Why did I lose the mark?

The answer that scoresThe cylinder should be standing on a level bench and the eye should be level with the mark, looking straight at the scale. The volume is read at the bottom of the meniscus, the lowest point of the curved water surface. Read this way, the value is the true volume of liquid in the cylinder.

The answer that scoresTime 20 complete oscillations and divide the total time by 20 to get the period. The total time is much longer, so the reaction-time error is only a small fraction of it, and the period comes out far more accurately. Repeat the measurement and average the results to reduce random error further.

The answer that scoresresultant = sqrt(6.0 x 6.0 + 8.0 x 8.0) = sqrt(36 + 64) = sqrt(100) = 10 N. The direction is found from tan theta = 6.0 / 8.0 = 0.75, so the resultant is 10 N at 37 deg to the 8.0 N direction, between the two original forces.

The answer that scoresSpeed is a scalar quantity, because it has magnitude only: 8 m/s tells you how fast the car moves but not which way. Velocity is a vector quantity, because it is speed in a stated direction, for example 8 m/s due north. A car going round a roundabout at a steady speed has a changing velocity, because its direction is changing.

The answer that scoresOn a speed-time graph the gradient is the acceleration, because acceleration is the change in velocity divided by the time. The distance travelled is the area under the line, because distance is speed multiplied by time. On a distance-time graph it is the other way round: the gradient there is the speed.

The answer that scoresAt terminal velocity the downward weight is balanced by the upward air resistance (drag). The resultant force is zero, so the acceleration is zero and the velocity stays constant. The forces are still there - they simply cancel out.

The answer that scoresa = (v - u) / t = (0 - 20) / 4 = -5 m/s2. This can be written as an acceleration of -5 m/s2, or as a deceleration of 5 m/s2. Both are correct; combining the two signs is not.

The answer that scoresThe distance is the area under the speed-time graph, not the height of the line. A car at a constant 15 m/s for 10 s travels the area of the rectangle, 15 x 10 = 150 m. If the speed is changing, split the area into triangles and rectangles before adding.

The answer that scoresThe mass is 60 kg. The weight is the gravitational force on that mass, so W = m x g = 60 x 10 = 600 N on the Earth. The mass and the weight are numerically different and have different units, and only the weight changes if the student moves to another planet.

The answer that scoresThe value of g depends on the body. It is about 10 N/kg on the Earth, but only 1.6 N/kg on the Moon, 3.7 N/kg on Mars and about 25 N/kg on Jupiter. Since W = m x g, an object of fixed mass has a different weight at the surface of each of these bodies.

The answer that scoresA balance compares the mass of an object with known masses. Because both pans are pulled by the same value of g, the comparison gives the same result on the Earth and on the Moon, so a balance measures mass in kilograms. A newton meter is the instrument that measures weight, in newtons, from the extension of a spring.

The answer that scoresThe mass of the astronaut is unchanged, because mass is a measure of the quantity of matter and does not depend on position. The weight is smaller on the Moon because the gravitational field strength is smaller: g is 1.6 N/kg instead of 10 N/kg, so W = m x g gives a smaller force for the same mass.

The answer that scoresDensity is the mass per unit volume, given by density = mass / volume. A kilogram of lead and a kilogram of feathers have the same mass, but the lead has the greater density because that mass is packed into a much smaller volume.

The answer that scoresThe volume of the stone is the rise in the water level, that is the final reading minus the starting reading. If the water rose from 50 cm3 to 74 cm3 the volume of the stone is 24 cm3, so the density is 60 / 24 = 2.5 g/cm3.

The answer that scoresA ship is hollow and contains a large volume of air, so its total mass is divided by a large total volume. The average density of the ship is less than the density of water, so it floats. Steel only sinks when it is solid, with no trapped air.

The answer that scoresThe answer is 2.7 g/cm3, which is the same as 2700 kg/m3. State the unit every time, and check whether the question asked for the density in g/cm3 or in kg/m3.

