Maths Formula Sheet

This maths formula sheet provides a clear, quick-reference list of commonly used formulas across algebra, geometry, trigonometry, coordinate geometry, and statistics. Ideal for revision, homework, and exam preparation.

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📐 Algebra

Linear equation

y = mx + c

Quadratic equation

y = ax² + bx + c

Quadratic formula

x = (−b ± √(b² − 4ac)) / (2a)

Factor identities

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a − b)(a + b)

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📊 Coordinate Geometry

Gradient (slope)

m = (y₂ − y₁) / (x₂ − x₁)

Midpoint formula

Midpoint = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

Distance formula

Distance = √((x₂ − x₁)² + (y₂ − y₁)²)

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📐 Geometry (2D)

Triangle area

Area = ½bh

Parallelogram area

Area = bh

Trapezium area

Area = ½(a + b)h

Circle

• Area = πr²
• Circumference = 2πr

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📦 Mensuration (3D)

Volume of a cuboid

V = lwh

Volume of a cylinder

V = πr²h

Surface area of a cylinder

TSA = 2πr² + 2πrh

Volume of a sphere

V = 4/3 πr³

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📐 Trigonometry

Basic ratios (right-angled triangle)

• sin θ = opposite / hypotenuse
• cos θ = adjacent / hypotenuse
• tan θ = opposite / adjacent

Pythagoras’ theorem

a² + b² = c²

Sine rule

a/sin A = b/sin B = c/sin C

Cosine rule

c² = a² + b² − 2ab cos C

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📈 Statistics

Mean

Mean = (sum of values) / (number of values)

Range

Range = highest − lowest

Probability

P(event) = favourable outcomes / total outcomes

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Quick tips

• Always include units (cm², m³, etc.).
• Use the correct formula for the shape or situation.
• Keep answers exact (π, √) unless rounding is requested.

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Disclaimer: This maths formula sheet is provided for general educational reference only. Syllabuses and notation may vary by country, school, or exam board. Always follow the formulas and conventions specified by your teacher or examining authority.