Apply current and resistance relationships in a circuitPartial supportCore
Scope: Core · Unit 1 §1.1: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
For a component, potential difference, current and resistance are linked by the printed relation I = V/R.
Current is measured in amperes, potential difference in volts and resistance in ohms.
Series and parallel layouts change how current and potential difference are shared; identify the circuit before applying a rule.
What to do in an assessment
Read the diagram to identify series paths and branch junctions.
Substitute SI quantities and state the unit; if a result is unexpected, check whether the requested quantity is total or branch current.
In plain language
A circuit carries current through its components. Potential difference measures energy transferred per charge, while resistance affects how much current flows for a given potential difference.
Self-check
A component has 12 V across it and 4 Ω resistance. Find its current.
Show the answer
I = V/R = 12/4 = 3 A.
Explain current as moving chargePartial supportCore
Scope: Core · Unit 1 §1.1: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Current is charge flow per second, I = Q/t; charge is measured in coulombs and current in amperes.
Potential difference is energy transferred per unit charge, V = E/Q.
In a series path the current is the same at every point; at a junction, total incoming current equals total outgoing current.
What to do in an assessment
Select I = Q/t or V = E/Q based on the quantity asked and use seconds/coulombs.
Use junction conservation before calculating unknown branch currents.
In plain language
Current tells how much charge passes each second. Potential difference tells how much energy each coulomb transfers between two points.
Self-check
A 10 C charge passes in 5 s. Find the current.
Show the answer
I = Q/t = 10/5 = 2 A.
Recognise and select electrical circuit symbolsCore
Scope: Core · Unit 1 §1.1(a)
Open revision guidance
What to know
Know the symbols for a cell, switch, lamp, voltmeter, ammeter, resistor, variable resistor, fuse, LED, thermistor, LDR and diode.
An ammeter measures current through a component and is placed in series; a voltmeter measures potential difference across a component and is connected in parallel.
What to do in an assessment
Translate each named component into its circuit symbol and trace the complete circuit path before interpreting it.
Check that meters are in the correct position and that a diode/LED is oriented for the permitted current direction.
In plain language
Circuit diagrams use agreed symbols so a component and its electrical connection can be recognised without drawing a picture of the real device.
Self-check
Which two meters measure current and potential difference, and how is each connected?
Show the answer
An ammeter measures current in series; a voltmeter measures potential difference across a component in parallel.
View diagrams
Cell
Battery of cells
Switch
Lamp
Ammeter
Voltmeter
Fixed resistor
Variable resistor
Fuse
Light-emitting diode
Thermistor
Light-dependent resistor
Diode
Read standard circuit symbols and compare the series ammeter with the parallel voltmeter connections.
Apply current and potential-difference rules in series and parallel circuitsCore
Scope: Core · Unit 1 §1.1(b)
Open revision guidance
What to know
In a series circuit the current is the same at every point and the potential differences across components add to the supply potential difference.
In parallel branches the potential difference across each branch is the same; branch currents add to the supply current.
What to do in an assessment
Mark junctions and trace branches before deciding whether a component is in series or parallel.
Use conservation at a junction and the supply-voltage sum, then state whether a value is total or branch-specific.
In plain language
A single series path carries one current. Parallel branches share the same voltage but the current splits and recombines.
Self-check
A 6 V supply feeds two parallel branches. What is the potential difference across each branch?
Show the answer
6 V across each branch.
Apply Higher-tier parallel and combined-circuit resistance calculationsCore
Scope: Core · Unit 1 written-paper tier: Higher tier · Unit 1 §1.1(g), printed bold fragments: “a parallel circuit” and “circuits consisting of combinations of series and parallel connections”
Open revision guidance
What to know
The bold fragments of §1.1(g) extend the common series-circuit calculations to parallel circuits and combinations of series and parallel connections.
For a parallel section, 1/R=1/R₁+1/R₂, every branch has the same potential difference and branch currents add; series sections carry the same current and their potential differences add.
What to do in an assessment
Reduce one series/parallel section at a time; calculate an equivalent resistance or branch value, then check current and potential-difference conservation at every connection.
In plain language
A mixed circuit is solved by identifying each series section and parallel branch rather than treating the whole network as one undifferentiated path.
Self-check
Two 6 Ω resistors are in parallel. What is their equivalent resistance?
Show the answer
3 Ω, because 1/R=1/6+1/6=1/3.
Measure current and potential difference in a circuitCore
Scope: Core · Unit 1 §1.1(c)
Open revision guidance
What to know
Current is measured in amperes (A) using an ammeter connected in series. Potential difference is measured in volts (V) using a voltmeter in parallel across the component.
Use a suitable range, read the scale without parallax, and include the unit with every recorded value.
What to do in an assessment
Draw or inspect the circuit and put the ammeter in the path whose current is wanted; connect the voltmeter across the named component.
Record meter readings with units and identify whether readings are supply, component or branch values.
In plain language
The ammeter joins the path so the same charge flow passes through it; the voltmeter compares the electrical energy per charge on the two sides of a component.
Self-check
Where is a voltmeter connected to measure a lamp’s potential difference?
Show the answer
In parallel across the lamp.
Investigate current–voltage characteristics of circuit componentsCore
Scope: Core · Unit 1 §1.1(d)
Open revision guidance
What to know
The required comparisons include a resistor or wire at constant temperature, a filament lamp and a diode.
For a fixed-temperature ohmic resistor, current is proportional to potential difference; a filament’s increasing temperature raises resistance, while a diode conducts readily in one direction and has little reverse current.
What to do in an assessment
Change the potential difference, measure current and voltage for repeated settings, reverse polarity where appropriate, and plot current against voltage with axes/units.
Keep the resistor’s temperature approximately constant; use a suitable series resistor and low-voltage supply to protect components.
In plain language
The graph shows whether a component lets current increase in the same proportion as the applied voltage or behaves differently as it heats or blocks one direction.
Self-check
What happens to a filament lamp’s resistance as its current and temperature rise?
Show the answer
Its resistance increases, so its current–voltage graph is not a straight line through the origin.
Relate current, potential difference and resistanceCore
Scope: Core · Unit 1 §1.1(e)
Open revision guidance
What to know
The specification prints I=V/R. Potential difference is energy transferred per unit charge, and resistance describes opposition to current.
Use volts, amperes and ohms consistently; a larger resistance at fixed voltage gives a smaller current.
What to do in an assessment
Use the stated form I=V/R when calculating current from a supplied potential difference and resistance; substitute SI values and show the arithmetic.
Check the result with the qualitative trend (current rises with voltage and falls with resistance when the other variable is fixed).
In plain language
The relationship predicts how much current flows when a voltage is applied to a component with a known resistance.
Self-check
A 12 V component has resistance 4 Ω. Find its current.
Show the answer
I=V/R=12/4=3 A.
Explain how circuit layout affects total resistanceCore
Scope: Core · Unit 1 §1.1(f)
Open revision guidance
What to know
Adding components in series increases total resistance.
Adding components in parallel decreases the equivalent resistance because there is an additional path for charge.
What to do in an assessment
Identify which resistors share a single path and which share the same two junctions; do not apply the series rule to branches.
Predict the direction of the total-resistance change before calculating.
In plain language
More series components make one path harder for charge to pass through; parallel paths give charge additional routes.
Self-check
What happens to equivalent resistance when a second resistor is added in parallel?
Show the answer
It decreases.
Calculate total resistance and current in series circuitsCore
Scope: Core · Unit 1 §1.1(g)
Open revision guidance
What to know
In a series circuit, total resistance is R=R₁+R₂ and the same current passes each resistor; use the printed I=V/R relationship to calculate current.
The common portion is the series calculation; the source prints the parallel and mixed-circuit calculation extensions in bold for Higher.
What to do in an assessment
Add series resistances directly, then use the circuit's total potential difference to calculate current.
Keep the parallel/mixed equivalent-resistance calculation for the separately gated Higher extension.
In plain language
Series resistances add directly, and the same current passes through every component in that single path.
Self-check
Find the total resistance of 2 Ω and 4 Ω in series.
Show the answer
6 Ω.
Calculate electrical energy transferred using power and timeCore
Scope: Core · Unit 1 §1.1(h)
Open revision guidance
What to know
Electrical energy transferred is E=Pt: power is energy transferred per unit time.
Use joules with watts and seconds, or a consistent energy/power/time unit set; convert before combining incompatible units.
What to do in an assessment
Use E=Pt to calculate transferred energy from a supplied power and interval; convert the time unit explicitly before multiplying.
Distinguish the appliance's power from energy consumed over a time interval.
In plain language
A more powerful appliance transfers more energy each second, so running it longer transfers more energy.
Self-check
A 60 W lamp runs for 30 s. How much energy is transferred?
Show the answer
E=Pt=60×30=1800 J.
Calculate power from voltage and currentCore
Scope: Core · Unit 1 §1.1(i), power=voltage×current; P=VI
Open revision guidance
What to know
Electrical power P=VI; use potential difference in volts and current in amperes to obtain power in watts.
Power is the rate of energy transfer, so P=E/t is consistent with E=Pt.
What to do in an assessment
Select the potential difference across the appliance and the current through it, then substitute into P=VI.
Check W=V×A and convert any prefixes before calculating.
In plain language
The voltage gives energy transferred per charge and current gives charge flowing each second; multiplying gives energy transferred each second.
Self-check
A device operates at 12 V with a current of 2 A. Find its power.
Show the answer
P=VI=12×2=24 W.
Calculate power using current and resistance (Higher)Core
Scope: Core · Unit 1 written-paper tier: Higher tier · Unit 1 §1.1(i), printed bold Higher-tier formula power=current²×resistance; P=I²R
Open revision guidance
What to know
The specification also gives P=I²R, with current in amperes and resistance in ohms.
It follows from P=VI and V=IR for an ohmic relationship; use only when current and resistance are known or can be found.
What to do in an assessment
Square the current before multiplying by resistance and show the squared-current step.
Compare with P=VI when both forms are available as a check.
In plain language
This form finds the rate of energy transfer from how much current flows and the resistance of the component.
Self-check
A 3 Ω resistor carries 2 A. Find its power.
Show the answer
P=I²R=2²×3=12 W.
Investigate how resistance varies in lamps, diodes, thermistors and LDRsCore
Scope: Core · Unit 1 §1.1(j)
Open revision guidance
What to know
A filament lamp's resistance rises as its filament heats; an NTC thermistor's resistance falls as temperature rises; an LDR's resistance falls as light intensity rises.
A diode has strongly direction-dependent current. The investigating-circuit outcome includes lamps, diodes, NTC thermistors and LDRs.
What to do in an assessment
Vary one condition at a time, measure V and I, calculate R=V/I and record the relevant temperature or light condition.
Use a circuit diagram, repeat readings where useful and plot the relationship so component behaviour can be compared.
In plain language
Some components change resistance when warmed or illuminated, while a diode mainly changes how easily current flows with direction.
Self-check
What happens to an NTC thermistor's resistance when it is warmed?
Show the answer
It decreases.
Investigate current–voltage characteristics for a componentCore
Scope: Core · Unit 1 §1.1 specified practical work: investigation of current–voltage (I–V) characteristics, printed p. 10
Open revision guidance
What to know
Measure current through and potential difference across the test component; use an ammeter in series and voltmeter in parallel.
The investigation records paired voltage/current readings over a range and reveals whether a component is ohmic or has a curved/directional response.
What to do in an assessment
Build a low-voltage circuit with variable supply/resistor, record V and I across a range, reverse polarity where appropriate, and plot I against V with units.
Keep resistor temperature approximately constant, repeat readings, and evaluate range, resolution, heating, anomalies and measurement uncertainty.
In plain language
Change voltage in controlled steps, measure the resulting current, and graph the paired values to reveal component behaviour.
Self-check
Where should the ammeter and voltmeter be placed for an I–V investigation?
Show the answer
Ammeter in series with the component; voltmeter in parallel across it.

