GCSE Physics resources

AQA GCSE Physics exam skills

GCSE Physics Equations and Maths Skills

Use this page as the equation and unit reference. The neighbouring calculation guide supplies complete multi-step practice rather than repeating the reference.

AQA 8463AQA 8464 GCSE PhysicsCombined Science: Trilogy FoundationHigher

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The revision snapshot

Use this page as the equation and unit reference. The neighbouring calculation guide supplies complete multi-step practice rather than repeating the reference.

By the end, you should be able to:

  • Select and rearrange equations for the required variable.
  • Convert prefixes, squared and cubed units.
  • Check course scope and the supplied equation-sheet policy.

Before you revise

Diagnostic question

Choose an answer from memory. Your result tells you what to watch for in the guide.

Rearrange E = mcΔθ for c. Which is correct?

Read the feedback for every option
  1. Both multiplying factors divide E.
  2. This multiplies by Δθ instead of dividing.
  3. Both factors should divide.
  4. This gives the reciprocal.

Core revision guide

Learn the model, then use it

Use this page as the equation and unit reference. The neighbouring calculation guide supplies complete multi-step practice rather than repeating the reference.

Read and rearrange relationships

Scope: 8463 and 8464 · Foundation and Higher

Identify the requested symbol and the physical quantities available. From P = E/t, multiply by t then divide by P to get t = E/P. From E = ½mv², v = √(2E/m); square roots and brackets matter. From E = mcΔθ, c = E/(mΔθ), not (E/m)Δθ. Ratio equations should be multiplied across symbolically before values are substituted.

Prefixes, powers and ratios

Scope: 8463 and 8464 · Foundation and Higher

kilo = 10³; milli = 10⁻³; micro = 10⁻⁶. Convert centimetres to metres before squaring/cubing: 1 cm² = 10⁻⁴ m², 1 cm³ = 10⁻⁶ m³. A km/h speed is divided by 3.6 to become m/s. Efficiency and magnification are dimensionless ratios. In standard form 0.00486 = 4.86 × 10⁻³; to two significant figures it is 0.0049.

Core reference by topic

Scope: 8463 and 8464 · Foundation and Higher

Energy: Ek = ½mv²; Ep = mgh; Ee = ½ke²; E = mcΔθ; W = Fs; P = E/t or W/t; efficiency = useful/total energy or power. Electricity: Q = It; V = IR; P = VI = I²R; E = Pt = QV; series R = R₁ + R₂. Particle model: ρ = m/V; E = mL. Forces/motion: Wweight = mg; F = ke; speed = distance/time; a = Δv/t; Fresultant = ma. Waves: v = fλ; T = 1/f. Use the exact current course equation sheet linked below for the full official set and printed symbols.

Apply scope before choosing an equation

Scope: 8463 and 8464 · Foundation and Higher

Physics-only additions include moments, basic pressure, pV = constant and lens magnification at both tiers; hρg, force from momentum change and transformer turns ratio are Physics Higher. Momentum p = mv, motor force BIl and ideal-transformer power equality VpIp = VsIs are Higher for both courses. Use each subsection label rather than assuming every equation belongs to every tier.

Equation-sheet policy reviewed 7 October 2026

Scope: 8463 and 8464 · Foundation and Higher

AQA’s September 2026 announcement confirms supplied equation sheets for 2027 and continuing support for 2028 onwards. Learners still need to select and apply relationships, rearrange and convert units. Check the sheet for your exact examination year and qualification; older “recall” wording in the specification does not alone describe the current support policy.

A kinetic-energy calculation shows the equation, values, substitution, 9.0 joule answer and unit check.
Keep the equation, substitution, answer, unit and sense check visible as separate stages.Open the full-size exam diagram
Kinetic energyEₖ = ½mv²J, kg, m/s8463 and 8464 · Foundation and Higher
Gravitational energy changeEₚ = mghJ, kg, N/kg, m8463 and 8464 · Foundation and Higher
Elastic energyEₑ = ½ke²J, N/m, m; proportional region8463 and 8464 · Foundation and Higher
Temperature changeE = mcΔθJ, kg, J/(kg °C), °C8463 and 8464 · Foundation and Higher
WorkW = FsJ, N, m along force8463 and 8464 · Foundation and Higher
PowerP = E/t = W/tW, J, s8463 and 8464 · Foundation and Higher
Efficiencyuseful energy/total energy or useful power/total powerno unit; ×100 for %8463 and 8464 · Foundation and Higher
ChargeQ = ItC, A, s8463 and 8464 · Foundation and Higher
ResistanceV = IRV, A, Ω; ratio at non-zero I8463 and 8464 · Foundation and Higher
Series resistanceRtotal = R₁ + R₂Ω8463 and 8464 · Foundation and Higher
Electrical powerP = VI = I²RW, V, A, Ω8463 and 8464 · Foundation and Higher
Electrical energyE = Pt = QVJ, W, s, C, V8463 and 8464 · Foundation and Higher
Densityρ = m/Vkg/m³, kg, m³8463 and 8464 · Foundation and Higher
Latent heatE = mLJ, kg, J/kg; state change8463 and 8464 · Foundation and Higher
WeightW = mgN, kg, N/kg8463 and 8464 · Foundation and Higher
Spring forceF = keN, N/m, m; proportional region8463 and 8464 · Foundation and Higher
Steady speeds = vtm, m/s, s8463 and 8464 · Foundation and Higher
Accelerationa = (v − u)/tm/s², m/s, s8463 and 8464 · Foundation and Higher
Uniform accelerationv² − u² = 2asm/s, m/s², m8463 and 8464 · Foundation and Higher
Resultant forceF = maN, kg, m/s²8463 and 8464 · Foundation and Higher
Wave speedv = fλm/s, Hz, m8463 and 8464 · Foundation and Higher
Wave periodT = 1/fs, Hz8463 and 8464 · Foundation and Higher
Momentump = mvkg m/s, kg, m/s8463 and 8464 · Higher only
Motor forceF = BIlN, T, A, m; conductor perpendicular to field8463 and 8464 · Higher only
Momentmoment = FdperpendicularN m, N, m8463 Physics only · Foundation and Higher
Fluid pressurep = F/APa, N, m²8463 Physics only · Foundation and Higher
Gas at constant temperaturep₁V₁ = p₂V₂absolute Pa; consistent volume8463 Physics only · Foundation and Higher
Magnificationimage height/object heightno unit; same length units8463 Physics only · Foundation and Higher
Liquid-depth pressurep = hρgPa, m, kg/m³, N/kg8463 Physics only · Higher only
Average force from momentumFaverage = Δp/ΔtN, kg m/s, s8463 Physics only · Higher only
Transformer voltageVp/Vs = Np/NsV, turns8463 Physics only · Higher only
Ideal transformer powerVpIp = VsIsW (V × A)8463 and 8464 · Higher only