The answer that scoresAn object continues to move in a straight line at a constant speed unless a resultant force acts on it. A book sliding across a table slows down because friction from the table acts on it in the opposite direction to its motion. In the absence of any resultant force, such as in deep space far from a planet, the object would carry on at the same speed for ever.

The answer that scoresEvery distance must be measured from the pivot. If a 4.0 N weight hangs at the 20 cm mark of a rule pivoted at the 50 cm mark, its distance from the pivot is 50 - 20 = 30 cm = 0.30 m, so its moment is 4.0 x 0.30 = 1.20 N m. Measure from the pivot, at right angles to the line of action of the force.

The answer that scoresForces acting along the same straight line in the same direction add, so 5 N and 3 N in the same direction give 8 N. If the forces act in opposite directions they subtract, so 5 N one way and 3 N the other way give a resultant of 2 N in the direction of the 5 N force. If the forces are equal and opposite the resultant is zero and the forces are balanced.

The answer that scoresThe spring constant is defined as the force per unit extension, k = F / x, where x is the extension and not the total length. A spring of original length 12 cm that stretches to 15 cm when a 3.0 N load is added has an extension of 3 cm = 0.03 m, so k = 3.0 / 0.03 = 100 N/m. Using 15 cm in the calculation would give the wrong answer.

The answer that scoresMomentum is the product of mass and velocity: p = mv, where m is in kg and v is in m/s, so the unit is kg m/s. A 1200 kg car travelling at 15 m/s has p = 1200 x 15 = 18 000 kg m/s in the direction of travel. Mass x acceleration gives force in newtons, which is a different quantity.

The answer that scoresTake the original direction as positive. Initial momentum = 0.20 x 8.0 = 1.6 kg m/s; final momentum = 0.20 x (-6.0) = -1.2 kg m/s. Change in momentum = -1.2 - 1.6 = -2.8 kg m/s, so the magnitude is 2.8 kg m/s and the change is in the direction away from the wall.

The answer that scoresThe passenger's momentum must fall to zero, and that change in momentum is the same with or without an airbag. The airbag inflates and then collapses, so the passenger takes a longer time to stop. Because F = delta p / delta t, the same change in momentum over a longer time gives a smaller average force, so the passenger is injured less.

The answer that scoresThe collision is inelastic, so kinetic energy is transferred to thermal energy and sound. Momentum, however, is still conserved because the only forces are the equal and opposite forces between the two wagons. The total momentum before the collision equals the total momentum after, and the coupled wagons move off with the combined mass and a lower velocity.

The answer that scoresEk = 1/2 mv2 = 1/2 x 1200 x 20 x 20 = 1/2 x 1200 x 400 = 240000 J, which is 240 kJ. Work out the square of the speed first, then multiply by the mass, then halve, and always finish with the unit.

The answer that scoresThe force you exert is upward while the box moves sideways, so the component of the force along the motion is zero and no work is done against gravity. Your muscles still transfer chemical energy to the internal store of your body by heating, which is why you feel tired, but that is not mechanical work done on the box.

The answer that scoresEnergy is never destroyed. The energy that is not transferred to the electrical output is dissipated to the internal store of the cooling water and the surrounding air by heating. It is spread out and harder to use, but the total amount of energy is unchanged, because energy in = useful energy out + wasted energy out.

The answer that scoresefficiency = useful energy output / total energy input x 100% = 520 / 800 x 100% = 65%. The remaining 280 J is wasted as heat. An efficiency above 100% would mean more energy came out than went in, which the conservation of energy forbids.

The answer that scoresThe force on the wall is the same, but the point of the pin has a very small area of contact. Because p = F / A, a small area gives a very large pressure, and that high pressure pushes the point into the wall. The wide flat head has a large area, so the pressure on your thumb is small and it does not hurt.

The answer that scoresUse change in p = rho x g x change in h. The only quantities in the equation are the density of the liquid, the gravitational field strength and the depth. A tall narrow tube and a wide tank both filled to a depth of 2 m have the same pressure at the bottom, because the depth and the density are the same. The volume and the shape of the container do not appear in the equation.