Decide when total internal reflection can occurPartial supportCore
Scope: Core · Unit 1 §1.6: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Total internal reflection occurs at a boundary when light travels from an optically denser medium to a less dense medium and the incidence angle exceeds the critical angle.
At the critical angle the refracted ray travels along the boundary; above it, light is reflected inside.
Optical fibres use repeated total internal reflection to guide light.
What to do in an assessment
Draw the normal first and measure incidence from it.
Check both conditions before naming the effect: direction of travel and incidence angle greater than critical angle.
In plain language
At a shallow enough angle, light exits the denser material. As the angle grows, the refracted ray skims the boundary; beyond that point, it cannot leave and reflects back inside.
Self-check
Can light travelling from air into glass undergo total internal reflection at the first boundary?
Show the answer
No. Total internal reflection requires travel from a more optically dense medium to a less dense one.
Apply the conditions for total internal reflectionPartial supportCore
Scope: Core · Unit 1 §1.6: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Total internal reflection occurs when a wave travels from a medium where it is slower into one where it is faster, and incidence exceeds the critical angle.
At the critical angle the refracted ray travels along the boundary.
Optical fibres use total internal reflection to guide light.
What to do in an assessment
Draw the normal and measure incidence from it.
Check both travel direction and angle condition before predicting total internal reflection.
In plain language
Light inside glass can leave at small incidence angles. When the incidence angle is greater than the critical value, it reflects back inside instead of refracting out.
Self-check
Can total internal reflection happen when light travels from air into glass?
Show the answer
No. It must travel from the slower/optically denser medium to the faster/less dense medium.
Identify the conditions for total internal reflectionCore
Scope: Core · Unit 1 §1.6(a)
Open revision guidance
What to know
Total internal reflection occurs when light travels from a more optically dense medium toward a less optically dense medium and the angle of incidence exceeds the critical angle.
At the critical angle the refracted ray travels along the boundary; below it, light refracts out.
What to do in an assessment
Draw the normal at the boundary, measure incidence from the normal, and check both direction-of-travel and angle conditions.
Do not apply the effect to light entering a denser medium.
In plain language
Light is trapped and reflected inside only when it tries to leave a denser optical medium at an angle above the critical value.
Self-check
Can light travelling from air into glass undergo total internal reflection at the interface?
Show the answer
No; it is travelling into a more optically dense medium.
Explain how optical fibres use total internal reflectionCore
Scope: Core · Unit 1 §1.6(b)
Open revision guidance
What to know
An optical fibre guides light along a core by repeated total internal reflection at the core boundary.
The incidence angles at the boundary must satisfy the conditions for total internal reflection; the light can carry signals or form an image.
What to do in an assessment
Trace the ray through the fibre, show repeated reflection and identify the denser core and lower-density surrounding material.
Relate the effect to communication or remote imaging only where the question specifies the application.
In plain language
The fibre keeps light inside by making it reflect again and again at its inner boundary.
Self-check
What keeps light inside an optical fibre?
Show the answer
Repeated total internal reflection at the core boundary.
Compare optical fibres with satellites for long-distance communicationCore
Scope: Core · Unit 1 §1.6(c)
Open revision guidance
What to know
Compare advantages and disadvantages: fibres offer high-capacity guided transmission with little leakage/interference but require physical cable routes and maintenance; satellites provide wide-area coverage but add delay, launch/space infrastructure and weather/line-of-sight constraints.
The source names geosynchronous/geostationary satellites as the comparison; do not claim either technology is universally superior.
What to do in an assessment
Compare both systems using the same criteria—coverage, capacity, delay, installation/access and reliability—and apply the criterion to the scenario.
Distinguish signal route: a fibre guides light in cable; a satellite relays electromagnetic signals through space.
In plain language
A cable can carry many signals along a fixed route, while a satellite can connect distant places without a continuous cable.
Self-check
Which method needs a physical cable route between its endpoints?
Show the answer
Optical-fibre communication.
Compare endoscopy with CT imagingCore
Scope: Core · Unit 1 §1.6(d)
Open revision guidance
What to know
Endoscopes use optical fibres to carry light into the body and return an image for remote examination; this can provide direct views of accessible internal surfaces.
CT uses X-rays and computer processing to create cross-sectional images; compare information obtained, invasiveness, radiation exposure, cost and suitability.
What to do in an assessment
Match the imaging method to the requested internal information and state a benefit and limitation of each.
Note that CT uses ionising X-rays, while endoscopy requires insertion of an instrument and may need clinical preparation.
In plain language
An endoscope sends light and images through a flexible instrument; a CT scanner uses X-rays to build slices through the body.
Self-check
Which technique uses optical fibres for remote imaging?
Show the answer
Endoscopy.

