📄 Executive Summary
Designed for post-secondary students preparing for calculus and science disciplines, this textbook covers intermediate algebra, college algebra, and trigonometry. It assumes a basic background in arithmetic and introductory algebra, beginning with a review of real numbers, properties of operations, exponents, radicals, polynomials, and rational expressions. From these foundational prerequisites, the text systematically progresses through algebraic equations and inequalities, functions and their graphs, polynomial and transcendental models, trigonometry, analytic geometry, systems of equations, and discrete topics.
The central organizing concept throughout the book is the function. The text introduces general function properties—including domain and range, rates of change, composite operations, inverse relations, and geometric transformations—before examining specific function families. Readers study linear, quadratic, higher-degree polynomial, rational, exponential, and logarithmic functions through algebraic, tabular, and graphical representations. Analytical techniques taught across these chapters include polynomial division, zero-finding strategies using the Fundamental Theorem of Algebra and Descartes' Rule of Signs, and curve-fitting methods such as least squares linear regression and exponential modeling.
The trigonometry portion develops both right-triangle geometry and unit-circle definitions, establishing the six standard trigonometric functions and their periodic graphs. It covers fundamental and derived trigonometric identities, sum and difference formulas, double- and half-angle formulas, and techniques for solving trigonometric equations. These principles extend into oblique triangle trigonometry with the Laws of Sines and Cosines, polar coordinates and polar curves, complex numbers in polar form via De Moivre's Theorem, parametric equations for motion modeling, and two-dimensional vectors using component form and dot products.
In its final sections, the textbook addresses systems of linear and nonlinear equations and inequalities, providing solution methods through algebraic substitution, Gaussian elimination, matrix inverses, and Cramer's Rule, alongside partial fraction decomposition. It also examines conic sections in Cartesian and polar forms, arithmetic and geometric sequences, series and annuities, counting principles, the Binomial Theorem, and introductory probability. Upon completing the text, readers should be able to analyze and graph diverse mathematical functions, solve complex equations and multi-variable systems, and model real-world phenomena such as projectile motion, population growth, and financial growth. The book focuses strictly on precalculus algebra and trigonometry, leaving calculus topics—such as limits, derivatives, and integrals—as well as three-dimensional vector operations outside its scope.