The answer that scoresp = F / A = 450 / 0.15 = 3000 Pa. This can also be written as 3000 N/m2, or as 3 kPa. Always write the unit with the answer and check that it matches the quantity the question asked you to find.

The answer that scoresAt any point below the surface the pressure acts equally in all directions. It is greater than the pressure at the surface because of the weight of liquid above, but it pushes sideways and upwards as well as downwards. That is why water escapes sideways from a hole in the side of a container and why a submarine hull is squeezed from every side.

The answer that scoresHeating transfers energy to the gas particles, so their average kinetic energy increases and they move faster. The particles themselves stay the same size; it is the average distance between them that increases, so the gas expands. If the gas is trapped in a container of fixed volume, the faster particles collide with the walls more often and with more force, and the pressure rises instead.

The answer that scoresHeating gives the particles more kinetic energy, so they move faster. They therefore collide with the walls of the container more frequently, and each collision exerts a larger force on the wall. The total force per unit area on the walls increases, so the pressure of the gas rises.

The answer that scoresThe smoke particles are bombarded by the much smaller, much faster-moving molecules of the air. The collisions are random and uneven, so at any instant the pushes on one side do not balance the pushes on the other, and the net force changes direction from moment to moment. The smoke particle therefore follows a random zigzag path. This is Brownian motion, and it is evidence that the air molecules are in constant random motion.

The answer that scoresT (in K) = theta (in °C) + 273, so rearranging gives theta (in °C) = T (in K) - 273. For 25 K: theta = 25 - 273 = -248 °C. A negative answer is possible in degrees Celsius but never in kelvin, because 0 K is absolute zero, the lowest temperature there is.

The answer that scoresWhen the metal is heated its particles gain kinetic energy and vibrate more strongly about their fixed positions. The average distance between neighbouring particles therefore increases, so the metal expands. The particles stay the same size throughout.

The answer that scoresThe energy supplied increases the potential energy of the particles as they are pulled apart against the forces between them, rather than their kinetic energy. Because the average kinetic energy does not increase, the temperature stays at 100 °C, but the internal energy of the water is increasing throughout.

The answer that scoresConvert the mass first: 500 g = 0.50 kg. Then change in E = 0.50 x 4200 x change in theta. Always check that the mass is in kilograms, the temperature change is in °C and the energy you calculate will come out in joules.

The answer that scoresEvaporation happens at any temperature because the most energetic particles at the surface can escape whatever the temperature of the liquid. Raising the temperature, increasing the surface area and moving air over the surface all make evaporation faster, but a puddle left at 10 °C will still dry up in time.

The answer that scoresThe metal spoon feels colder because metal is a much better thermal conductor than wood. It conducts thermal energy away from your hand quickly, and your skin detects that rapid loss of energy as cold. The wooden spoon is a poor conductor, so it takes energy from your hand only slowly and feels warmer, even though both spoons are at the same temperature.

The answer that scoresConvection happens only in liquids and gases, because it depends on the particles being free to move so that the warmer, less dense fluid can rise and the cooler, denser fluid can sink. In a solid the particles vibrate about fixed positions and cannot travel, so the only method of thermal energy transfer available is conduction.

The answer that scoresA vacuum flask does not produce energy; it slows the transfer of thermal energy so that the drink stays near its starting temperature for longer. The vacuum between the walls stops conduction and convection, the silvered walls reflect infrared radiation back inside, and the plastic stopper and insulating supports reduce conduction. Energy is still transferred out, so the drink does eventually cool.

The answer that scoresThe panel should be painted black and matt, because a black, dull surface is the best absorber of infrared radiation, so it absorbs the maximum energy from the Sun. That energy is then transferred by conduction through the metal to the water, and convection circulates the warmed water. A shiny white surface would reflect most of the radiation away and heat the water far more slowly.

The answer that scoresWhen a wave crosses into a new medium its speed changes, so the wave bends. Because v = f x wavelength and the frequency is fixed by the source, the wavelength must change by the same factor as the speed. If the wave slows down the wavelength becomes shorter, but the frequency stays the same.

