Precalculus

What Students Learn

Precalculus develops fluency in algebra and trigonometry through the study of functions, preparing students for calculus. Students explore polynomial and rational functions, followed by exponential and logarithmic functions. They extend their understanding of trigonometric functions and their applications, alongside sequences and analytic geometry. The course emphasizes interpreting graphs and using mathematical models to analyze practical problems, with clear explanations of mathematical reasoning.

Key Topics

Functions and graphs: domain and range, transformations, composition, and inverse functions.

Polynomial and rational functions: zeros and asymptotes, with methods for solving equations and inequalities.

Exponential and logarithmic functions: properties and equations, applied to growth and decay models.

Trigonometry: the unit circle and function graphs, identities and equations, and models of periodic phenomena.

Sequences: arithmetic and geometric sequences, recurrence relations, and summation methods.

Analytic geometry: vectors, matrices, conic sections, and introductory representations using parametric equations and polar coordinates.