Formulas and rules

Algebraic notation

2x means 2 times x. x^2 means x squared. Like terms can be collected.

Expanding brackets

a(b + c) = ab + ac

Multiply the term outside by every term inside.

Factorising

ab + ac = a(b + c)

Take the highest common factor outside the brackets.

Solving linear equations

ax + b = c -> x = (c - b) / a

Do the same operation to both sides to keep the balance and isolate x.

Inequalities

Solve like an equation, but reverse the sign when multiplying or dividing by a negative.

Systems of linear equations

Two equations, two unknowns: eliminate one variable by adding or substituting.

Quadratic formula

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

Solves ax^2 + bx + c = 0. The discriminant b^2 - 4ac tells how many roots.

Difference of two squares

a^2 - b^2 = (a - b)(a + b)

A square subtracted from a square factorises into a product of a difference and a sum.

Sequences

arithmetic: u_n = a + (n-1)d ; geometric: u_n = a x r^(n-1)

Arithmetic sequences add a constant, geometric ones multiply by a constant.