The answer that scoresThe amplitude is the maximum displacement of a point from its rest position, measured from the middle line of the wave up to a crest or down to a trough. The distance from a crest to the next trough is twice the amplitude, not the amplitude itself.

The answer that scoresA wave transfers energy from one place to another without transferring matter. In a water wave the water particles move up and down and end where they began, so it is the energy of the wave that travels forward. A floating ball bobs up and down as a wave passes but is not carried along with it.

The answer that scoresDiffraction is the spreading of waves as they pass through a gap. The spreading is greatest when the width of the gap is similar to or smaller than the wavelength. If the gap is much wider than the wavelength the waves pass through with very little spreading, so widening the gap reduces diffraction.

The answer that scoresThe angle of incidence is the angle between the incident ray and the normal. The normal is drawn perpendicular to the surface at the point where the ray strikes it. The angle of reflection is measured in the same way, from the normal, and the two angles are equal.

The answer that scoresA plane mirror forms a virtual image. The reflected rays diverge, so they only appear to come from a point behind the mirror, and a screen placed there would show nothing. The image is the same size as the object, upright, laterally inverted, and as far behind the mirror as the object is in front of it.

The answer that scoresGlass is denser than air, so light travels more slowly in it. When the ray enters the glass it slows down and bends towards the normal. When it leaves the glass on the other side it speeds up again and bends away from the normal, so the emergent ray is parallel to the incident ray but displaced sideways.

The answer that scoresTotal internal reflection happens only when light travels from a denser to a less dense medium and the angle of incidence is greater than the critical angle. At angles below the critical angle most of the light is refracted out of the glass. This is why light is trapped in the core of an optical fibre and can carry a signal for many kilometres.

The answer that scoresIn order of increasing frequency the spectrum is radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Reversing the list gives the order of increasing wavelength, with gamma rays shortest and radio waves longest.

The answer that scoresEvery electromagnetic wave travels at 3.0 x 108 m/s in a vacuum. X-rays are more dangerous than microwaves because they have a much higher frequency and carry much more energy per wave, which makes them ionising: they can knock electrons out of atoms and damage DNA, causing mutation or damage to cells. Microwaves are not ionising, but excessive exposure still heats body cells internally.

The answer that scoresUltraviolet is used to sterilise water, because it damages the genetic material of microorganisms in the water so they cannot reproduce. Gamma rays are used to sterilise food and medical equipment, because their great penetrating power lets them pass through packaging and kill microorganisms inside a sealed packet without heating it.

The answer that scoresA digital signal has only two values, 0 and 1, so the receiver only has to decide which of the two it has received. Even a distorted pulse can still be recognised, so the signal can be regenerated accurately and the noise does not build up, which gives a greater range. The stream of pulses also allows a higher rate of transmission of data, so more information can be sent in the same time.

The answer that scoresSound travels fastest in solids, more slowly in liquids and slowest in gases. In a solid the particles are packed close together and held by strong forces, so a vibration is passed on very quickly; in a gas the particles are far apart and only weakly interacting, so the disturbance travels slowly. The speed of sound in steel is about 5900 m/s, in water about 1500 m/s and in air about 340 m/s.

The answer that scoresLoudness is controlled by the amplitude of the wave: a bigger amplitude means bigger pressure changes and a louder sound. Pitch is controlled by the frequency: a higher frequency means more compressions and rarefactions per second and a higher note. The two are independent, so a sound can be loud and low-pitched, or quiet and high-pitched.

The answer that scoresThe sound travels to the wall and back, so the total distance travelled is 340 x 2.0 = 680 m. The distance to the wall is half of this, 680 / 2 = 340 m. Write distance to the reflector = (speed of sound x time) / 2 and the factor of two is never forgotten.

The answer that scoresUltrasound is sound with a frequency higher than 20 kHz, above the upper limit of human hearing, so it is inaudible to humans whatever its amplitude. Doctors use it to scan soft tissue because the pulses are reflected at boundaries between tissues of different density and the echoes build up an image, and because ultrasound does not use ionising radiation, so it is safer than X-rays, especially for a foetus.

