Physics Equations Sheet - GCSE Combined Science (Trilogy and Synergy)

For Use in June 2025 Only

This equations sheet is applicable for students taking GCSE Combined Science: Trilogy (8464) and Synergy (8465) exams in June 2025.

Key Physics Equations

Energy Equations

• Kinetic Energy: [ Ek = \frac{1}{2} m v^2 ]
  • Kinetic energy is half the product of mass and the square of speed.
• Elastic Potential Energy: [ Ee = \frac{1}{2} k e^2 ]
  • Elastic potential energy is half the product of spring constant and the square of extension.
• Gravitational Potential Energy: [ Ep = m g h ]
  • Product of mass, gravitational field strength, and height.
• Change in Thermal Energy: [ \Delta E = mc \Delta \theta ]
  • Product of mass, specific heat capacity, and temperature change.

Power and Efficiency

• Power (Energy Transfer): [ P = \frac{E}{t} ]
  • Power equals energy transferred divided by time.
• Power (Work Done): [ P = \frac{W}{t} ]
  • Power equals work done divided by time.
• Efficiency (Energy Transfer): [ \text{Efficiency} = \frac{\text{useful output energy transfer}}{\text{total input energy transfer}} ]
• Efficiency (Power Output): [ \text{Efficiency} = \frac{\text{useful power output}}{\text{total power input}} ]

Electricity

• Charge Flow: [ Q = I t ]
  • Charge flow is the product of current and time.
• Potential Difference: [ V = I R ]
  • Potential difference equals current times resistance.
• Power (Electrical): [ P = V I ] [ P = I^2 R ]
  • Power equals potential difference times current or current squared times resistance.
• Energy Transferred: [ E = P t ] [ E = Q V ]
  • Energy transferred equals power times time or charge flow times potential difference.

Advanced Electricity (HT Only)

• Transformer Equation (For Higher Tier): [ V_p I_p = V_s I_s ]
  • Potential difference across the primary coil times current in primary coil equals potential difference across secondary coil times current in secondary coil.

Miscellaneous

• Density: [ \rho = \frac{m}{V} ]
  • Density equals mass divided by volume.
• Thermal Energy for Change of State: [ E = m L ]
  • Thermal energy equals mass times specific latent heat.
• Weight: [ W = m g ]
  • Weight equals mass times gravitational field strength.
• Work Done: [ W = F s ]
  • Work done equals force times distance along the direction of the force.
• Force on a Spring: [ F = k e ]
  • Force equals spring constant times extension.

Motion

• Distance Travelled: [ s = v t ]
  • Distance equals speed times time.
• Acceleration: [ a = \frac{\Delta v}{t} ]
  • Acceleration equals change in velocity divided by time taken.
• Motion Equations: [ v^2 - u^2 = 2 a s ]
  • Final velocity squared minus initial velocity squared equals two times acceleration times distance.
• Resultant Force: [ F = ma ]
  • Resultant force equals mass times acceleration.

Advanced Motion (HT Only)

• Momentum: [ p = mv ]
  • Momentum equals mass times velocity.

Waves

• Period: [ T = \frac{1}{f} ]
  • Period equals one over frequency.
• Wave Speed: [ v = f \lambda ]
  • Wave speed equals frequency times wavelength.

Magnetism (HT Only)

• Force on a Conductor: [ F = B I l ]
  • Force on a conductor at right angles to a magnetic field carrying current equals magnetic flux density times current times length.