- Course Type CLEP
- Subject Science and Mathematics
- Level Introductory
- Length 4 Modules
- Video Length 5h 54m
- Reading Pages 1634
- Institution Modern States
ABOUT THIS COURSE
College Algebra reviews the fundamentals typically taught in a one-semester college course. The course develops algebraic skills and builds knowledge of core concepts, including vocabulary, symbols, and notation. Topics include algebraic operations, equations and inequalities, algebraic, exponential, and logarithmic functions, and number systems.
This is a free, self-paced Modern States course with no prerequisites. It is aligned to the CLEP® College Algebra exam and is designed to prepare you to succeed on the test and earn college credit at no cost.
Modern States originally developed this course in collaboration with James M. Murphy, now at Tufts University, Department of Mathematics. Andrew Misseldine, Ph.D. of Southern Utah University supported course enhancements published in 2025.
Course Overview
College Algebra Course Overview - Modern States
| Module | Topic | Video Length | Total pages of required reading |
| Module 1: Algebraic operations (25%) 01:24:35 total video length 465 total reading pages |
1: Introduction to Algebraic Operations | 0:00:49 | – |
| 1.1.1: Algebraic Operations | 0:05:45 | 24 | |
| 1.1.2: Manipulating Fractions | 0:08:17 | 24 | |
| 1.1.3: Powers and Roots | 0:04:55 | 24 | |
| 1.2.1: Factoring and Expanding Polynomials | 0:04:27 | 26 | |
| 1.2.2: Linear Polynomials | 0:02:19 | 26 | |
| 1.2.3: Quadratic Polynomials | 0:02:31 | 26 | |
| 1.2.4: Roots of Quadratics | 0:10:44 | 26 | |
| 1.2.5: Higher Order Polynomials | 0:03:18 | 26 | |
| 1.2.6: Expanding Polynomials | 0:05:27 | 26 | |
| 1.3.1: Introduction to Exponentials | 0:02:30 | 43 | |
| 1.3.2: Properties of Exponents | 0:12:07 | 43 | |
| 1.3.3: Plots of Exponentials | 0:04:01 | 43 | |
| 1.4.1: Logarithms | 0:05:03 | 36 | |
| 1.4.2: Properties of Logarithms | 0:08:02 | 36 | |
| 1.4.3: Logarithm as Inverse of Exponential | 0:04:20 | 36 | |
| 1: Summary | – | – | |
| Module 2: Equations and inequalities (25%) 01:21:25 total video length 249 total reading pages |
2: Equations and Inequalities | 0:01:11 | – |
| 2.1.1: Linear Equations and Inequalities | 0:07:02 | 29 | |
| 2.1.2: Linear Inequalities | 0:05:20 | 29 | |
| 2.2.1: Quadratic Equations | 0:05:31 | 12 | |
| 2.2.2: Quadratic Formula | 0:06:11 | 12 | |
| 2.2.3: Quadratic Inequalities | 0:07:53 | 12 | |
| 2.3.1: Exponential and Logarithmic Equations | 0:10:48 | 27 | |
| 2.4.1: Introduction to Absolute Value | 0:03:44 | 13 | |
| 2.4.2: Equations with Absolute Values | 0:05:54 | 13 | |
| 2.4.3: Inequalities Involving Absolute Values | 0:07:57 | 13 | |
| 2.5.1: Systems of Equations | 0:09:10 | 13 | |
| 2.5.2: Systems of Linear Equations | 0:04:44 | 38 | |
| 2.5.3: Higher Order Systems | 0:06:00 | 38 | |
| 2: Summary | – | – | |
| Module 3: Functions and their properties (30%) 01:46:11 total video length 478 total reading pages |
3: Functions and Their Properties | 0:00:55 | – |
| 3.1.1: What is a Function? | 0:10:53 | 21 | |
| 3.1.2: Function or Not? | 0:02:55 | 21 | |
| 3.1.3: Vertical Line Test | 0:04:22 | 21 | |
| 3.2: Representing with Functions | 0:04:21 | 51 | |
| 3.2.1: Linear Modeling | 0:05:02 | 51 | |
| 3.2.2: Exponential Modeling | 0:06:25 | 51 | |
| 3.3.1: Domain and Range of a Function | 0:01:31 | 17 | |
| 3.3.1.1: Intrinsic Domain Limitations | 0:08:45 | 17 | |
| 3.3.2: Visualizing Domain and Range | 0:07:18 | 17 | |
| 3.4: Algebra of Functions | 0:02:03 | 14 | |
| 3.4.1: Composition of Functions | 0:11:25 | 14 | |
| 3.5.1: Plotting Functions | 0:06:58 | 47 | |
| 3.5.2: Symmetry of Functions | 0:08:46 | 47 | |
| 3.5.3: Transformation of Functions | 0:07:12 | 47 | |
| 3.6: Inverse Functions | 0:06:06 | 14 | |
| 3.6.1: Remarks on Inverse Functions | 0:02:30 | 14 | |
| 3.6.2: Horizontal Line Test | 0:08:44 | 14 | |
| 3: Summary | – | – | |
| Module 4: Number systems and operations (20%) 01:21:35 total video length 442 total reading pages |
4: Number Systems and Operations | 0:00:54 | – |
| 4.1.1: Real Numbers | 0:01:12 | 16 | |
| 4.1.2: Integers | 0:01:32 | 16 | |
| 4.1.3: Rational Numbers | 0:02:44 | 16 | |
| 4.1.4: Irrational Numbers | 0:05:26 | 16 | |
| 4.2.1: Complex Numbers | 0:05:22 | 9 | |
| 4.2.2: Arithmetic with Complex Numbers | 0:05:13 | 9 | |
| 4.2.3: Division of Complex Numbers | 0:05:18 | 9 | |
| 4.3.1: Sequences and Series | 0:02:21 | 45 | |
| 4.3.2: Notation | 0:02:35 | 45 | |
| 4.3.3: Arithmetic Series | 0:05:42 | 45 | |
| 4.3.3.1: Arithmetic Series (continued) | 0:02:11 | 45 | |
| 4.3.4: Geometric Series | 0:05:55 | 45 | |
| 4.4.1: Factorials and Binomial Theorem | 0:02:51 | 18 | |
| 4.4.2: Factorial! | 0:05:13 | 18 | |
| 4.4.3: Counting with Factorials | 0:04:24 | 18 | |
| 4.4.3.1: Counting with Factorials | 0:05:25 | 18 | |
| 4.4.4: Binomial Theorem | 0:07:05 | 18 | |
| 4.5.1: Matrices | 0:03:15 | 12 | |
| 4.5.2: Matrix Algebra | 0:03:24 | 12 | |
| 4.5.3: Determinant | 0:03:33 | 12 | |
| 4: Summary | – | – | |
| Course Conclusion | – | – |