Calculate acceleration from velocity changePartial supportCore
Scope: Core · Unit 2 §2.1: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Acceleration = change in velocity ÷ time, a = (v − u)/t.
Use m/s for velocity and seconds for time to obtain m/s².
A negative acceleration sign depends on the chosen direction; describe the motion in context rather than treating “negative” as always slowing down.
What to do in an assessment
Convert any km/h values to m/s when required and show the change in velocity.
On a velocity-time graph, use gradient for acceleration and signed area for displacement.
In plain language
Acceleration measures how quickly velocity changes. If you choose forward as positive, a slowing car has a negative change in forward velocity; a car reversing may have negative velocity while speeding up.
Self-check
A runner changes velocity from 2 m/s to 8 m/s in 3 s. Find acceleration.
Show the answer
(8 − 2)/3 = 2 m/s².
Interpret motion graphs and calculate accelerationPartial supportCore
Scope: Core · Unit 2 §2.1: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Speed = distance/time; acceleration = change in velocity/time.
Distance-time graph gradient gives speed; velocity-time graph gradient gives acceleration and its area gives displacement.
A negative velocity or acceleration needs a stated direction convention.
What to do in an assessment
Use two points on a straight graph section and include the graph units.
Calculate acceleration from final minus initial velocity, not from speed alone when direction changes.
In plain language
Graph gradients turn a visual change into a rate. On a velocity-time graph, a steep slope means velocity changes quickly and the area shows signed displacement.
Self-check
Velocity changes from 2 m/s to 14 m/s in 4 s. Find acceleration.
Show the answer
a = (14 − 2)/4 = 3 m/s².
Describe motion, interpret graphs and assess stopping distanceCore
Scope: Core · Unit 2 §2.1(a)–(f), printed pp. 25–26
Open revision guidance
What to know
Distance is scalar; displacement includes direction. Speed is distance travelled per unit time; velocity is displacement per unit time. Acceleration is change in velocity per unit time, including deceleration.
On a distance–time graph, gradient is speed. On a velocity–time graph, gradient is acceleration; Higher adds finding distance travelled from the area; the bold distance-travelled graph skill is Higher-only in the separate Unit 2 extension.
Thinking distance is travelled during the driver's reaction time; braking distance is travelled after braking begins; stopping distance is their sum. Speed, tiredness, alcohol/drugs and distractions can affect thinking distance; road, tyre, brake and weather conditions affect braking distance.
Stopping-distance decisions combine measured evidence and physical reasoning with social views about traffic control, speed limits and seat belts; distinguish evidence from opinion.
What to do in an assessment
For 150 m in 10 s, speed = distance/time = 15 m/s. For velocity changing from 4 m/s to 16 m/s in 3 s, acceleration = (16−4)/3 = 4 m/s².
On a graph, read axes and units first, then identify the requested gradient; Higher also finds distance from area. A velocity–time gradient of (12−2) m/s over 5 s is 2 m/s².
When investigating acceleration, release the same object consistently, record repeated times with a stopwatch or use light gates/data loggers, and calculate a mean; identify reaction time or gate alignment as limitations.
Compare stopping-distance proposals using the same conditions and separate measured stopping distances from value judgements.
In plain language
Motion can be described by how position changes with time. A moving vehicle needs distance to respond and brake, so its stopping distance depends both on speed and on driver and road conditions.
Self-check
A car's thinking distance is 12 m and braking distance is 24 m. What is the stopping distance, and which part changes if the driver takes longer to react?
Show the answer
Stopping distance = 12 + 24 = 36 m. Longer reaction time increases thinking distance.
Higher: find distance travelled from a velocity–time graphCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.1(d), printed p. 26; bold fragment 'and distance travelled'
Open revision guidance
What to know
The area between a velocity–time graph and the time axis gives displacement. For motion that stays in one direction, its magnitude is distance travelled; if velocity changes sign, calculate total distance from the magnitudes of the separate areas.
Use a triangle, rectangle or trapezium area as appropriate and read both axes and units before calculating.
What to do in an assessment
A constant 6 m/s for 4 s gives rectangular area 6 × 4 = 24 m displacement and distance.
For a triangular velocity section rising from zero to 8 m/s over 3 s, area = ½ × 3 × 8 = 12 m. Add signed areas for displacement; add magnitudes for total distance when direction reverses.
In plain language
A velocity–time graph's area counts how far motion accumulates; a reversal changes the sign of displacement but not the amount of distance travelled.
Self-check
A graph shows 5 m/s for 6 s in one direction. Find distance travelled.
Show the answer
Area = 5 × 6 = 30 m.
Investigate acceleration and stopping-distance factorsCore
Scope: Core · Unit 2 §2.1 Working Scientifically, printed p. 25; acceleration/stopping-distance experimental contexts (not separately labelled specified practical work)
Open revision guidance
What to know
The English legacy §2.1 Working Scientifically paragraph presents opportunities to use stopwatches, light gates and data loggers to measure acceleration, and to investigate factors affecting stopping distance; it does not label this paragraph as a separately specified practical.
A useful motion investigation defines the measured quantities, controls conditions and uses repeated readings; a stopping-distance comparison must keep test conditions clear and distinguish driver reaction effects from road/braking effects.
What to do in an assessment
Use a stopwatch for a longer timed interval or light gates/data logging for short intervals; calculate speed/acceleration from recorded distance, velocity and time, and state measurement resolution.
For stopping-distance factors, vary one factor at a time where appropriate, record the conditions and distances, repeat readings, and discuss safety; do not conduct unsafe vehicle tests on public roads.
Evaluate reaction time, release consistency, calibration, surface condition and repeatability as possible limitations only when they apply to the actual chosen method.
In plain language
Measure motion with an instrument suited to the time scale, and compare stopping-distance evidence under clearly stated, safe conditions.
Self-check
Why might a light gate be preferred to a handheld stopwatch for a very short motion interval?
Show the answer
Its timing is less affected by a person's reaction time.

Explain motion using the resultant forcePartial supportCore
Scope: Core · Unit 2 §2.2: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
A resultant force changes an object’s velocity; if resultant force is zero, velocity remains constant.
For an object of mass m, F = ma links resultant force in newtons, mass in kilograms and acceleration in m/s².
Forces in an interaction pair act on different objects and are equal in magnitude and opposite in direction.
What to do in an assessment
Combine forces with direction before substituting into F = ma.
For action–reaction, name both objects and the force each exerts; two forces on one object cannot be an interaction pair.
In plain language
Motion changes only when forces do not balance. A moving object does not need a forward force to keep going at constant velocity; it needs a resultant force to change that velocity.
Self-check
A 2 kg cart has 10 N forward and 4 N backward. Find acceleration.
Show the answer
Resultant force = 10 − 4 = 6 N forward; a = F/m = 6/2 = 3 m/s² forward.
Connect resultant force, mass and accelerationPartial supportCore
Scope: Core · Unit 2 §2.2: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
A zero resultant force means constant velocity; a non-zero resultant changes velocity.
Newton’s second law gives F = ma for resultant force, mass and acceleration.
Forces in an interaction pair are equal and opposite and act on different objects.
What to do in an assessment
Draw forces on one object, combine them with directions and then use F = ma.
Name both objects when describing an action-reaction pair.
In plain language
A moving object can keep its velocity without a forward force if opposing forces balance. A net force is needed to speed it up, slow it down or change its direction.
Self-check
A 5 kg object has a resultant force of 15 N. Find its acceleration.
Show the answer
a = F/m = 15/5 = 3 m/s² in the direction of the resultant force.
Apply Newton’s laws, weight and terminal speedCore
Scope: Core · Unit 2 §2.2(a)–(g), printed p. 27
Open revision guidance
What to know
Mass is a measure of inertia; weight is the gravitational force on a mass. Near Earth's surface, 1 kg has weight approximately 10 N; use the g value given or specified.
A resultant force changes velocity. Acceleration is directly proportional to resultant force and inversely proportional to mass; combine forces with direction before using F = ma. Interaction forces act on different bodies, are equal in magnitude and opposite in direction.
A falling object accelerates while its weight exceeds air resistance. As speed rises, drag rises; terminal speed occurs when drag balances weight, resultant force is zero and velocity is constant.
The separately bold phrases requiring candidates to state Newton's first, second and third laws are Higher-only; common explanations and calculations remain common.
What to do in an assessment
A 2 kg cart with 10 N forward and 4 N backward has resultant force 6 N forward, so a = F/m = 6/2 = 3 m/s² forward.
Use W = mg: for m = 2.0 kg and g = 9.8 N/kg, W = 19.6 N; if the question specifies g = 10 N/kg, W = 20 N.
Draw a free-body diagram before reasoning about motion. At terminal speed, draw equal upward drag and downward weight; do not infer zero velocity from zero resultant force.
Describe each Newton-law interaction by naming both bodies and the force each exerts; two forces on one body are not a third-law pair.
In plain language
Forces explain changes in motion. A balanced set of forces can leave an object moving steadily, while a non-zero resultant changes its velocity.
Self-check
A 60 kg skydiver is falling at terminal speed. If g = 10 N/kg, what is the air-resistance force?
Show the answer
Weight is 60 × 10 = 600 N downward. At terminal speed the resultant force is zero, so air resistance is 600 N upward.
Higher: state Newton’s first, second and third lawsCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.2(b), (d), (g), printed p. 27; bold 'and be able to state it' fragments
Open revision guidance
What to know
First law: an object remains at rest or continues at constant velocity unless acted on by a resultant external force.
Second law: the resultant force equals the rate of change of momentum; for constant mass, F = ma.
Third law: when two bodies interact, they exert equal and opposite forces on one another; the forces act on different bodies.
What to do in an assessment
State the condition and consequence, not just a law's name: for zero resultant force, velocity is constant (which includes rest).
For the third law, identify both bodies, both forces and their opposite directions. For the second law, distinguish resultant force from one individual force.
In plain language
Higher candidates must be ready to express all three laws accurately, as well as apply the common ideas to motion.
Self-check
State Newton's first law.
Show the answer
An object remains at rest or continues moving at constant velocity unless acted on by a resultant external force.
Specified practical: investigate terminal speed of a falling objectCore
Scope: Core · Unit 2 §2.2 Specified Practical Work, printed p. 27
Open revision guidance
What to know
As an object falls, its speed rises while weight exceeds drag; increasing drag eventually balances weight, producing constant terminal speed.
To show terminal speed, measure motion at successive positions/times and test whether equal distances are covered in equal time intervals. Use an appropriate safe object and apparatus.
What to do in an assessment
Set up a safe, repeatable drop and mark or measure known distances. Record times for the object to pass successive intervals using a suitable timing method (such as video, light gates or data logging when appropriate).
Calculate interval speeds as distance/time and compare later intervals; approximately equal speeds indicate terminal motion. Repeat and average where appropriate.
Keep object shape/mass and medium fixed when comparing a run; explain timing resolution, release consistency and alignment as possible sources of uncertainty.
In plain language
Terminal speed means the falling object has stopped speeding up, so equal distance sections take about equal times.
Self-check
An object travels 0.40 m in each of two successive 0.20 s intervals. What evidence does this provide?
Show the answer
Both interval speeds are 0.40/0.20 = 2.0 m/s, consistent with constant speed over those intervals.

