The exam gives you a small number of equations where a question needs them, but you are expected to recall most of the rest. This sheet lists the equations and facts to learn by heart, grouped by topic, and does not copy the paper's own list. Use it for daily recall practice, covering the symbols and units as well as the formula itself.
Motion
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| speed = distance ÷ time | speed in m/s, distance in m, time in s | Constant speed and average speed |
| acceleration = change in velocity ÷ time | a = (v − u) ÷ t; a in m/s², v and u in m/s, t in s | Any change of velocity over a time |
| v² = u² + 2as | v final and u initial velocity (m/s), a acceleration (m/s²), s displacement (m) | Constant acceleration when time is not given |
| gradient of a distance–time graph | Gradient equals speed (m/s) | Reading speed from a graph |
| area under a velocity–time graph | Area equals distance travelled (m) | Finding distance from a graph |
| gradient of a velocity–time graph | Gradient equals acceleration (m/s²) | Reading acceleration from a graph |
Forces and momentum
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| F = ma | Resultant force F (N), mass m (kg), acceleration a (m/s²) | Unbalanced forces and Newton's second law |
| W = mg | Weight W (N), mass m (kg), gravitational field strength g (N/kg) | Converting between mass and weight |
| p = mv | Momentum p (kg m/s), mass m (kg), velocity v (m/s) | Collisions and explosions (Paper 2 only) |
| F = (mv − mu) ÷ t | Force equals rate of change of momentum; F (N), t (s) | Impact forces and safety features (Paper 2 only) |
| momentum before = momentum after | Total momentum of a closed system is conserved | Collision and recoil problems (Paper 2 only) |
| moment = force × perpendicular distance | Moment in N m, force in N, distance in m from the pivot | Levers, balances and turning effects (Paper 2 only) |
| clockwise moments = anticlockwise moments | Sum about the same pivot when in equilibrium | Balanced beams and seesaws (Paper 2 only) |
| thinking distance = speed × reaction time | Distances in m, speed in m/s, time in s | Stopping distances |
| stopping distance = thinking + braking distance | Both distances in m | Road safety questions |
Energy, work and power
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| work done = force × distance moved | W in J, F in N, distance in m along the force | Mechanical work |
| KE = ½mv² | Kinetic energy (J), mass (kg), speed (m/s) | Moving objects |
| GPE = mgh | Gravitational potential energy (J), mass (kg), g (N/kg), height change h (m) | Lifting and falling objects |
| power = energy transferred ÷ time | P in W, E in J, t in s | Rates of energy transfer |
| power = work done ÷ time | Same idea, with work done in J | Machines and lifting |
| efficiency = useful output ÷ total input | Energy or power; give as a fraction or multiply by 100% | Energy transfer devices |
| ΔE = mcΔθ | Energy change (J), mass (kg), specific heat capacity c (J/kg °C), temperature change (°C) | Heating and cooling (Paper 2 only) |
Solids, liquids and gases
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| density = mass ÷ volume | ρ in kg/m³ (or g/cm³), mass in kg (g), volume in m³ (cm³) | Floating, sinking and material identification |
| p = F ÷ A | Pressure p (Pa), force F (N), area A (m²) | Solids pressing on a surface |
| p = hρg | Pressure from a liquid column (Pa), depth h (m), density ρ (kg/m³), g (N/kg) | Pressure in fluids |
| pV = constant | Fixed mass and temperature; p and V in consistent units | Boyle's law problems |
| p₁V₁ = p₂V₂ | Pressure and volume before and after a change | Compressing or expanding a gas |
| p ÷ T = constant | Fixed volume and mass; T in kelvin | Gas heated in a rigid container |
| T(K) = θ(°C) + 273 | Kelvin and Celsius conversion | Any gas law calculation |
Waves and light
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| v = fλ | Wave speed v (m/s), frequency f (Hz), wavelength λ (m) | All wave calculations |
| f = 1 ÷ T | Frequency f (Hz), period T (s) | Linking period and frequency |
| n = sin i ÷ sin r | Refractive index n, angle of incidence i, angle of refraction r | Refraction at a boundary |
| sin c = 1 ÷ n | Critical angle c for total internal reflection | Optical fibres and prisms |
| speed = distance ÷ time (for sound and echoes) | Total path travelled is twice the distance to the reflector | Echo and speed-of-sound questions |
Electricity
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| Q = It | Charge Q (C), current I (A), time t (s) | Charge flow |
| V = IR | Potential difference V (V), current I (A), resistance R (Ω) | Any resistor circuit |
| P = IV | Power P (W), current I (A), potential difference V (V) | Electrical power |
| P = I²R | Power in a resistor (W) | When current and resistance are known |
| E = IVt | Energy transferred (J), time t (s) | Energy used by an appliance |
| E = QV | Energy (J), charge (C), potential difference (V) | Energy change per charge |
| R = R₁ + R₂ | Total resistance in series (Ω) | Series circuits |
| Vp ÷ Vs = Np ÷ Ns | Transformer voltages and turns on primary and secondary coils | Step-up and step-down transformers (Paper 2 only) |
| VpIp = VsIs | Power in equals power out for an ideal transformer | Transformer current calculations (Paper 2 only) |
Radioactivity and astrophysics
| Formula | Meaning, symbols and units | When you use it |
|---|---|---|
| A = Z + N | Mass number A, proton number Z, neutron number N | Writing nuclear symbols |
| remaining fraction = (½)ⁿ | n is the number of half-lives elapsed | Half-life calculations |
| n = total time ÷ half-life | Number of half-lives passed | Setting up decay questions |
| alpha: A − 4, Z − 2 | Changes in a nucleus after alpha emission | Balancing decay equations |
| beta minus: A same, Z + 1 | Changes in a nucleus after beta minus emission | Balancing decay equations |
| Δλ ÷ λ = v ÷ c | Change in wavelength ÷ reference wavelength = galaxy speed ÷ speed of light | Red-shift of galaxies (Paper 2 only) |
| orbital speed = 2πr ÷ T | Speed v (m/s), orbital radius r (m), period T (s) | Planets and satellites |