Misconception clinic

Replace the tempting answer

Read each belief, say what is wrong with it, then compare your correction.

Tempting idea: c = (E/m)Δθ.

Use instead: This multiplies by Δθ instead of dividing. Both multiplying factors divide E.

Tempting idea: 1 cm³ = 10⁻² m³.

Use instead: The conversion is cubed. (10⁻²)³ = 10⁻⁶.

Retrieval practice

Quick checks

1. Which conversion is correct?

Read the feedback for every option
  1. The conversion is cubed.
  2. Each length converts by 10⁻².
  3. (10⁻²)³ = 10⁻⁶.
  4. A cubic centimetre is smaller than a cubic metre.

Worked examples

See the method being built

Apply read and rearrange relationships in the worked reasoning, then try the changed-context questions below.

Example 1 · Prefix conversion

Scope: 8463 and 8464 · Foundation and Higher

Convert 3.5 kJ to joules.

  1. The prefix kilo means ×1 000.
  2. 3.5 × 1 000 = 3 500.
Show the answer

3 500 J.

Example 2 · Rearranging

Scope: 8463 and 8464 · Foundation and Higher

Rearrange P = E ÷ t to make t the subject.

  1. Multiply both sides by t.
  2. Divide both sides by P.
Show the answer

t = E ÷ P.

Example 3 · Sense check

Scope: 8463 and 8464 · Foundation and Higher

A 2 kg object moving at 3 m/s has a calculated kinetic energy of 90 J. What should you check first?

  1. Write Eₖ = ½mv².
  2. The speed must be squared before multiplying.
Show the answer

Check that v² was used; the correct value is 9 J.

Exam precision

Use the physics precisely

Do this: Rearrange symbolically, then convert and substitute. Use the equation’s scope label and check the examination-year sheet.

Independent practice

Exam-style questions

Write an answer before opening the marking guidance. Then edit the exact phrase or step that would gain the next mark.

1. Rearrange E = ½mv² for v and state the SI mass unit.

[3 marks]

Scope: 8463 and 8464 · Foundation and Higher

Show marking guidance and model answer

Original PhysicsUK mark scheme: Point 1 (1 mark): v² = 2E/m. Point 2 (1 mark): v = √(2E/m). Point 3 (1 mark): Mass must be in kg. Award each distinct point once. Accept equivalent scientifically correct wording. No half marks.

  1. v² = 2E/m. (1 mark)
  2. v = √(2E/m). (1 mark)
  3. Mass must be in kg. (1 mark)

Model answer: v = √(2E/m), with mass in kg.

2. Convert 250 mA to A and 20 cm³ to m³.

[2 marks]

Scope: 8463 and 8464 · Foundation and Higher

Show marking guidance and model answer

Original PhysicsUK mark scheme: Point 1 (1 mark): 250 mA = 0.250 A. Point 2 (1 mark): 20 cm³ = 20 × 10⁻⁶ m³ = 2.0 × 10⁻⁵ m³. Award each distinct point once. Accept equivalent scientifically correct wording. No half marks.

  1. 250 mA = 0.250 A. (1 mark)
  2. 20 cm³ = 20 × 10⁻⁶ m³ = 2.0 × 10⁻⁵ m³. (1 mark)

Model answer: 0.250 A; 2.0 × 10⁻⁵ m³.

Questions pupils ask

GCSE Physics Equations and Maths Skills FAQs

Do I still need to learn how to use equations when a sheet is supplied?

Yes. A sheet supplies relationships; you must recognise the correct quantities, rearrange when required, convert units and interpret the answer.

Why does cm³ need a different conversion factor from cm?

Volume involves three lengths. Each length contributes a factor of 0.01, giving 0.01³ = 10⁻⁶.

Useful next steps

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