Calculate work done and gravitational energyPartial supportCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.3: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Work done by a constant force parallel to displacement is W = Fd.
A lift in height changes gravitational potential energy by ΔE = mgΔh, using mass in kg and gravitational field strength in N/kg.
Work and energy are measured in joules.
What to do in an assessment
Use the distance moved in the direction of the force; for weight gain, use vertical height.
Check whether the question asks for work by a force or change in gravitational energy.
In plain language
Work is energy transferred when a force moves something. Lifting a bag transfers energy into its gravitational store; moving it sideways at the same height does not change that store.
Self-check
A 3 kg object rises by 2 m where g = 10 N/kg. Find its gain in gravitational potential energy.
Show the answer
ΔE = mgΔh = 3 × 10 × 2 = 60 J.
Calculate work and changes in energy storesPartial supportCore
Scope: Core · Unit 2 §2.3: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Work done transfers energy: W = Fs for force along displacement.
Kinetic energy is Ek = ½mv² and gravitational potential energy change is ΔEp = mgΔh.
Power is energy transferred per time; efficiency is useful output divided by total input.
What to do in an assessment
Use SI units and show the energy store that changes.
Account for dissipated energy rather than assuming input energy equals useful output.
In plain language
Pushing an object transfers energy through work. If it speeds up, kinetic energy rises; if lifted, gravitational potential energy rises.
Self-check
What kinetic energy does a 4 kg object have at 2 m/s?
Show the answer
Ek = ½ × 4 × 2² = 8 J.
Explain work, energy stores, springs and vehicle efficiencyCore
Scope: Core · Unit 2 §2.3(a)–(i), printed pp. 28–29
Open revision guidance
What to know
When a force acts on a moving object, energy transfers between stores; total energy is conserved. Work is energy transferred by a force acting through a distance in its direction, W = Fd, measured in joules.
An object can have kinetic, gravitational-potential and elastic energy. A stretched spring stores elastic energy; in the linear region, force is proportional to extension and F = kx, where k is spring constant.
Vehicle efficiency can be improved by reducing aerodynamic drag, rolling resistance and idling losses. Apply force, energy and motion ideas to safety features such as seat belts, airbags and crumple zones.
The printed bold kinetic-energy and gravitational-potential-energy equations in (e), and the bold area-under-force–extension-graph method in (g), are Higher-only and taught separately.
What to do in an assessment
If a 12 N force moves an object 3 m in the force direction, W = Fd = 36 J. A force perpendicular to displacement does no work by this simple relation.
Plot force against extension using repeated readings and show the elastic region. For k = 20 N/m and extension x = 0.10 m, F = kx = 2.0 N; do not extend the linear rule beyond the measured proportional region.
For efficiency, state useful energy output and total energy input, then calculate a percentage; identify where energy is dissipated rather than saying energy is destroyed.
Relate a safety feature to the force/time or energy-transfer change it provides, and distinguish protection of occupants from prevention of a collision.
In plain language
Work transfers energy when a force moves something. Springs store energy when stretched, and design choices can make useful energy transfers safer or more efficient.
Self-check
A 15 N force moves a box 4 m in the direction of the force. How much work is done?
Show the answer
W = Fd = 15 × 4 = 60 J.
Higher: calculate kinetic, gravitational and spring energy transferCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.3(e), (g), printed p. 29; bold energy equations and force–extension area method
Open revision guidance
What to know
Kinetic energy KE = ½mv² (mass m in kg, speed v in m/s). Change in gravitational potential energy ΔPE = mgh (g in N/kg or m/s², vertical height change h in m). Both energy changes are in joules.
For a linear force–extension relationship, work done stretching is the area under the force–extension graph: W = ½Fx when force rises from zero to F over extension x. Use measured area for a non-linear graph, as the question requires.
What to do in an assessment
For m = 2.0 kg moving at 3.0 m/s, KE = ½ × 2.0 × 3.0² = 9.0 J.
For a 3.0 kg mass lifted 2.0 m with g = 10 N/kg, ΔPE = 3.0 × 10 × 2.0 = 60 J.
For a linear spring reaching 20 N at 0.10 m extension, W = ½ × 20 × 0.10 = 1.0 J. The triangular area is valid only for a straight-line graph from the origin.
In plain language
These Higher-only equations calculate energy from motion, lifting and stretching; match the formula to the physical change and use consistent SI units.
Self-check
Find the kinetic energy of a 4 kg object moving at 5 m/s.
Show the answer
KE = ½ × 4 × 5² = 50 J.
Specified practical: investigate a spring force–extension graphCore
Scope: Core · Unit 2 §2.3 Specified Practical Work, printed p. 29
Open revision guidance
What to know
Measure original and loaded lengths to find extension; a known hanging mass provides force from F = mg using the stated g value.
Plot force against extension and look for the straight-line region where force is proportional to extension. The gradient can determine the spring constant when the graph axes are force and extension.
What to do in an assessment
Secure the spring safely, record its unloaded length, add known loads in measured steps and read the new length at eye level. Calculate extension by subtracting the original length and weight by multiplying mass by g.
Repeat readings where practical, tabulate mass/force/length/extension with units and plot force against extension. Mark any departure from proportional behaviour; do not keep loading beyond safe elastic limits.
Use the measured gradient only in the linear region; identify parallax, ruler resolution, oscillation and spring hysteresis as possible limitations when relevant.
In plain language
Add known loads, measure how much the spring lengthens and use the graph to test whether force and extension remain proportional.
Self-check
A spring has unloaded length 12.0 cm and loaded length 15.5 cm. What is its extension?
Show the answer
15.5−12.0 = 3.5 cm = 0.035 m.

Read a radioactive decay curvePartial supportCore
Scope: Core · Unit 2 §2.8: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Half-life is the time for the number of undecayed nuclei or the activity to fall to half its initial value.
For n half-lives, activity fraction remaining is (1/2)^n.
Count-rate data may include background radiation, which should be subtracted before calculating source activity.
What to do in an assessment
Read the initial and halved values from the decay curve, then measure the time interval.
Use corrected count rates if background is stated and show the repeated-halving steps.
In plain language
A radioactive source does not decay on a timetable for each nucleus. In a large sample, however, a predictable fraction remains after each half-life.
Self-check
A source has 640 counts/min above background. What rate remains after two half-lives?
Show the answer
640 ÷ 2 ÷ 2 = 160 counts/min above background.
Calculate decay using half-lifePartial supportCore
Scope: Core · Unit 2 §2.8: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Half-life is the time for half the undecayed nuclei in a sample to decay or for activity to halve.
The decay of an individual nucleus is random, but the average behaviour of a large sample is predictable.
After each half-life, the remaining activity or nuclei count is halved.
What to do in an assessment
Find the number of elapsed half-lives and repeatedly halve the starting activity.
Subtract background count where given before comparing source count rates.
In plain language
A sample with 1000 undecayed nuclei is expected to have about 500 after one half-life and 250 after two. That does not identify which individual nuclei decay.
Self-check
A sample’s activity is 240 Bq. What is it after two half-lives?
Show the answer
240 → 120 → 60 Bq.
Model radioactive decay and use half-lifeCore
Scope: Core · Unit 2 §2.8(a)–(d), printed p. 35
Open revision guidance
What to know
Radioactive decay is random for each nucleus but can be modelled by a constant probability per unit time for a large sample. A dice or spreadsheet model is an analogy, not radioactive material.
Half-life is the time for the number of undecayed nuclei or activity to halve. The same half-life can be read from a decay curve at successive values.
After n half-lives, the fraction remaining is (1/2)^n. Activity/count-rate calculations and carbon-dating contexts use the ratio remaining and the stated half-life; correct for background where count data include it.
Uses of radioactive materials depend on half-life, penetration and biological effect; relate each property to the named tracer, treatment or application.
What to do in an assessment
If initial activity is 800 Bq, after 3 half-lives it is 800/2³ = 100 Bq. On a graph, read two activity values in a 2:1 ratio and measure their time separation.
For the dice practical, define the decay rule, such as removing dice showing one specified face; count survivors after each throw, repeat enough trials, and plot survivors against throws. A single trial fluctuates; a larger sample better displays the model trend.
For an unknown curve, subtract a stated background count before halving activity and use matching units on both axes.
Explain why individual decay times cannot be predicted while a large sample's average behaviour can be modelled.
In plain language
Half-life describes the predictable halving of a large sample, not a timer that tells when one particular nucleus will decay.
Self-check
A sample begins at 480 nuclei. How many are expected after two half-lives?
Show the answer
480/2/2 = 120 nuclei.
Specified practical: model half-life with a radioactive-source analogueCore
Scope: Core · Unit 2 §2.8 Specified Practical Work, printed p. 35
Open revision guidance
What to know
The WJEC practical is determination of model half-life, for example using dice. A model applies a fixed chance of 'decay' each throw; it does not reproduce the exact timing of each radioactive nucleus.
For a large set, plot number remaining against throws or model time; estimate half-life from the interval for the population to halve. Repeated runs vary because the model is random.
What to do in an assessment
Choose and record a decay rule (for example, remove each die showing a designated face), shake/roll consistently and count the remaining objects after each throw.
Repeat the process through several throws, table every count and graph count remaining against throws. Repeat a whole run or use a larger starting sample to see the average pattern more clearly.
Estimate a halving interval from the graph; explain random scatter and why an individual die/nucleus cannot be assigned a predictable decay time.
In plain language
The dice are a safe model of unpredictable individual decay and predictable large-sample behaviour.
Self-check
A model begins with 120 dice. If each throw leaves about half on average, how many remain after three throws?
Show the answer
120/2³ = 15 dice on average.

