Object inside the focal length of a converging lens gives a virtual, upright, enlarged image.
- When a ray reflects from two mirrors that are at 90 degrees to each other, the law of reflection applied twice turns the ray through a total of 180 degrees. The emerging ray is therefore parallel to the incident ray but travelling in the opposite direction. This is the principle of a corner reflector.Method:Apply reflection at both mirrors; the ray turns 180 degrees and emerges parallel but opposite.Examiner tips
- Two mirrors at 90 degrees reverse a ray's direction (corner reflector).
- Refractive index n = speed of light in air divided by speed of light in the material. If the speed in the material is one half of the speed in air, then n = 1 divided by 0.5 = 2.0.Method:Apply n = speed in air / speed in material = 1 / 0.5 = 2.0.Examiner tips
- Refractive index = speed in vacuum (or air) divided by speed in the medium, always greater than 1.
- Dispersion is the separation of white light into its component colours. It happens because each colour has a slightly different speed in glass and so is refracted by a different amount, spreading the colours into a spectrum.Method:Recall the definition of dispersion as splitting white light into its spectrum.Examiner tips
- Dispersion = splitting of white light into a spectrum by refraction.
- Television broadcasting uses geostationary satellites, which stay above the same point on the Earth so the receiving dish can stay fixed. The signals are carried by microwaves, which pass easily through the atmosphere and carry large amounts of information.Method:Match satellite TV to a geostationary satellite and microwave electromagnetic waves.Examiner tips
- Satellite TV uses geostationary satellites and microwave signals.
- Sound travels much faster in a solid such as steel than in air. The frequency is set by the source and does not change. Since speed = frequency multiplied by wavelength, and the speed increases while the frequency stays the same, the wavelength must also increase.Method:Speed rises in steel, frequency constant, so wavelength rises by v = f x wavelength.Examiner tips
- When a wave changes medium, frequency stays constant; speed and wavelength change together.
- The closeness of magnetic field lines represents the strength of the field. Where the lines are closest together, near the poles, the field is strongest. Where the lines are widely spaced the field is weaker.Method:Relate field strength to line spacing; closest lines mean the strongest field.Examiner tips
- Closely spaced field lines mean a strong magnetic field.
- An electric field is a region in which an electric charge experiences a force. By convention, the direction of the electric field at a point is the direction of the force that would act on a small positive test charge placed there.Method:State the definition of an electric field and the positive-test-charge direction convention.Examiner tips
- Electric field direction is always defined by the force on a positive test charge.
- Resistance is inversely proportional to the cross-sectional area of a wire. The cross-sectional area of a circular wire is proportional to the diameter squared. So resistance is inversely proportional to the diameter squared: doubling the diameter reduces the resistance to one quarter.Method:R is inversely proportional to area; area proportional to d squared, so R inversely proportional to d squared.Examiner tips
- Link resistance to area, then area to the square of the diameter.
- In a series circuit the supply voltage is shared between the components. Two equal resistors share the 12 V equally, so each has a potential difference of 12 divided by 2 = 6.0 V.Method:Two equal series resistors split the 12 V supply equally: 12 / 2 = 6.0 V each.Examiner tips
- In a series circuit the potential differences add up to the supply voltage.
- A diode, including an LED, only allows current to flow in one direction. It conducts and an LED lights only when it is forward biased, that is connected the correct way round so that current can pass. When reverse biased it blocks the current and stays off.Method:Recall diode behaviour: an LED lights only when forward biased.Examiner tips
- A diode conducts only when forward biased; reverse bias blocks current.
- The induced e.m.f. depends on how quickly the wire cuts magnetic field lines. Moving the wire faster cuts the field lines at a greater rate, so a larger e.m.f. is induced. A stronger magnet or more turns would also increase it.Method:Relate induced e.m.f. to the rate of cutting field lines; moving faster increases it.Examiner tips
- Induced e.m.f. increases with faster motion, stronger field or more turns.
