GCSE Combined Science equations you must know

All 31 physics equations that can appear in GCSE Combined Science, grouped by topic, with every symbol and its unit. 9 are marked given (you are given them, so practise using them) and 22 are marked recall (learn them). The Biology and Chemistry formulae follow.

Always check your own board's equation sheet for the final word. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Motion · Forces · Energy · Particles · Waves · Electricity · Magnetism and transformers · Biology · Chemistry

AQA and Edexcel: what differs

On Edexcel Combined Science but only Separate Science for AQA: moment of a force, pressure, momentum, force and change in momentum, transformer voltage and turns, transformer power.

Everything else listed here is in the Combined Science content of both boards. Higher-tier-only equations are marked on their card.

Motion

Distance travelled

distance travelled = speed × time

In symbols: s = v t

s is distance travelled, in m
v is speed, in m/s
t is time, in s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Acceleration

acceleration = change in velocity ÷ time taken

In symbols: a = Δv ⁄ t

a is acceleration, in m/s²
Δv is change in velocity, in m/s
t is time taken, in s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Constant acceleration

(final velocity)² − (initial velocity)² = 2 × acceleration × distance

In symbols: v² − u² = 2 a s

v is final velocity, in m/s
u is initial velocity, in m/s
a is acceleration, in m/s²
s is distance, in m

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Forces

Resultant force

resultant force = mass × acceleration

In symbols: F = m a

F is resultant force, in N
m is mass, in kg
a is acceleration, in m/s²

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Weight

weight = mass × gravitational field strength

In symbols: W = m g

W is weight, in N
m is mass, in kg
g is gravitational field strength, in N/kg

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Work done

work done = force × distance (along the line of action of the force)

In symbols: W = F s

W is work done, in J
F is force, in N
s is distance moved along the line of action, in m

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Force applied to a spring

force applied to a spring = spring constant × extension

In symbols: F = k e

F is force, in N
k is spring constant, in N/m
e is extension, in m

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Elastic potential energy

elastic potential energy = ½ × spring constant × extension²

In symbols: Eₑ = ½ k e²

Eₑ is elastic potential energy, in J
k is spring constant, in N/m
e is extension, in m

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Moment of a force

moment of a force = force × distance (normal to the direction of the force)

In symbols: M = F d

M is moment, in Nm
F is force, in N
d is distance from the pivot, in m

Recall: learn this one. Do not expect it to be printed for you. AQA: Separate Science only. Edexcel: Combined Science, both tiers.

Pressure

pressure = force normal to a surface ÷ area of that surface

In symbols: p = F ⁄ A

p is pressure, in Pa
F is force normal to the surface, in N
A is area of the surface, in m²

Recall: learn this one. Do not expect it to be printed for you. AQA: Separate Science only. Edexcel: Combined Science, both tiers.

Momentum

momentum = mass × velocity

In symbols: p = m v

p is momentum, in kg m/s
m is mass, in kg
v is velocity, in m/s

Recall: learn this one. Do not expect it to be printed for you. AQA: Separate Science only. Edexcel: Combined Science, both tiers.

Force and change in momentum

force = change in momentum ÷ time taken

In symbols: F = Δp ⁄ Δt

F is force, in N
Δp is change in momentum, in kg m/s
Δt is time taken, in s

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Separate Science Higher only. Edexcel: Combined Science, Higher tier only.

Energy

Kinetic energy

kinetic energy = ½ × mass × speed²

In symbols: Eₖ = ½ m v²

Eₖ is kinetic energy, in J
m is mass, in kg
v is speed, in m/s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Gravitational potential energy

change in gravitational potential energy = mass × gravitational field strength × change in height

In symbols: Eₚ = m g h

Eₚ is gravitational potential energy, in J
m is mass, in kg
g is gravitational field strength, in N/kg
h is height, in m

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Power (energy transferred)

power = energy transferred ÷ time

In symbols: P = E ⁄ t

P is power, in W
E is energy transferred, in J
t is time, in s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Power (work done)

power = work done ÷ time

In symbols: P = W ⁄ t

P is power, in W
W is work done, in J
t is time, in s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Efficiency

efficiency = useful output energy transfer ÷ total input energy transfer

In symbols: efficiency = E(useful) ⁄ E(total)

efficiency is efficiency (a fraction, or × 100 for a percentage), in
E(useful) is useful output energy transfer, in J
E(total) is total input energy transfer, in J

