Algebra

Algebra is the branch of mathematics in which letters and symbols stand for numbers, allowing general relationships and unknown quantities to be expressed and manipulated. Rather than working only with specific values, algebra states rules that hold for whole classes of numbers, making it possible to describe patterns, formulate problems, and find unknowns systematically. It forms the foundation for most higher mathematics and for the mathematical modelling used in science and engineering.

A central task in algebra is solving equations, that is, finding the values of the unknowns that make a statement true. Linear equations are the simplest, while quadratic equations, which involve a squared term, can be solved by factorisation, completing the square, or a general formula. The study of polynomials extends these ideas, including the factorisation of expressions and the search for their roots. Inequalities, which compare quantities rather than set them equal, are solved using related but distinct methods.

Algebra also introduces important families of functions and structures. Inverse functions reverse the effect of a given function, and logarithms are the inverses of exponential functions, providing a powerful way to handle growth, decay, and very large or small numbers. Matrices, rectangular arrays of numbers, give a compact way to represent and solve systems of equations and to describe transformations. Reference tables of curves and formulas support work across all of these topics.

Frequently asked questions

What does it mean to solve an equation?

It means finding the value or values of the unknown that make both sides of the equation equal.

How is a quadratic equation different from a linear one?

A linear equation has only first-power terms, while a quadratic equation contains a squared term and can have up to two solutions.

What is a logarithm?

A logarithm is the inverse of an exponential function; it tells you the power to which a base must be raised to produce a given number.