- An a.c. generator uses a coil of wire rotating between magnetic poles, with slip rings to connect the coil to the external circuit. A split-ring commutator is used in a d.c. motor or dynamo to reverse connections; it is not part of an a.c. generator.Method:Recall a.c. generator parts; the split-ring commutator belongs to a d.c. machine.Examiner tips
- Slip rings go with a.c. generators; split-ring commutators go with d.c. machines.
- A current in a long straight wire produces a magnetic field made up of concentric circles centred on the wire, lying in planes at right angles to the wire. The circles are closer together near the wire, where the field is strongest.Method:Recall the circular field pattern around a straight current-carrying wire.Examiner tips
- The field around a straight current-carrying wire is circular.
- The soft iron core concentrates and guides the changing magnetic field (flux) produced by the primary coil so that almost all of it passes through the secondary coil. This strong magnetic linkage allows an alternating voltage to be induced efficiently in the secondary coil. The core does not carry electric current between the coils.Method:State that the soft iron core links the changing magnetic flux from primary to secondary.Examiner tips
- The iron core provides a path for magnetic flux, linking the two coils.
- Most of the atom is empty space, so the great majority of alpha particles pass straight through the thin gold foil with little or no deflection. Only a very small number come close to the tiny, dense, positively charged nucleus and are deflected through large angles or bounced back.Method:Recall the scattering result: most alpha particles pass straight through the foil.Examiner tips
- Most alpha particles pass straight through, showing the atom is mostly empty space.
- The nucleon number is the total number of protons and neutrons. So the number of neutrons = nucleon number minus proton number = 15 - 7 = 8.Method:Subtract the proton number from the nucleon number: 15 - 7 = 8.Examiner tips
- Neutrons = nucleon number minus proton number.
- First subtract the background: source count rate = 520 - 40 = 480 counts per minute. In 4 hours there are 4 divided by 2 = 2 half-lives, so the source rate falls to 480 then 240 then 120 counts per minute. The detector also reads the background, so the reading is 120 + 40 = 160 counts per minute.Method:Source 480 cpm, 2 half-lives gives 120 cpm, add 40 background to get 160 cpm.Examiner tips
- Always correct for background before and after applying half-lives.
- In beta-minus decay a neutron changes into a proton and an electron, and the electron (the beta particle) is emitted. The proton number increases by 1, from 11 to 12, while the nucleon number stays at 24. So sodium-24 becomes magnesium-24 with proton number 12.Method:Apply beta-minus rules: proton number 11 to 12, nucleon number 24, giving magnesium-24.Examiner tips
- Beta-minus decay: proton number plus 1, nucleon number unchanged.
- Exposure to gamma radiation is reduced by keeping a large distance from the source, spending the shortest possible time near it, and placing dense shielding such as lead or thick concrete between the source and the person. Moving closer or staying longer would increase the exposure.Method:Apply the three safety measures: more distance, less time, and shielding.Examiner tips
- Reduce radiation dose by increasing distance, reducing time and using shielding.
- TR is one day (the Earth spinning once), TM is about 27 days (the Moon orbiting the Earth) and TS is one year (the Earth orbiting the Sun). The shortest period is the day, TR, and the longest period is the year, TS.Method:Compare a day, a month and a year; shortest is TR, longest is TS.Examiner tips
- Order the periods: day (rotation) < month (Moon orbit) < year (Earth orbit).
- Light from distant galaxies is observed to be redshifted, meaning its wavelength is increased (shifted towards the red end of the spectrum). This is because those galaxies are moving away from us, and it is evidence that the Universe is expanding.Method:Identify the correct redshift statement: distant galaxy light is redshifted.Examiner tips
- Redshift = longer observed wavelength, evidence the Universe is expanding.
- The cosmic microwave background radiation was produced in the very early Universe with much shorter wavelengths. As the Universe expanded, the radiation was stretched, so its wavelength has increased over time and it is now in the microwave region. This means it had a shorter wavelength in the past.Method:Expansion stretches the CMBR wavelength over time, so it was shorter in the past.Examiner tips
- Cosmic expansion stretches the CMBR, so its wavelength was shorter in the past.
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