National 5 Mathematics formula reference

a^m x aⁿ = a^m+n

a^maⁿ = a^m−n

(a^m)ⁿ = a^mn

a^(mn) = nth root of a^m

√(ab) = √a√b

a√b = a√bb

m = y2 − y1x2 − x1

y − b = m(x − a)

y = mx + c

D = b² − 4ac

D > 0: two real and distinct roots

D = 0: one repeated real root

D < 0: no real roots

V = 43 πr³

V = 13 πr² h

V = 13 x base area x perpendicular height

arc length = angle/360 × 2πr

sector area = angle/360 x πr²

length factor = k

area factor = k²

volume factor = k³

sin x = opposite ÷ hypotenuse

cos x = adjacent ÷ hypotenuse

tan x = opposite ÷ adjacent

sin² x + cos² x = 1

tan x = sin xcos x

a² = b² + c² − 2bc cos A

cos A = b² + c² − a²2bc

AB = b − a

|(x, y)| = √(x² + y²)

|(x, y, z)| = √(x² + y² + z²)