Conserve mass and charge in nuclear equationsPartial supportCore
Scope: Core · Unit 2 §2.9: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Nuclear equations conserve total nucleon number (mass number) and total proton number (atomic number).
Alpha emission lowers the parent’s mass number by 4 and atomic number by 2; beta-minus emission raises atomic number by 1 while mass number is unchanged.
Nuclear fission splits a heavy nucleus; fusion combines light nuclei, with energy released from mass-energy changes.
What to do in an assessment
Balance top numbers and bottom numbers independently, then check the daughter element from its proton number.
Explain energy release using mass defect and E = mc² only within the extent required by the paper.
In plain language
A nuclear equation is particle bookkeeping: the totals on each side must match. The identity of an element follows its proton number, so beta-minus decay changes which element the nucleus is.
Self-check
What happens to mass number and atomic number in beta-minus decay?
Show the answer
Mass number stays the same; atomic number increases by one.
Balance nuclear equations and compare fission with fusionPartial supportCore
Scope: Core · Unit 2 §2.9: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Nuclear equations conserve total mass number and total atomic number.
Fission splits a heavy nucleus and may release neutrons; fusion joins light nuclei under extreme conditions.
Nuclear reactions can release energy because the products have lower mass, with the difference transferred as energy.
What to do in an assessment
Balance nucleon and proton numbers separately.
Compare fission and fusion by whether nuclei split or combine, and by the conditions involved.
In plain language
Nuclear reactions rearrange nuclei. In fission a heavy nucleus splits; in fusion light nuclei join. Both can release energy through a small mass change.
Self-check
What must be conserved on both sides of a nuclear equation?
Show the answer
The total mass number (nucleon number) and total atomic number (proton number).
Explain nuclear fission, fusion and reactor containmentCore
Scope: Core · Unit 2 §2.9(a)–(f), printed p. 36
Open revision guidance
What to know
In a fissile nucleus, absorption of a slow neutron can cause fission into smaller nuclei and further neutrons. A controlled chain reaction is sustained when, on average, an emitted neutron causes another fission.
A moderator slows neutrons; control rods absorb neutrons to regulate or stop the chain reaction. Fission products may be radioactive and have a range of half-lives.
Fusion joins light nuclei such as hydrogen isotopes and can release energy. Fission splits heavy nuclei; in both processes a small mass change is associated with released energy.
Reactor challenges differ: fission needs containment of neutron/gamma radiation and radioactive products; fusion needs confinement at high temperature. Pressure, shielding and containment address distinct hazards.
Energy release comes from a decrease in total mass; the nuclear equation still conserves nucleon and proton numbers, not the separate rest masses. Fusion reactors face the technical challenge of maintaining/confining extremely hot fuel long enough for useful energy output.
What to do in an assessment
Balance supplied nuclear data by conserving total nucleon number and proton number. For example, ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n; check 236 nucleons and 92 protons on each side.
Use the neutron symbol ¹₀n and apply the same number-conservation check when given different products or fusion data; do not assume every fission yields the same fragments.
Compare fission and fusion by fuel nuclei, conditions, products, chain reaction/control and containment—not simply by saying one is 'clean'.
In plain language
Fission releases neutrons that can trigger more splitting; fusion joins small nuclei. Both need carefully controlled conditions and containment.
Self-check
What is the function of a moderator in a fission reactor?
Show the answer
It slows neutrons so they are more likely to cause further fission in the fissile fuel.
Higher: produce fission and fusion equationsCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.9(e), bold produce fragment; supplied-equation balancing remains common
Open revision guidance
What to know
To produce a fission or fusion equation, choose the stated parent/fuel and products, then conserve nucleon and proton numbers. Include the correct number of neutrons, using ¹₀n; different fission fragments are possible.
What to do in an assessment
Construct the supplied example process: ²³⁵₉₂U absorbs ¹₀n and splits into ¹⁴¹₅₆Ba and ⁹²₃₆Kr. The masses sum to 233, so three ¹₀n are emitted: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n. Protons sum to 92 on both sides.
For fusion of deuterium and tritium into helium-4: ²₁H + ³₁H → ⁴₂He + ¹₀n. Check five nucleons and two protons on each side. Identify released energy separately rather than assigning it a nucleon number.
In plain language
Higher adds constructing a nuclear-process equation from the described process; both tiers still balance an equation they are given.
Self-check
What particle completes ²₁H + ³₁H → ⁴₂He + ?
Show the answer
A neutron, ¹₀n, conserves five nucleons and two protons.

