College Algebra
Course updated in January 2025
Lumen Learning’s College Algebra in OHM provides an interactive exploration of topics to help students lay a firm groundwork for success in subsequent math courses. Designed with the needs of today’s students in mind, our embedded algorithmically generated practice questions engage students with active learning through real-world application problems, Desmos interactives, streamlined content, and outcome-aligned videos. Faculty can customize the course content to meet the needs of their institutional learning outcomes.
OHM utilizes machine-grading, interactive content and practice with immediate feedback to maximize student understanding and retention. The instructor resources package is robust and includes easy-to-use, engaging PowerPoint slides, and in-class activities, with suggested modifications based on the modality of the course.
Lumen Learning applies learning science research to the design of affordable digital courseware to engage students and empower them in building a strong foundation in Mathematics. OHM has fully digital course materials focused on hands-on practice, customizable template courses, interactive full e-text with immediate feedback that stands alone or integrates seamlessly into Brightspace, Canvas, Blackboard, or Moodle.
Contributors: Lumen Learning curated a variety of sources for this course including the OpenStax textbooks, College Algebra and Precalculus by Jay Abramson, et al. and videos by James Sousa.
Content
Algebra Essentials
- Real Numbers
- Algebraic Expressions
- Exponents and Scientific Notation
- Radical Expressions
- Rational Exponents
Polynomial and Rational Expressions
- Polynomial Expressions
- Factoring Polynomial Expressions
- Rational Expressions
Linear Equations and Inequalities
- Graphing and Analyzing Linear Equations
- Equations of Lines
- Modeling Linear Equations
- Linear Inequalities
Non-Linear Equations
- Quadratic Equations
- Radical Equations
- Rational Equations
- Polynomial Equations
- Absolute Value Equations
- Modeling Non-Linear Equations
- Absolute Value Inequalities
Function Basics
- Common or Toolkit Functions
- Characteristics of Common Functions
- Domain and Range of Functions
- Rates of Change and Graph Behaviors
Algebraic Operations on Functions
- Combining Functions Algebraically
- Compositions of Functions
- Transformations of Functions
- Inverse of Functions
Linear Functions
- Linear Functions
- Graphing and Writing Linear Equations
- Modeling with Linear Functions
Quadratic Functions
- Quadratic Functions
- Complex Numbers
- Solving Quadratic Problems
Power and Polynomial Functions
- Power Functions
- Polynomial Functions
- Graphing and Writing Equations for Polynomial Functions
- Dividing Polynomial Functions
- Finding Zeros of Polynomial Functions
Rational and Radical Functions
- Rational Functions
- Inverse of Polynomial Functions
- Radical Functions
- Inverse of Radical Functions
- Solving Variation Functions
Exponential and Logarithmic Functions
- Exponential Functions
- Evaluation and Application of Exponential Functions
- Logarithmic Functions
- Conversion Between Forms
- Evaluation of Logarithms
Exponential and Logarithmic Equations and Models
- Logarithmic Rules
- Expanding and Condensing Logarithmic Expressions
- Change of Base Formula
- Exponential Equations
- Logarithmic Equations
- Graphing and Modeling with Exponential and Logarithmic Functions
Systems of Equations and Inequalities
- Systems of Linear Equations with Two Variables
- Systems of Nonlinear Equations
- Systems of Equations Involving Three Variables
- Decomposition of Rational Expressions Using Systems of Equations
Solving Systems With Matrices
- Matrices
- Matrix Operations
- Using Matrices to Solve Systems of Equations
- Solving Systems Using Inverse Matrices
Conic Sections
- Circles
- Ellipses
- Hyperbolas
- Parabolas
Sequences and Series
- Sequences
- Arithmetic Sequences
- Geometric Sequences
- Series and Summation
Probability and Counting Principles
- Counting Principles
- Addition and Multiplication Principles
- Permutations
- Combinations
- Binomial Theorem
- Probability Models
Additional Course Features
These course materials include:
- Online Homework Manager (OHM): A flexible, user-friendly math homework system with customizable learning content, assessments, and activities you can tailor to fit your needs. Request an OHM instructor account.
- Outcome-aligned OER: Designed to replace expensive textbooks, this course curates open educational resources (OER) aligned with learning outcomes. Teach as-is or customize to fit your needs.
- LMS Integration: This course may be delivered with seamless LMS integration and automatic grade return for Canvas, Blackboard, Brightspace, and Moodle.
- Accessibility: Lumen is 100% committed to providing learning materials that are accessible to all learners. Lumen course materials are mobile-friendly.
- View Course Content and Outcomes
What People Are Saying
“OHM is fantastic for providing students with immediate feedback and remediation. It has helped my students improve their precision in answers.” – Royce Shelley, Salt Lake Community College
“Since using OHM, my students have a better understanding of the course topics.” – Bethzabeth Berrios, SUNY Rockland
“Since using OHM, I have achieved greater efficiency in giving feedback to students. OHM helps me to quickly let students know how well they are progressing through the course.” – Noel Whelchel, Atlanta Metropolitan State College
“Since using OHM, I have been able to hold students accountable for their homework. It is extremely comprehensive for the students and it saves me an immense amount of time.” – Mac Psachie, Hunter College CUNY
“OHM has greatly reduced the cost of an online homework program for our students.” – Jim Smart, Tallahassee Community College
Teaching with Lumen Course Materials
- Replace expensive textbooks | Ready-to-adopt open educational resources (OER) include text, videos, simulations, self-checks, and other interactives.
- Choose affordability | Low cost to students.
- Use better content | Continuous, data-driven improvements make OER content more effective at supporting learning.
- Simplify access | Easy access to course materials in your LMS (Blackboard, Canvas, D2L, and Moodle) plus automatic grade return.
- Improve student outcomes | Research shows Lumen course materials can improve academic performance, passing rates, and course completion.
FOR INSTRUCTORS
- Connect with students | Instructor and student tools designed to help strengthen communication.
- Save time | Start with curated, outcome-aligned OER and supplemental instructor resources like quiz banks, assignments, slide decks, etc.
- Customize your course | Freedom to tailor course content to fit your learning outcomes and instructional approach.
- Enjoy awesome support | Faculty-friendly onboarding, training, and support.
FOR STUDENTS
- Learn by doing | Online homework, self-check activities, and other interactive tools strengthen learning.
- Engage from day one | Avoid falling behind with access to course materials from the first day of class.
- Retain materials | Download a digital copy of course content to keep forever.
- Become a better learner | Real-time feedback guides students on where to focus and how to improve.
Are you ready to get started with Lumen Learning digital courseware?
Great! Fill out our Explore a Course form, and our team will contact you promptly.