Motion
| Quantity | Formula | SI unit |
|---|---|---|
| Speed | v = distance ÷ time | m/s |
| Acceleration | a = (v - u) ÷ t | m/s2 |
| First equation of motion | v = u + at | m/s |
| Second equation of motion | s = ut + ½at2 | m |
| Third equation of motion | v2 = u2 + 2as | m2/s2 |
| Average speed | Total distance ÷ total time | m/s |
u is the initial velocity, v the final velocity, a the acceleration, t the time and s the distance travelled.
Force, work, energy and power
| Quantity | Formula | SI unit |
|---|---|---|
| Momentum | p = m × v | kg m/s |
| Force (Newton second law) | F = m × a | newton (N) |
| Work | W = F × s | joule (J) |
| Kinetic energy | KE = ½mv2 | joule (J) |
| Potential energy | PE = mgh | joule (J) |
| Power | P = W ÷ t | watt (W) |
| Pressure | P = F ÷ A | pascal (Pa) |
| Density | ρ = m ÷ V | kg/m3 |
| Weight | W = m × g | newton (N) |
g is about 9.8 m/s2 near the Earth surface (often taken as 10 m/s2 in problems).
Gravitation
| Idea | Formula or value |
|---|---|
| Universal law of gravitation | F = G m1 m2 ÷ r2 |
| Value of G | 6.67 × 10-11 N m2/kg2 |
| Acceleration due to gravity on Earth | g about 9.8 m/s2 |
| Archimedes principle | Buoyant force = weight of the liquid displaced |
Light
| Idea | Formula |
|---|---|
| Mirror formula | 1/v + 1/u = 1/f |
| Magnification by a mirror | m = h' ÷ h = -v ÷ u |
| Lens formula | 1/v - 1/u = 1/f |
| Power of a lens | P = 1 ÷ f (f in metres); unit dioptre (D) |
| Refractive index | n = sin i ÷ sin r = speed of light in air ÷ speed of light in the medium |
| Focal length of a spherical mirror | f = R ÷ 2 |
Use the sign convention from your textbook: distances are measured from the pole or optical centre, and the direction of incident light is taken as positive.
Electricity
| Quantity | Formula | SI unit |
|---|---|---|
| Charge | Q = I × t | coulomb (C) |
| Potential difference | V = W ÷ Q | volt (V) |
| Ohm's law | V = I × R | ohm (Ω) |
| Resistance of a wire | R = ρ l ÷ A | ohm (Ω) |
| Resistors in series | R = R1 + R2 + R3 | ohm (Ω) |
| Resistors in parallel | 1/R = 1/R1 + 1/R2 + 1/R3 | ohm (Ω) |
| Electric power | P = V × I = I2R = V2 ÷ R | watt (W) |
| Heat produced | H = I2Rt | joule (J) |
| Electrical energy | E = P × t | joule (J) or kWh |
1 kWh (one unit of electricity) = 3.6 × 106 J.
Waves and sound
| Idea | Formula |
|---|---|
| Wave speed | v = f × λ |
| Frequency and time period | f = 1 ÷ T |
| Distance using an echo | d = (v × t) ÷ 2 |
Chemistry
| Idea | Formula or fact |
|---|---|
| Number of moles | n = given mass ÷ molar mass |
| Number of particles | n × 6.022 × 1023 (Avogadro number) |
| Photosynthesis | 6CO2 + 6H2O → C6H12O6 + 6O2 (with sunlight) |
| Neutralisation | Acid + base → salt + water |
| Acid with a metal | Acid + metal → salt + hydrogen |
| pH scale | Below 7 acidic, 7 neutral, above 7 basic |
| Law of conservation of mass | Total mass of the reactants equals total mass of the products |