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Thermal energy change

change in thermal energy = mass × specific heat capacity × temperature change

In symbols: ΔE = m c Δθ

ΔE is change in thermal energy, in J
m is mass, in kg
c is specific heat capacity, in J/kg°C
Δθ is temperature change, in °C

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Latent heat

thermal energy for a change of state = mass × specific latent heat

In symbols: E = m L

E is thermal energy for a change of state, in J
m is mass, in kg
L is specific latent heat, in J/kg

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Particles

Density

density = mass ÷ volume

In symbols: ρ = m ⁄ V

ρ is density, in kg/m³
m is mass, in kg
V is volume, in m³

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Waves

Wave speed

wave speed = frequency × wavelength

In symbols: v = f λ

v is wave speed, in m/s
f is frequency, in Hz
λ is wavelength, in m

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Period

period = 1 ÷ frequency

In symbols: T = 1 ⁄ f

T is period, in s
f is frequency, in Hz

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Electricity

Charge flow

charge flow = current × time

In symbols: Q = I t

Q is charge flow, in C
I is current, in A
t is time, in s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Potential difference (Ohm's law)

potential difference = current × resistance

In symbols: V = I R

V is potential difference, in V
I is current, in A
R is resistance, in Ω

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Electrical power (V and I)

power = potential difference × current

In symbols: P = V I

P is power, in W
V is potential difference, in V
I is current, in A

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Electrical power (I squared R)

power = (current)² × resistance

In symbols: P = I² R

P is power, in W
I is current, in A
R is resistance, in Ω

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Energy transferred (power and time)

energy transferred = power × time

In symbols: E = P t

E is energy transferred, in J
P is power, in W
t is time, in s

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Energy transferred (charge and p.d.)

energy transferred = charge flow × potential difference

In symbols: E = Q V

E is energy transferred, in J
Q is charge flow, in C
V is potential difference, in V

Recall: learn this one. Do not expect it to be printed for you. AQA: Combined Science, both tiers. Edexcel: Combined Science, both tiers.

Magnetism and transformers

Motor effect

force on a conductor at right angles to a magnetic field carrying a current = magnetic flux density × current × length

In symbols: F = B I l

F is force, in N
B is magnetic flux density, in T
I is current, in A
l is length of conductor in the field, in m

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Combined Science, Higher tier only. Edexcel: Combined Science, Higher tier only.

Transformer voltage and turns

potential difference across the primary coil ÷ potential difference across the secondary coil = number of turns on the primary ÷ number of turns on the secondary

In symbols: Vₚ ⁄ Vₛ = nₚ ⁄ nₛ

Vₚ is primary potential difference, in V
Vₛ is secondary potential difference, in V
nₚ is turns on the primary coil, in turns
nₛ is turns on the secondary coil, in turns

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Separate Science Higher only. Edexcel: Combined Science, Higher tier only.

Transformer power

potential difference across the primary × current in the primary = potential difference across the secondary × current in the secondary

In symbols: Vₚ Iₚ = Vₛ Iₛ

Vₚ is primary potential difference, in V
Iₚ is primary current, in A
Vₛ is secondary potential difference, in V
Iₛ is secondary current, in A

Given: treat this as an equation printed on the equation sheet. Practise using it, not memorising it. AQA: Separate Science Higher only. Edexcel: Combined Science, Higher tier only.

Biology formulae

Magnification

magnification = size of image ÷ size of real object

both sizes in the same unit

Recall: learn this one.

Percentage change

percentage change = (final − original) ÷ original × 100

Recall: learn this one.

Rate of change

rate = change in quantity ÷ time

Recall: learn this one.

Cardiac output

cardiac output = stroke volume × heart rate

stroke volume in cm³ per beat, heart rate in beats per minute

Recall: learn this one.

Mean

mean = total of the values ÷ number of values

Recall: learn this one.

Chemistry formulae

Amount in moles

moles = mass (g) ÷ relative formula mass (Mr)

Recall: learn this one.

Concentration

concentration (g/dm³) = mass of solute (g) ÷ volume (dm³)

Recall: learn this one.

Percentage yield

percentage yield = actual mass of product ÷ maximum theoretical mass × 100

Recall: learn this one.

Atom economy

atom economy = Mr of the wanted product ÷ sum of Mr of all products × 100

Recall: learn this one.

Rf value

Rf = distance moved by the substance ÷ distance moved by the solvent

Recall: learn this one.

Mean rate of reaction

mean rate = amount of reactant used (or product made) ÷ time

Recall: learn this one.

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