Precalculus

Precalculus is a mathematics course offered in secondary and early university education. Its purpose is to provide students with the knowledge and skills required before beginning calculus (the mathematics of change and rates). It combines advanced algebra and trigonometry.

The term "precalculus" is primarily used in North America and other countries that have adopted this approach. In other countries, the same topics are taught within separate algebra and trigonometry courses, and no single designation is used.

Main topics

The course is centered on the concept of functions (a mathematical relationship that assigns a single output value to each input value). Students study domains and ranges, function composition, and inverse functions. Various types are examined: linear functions, quadratic functions, polynomials, rational functions, exponential functions, and logarithms.

Trigonometry forms a significant component: the measurement of angles, the unit circle, the functions sine, cosine and tangent, their graphs, and trigonometric identities. Also commonly included are vectors, complex numbers, matrices, sequences and series, and parts of analytic geometry such as conic sections.

Connection to calculus

Calculus depends on students being able to work fluently with functions and understand their graphs. For this reason, precalculus emphasizes algebraic skills that are essential for derivatives and integrals. Some curricula introduce the concept of limits (the value a function approaches), though this is covered more thoroughly in a calculus course.

Educational structure

Precalculus is sometimes divided into two parts: one focused on algebra and one on trigonometry. Some schools use a course structured to assess student readiness, while others view it as a unified course giving students broad mathematical skills relevant to science, engineering, and economics.