Explain fuse, earth and mains-wire safetyPartial supportCore
Scope: Core · Unit 1 §1.4: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
The live wire is dangerous relative to earth; neutral completes the mains circuit and earth is a protective path.
A fuse or circuit breaker interrupts excessive current; an earth wire lets a fault current operate the protection.
Appliances are connected in parallel so each receives the mains potential difference and can be controlled independently.
What to do in an assessment
Describe a fault from live wire to metal case and explain how earth plus fuse/breaker disconnects the supply.
State why a fuse or switch must break the live connection.
In plain language
If the live wire touches a metal casing, the earth wire provides a low-resistance fault path. The resulting current should melt the fuse or trip the breaker before the casing can seriously shock a user.
Self-check
Why are household appliances normally connected in parallel?
Show the answer
Each appliance receives the full mains potential difference and can operate independently; switching one off does not break the others’ circuits.
Use kilowatts and kilowatt-hours for domestic electricityCore
Scope: Core · Unit 1 §1.4(a)
Open revision guidance
What to know
A kilowatt (kW) is a convenient domestic power unit: 1 kW=1000 W. A kilowatt-hour (kWh) is energy, not power.
Energy in kWh = power in kW × time in hours.
What to do in an assessment
Convert watts to kilowatts and minutes to hours before calculating kWh; distinguish a device's kW rating from energy consumed.
Use kWh as the energy unit in household cost calculations.
In plain language
A kW tells how quickly an appliance transfers energy; a kWh tells how much energy it transfers over time.
Self-check
A 2 kW heater runs for 3 h. How much energy does it use?
Show the answer
2×3=6 kWh.
Calculate domestic electricity use and costCore
Scope: Core · Unit 1 §1.4(b)
Open revision guidance
What to know
Units used (kWh)=power (kW)×time (h); cost=units used×cost per unit.
Use the tariff unit price in the matching currency per kWh; a pence-per-unit price gives a cost in pence unless converted to pounds.
What to do in an assessment
Convert appliance power and operating time to kW and hours; calculate energy first, then multiply by the given cost per unit.
For multiple appliances sum their kWh before applying a common tariff; do not multiply cost directly by watts.
In plain language
First find how many kilowatt-hours the appliance uses, then multiply by the price charged for each kilowatt-hour.
Self-check
A 1.5 kW appliance runs 2 h at 30 p/kWh. Find its cost.
Show the answer
3 kWh×30 p=90 p (£0.90).
Use appliance data to investigate domestic energy costCore
Scope: Core · Unit 1 §1.4(c)
Open revision guidance
What to know
Appliance data may be obtained directly or from secondary sources, including energy banding (A–G) and power ratings.
A rating/power value alone does not specify cost: use operating time, energy use and the electricity tariff.
What to do in an assessment
Select relevant appliance power and usage data, calculate kWh and cost, and identify whether each value was measured or taken from a source.
Compare appliances for the same task and report assumptions about duration and frequency of use.
In plain language
An appliance label helps estimate energy use, but cost depends on how long and how often the appliance runs.
Self-check
What additional information is needed to calculate cost from an appliance's power rating?
Show the answer
Its operating time and the cost per unit of electricity.
Distinguish alternating current from direct currentCore
Scope: Core · Unit 1 §1.4(d)
Open revision guidance
What to know
Direct current flows in one direction; alternating current repeatedly reverses direction.
Domestic mains supply is alternating current; cells and batteries provide direct current.
What to do in an assessment
Identify the direction of charge flow over time rather than using voltage magnitude alone.
Use the source/device context to identify AC or DC in a circuit.
In plain language
DC keeps the same direction; AC changes direction repeatedly.
Self-check
Does current from a cell alternate direction?
Show the answer
No. A cell supplies direct current.
Explain fuses and circuit breakers and calculate fuse ratingCore
Scope: Core · Unit 1 §1.4(e)
Open revision guidance
What to know
A fuse melts when excessive current heats its element; an MCB trips when current exceeds its operating threshold; an RCCB detects an imbalance between live and neutral currents that can indicate leakage.
For a resistive appliance, operating current I=P/V can guide a suitable fuse rating: choose a rating above normal operating current but not so high that the cable/appliance is left unprotected.
What to do in an assessment
Calculate the operating current using consistent W and V; choose the smallest suitable standard fuse rating above that current when options are supplied.
Explain the device's response to overcurrent or leakage and that it interrupts the circuit to reduce fire/electric-shock risk.
In plain language
Safety devices disconnect a circuit when current is unsafe: a fuse melts, a breaker trips, and an RCCB responds to current leaking away from its intended path.
Self-check
A 1.2 kW appliance runs at 240 V. Estimate its normal current.
Show the answer
I=P/V=1200/240=5 A; choose a suitable rating just above 5 A from the available options.
Explain the ring main and live, neutral and earth wiresCore
Scope: Core · Unit 1 §1.4(f)
Open revision guidance
What to know
The live wire is at alternating potential relative to earth and supplies energy; the neutral wire completes the circuit and is close to earth potential; the earth wire is a safety path for fault current.
A domestic ring main forms a loop from and back to the supply, allowing appliances to be supplied around the circuit; fuse/MCB protection interrupts excessive current.
What to do in an assessment
Label the three conductors by function and trace the intended operating-current path through live and neutral.
For a fault to a metal case, explain that earth provides a low-resistance path that produces a large enough current to operate the protective device.
In plain language
Live and neutral normally carry current through an appliance; earth is a safety connection used if a fault makes an exposed case live.
Self-check
Why is the earth wire connected to a metal appliance case?
Show the answer
It provides a fault-current path so the protective device disconnects the supply instead of leaving the case dangerously live.
Evaluate domestic solar and wind equipment using payback dataCore
Scope: Core · Unit 1 §1.4(g)
Open revision guidance
What to know
Compare the cost-effectiveness of domestic solar and wind equipment using fuel/electricity cost savings and payback time from data.
Generation depends on local resource and installation conditions; capital/maintenance cost and expected service life affect the decision.
What to do in an assessment
Calculate annual savings from the supplied data, then simple payback=initial cost/annual saving; compare payback with expected lifetime.
Use the same assumptions and include both cost savings and resource/environmental limitations.
In plain language
A home system may reduce purchased energy, but its value depends on installation cost, local sunlight or wind and how long savings continue.
Self-check
A home wind system costs £2400 and saves £300 per year. What is its simple payback?
Show the answer
2400/300=8 years.
Investigate energy transfers and evaluate data and methodsCore
Scope: Core · Unit 1 §1.4(h)
Open revision guidance
What to know
Investigations include interpreting and analysing data and evaluating validity of both data and methods.
Specified contexts include renewable-source output (for example wind-turbine construction/location) and energy-transfer efficiency (for example an electric kettle).
What to do in an assessment
For a kettle, compare useful heating energy mcΔθ with electrical input Pt; for a wind turbine, control or record wind speed, blade/construction and location conditions.
Plot/compare repeated results, identify controls and measurement limits, and distinguish validity (method answers the question) from repeatability or precision.
In plain language
Measure energy entering and leaving a system, then decide whether the method and evidence support the efficiency or output claim.
Self-check
For a kettle, what energy can be treated as useful output when heating water?
Show the answer
The water's increase in thermal energy, approximately mcΔθ.

Use seismic waves to infer Earth structurePartial supportCore
Scope: Core · Unit 1 §1.7: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Earthquakes generate seismic waves that travel through Earth and are recorded by seismometers.
Longitudinal P-waves travel through solids and liquids; transverse S-waves travel through solids but not through liquids.
Different arrival times and shadow regions provide evidence about Earth’s internal layers.
What to do in an assessment
Compare wave travel times and identify which wave arrives first.
Use absence of S-waves through a region as evidence that the region is liquid.
In plain language
A seismometer far from an earthquake can receive P-waves but not S-waves through Earth’s outer core. This pattern supports the conclusion that the outer core is liquid.
Self-check
Why do S-waves not pass through Earth’s liquid outer core?
Show the answer
S-waves are transverse shear waves and a liquid cannot sustain the required shear deformation.
Compare seismic P, S and surface wavesCore
Scope: Core · Unit 1 §1.7(a)
Open revision guidance
What to know
P waves are longitudinal and travel through solids and liquids; S waves are transverse and cannot travel through liquids; surface waves travel along Earth's surface.
P waves are generally faster than S waves; surface waves are slower and often cause strong ground motion. Compare their nature, speed and ability to pass through materials.
What to do in an assessment
Use arrival order to identify P before S at a station and use whether a liquid layer is present to test whether S waves can pass.
Do not infer an exact speed from material density/stiffness unless data are provided.
In plain language
Earthquakes send different seismic waves: fast P waves pass through liquid and solid, while S waves cannot cross liquid.
Self-check
Which seismic wave cannot travel through a liquid?
Show the answer
An S wave.
Identify P waves as longitudinal and S waves as transverseCore
Scope: Core · Unit 1 §1.7(b)
Open revision guidance
What to know
Particle oscillations in a P wave are parallel to its travel direction; oscillations in an S wave are perpendicular.
This distinction explains why shear S waves do not propagate through liquids.
What to do in an assessment
Draw travel direction and particle displacement arrows, then classify the wave from their relationship.
Do not confuse the direction a wave travels with the direction a particle oscillates.
In plain language
P compressions move along the direction the wave travels; S-wave motion is across that direction.
Self-check
Which wave has perpendicular oscillations and travel direction?
Show the answer
The transverse S wave.
Use seismic records to find earthquake lag time and epicentreCore
Scope: Core · Unit 1 §1.7(c)
Open revision guidance
What to know
On a simplified seismogram, the P–S lag is the time between the first P arrival and first S arrival; greater lag indicates a greater distance from the epicentre.
Use records from several stations to find the epicentre; each station gives a distance circle and the intersection locates the source.
What to do in an assessment
Read both arrival times from one time axis, subtract P from S, then use a supplied travel-time graph/table to convert lag to distance.
Draw/map distance circles from at least three stations and identify their common intersection; include map scale units.
In plain language
The time gap between fast P waves and slower S waves reveals how far the earthquake was from a station; several stations pinpoint it.
Self-check
P waves arrive at 10:02 and S waves at 10:05. What is the lag?
Show the answer
3 minutes.
Trace P- and S-wave paths through EarthCore
Scope: Core · Unit 1 §1.7(d)
Open revision guidance
What to know
Use diagrams/records to describe P- and S-wave paths through Earth and where waves are detected or absent.
The specification explicitly excludes examination of how seismic-wave speed depends on material density and stiffness; do not add that as a required explanation.
What to do in an assessment
Trace each wave path and mark where an S wave is blocked by liquid; distinguish a path diagram from a detailed quantitative Earth model.
If given an observed travel-time or shadow-zone pattern, use it as evidence rather than inventing material-speed calculations.
In plain language
Earthquake records show that wave paths change inside Earth and that some regions do not receive S waves.
Self-check
Is the speed dependence on density and stiffness required in this specification point?
Show the answer
No; the source explicitly says that dependence will not be examined.
Use the S-wave shadow zone as evidence about Earth's interiorCore
Scope: Core · Unit 1 §1.7(e)
Open revision guidance
What to know
S waves cannot pass through liquid; their shadow zone in seismic records indicates a liquid region within Earth.
The specified inference is a solid mantle and liquid core; use the absence/presence pattern as the evidence for the model.
What to do in an assessment
Connect observation (S waves absent in a region) to the limitation (no S-wave transmission through liquid), then state the inferred interior structure.
Distinguish direct seismic evidence from a model of inaccessible internal layers.
In plain language
A region with no recorded S waves suggests that the waves encountered liquid inside Earth; this supports the model of a solid mantle around a liquid core.
Self-check
What does an S-wave shadow zone support about Earth's interior in this syllabus?
Show the answer
A model with a solid mantle and a liquid core.