The answer that scoresCopper is a metal, but it is non-magnetic, so a magnet does not attract it at all. The magnetic materials are iron, steel, cobalt and nickel. A magnet attracts these because their atoms behave like tiny magnets that can be lined up by the field, while the atoms of copper, aluminium and brass cannot be lined up in this way.

The answer that scoresThe compass needle is a small magnet that is free to turn. The magnetic pole of the Earth near the geographic north is a magnetic south pole, so it attracts the north-seeking pole of the needle. That is why the needle comes to rest pointing north-south, and why the end that points north is called the north pole of the magnet.

The answer that scoresOutside the magnet the field lines are drawn from the N pole to the S pole, because the direction of the field at a point is the direction of the force on a north pole placed there. The lines are closest together at the two poles and further apart in the space around the middle of the magnet, and the spacing of the lines shows the relative strength of the field.

The answer that scoresThe crane uses an electromagnet, which is a coil of wire wound on a soft iron core. It can be switched on and off with the current, so the crane can pick up the scrap and then drop it, and its strength can be changed to suit the load. An electromagnet can also be made much stronger than any permanent magnet, because its strength increases with the current and with the number of turns of wire.

The answer that scoresRubbing transfers electrons from the cloth to the polythene rod. The rod gains electrons and becomes negatively charged, and the cloth loses the same number of electrons and is left positively charged. The total amount of charge is unchanged, so the rod and the cloth now attract each other.

The answer that scoresConvert the time first: t = 5.0 x 60 = 300 s. Then Q = I x t = 2.0 x 300 = 600 C. Always convert minutes to seconds before substituting into I = Q / t, and check that the answer is in coulombs.

The answer that scoresResistance is directly proportional to length, so doubling the length doubles the resistance, because the electrons have to push past twice as many ions. Resistance is inversely proportional to cross-sectional area, so doubling the area halves the resistance, because there is a wider path for the electrons.

The answer that scoresEnergy in kW h = power in kW x time in hours = 2.0 x 3.0 = 6.0 kW h. To express that in joules, use E = IVt with the power in watts and the time in seconds: E = 2000 x 3.0 x 3600 = 21600000 J, which is 21.6 MJ. As a check, 6.0 kW h x 3.6 MJ = 21.6 MJ, so the two methods agree.

The answer that scoresTwo lamps in parallel have a combined resistance less than either lamp alone, because the second branch gives the current another path and the current drawn from the supply increases. Each lamp is connected across the same two points, so each has the full supply p.d. across it and is just as bright as it would be on its own. In series the lamps would share the p.d. between them and both would be dimmer.

The answer that scoresThe current at every point in a series circuit is the same. If 0.20 A leaves the cell then 0.20 A passes through every component and 0.20 A returns to the cell, because there is only one path and charge cannot pile up or disappear. The supply p.d. is shared between the components, so V = V1 + V2 + V3, and it is the potential difference, not the current, that the components divide between them.

The answer that scoresThe same current passes through both resistors, so the p.d. across each is proportional to its resistance: the larger resistance takes the larger share of the supply p.d. The equation is R1 / R2 = V1 / V2. For a 300 ohm resistor and a 100 ohm resistor on a 12 V supply, R1 / R2 = 3.0, so V1 = 3.0 x V2 and, since V1 + V2 = 12 V, the p.d.s are 9.0 V and 3.0 V.

The answer that scoresAn NTC thermistor has a resistance that falls as the temperature rises. In a potential divider it therefore takes a smaller share of the total resistance, so the p.d. across it falls and the p.d. across the fixed resistor rises. That rise in the p.d. across the fixed resistor is the signal the circuit uses to switch on a cooling fan or to display a temperature.

The answer that scoresThe fuse protects the circuit and the cable. If too much current flows, the fuse melts and breaks the circuit before the cable can overheat and start a fire. The user is protected from a shock either by the earth wire, which makes a fault current flow and blows the fuse, or by double insulation, which stops the case becoming live in the first place.

