Algebra
Here is a set of notes used by Paul Dawkins to teach his Algebra course at Lamar University. Included area a review of exponents, radicals, polynomials as well as indepth discussions of solving equations (linear, quadratic, absolute value, exponential, logarithm) and inqualities (polynomial, rational, absolute value), functions (definition, notation, evaluation, inverse functions) graphing (lines, circles, parabolas, ellipses, hyperbolas, functions), exponential and logarithms and solving systems of equations.
En bref
Ajouté le
18 mars 2026
Matière et domaine
math · trigonometry
Niveaux scolaires
8e année–12e année (Terminale)
Type de page
Article
Mots-clés
integer exponents rational exponents exponents radicals polynomials factoring rational expressions complex numbers solving equations solving linear equations solving quadratic equations solving inequalities solving absolute value equations solving absolute value inequalities solving polynomial inequalities solving rational inequalities applications of linear equations completing the square quadratic formula line circle graph line graph circle piecewise function function definition function notation function composition composition inverse function function inverse parabolas ellipses hyperbolas rational functions transformations symmetry polynomials zeroes of polynomials roots of polynomials graphing polynomials partial fractions systems of equations substitution method elimination method augmented matrix nonlinear systems
Introduction
Algebra Course Notes Overview
- Source: Online course notes provided by a Lamar University instructor.
- Purpose: Designed as a self-contained resource for learning Algebra or as a refresher; does not require a specific textbook.
- Prerequisites: Assumes basic prior exposure to algebra (exponents, factoring, graphing).
- Student Warning: These notes are not a substitute for attending class; they may contain extra material not covered in lectures or omit specific insights discussed in class.
Key Topics Covered
1. Preliminaries
- Exponents (integer and rational) and radicals.
- Polynomials: definitions, degree, and arithmetic.
- Factoring: GCF, grouping, quadratics, and higher-degree polynomials.
- Rational expressions and complex numbers.
2. Solving Equations and Inequalities
- Linear Equations: Solving processes, applications (pricing, distance/rate, work, mixing), and multi-variable equations.
- Quadratic Equations: Factoring, square root property, completing the square, the quadratic formula, and the discriminant.
- Advanced Equations: Equations reducible to quadratic form and equations with radicals.
- Inequalities: Linear, polynomial, and rational inequalities (including interval notation).
- Absolute Value: Mathematical/geometric definitions and solving absolute value equations and inequalities.
3. Graphing and Functions
- Coordinate Systems: Cartesian/rectangular systems for graphing lines and circles.
- Lines: Slope, standard form, point-slope form, slope-intercept form, and parallel/perpendicular lines.
- Circles: Standard form and completing the square.
- Functions: Formal definitions, function notation, domain and range, piecewise functions, graphing, and combining functions.
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