Explain circular motion and momentum in contextPartial supportCore
Scope: Core · Unit 2 §2.4: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
An object travelling in a circle at constant speed changes velocity because direction changes.
An inward resultant force is needed for circular motion.
Momentum p = mv includes direction; an isolated system’s total momentum is conserved in an interaction.
What to do in an assessment
Draw the centripetal force toward the circle’s centre, not along the direction of motion.
Use signed velocities to solve one-dimensional collision problems.
In plain language
A satellite can move at steady speed yet accelerate because it is constantly turning. Gravity supplies the inward force that keeps the path curved.
Self-check
What direction does the centripetal resultant force point?
Show the answer
Toward the centre of the circular path.
Use momentum, motion equations and momentsCore
Scope: Core · Unit 2 §2.4(a)–(f), printed pp. 30–31
Open revision guidance
What to know
Momentum p = mv depends on mass and velocity. For an isolated system, total momentum is conserved; link this to Newton's third law and compare before/after states for collisions; the explosion extension is Higher-only.
Newton's second law can be written force = change in momentum/time. The common uniformly accelerated-motion equations are v = u + at and x = (u + v)t/2; the two separately bold equations are Higher-only.
Moments describe turning effect about a pivot: moment = force × perpendicular distance from pivot, M = Fd. The Principle of Moments is limited here to a pivot and parallel forces.
The printed bold instruction to select kinetic energy and compare before and after a collision/explosion is Higher-only; other conservation and momentum outcomes remain common.
What to do in an assessment
For a 0.20 kg ball travelling at 5 m/s, p = mv = 1.0 kg m/s. Keep direction/signs consistent when adding momenta.
A body changes velocity from 3 m/s to 15 m/s in 4 s: v = u + at gives a = (15−3)/4 = 3 m/s². Convert distances and times to SI before selecting an equation.
A 5 N force acting 0.30 m perpendicular to a pivot gives M = Fd = 1.5 N m. For balance with parallel forces, take clockwise and anticlockwise moments about the same pivot.
For the moments practical, measure lever arms perpendicular to each force and repeat balances; record how pivot location and apparatus mass are controlled.
In plain language
Momentum keeps track of motion in a collision, while a moment measures how strongly a force turns an object about a pivot.
Self-check
A 4 N force acts 0.25 m from a pivot at right angles. Find its moment.
Show the answer
M = Fd = 4 × 0.25 = 1.0 N m.
Higher: compare collision energy and use additional motion equationsCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.4(c), (d), printed p. 31; bold collision-energy and two-equation fragments
Open revision guidance
What to know
The two additional uniformly accelerated-motion equations printed bold are x = ut + ½at² and v² = u² + 2ax. Here u and v are initial/final velocity, a acceleration, t time and x displacement; use them only for constant acceleration.
Use KE = ½mv² to compare kinetic energy before and after a collision or explosion. A change in total kinetic energy does not mean momentum conservation has failed; energy can transfer to other stores.
What to do in an assessment
A body starts from rest, accelerates at 2 m/s² for 4 s: x = 0 + ½ × 2 × 4² = 16 m.
A body with u = 3 m/s accelerates at 2 m/s² over 4 m: v² = 3² + 2 × 2 × 4 = 25, so v = 5 m/s in the stated direction.
For a collision, calculate each object's KE before and after with consistent units and compare totals; keep velocity signs for momentum separate from speed in KE.
For an explosion of a previously stationary system, total initial momentum is zero. Two 2 kg fragments moving apart at 3 m/s and −3 m/s have momenta +6 and −6 kg m/s, conserving total zero; their kinetic energy is supplied by the stored energy released.
In plain language
The extra equations make it possible to connect displacement, speed and acceleration without a time value; the energy comparison describes one possible transfer in a collision.
Self-check
Starting from rest, an object accelerates at 3 m/s² for 2 s. Find displacement using the Higher equation.
Show the answer
x = ut + ½at² = 0 + ½ × 3 × 2² = 6 m.
Specified practical: investigate the Principle of MomentsCore
Scope: Core · Unit 2 §2.4 Specified Practical Work, printed p. 31
Open revision guidance
What to know
For parallel forces, calculate each moment about the same pivot using force multiplied by perpendicular distance. In balance, total clockwise moment equals total anticlockwise moment.
A metre rule or similar balanced beam allows the pivot, forces and distances to be identified; include the apparatus' own weight where its line of action matters.
What to do in an assessment
Balance the rule on a pivot and note the pivot position. Add known masses at measured distances on each side; convert mass to force using the stated g value.
Measure perpendicular distances from pivot to force line, adjust until the rule balances, then total clockwise and anticlockwise moments in N m.
Repeat with different mass/distance combinations and compare totals. Keep the pivot and applied-force directions clear; account for zero error, mass of the rule and reading uncertainty.
In plain language
A balanced beam has equal turning effects in opposite directions about the same pivot.
Self-check
A 2 N force acts 0.30 m from a pivot. What opposing moment is needed for balance?
Show the answer
2 × 0.30 = 0.60 N m anticlockwise or clockwise opposite to the first moment.

Describe star life cycles by starting massPartial supportCore
Scope: Core · Unit 2 §2.5: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Stars form from collapsing gas and dust and release energy by nuclear fusion.
A star’s later stages depend on initial mass: a Sun-like star becomes a red giant then white dwarf; a massive star can become a supernova and leave a neutron star or black hole.
Gravity provides the force that keeps planets and satellites in orbit.
What to do in an assessment
Choose the correct evolution branch based on mass and order the stages.
Explain stable star structure as balance between inward gravity and outward pressure.
In plain language
Stars do not all finish the same way. A massive star has enough gravity to follow a supernova route, while a star like the Sun ends as a white dwarf.
Self-check
What is the likely remnant of a Sun-like star?
Show the answer
A white dwarf, after the red-giant stage and loss of its outer layers.
Describe the Solar System, stars and stellar evolutionCore
Scope: Core · Unit 2 §2.5(a)–(g), printed p. 32
Open revision guidance
What to know
The Solar System contains the Sun, planets and their moons, dwarf planets, comets and asteroids; describe their relative order, scale, orbits and composition as required.
Astronomical distance units include kilometres, astronomical units (AU) and light-years. A light-year is a distance light travels in one year, not a time; use conversions or values supplied in the question.
A star forms from a collapsing cloud of gas and dust. Its life path depends mainly on initial mass: stars pass through a main-sequence stage, then lower-mass stars become red giants and white dwarfs; higher-mass stars can become supergiants, explode as supernovae and leave neutron stars or black holes.
A star's stability reflects a balance between inward gravity and outward gas/radiation pressure. Fusion builds heavier elements in stars; supernovae return elements to space. The bold H–R diagram outcome is Higher-only.
A protostar forms when gravity draws together gas and dust. In the main sequence, hydrogen fusion supports the star; later stages depend on initial mass. A Sun-like star becomes a red giant then a white dwarf, whereas a massive star can become a supergiant, explode as a supernova, and leave a neutron star or black hole.
What to do in an assessment
When ordering objects, distinguish orbital distance, physical size and composition; use an appropriate supplied scale and retain its precision.
Explain stellar stages as a branching path by starting mass rather than one sequence for all stars.
Connect observations to claims: a diagram classifies measured stellar properties, while a life-cycle model is an explanation supported by evidence.
In plain language
Stars change over time, and their starting mass determines which later stages they can reach. Gravity and pressure compete inside a star.
Self-check
Does a light-year measure time or distance?
Show the answer
Distance: it is how far light travels in one year.
Higher: interpret the Hertzsprung–Russell diagramCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.5(g), printed p. 32; entire statement printed bold
Open revision guidance
What to know
An H–R diagram displays stellar properties, conventionally luminosity against surface temperature or spectral class. Temperature conventionally decreases from left to right; luminosity increases upward.
Stars occupy regions associated with life stages; evolutionary paths connect stages and depend on starting mass. Use plotted position and labels rather than assuming all stars follow the same path.
What to do in an assessment
Read the axis direction before interpreting position. A star high on the diagram is more luminous; on a conventional temperature axis, a point farther left is hotter.
Use the plotted region and the specified life-cycle model to describe a star's properties or likely path; retain qualifiers such as 'main sequence' or 'red giant'.
In plain language
The H–R diagram groups stars by brightness and temperature so their different evolutionary stages can be compared.
Self-check
On the conventional H–R diagram with temperature decreasing left to right, which is hotter: a star on the left or right?
Show the answer
A star farther left is hotter.
View diagrams
Hertzsprung-Russell diagram and stellar classification
Luminosity is plotted logarithmically upward and surface temperature decreases from left to right. The labelled illustrative points classify the Sun on the main sequence, a hot dim white dwarf, and a cool luminous red giant; no observational star catalogue data are implied.
Compare luminosity and surface temperature, noting that the temperature axis runs from hot on the left to cool on the right.

