The GCSEs are a significant milestone, and having the right resources at your fingertips is crucial for success. This guide provides a comprehensive overview of the key formulas you'll encounter in your 2025 GCSE exams, categorized for easy reference. Remember that this is a general guide, and specific requirements may vary slightly depending on the exam board. Always refer to your exam board's official specifications for the most accurate and up-to-date information.
Mathematics GCSE Equation Sheet
Mathematics is a core subject, and mastering its formulas is essential for achieving high marks. Here's a breakdown of key areas and their associated equations:
Number
- Percentage Change:
Percentage change = [(New Value - Original Value) / Original Value] x 100 - Simple Interest:
Simple Interest = (Principal x Rate x Time) / 100 - Compound Interest:
A = P (1 + r/n)^(nt)where:- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
Algebra
- Quadratic Formula:
x = (-b ± √(b² - 4ac)) / 2a(used to solve quadratic equations of the form ax² + bx + c = 0) - Equation of a Straight Line:
y = mx + cwhere:- m = gradient
- c = y-intercept
- Gradient of a Line:
m = (y₂ - y₁) / (x₂ - x₁)(given two points (x₁, y₁) and (x₂, y₂))
Geometry
- Area of a Triangle:
Area = (1/2) x base x height - Area of a Circle:
Area = πr² - Circumference of a Circle:
Circumference = 2πrorCircumference = πd - Volume of a Cuboid:
Volume = length x width x height - Volume of a Cylinder:
Volume = πr²h - Pythagoras' Theorem:
a² + b² = c²(for right-angled triangles) - Trigonometric Ratios (SOH CAH TOA):
sin θ = opposite / hypotenusecos θ = adjacent / hypotenusetan θ = opposite / adjacent
Statistics
- Mean:
Mean = (Sum of values) / (Number of values) - Median: The middle value when the data is ordered.
- Mode: The most frequent value.
- Range:
Range = Highest value - Lowest value
Science GCSE Equation Sheet
Science GCSEs often require the application of specific formulas. Remember to always use the correct units!
Physics
- Speed:
Speed = Distance / Time - Force:
Force = Mass x Acceleration(Newton's Second Law) - Work Done:
Work Done = Force x Distance - Kinetic Energy:
Kinetic Energy = (1/2)mv² - Potential Energy:
Potential Energy = mgh(where g is acceleration due to gravity) - Power:
Power = Work Done / Time
Chemistry
Many chemical calculations rely on molar mass and stoichiometry, requiring an understanding of the mole concept rather than specific formulas in the same way as Physics or Maths. Specific formulas will be context-dependent and provided within the exam questions themselves.
Biology
Similar to Chemistry, biological calculations in GCSEs often involve ratios and percentages rather than relying on a set list of equations.
Preparing for Your Exams
This equation sheet serves as a helpful starting point. However, effective exam preparation involves more than just memorizing formulas. Practice applying these formulas to various problems, understand the underlying concepts, and work through past papers to build confidence and familiarity with the exam format. Good luck!
