- Course Type CLEP
- Subject Science and Mathematics
- Level Introductory
- Length 6 Modules
- Video Length 7h 8m
- Reading Pages 1070
- Institution Modern States
ABOUT THIS COURSE
Precalculus reviews the material typically taught in a first-semester college-level precalculus course. The course emphasizes algebra, function theory, and trigonometry, preparing learners for the transition into calculus. Topics include the properties of linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, piecewise-defined, absolute value, and square root functions.
This is a free, self-paced Modern States course with no prerequisites. It is aligned to the CLEP® Precalculus 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. Dr. Dywayne A Nicely, The Ohio State University – Marion Campus supported course enhancements published in 2025.
Course Overview
Precalculus Course Overview - Modern States
| Module | Topic | Video Length | Total pages of required reading |
| Module 1: Algebra 02:06:03 total video length 385 total reading pages |
1: Algebra | 0:01:26 | – |
| 1.1: Basic Algebra | 0:00:40 | – | |
| 1.1.1: Algebraic Operations | 0:15:23 | 133 | |
| 1.1.2: Factoring and Expanding Polynomials | 0:16:57 | 31 | |
| 1.1.3: Introduction to Exponentials | 0:09:13 | 27 | |
| 1.1.4: Logarithms | 0:08:27 | 35 | |
| 1.2: Equations | 0:00:49 | – | |
| 1.2.1: Linear Equations and Inequalities | 0:06:49 | 61 | |
| 1.2.2: Quadratic Equations | 0:14:24 | 16 | |
| 1.2.3: Higher Order Polynomials | 0:12:48 | 33 | |
| 1.2.4: Exponential and Logarithmic Equations | 0:08:53 | 11 | |
| 1.2.5: Absolute Value Equations | 0:11:02 | 11 | |
| 1.3: Systems of Equations | 0:01:11 | – | |
| 1.3.1: Systems of Equations and Inequalities | 0:10:54 | 16 | |
| 1.3.2: Higher Order Systems | 0:07:07 | 11 | |
| 1: Summary | – | – | |
| Module 2: Function Theory 00:43:10 total video length 62 total reading pages |
2: Function Theory | 0:00:36 | – |
| 2.1: Introduction to Functions | 0:09:35 | 20 | |
| 2.2: Algebra of Functions | 0:08:17 | 13 | |
| 2.3: Domain and Range of a Function | 0:13:24 | 16 | |
| 2.4: Inverse Functions | 0:11:18 | 13 | |
| 2: Summary | – | – | |
| Module 3: Trigonometry 01:48:19 total video length 400 total reading pages |
3: Trigonometry | 0:01:16 | – |
| 3.1: Introduction to Trigonometry | 0:01:07 | – | |
| 3.1.1: Idea of Trigonometry | 0:04:51 | 29 | |
| 3.1.2: Trigonometric Functions | 0:09:00 | 41 | |
| 3.2: Trigonometric Examples | 0:07:16 | 12 | |
| 3.3: Radians | 0:05:19 | 17 | |
| 3.4: Periodicity and Plotting Trigonometric Functions | 0:08:32 | 36 | |
| 3.5: Trigonometric Identities | 0:07:51 | 75 | |
| 3.6: Inverse Trigonometric Functions | 0:10:12 | 11 | |
| 3.7: Domain and Range of Trigonometric Functions | 0:01:21 | – | |
| 3.7.1: Domain and Range of Trigonometric Functions | 0:17:20 | 84 | |
| 3.7.2: Domain and Range of Inverse Trigonometric Functions | 0:13:31 | 11 | |
| 3.8: Law of Sines and Cosines | 0:08:25 | 26 | |
| 3.9: Trigonometric Equations | 0:12:18 | 58 | |
| 3: Summary | – | – | |
| Module 4: Function Representations 00:41:02 total video length 85 total reading pages |
4: Function Representations | 0:01:08 | – |
| 4.1: Plotting Functions | 0:01:13 | – | |
| 4.1.1: Plotting with Symmetry and Transformations | 0:16:21 | 25 | |
| 4.1.2: Plotting with Asymptotes and Extrema | 0:08:24 | 13 | |
| 4.2: Return to Function Algebra | 0:06:32 | 13 | |
| 4.3: Tabular Representations | 0:07:24 | 34 | |
| 4: Summary | – | – | |
| Module 5: Modeling with Functions 00:49:15 total video length 45 total reading pages |
5: Modeling with Functions | 0:01:50 | – |
| 5.1: Linear Growth | 0:08:44 | 13 | |
| 5.2: Exponential Growth | 0:21:26 | 15 | |
| 5.3: Trigonometric Models | 0:17:15 | 17 | |
| 5: Summary | – | – | |
| Module 6: Analytic Geometry 00:59:41 total video length 93 total reading pages |
6: Analytic Geometry | 0:01:25 | – |
| 6.1: Lines | 0:09:01 | 19 | |
| 6.2: Idea of Conic Sections | 0:04:13 | 15 | |
| 6.3: Circles | 0:11:17 | 13 | |
| 6.4: Ellipses | 0:14:02 | 16 | |
| 6.5: Parabolas | 0:09:19 | 13 | |
| 6.6: Hyperbolas | 0:10:24 | 17 | |
| 6: Summary | – | – | |
| Course Conclusion | – | – |