The answer that scoresThe switch must be connected in the live wire. Then, when the switch is open, the appliance is disconnected from the 230 V supply and everything beyond the switch, including the case, is at 0 V, so touching it gives no shock. With the switch in the neutral wire the appliance would still be at 230 V and could give a fatal shock.

The answer that scoresThe normal current is I = P / V = 60 / 230 = 0.26 A, so a 3 A fuse is the correct choice, being the next standard rating above 0.26 A. A 13 A fuse would not protect the thin flex of the lamp from overheating.

The answer that scoresWhen several high-power appliances share one socket through an adaptor, the total current can exceed the 13 A rating of the socket and the lead. The cable then overheats, the insulation can melt or burn, and the result can be a fire. The fuse in each plug protects that appliance only and does not protect the shared lead.

The answer that scoresThe commutator is a ring cut into two halves, with a carbon brush pressing on each half. Every half turn the gaps between the halves pass the brushes, so the connections to the battery swap over and the current in the coil reverses direction. The forces on the two sides of the coil therefore swap sides, so the coil is always pushed round in the same rotational direction and keeps spinning. The size of the current is set by the battery and the resistance of the coil, not by the commutator.

The answer that scoresThe field lines around a long straight wire are concentric circles centred on the wire. Close to the wire the circles are close together, so the field is strong; further away the circles are further apart, so the field is weaker. Increasing the current makes the field stronger everywhere, and reversing the current reverses the direction of the field without changing its strength.

The answer that scoresWith a direct current the current in the primary coil is steady, so the magnetic field in the core is steady and does not change. A steady field induces no e.m.f., so no voltage appears across the secondary coil. With an alternating current the field in the core changes continuously, and it is that changing field linking the secondary coil that induces an alternating e.m.f. in it.

The answer that scoresThe e.m.f. is a maximum when the plane of the coil is parallel to the magnetic field, because the sides of the coil are then moving at right angles to the field lines and cutting them at the greatest rate. The e.m.f. is zero when the plane of the coil is perpendicular to the field, because the sides are then moving parallel to the field lines and do not cut them. So the graph of e.m.f. against time is a sine curve with the peaks at the parallel positions and the zeros at the perpendicular positions.

The answer that scoresAn alpha particle is a helium nucleus with a relative mass of 4 and a relative charge of +2. An electron is about 1840 times lighter than a proton, so it cannot deflect an alpha particle through a large angle. The particles that came almost straight back had passed very close to a very small, dense, positively charged nucleus, which repelled them strongly because both the nucleus and the alpha particle are positive. Those rare large deflections are the evidence that the nucleus is small, massive and positive, while the many undeflected particles show that the atom is mostly empty space.

The answer that scoresIsotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Chlorine-35 and chlorine-37 both have 17 protons, so both are chlorine. Chlorine-35 has 35 - 17 = 18 neutrons and chlorine-37 has 37 - 17 = 20 neutrons. Because both have 17 electrons in a neutral atom, they have the same chemical properties, but their masses are different.

The answer that scoresA negative ion is formed when an atom gains one or more electrons. A chlorine atom has proton number 17, so it has 17 protons and 17 electrons; when it gains one electron it has 17 protons and 18 electrons, so there is one more negative charge than positive charge and the ion has a charge of 1-, written Cl-. The number of protons is unchanged when an ion forms.

The answer that scoresNuclear fission is the splitting of a heavy nucleus, such as uranium-235, into two smaller nuclei after it absorbs a neutron. It releases energy and more neutrons, so a chain reaction can build up, and this is the process used in a nuclear power station. Nuclear fusion is the joining of two light nuclei, such as hydrogen nuclei, to form a heavier nucleus such as helium, and it releases even more energy per kilogram of fuel. Fusion only happens at extremely high temperatures and pressures, as in the core of the Sun, so no fusion power station yet produces more energy than it uses.

