College Algebra
Free Online Course • Self-Paced Learning • For MATH 4/4C Students
Welcome to Your College Algebra Learning Journey!
This comprehensive course is designed specifically for students taking MATH 4/4C at Santa Monica College and anyone who wants to master college algebra fundamentals. Each module includes detailed lessons, interactive practice problems, self-check quizzes, and comprehensive study materials.
Self-Paced
Learn on your schedule. All materials available 24/7.
Interactive
Practice problems with instant feedback and detailed solutions.
Comprehensive
Study guides, quick reference cards, and worked examples.
Research-Based
Designed using evidence-based learning principles.
Course Modules
Functions & Coordinate Plane
Master the foundations: real numbers, coordinate plane, functions, and graph transformations.
- Real numbers, intervals, and the coordinate plane
- Relations and functions: domain, range, function notation
- Function arithmetic: addition, subtraction, multiplication, division, composition
- Graphs of functions and transformations
Linear & Quadratic Functions
Master linear equations, modeling, and quadratic functions with three solving methods.
- Linear functions: slope, intercepts, three equation forms
- Modeling with linear functions (real-world applications)
- Quadratic functions: parabolas, vertex form, transformations
- Solving quadratics: factoring, formula, completing the square
Polynomial & Rational Functions
Explore polynomial behavior, factoring, and rational function graphs.
- Polynomial functions: end behavior, zeros, multiplicity
- Factoring techniques and the Rational Root Theorem
- Rational functions: asymptotes and holes
- Polynomial and rational inequalities
Exponential & Logarithmic Functions
Master exponential growth/decay, logarithms, and real-world applications.
- Exponential functions: growth, decay, compound interest
- Logarithmic functions and properties
- Solving exponential and logarithmic equations
- Applications: population growth, radioactive decay, pH
Systems of Equations & Inequalities
Solve systems using multiple methods and apply to real-world optimization.
- Systems of linear equations: substitution and elimination
- Matrices and Gaussian elimination
- Nonlinear systems
- Systems of inequalities and linear programming
Sequences & Series
Master patterns, formulas, and applications of arithmetic and geometric sequences.
- Arithmetic sequences and series formulas
- Geometric sequences and infinite series
- Summation notation and special formulas
- Applications: finance, population growth, physics
Conic Sections
Explore the four conic sections: circles, parabolas, ellipses, and hyperbolas.
- Circles: standard form and completing the square
- Parabolas: focus, directrix, and applications
- Ellipses: major/minor axes, foci, and eccentricity
- Hyperbolas: asymptotes, graphing, and applications
Introduction to Matrices
Master matrix algebra, determinants, inverses, and real-world applications.
- Matrix operations: addition, multiplication, properties
- Determinants and their properties
- Finding and using inverse matrices
- Matrix equations, Cramer's Rule, and applications
Ready to Get Started?
Begin with Module 1 to build a strong foundation in functions and the coordinate plane. All materials are completely free!
Learning Tips
- Start with the pre-assessment to see what you already know
- Work through all lessons in order for best understanding
- Practice, practice, practice! Do all practice problems before the quiz
- Use the study guide to review before quizzes and exams
- Take your time – understanding is more important than speed
- Use Desmos to visualize functions and graph transformations
For MATH 4/4C Students at SMC
This platform is designed to complement your coursework. Use it to preview topics before class, review concepts, and practice for exams. The lessons align with your textbook and course objectives.
Note: This platform is a supplemental resource. Always refer to your course syllabus and Canvas page for official assignments, deadlines, and exam dates.