Maths Core

sin 30°

1/2

cos 30°

√3/2

tan 30°

1/√3 (= √3/3)

sin 45°

1/√2 (= √2/2)

cos 45°

1/√2 (= √2/2)

tan 45°

1

sin 60°

√3/2

cos 60°

1/2

tan 60°

√3

sin θ

opposite / hypotenuse

cos θ

adjacent / hypotenuse

tan θ

opposite / adjacent

Pythagoras' theorem

a² + b² = c² (c = hypotenuse)

Area of a triangle

½ × base × height

Area of a parallelogram

base × height

Area of a trapezium

½(a + b)h

Area of a rhombus

½ × d₁ × d₂ (half product of diagonals)

Area of a circle

πr²

Circumference of a circle

2πr (= πd)

Arc length

(θ/360) × 2πr

Area of a sector

(θ/360) × πr²

Volume of a cylinder

πr²h

Surface area of a cylinder

2πr² + 2πrh

Volume of a cone

⅓πr²h

Curved surface area of a cone

πrl (l = slant height)

Volume of a sphere

(4/3)πr³

Surface area of a sphere

4πr²

Volume of a pyramid

⅓ × base area × height

Equation of a straight line

y = mx + c

Gradient

(y₂ − y₁) / (x₂ − x₁)

Perpendicular gradients

m₁ × m₂ = −1

Length of a vector (a, b)

√(a² + b²)

Midpoint of (x₁,y₁) and (x₂,y₂)

((x₁+x₂)/2, (y₁+y₂)/2)

Quadratic formula

x = (−b ± √(b² − 4ac)) / 2a

Percentage change multiplier

(100 ± %) / 100

Compound interest

P(1 + r/100)ⁿ

Difference of two squares

a² − b² = (a + b)(a − b)

x⁰

1

Laws of indices (multiply)

xᵃ × xᵇ = xᵃ⁺ᵇ

Laws of indices (divide)

xᵃ ÷ xᵇ = xᵃ⁻ᵇ

Laws of indices (power)

(xᵃ)ᵇ = xᵃᵇ

Negative power

x⁻ⁿ = 1/xⁿ

Fractional power

xᵃ/ᵇ = ᵇ√(xᵃ)