Percentage Change
Calculate percentage increase or decrease.
Percentage Change = ((New Value - Original Value) / Original Value) × 100% AQA GCSE 2025
🧮 AQA GCSE Mathematics Formula Sheet
Essential formulas for number, algebra, geometry, statistics, and probability aligned to AQA GCSE Mathematics (8300/8301) specification.
Number & Algebra Geometry Statistics
Master GCSE Mathematics
This formula sheet covers key mathematical relationships from the AQA GCSE Mathematics specification, helping you solve problems efficiently and achieve top grades.
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Number operations
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Geometry formulas
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Statistics basics
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Algebra essentials
Number & Operations
Fundamental number relationships, percentages, ratios, and proportional reasoning for GCSE problem-solving.
Compound Interest
A final amount, P principal, r rate (as decimal), n compounding periods per year, t time in years.
A = P(1 + r/n)^(nt) Ratio & Proportion
If a : b = c : d, then a/b = c/d and ad = bc.
a : b = c : d ⟺ a/b = c/d Speed, Distance, Time
s speed, d distance, t time.
s = d / t Topic Focus
Percentage Applications
- Use percentage change to compare values over time or between quantities.
- Remember: percentage increase = ((new - old) / old) × 100%.
- For reverse calculations, use original = new / (1 + percentage/100).
Algebra & Equations
Linear and quadratic equations, algebraic manipulation, and solving strategies for GCSE assessments.
Linear Equation (Slope-Intercept)
m gradient, c y-intercept.
y = mx + c Gradient Formula
Calculate gradient from two points.
m = (y₂ - y₁) / (x₂ - x₁) Quadratic Formula
Solutions for ax² + bx + c = 0 where a ≠ 0.
x = [-b ± √(b² - 4ac)] / (2a) Distance Formula
Distance between two points (x₁, y₁) and (x₂, y₂).
d = √[(x₂ - x₁)² + (y₂ - y₁)²] Topic Focus
Linear Relationships
- Gradient (m) represents rate of change: positive = increasing, negative = decreasing.
- Y-intercept (c) shows the value when x = 0.
- Parallel lines have equal gradients; perpendicular lines have gradients that multiply to -1.
Geometry & Measurement
Area, perimeter, volume, and geometric relationships for 2D and 3D shapes.
Area of Rectangle
l length, w width.
A = l × w Area of Triangle
b base, h height perpendicular to base.
A = ½ × b × h Area of Circle
r radius, π ≈ 3.14159.
A = πr² Circumference of Circle
r radius, d diameter.
C = 2πr C = πd Volume of Prism
A cross-sectional area, l length.
V = A × l Volume of Cylinder
r radius, h height.
V = πr²h Pythagorean Theorem
For right triangles, where c is the hypotenuse.
a² + b² = c² Topic Focus
Area Calculations
- Always use consistent units (all in cm, all in m, etc.) before calculating.
- For composite shapes, break them into simpler shapes and add/subtract areas.
- Remember: height must be perpendicular to the base for triangles and parallelograms.
Statistics & Probability
Basic statistical measures and probability calculations for data analysis.
Mean (Average)
Sum of all values divided by number of values.
Mean = (Sum of all values) / (Number of values) Median
Middle value when data is arranged in order.
For even number of values, median is the average of the two middle values.
Probability (Single Event)
P(A) probability of event A occurring.
P(A) = (Number of favorable outcomes) / (Total number of possible outcomes) Topic Focus
Measures of Central Tendency
- Mean is affected by outliers; median is more robust for skewed data.
- Mode is useful for categorical data or when finding the most common value.
- Choose the appropriate measure based on your data type and purpose.
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Practice Problem-Solving
Apply formulas to real-world GCSE problems. Don't just memorize—understand when and why to use each formula.
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Check Units
Always verify units match before substituting values. Convert units if necessary to ensure consistency.
Excel in AQA GCSE Mathematics
Achieve top grades with expert GCSE tutors who help you understand concepts deeply and apply formulas confidently.
Formulas align with AQA GCSE Mathematics specification (8300/8301) for UK students.
Always show your working and include units in your final answers.