The answer that scoresAlpha particles carry a charge of +2e and are deflected towards the negative plate, but only slightly, because their mass is large. Beta particles carry a charge of -1e and are deflected towards the positive plate, in the opposite direction, and their deflection is much greater because their mass is very small and their charge-to-mass ratio is very large. Gamma radiation is uncharged and is not deflected at all.

The answer that scoresHalve the count rate once for each half-life: 800 -> 400 -> 200 -> 100 counts per minute. After three half-lives the count rate is 100 counts per minute, which is one eighth of the original value, because (1/2) x (1/2) x (1/2) = 1/8.

The answer that scoresThe mass number decreases by 4 and the proton number decreases by 2. Radium-226 (88 protons, 138 neutrons) decays to radon-222 (86 protons, 136 neutrons), so the decay equation in words is: radium-226 -> radon-222 + alpha particle. Radium and radon are different elements, so the product is not radium-222.

The answer that scoresGamma radiation needs thick lead shielding. Beta particles are stopped by a few millimetres of aluminium, and alpha particles are stopped by a sheet of paper or a few centimetres of air. For gamma, keep as far away as possible, use tongs so the source is never touched, spend as little time near it as you can, and keep it behind lead. The three precautions are reducing the time, increasing the distance and using the correct shielding.

The answer that scoresThe Earth's axis is tilted, and the tilt keeps pointing in the same direction as the Earth orbits the Sun. When the northern hemisphere leans towards the Sun, the Sun's rays strike it more directly and the days are longer, so it is summer there. When it leans away, the rays arrive at a shallower angle and the days are shorter, so it is winter. Six months later the opposite hemisphere is tilted towards the Sun, so the seasons repeat once every orbit, about 365 days.

The answer that scoresThe Moon is lit by the Sun, so half of it is always lit and half is always dark. As the Moon orbits the Earth once a month, the fraction of the lit half that faces the Earth changes. At new moon the lit half faces away from us, at full moon it faces us completely, and in between we see crescents, half moons and gibbous shapes. The cycle repeats every orbit, which takes approximately one month.

The answer that scoresConvert the period first: T = 365 x 24 x 60 x 60 = 3.15 x 107 s. Then substitute: v = 2 x pi x r / T = (2 x 3.14 x 1.5 x 1011) / (3.15 x 107) = (9.42 x 1011) / (3.15 x 107) = 3.0 x 104 m/s. Always convert T to seconds before substituting, and check that the answer is a sensible size.

The answer that scoresThe Sun contains most of the mass of the Solar System, so its gravitational field is by far the strongest. The force that keeps a planet in its orbit is the gravitational attraction of the Sun, which pulls the planet towards the Sun and provides the force needed for it to follow a curved path. The same idea keeps moons in orbit around their planets and satellites in orbit around the Earth.

The answer that scoresA light-year is the distance travelled in the vacuum of space by light in one year. Light travels at 3.0 x 108 m/s and a year is 3.15 x 107 s, so one light-year = 3.0 x 108 x 3.15 x 107 = 9.5 x 1015 m. The Milky Way is about 100 000 light-years across, so that is a distance, not a time.

The answer that scoresRedshift is an increase in the observed wavelength of electromagnetic radiation emitted from a receding star or galaxy. The light from distant galaxies is redshifted compared with the same light emitted on the Earth, so those galaxies are moving away from us. The further away a galaxy is, the greater its redshift, which is evidence that the Universe is expanding.

The answer that scoresA red supergiant explodes as a supernova. The explosion forms a nebula containing hydrogen and new heavier elements, and leaves behind a neutron star or, for the most massive stars, a black hole. It is a red giant from a less massive star that forms a planetary nebula with a white dwarf at its centre. The nebula from a supernova may later collapse to form new stars with orbiting planets.

The answer that scoresThe CMBR is microwave radiation of a specific frequency that is observed at all points in space around us. It was produced shortly after the Universe was formed, when the Universe was extremely hot and the radiation had a very short wavelength. As the Universe expanded the radiation was stretched, moving it into the microwave region of the electromagnetic spectrum, so it is now detected as faint microwaves from every direction.