Use red-shift as evidence for an expanding universePartial supportCore
Scope: Core · Unit 2 §2.6: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Light from many distant galaxies is shifted to longer wavelengths compared with the same spectral lines measured in a laboratory.
Red-shift indicates recession; the more distant galaxies generally have greater recession speeds.
This evidence supports an expanding universe and a common origin model.
What to do in an assessment
State that observed wavelength has increased before drawing a conclusion about recession.
Distinguish evidence for expansion from an unsupported claim that Earth is the centre.
In plain language
A longer wavelength tells us a distant galaxy is moving away. Seeing this pattern widely across the Universe is evidence that space is expanding.
Self-check
What does red-shift tell us about the motion of a galaxy?
Show the answer
Its light has shifted to longer wavelength, indicating that it is receding from the observer.
Explain red shift and evidence for the Big BangCore
Scope: Core · Unit 2 §2.6(a)–(e), printed p. 33
Open revision guidance
What to know
Absorption spectra contain dark lines associated with particular elements. Compare line patterns with known spectra to identify gases; historical observations showed that stars contain familiar elements.
For distant galaxies, spectral lines shift toward longer wavelengths (red shift). Greater red shift is associated with greater distance in the stated Hubble relationship.
The cosmological interpretation is that space has expanded since the radiation was emitted, stretching wavelengths. Red shift provides evidence for an expanding Universe and supports the Big Bang model.
The Cosmic Microwave Background is relic radiation that supports a hot early Universe; state how it contributes evidence rather than presenting one observation as a complete proof.
What to do in an assessment
Compare observed and reference absorption-line positions, identify a consistent shift, then state what the pattern supports.
Keep observation and interpretation distinct: measured line displacement is evidence; expansion is the model used to explain it.
When a question supplies spectra or red-shift data, use its scale and quote the comparison instead of assuming an unsupplied numerical constant.
In plain language
Light from many distant galaxies arrives with its spectral pattern stretched toward longer wavelengths. Together with the cosmic microwave background, this supports a changing Universe with a hot, dense early stage.
Self-check
What happens to the wavelength of a spectral line when its light is red-shifted?
Show the answer
It is shifted to a longer wavelength.

Compare alpha, beta and gamma radiationPartial supportCore
Scope: Core · Unit 2 §2.7: additional worked support, not a second full requirement
This explanation covers part of the source requirement only. Its tick is separate and does not count as a fully revised requirement.
Open revision guidance
What to know
Alpha is a helium nucleus, beta-minus is an electron emitted from the nucleus, and gamma is electromagnetic radiation.
Alpha is most ionising and least penetrating; beta is intermediate; gamma is least ionising and most penetrating.
Ionising radiation can damage cells; exposure and contamination risks differ.
What to do in an assessment
Match the type to suitable shielding and describe both ionisation and penetration.
Explain safety using reduced time, greater distance and appropriate shielding.
In plain language
Alpha travels only a short distance in air and is stopped by paper, while gamma penetrates farther and needs thick dense shielding to reduce it.
Self-check
Which radiation is stopped by a thin sheet of paper?
Show the answer
Alpha radiation.
Compare radiation, nuclear notation and radiation risksCore
Scope: Core · Unit 2 §2.7(a)–(i), printed pp. 34–35
Open revision guidance
What to know
The nucleon (mass) number A counts protons plus neutrons; proton (atomic) number Z counts protons. Isotopes share Z but have different neutron numbers. Radioactive decay is spontaneous and random for individual nuclei.
Background radiation comes from natural and artificial sources, including rocks/radon, cosmic radiation and medical sources such as X-rays. Correct a measured count rate for background and consider variation between readings.
Alpha is a helium nucleus, beta radiation here is a high-energy electron and gamma is electromagnetic radiation. Compare penetration and ionisation qualitatively and connect these properties to shielding, exposure and storage of radioactive waste.
Both tiers balance supplied nuclear-decay equations: conserve nucleon number and proton number separately, using ⁴₂He (or ⁴₂α) and ⁰₋₁e (or ⁰₋₁β). Producing an equation yourself is the Higher-only fragment. Some radioactive waste remains radioactive for thousands of years; storage must account for radiation type and long-term risk.
What to do in an assessment
If source plus background is 72 counts/min and background is 18 counts/min, estimated source count rate is 72−18 = 54 counts/min.
Repeat count measurements for an appropriate period, compare variation and avoid treating one random reading as exact. State whether you report gross or background-corrected counts.
For nuclear notation, check proton and nucleon numbers separately and identify the element from Z; balance supplied equations at both tiers; produce an equation independently only when Unit 2 is Higher.
Evaluate risk by considering source activity, exposure time, distance, shielding and route of exposure; do not equate 'natural' with 'harmless'.
Complete a supplied alpha equation: ²³⁸₉₂U → ? + ⁴₂He. Subtract 4 from 238 and 2 from 92 to obtain ²³⁴₉₀Th. For supplied beta-minus decay, nucleon number is unchanged and daughter proton number rises by one. Radon levels vary with local geology, ventilation and building design; compare evidence rather than assuming a single national background rate.
In plain language
Radioactive decay is unpredictable for one nucleus but produces measurable patterns in large samples. Radiation types differ in what they are and how they interact with matter.
Self-check
A detector records 45 counts/min while background is 12 counts/min. What source count rate remains after correction?
Show the answer
45−12 = 33 counts/min.
Higher: produce and balance alpha- and beta-decay equationsCore
Scope: Core · Unit 2 written-paper tier: Higher tier · Unit 2 §2.7(h), printed p. 34; entire equation-production statement printed bold
Open revision guidance
What to know
Use ⁴₂He for an alpha particle and ⁰₋₁e for the beta-minus electron specified. Conserve nucleon number (top) and proton number (bottom) across the equation.
Alpha emission reduces the parent nucleon number by four and proton number by two. Beta-minus emission leaves nucleon number unchanged and increases the daughter proton number by one; the emitted electron carries −1 charge.
What to do in an assessment
Alpha example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He; check 238 = 234 + 4 and 92 = 90 + 2.
Beta-minus example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e; check 14 = 14 + 0 and 6 = 7 − 1.
After balancing, identify the daughter element from its proton number and check both rows independently.
In plain language
Nuclear equations are a bookkeeping check for protons and nucleons; the emitted particle determines how the nucleus changes.
Self-check
Complete alpha decay of ²²⁶₈₈Ra by conserving both numbers.
Show the answer
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He.

Appendix A: plan, measure, analyse and evaluate scientific workCore
Scope: Core · Legacy Appendix A §§1–4, printed pp. 41–42
Open revision guidance
What to know
Scientific thinking includes how methods, theories and models develop; using models to solve problems and make predictions; considering limits and ethics; evaluating technological/social/environmental consequences and risk; and communicating work subject to peer review.
Experimental skills include forming a hypothesis, planning procedures, selecting suitable apparatus and techniques, working accurately and safely, recording observations and measurements, and evaluating methods with specific improvements.
Analysis/evaluation includes presenting and translating data, mathematical analysis, estimating uncertainty, identifying patterns and trends, making inferences and conclusions linked to evidence/hypotheses, and judging accuracy, precision, repeatability, reproducibility and random/systematic error.
Use precise scientific vocabulary and definitions, recognise how quantities are determined, use SI units/prefixes and appropriate symbols, convert units and apply the separate bold Appendix A significant-figures fragment only under its Higher predicate.
What to do in an assessment
Plan a fair test by stating the independent variable, measured dependent variable, controls, range/repeats, apparatus resolution and one relevant hazard/control measure.
Record raw readings with units and suitable decimal places; process only after preserving the observations, show calculations and plots, then state a conclusion tied to the data.
Evaluate a limitation by explaining its direction/effect and propose a feasible targeted improvement; repeating readings reduces random scatter but does not remove a systematic zero error.
When using secondary data or a model, identify its source/assumptions and state what evidence would support or challenge the conclusion.
In plain language
A scientific answer moves from a clear question through a safe, suitable method and trustworthy measurements to a conclusion that the evidence can support.
Self-check
Why does repeating a measurement not remove a systematic zero error?
Show the answer
The same bias remains in every reading; correct or recalibrate the instrument/method rather than relying on a mean.

Revision points, with the explanation beside them

Unit 1 written-paper tier

Unit 2 written-paper tier

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know

What to do in an assessment

In plain language

Self-check

What to know