GCSE 2025 Formula Cheat Sheets: The Ultimate Guide to Acing Maths and Sciences!

The GCSE 2025 exams are fast approaching, and students across the UK are preparing to tackle challenging questions in Maths and Sciences. Success in these subjects often hinges on mastering essential formulae and equations. 

To help you streamline your revision process and boost your confidence, we have compiled the ultimate GCSE 2025 formula cheat sheets covering all the critical concepts. Whether you’re aiming for top grades or simply want to pass with flying colors, this comprehensive guide will be your roadmap to success. SAT 2025 Guide

GCSE Maths Formula Cheat Sheet

1. Algebra

• Quadratic Formula:
  x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

• Factorising Difference of Squares:
  a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)a2−b2=(a+b)(a−b)

• Expanding Binomials:
  (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2

2. Geometry 

• Volume of a Sphere:
  V=43πr3V = \frac{4}{3} \pi r^3V=34​πr3

• Volume of a Cylinder:
  V=πr2hV = \pi r^2 hV=πr2h

• Area of a Triangle:
  A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}A=21​×base×height

• Trigonometric Ratios (for right-angled triangles):
  sin⁡θ=oppositehypotenuse\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}sinθ=hypotenuseopposite​
  cos⁡θ=adjacenthypotenuse\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}cosθ=hypotenuseadjacent​
  tan⁡θ=oppositeadjacent\tan \theta = \frac{\text{opposite}}{\text{adjacent}}tanθ=adjacentopposite​

• Area of a Sector:
  A=θ360∘πr2A = \frac{\theta}{360^\circ} \pi r^2A=360∘θ​πr2

3. Probability and Statistics

• Mean:
  Mean=Sum of valuesNumber of values\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}Mean=Number of valuesSum of values​

• Probability:
  P(Event)=Favourable outcomesTotal outcomesP(\text{Event}) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}}P(Event)=Total outcomesFavourable outcomes​

4. Other Important Equations

• Speed-Distance-Time:
  Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}Speed=TimeDistance​

• Gradient of a Straight Line:
  m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​

GCSE Physics Formula Cheat Sheet

1. Motion

• Speed:
  v=stv = \frac{s}{t}v=ts​

• Acceleration:
  a=Δvta = \frac{\Delta v}{t}a=tΔv​

• Force (Newton’s Second Law):
  F=maF = maF=ma

2. Energy and Work

• Work Done:
  W=F×dW = F \times dW=F×d

• Kinetic Energy:
  KE=12mv2KE = \frac{1}{2} mv^2KE=21​mv2

• Gravitational Potential Energy:
  GPE=mghGPE = mghGPE=mgh

• Power:
  P=EtP = \frac{E}{t}P=tE​

3. Electricity

• Ohm’s Law:
  V=IRV = IRV=IR

• Power in Circuits:
  P=IVP = IVP=IV
  P=I2RP = I^2 RP=I2R

• Energy Transferred:
  E=PtE = PtE=Pt
  E=QVE = QVE=QV

4. Waves

• Wave Speed:
  v=fλv = f \lambdav=fλ
  (fff = frequency, λ\lambdaλ = wavelength)

GCSE Chemistry Formula Cheat Sheet

1. Moles and Concentrations

• Number of Moles:
  Moles=MassMolar Mass\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}Moles=Molar MassMass​

• Concentration:
  Concentration=Moles of soluteVolume of solution (dm3)\text{Concentration} = \frac{\text{Moles of solute}}{\text{Volume of solution (dm}^3\text{)}}Concentration=Volume of solution (dm3)Moles of solute​

2. Gas Calculations

• Ideal Gas Equation:
  PV=nRTPV = nRTPV=nRT

3. Reactivity

• Percentage Yield:
  Percentage Yield=Actual YieldTheoretical Yield×100\text{Percentage Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100Percentage Yield=Theoretical YieldActual Yield​×100

4. Empirical Formula

• Calculation Steps:

1. Divide the mass (or percentage) of each element by its relative atomic mass.

2. Simplify the ratios to the smallest whole numbers.

GCSE Biology Formula Cheat Sheet

1. Magnification

• Magnification=Image SizeActual Size\text{Magnification} = \frac{\text{Image Size}}{\text{Actual Size}}Magnification=Actual SizeImage Size​

2. Surface Area to Volume Ratio

• SA:V Ratio=Surface AreaVolume\text{SA:V Ratio} = \frac{\text{Surface Area}}{\text{Volume}}SA:V Ratio=VolumeSurface Area​

3. Population Growth

• Population Change=(Births+Immigration)−(Deaths+Emigration)\text{Population Change} = (\text{Births} + \text{Immigration}) - (\text{Deaths} + \text{Emigration})Population Change=(Births+Immigration)−(Deaths+Emigration)

4. Photosynthesis

• 6CO2+6H2O→C6H12O6+6O26CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_26CO2​+6H2​O→C6​H12​O6​+6O2​

5. Respiration

• Aerobic Respiration:
  C6H12O6+6O2→6CO2+6H2O+EnergyC_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + \text{Energy}C6​H12​O6​+6O2​→6CO2​+6H2​O+Energy

Top Tips for Memorizing Formulae and Equations

1. Use Flashcards: Write formulas on one side and applications on the other.

2. Practice Regularly: Solve past papers and mock exams.

3. Create Mnemonics: Make acronyms to simplify memorization.

4. Group Formulas by Topic: Organize formulas to make revision more systematic.

5. Teach Someone Else: Explaining concepts reinforces learning.

Final Thoughts: Your Success Starts Now!

Mastering the formulas and equations outlined in this guide can set you on the path to success in your GCSE 2025 Maths and Science exams. With our cheat sheets, you’ll feel more prepared, confident, and equipped to tackle any question that comes your way. Make these resources part of your daily revision routine, and you’ll maximize your chances of achieving top marks.