- Course Type CLEP
- Subject Science and Mathematics
- Level Introductory
- Length 4 weeks
- Effort 6 hours/week
- Institution Modern States
ABOUT THIS COURSE
This course, which covers the fundamentals taught in a first-semester calculus course, will provide you with an understanding of functions and their properties. Our goal as creators of this course is to prepare you to pass the College Board’s CLEP examination and obtain college credit for free.
“Precalculus is a transitional course. There is a big difference between life before and after calculus, and I want to prepare you as much as possible for this fascinating subject. The precalculus CLEP exam will require us to study algebra and function theory in great detail. A huge emphasis is also placed on trigonometry,” explains Dr. James Murphy, professor at Tufts University, and instructor of this course.
“Precalculus” is a completely self-paced course. It has no prerequisites and it is offered entirely for free.
Instructors
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James Murphy, Ph.D.Professor, Tufts University
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 |
Introduction to Algebra (Module 1) | 0:01:26 | – |
| Basic Algebra (Module 1.1) | 0:00:40 | – | |
| Algebraic Operations (Module 1.1.1) | 0:15:23 | 133 | |
| Factoring and Expanding Polynomials (Module 1.1.2) | 0:16:57 | 31 | |
| Introduction to Exponentials (Module 1.1.3) | 0:09:13 | 27 | |
| Logarithms (Module 1.1.4) | 0:08:27 | 35 | |
| Equations (Module 1.2) | 0:00:49 | – | |
| Linear Equations and Inequalities (Module 1.2.1) | 0:06:49 | 61 | |
| Quadratic Equations (Module 1.2.2) | 0:14:24 | 16 | |
| Higher Order Polynomials (Module 1.2.3) | 0:12:48 | 33 | |
| Exponential and Logarithmic Equations (Module 1.2.4) | 0:08:53 | 11 | |
| Absolute Value Equations (Module 1.2.5) | 0:11:02 | 11 | |
| Systems of Equations (Module 1.3) | 0:01:11 | – | |
| Systems of Equations and Inequalities (Module 1.3.1) | 0:10:54 | 16 | |
| Higher Order Systems (Module 1.3.2) | 0:10:54 | 11 | |
| Module 2: Function Theory 00:43:10 total video length 62 total reading pages |
Introduction (Module 2) | 0:00:36 | – |
| Introduction to Functions (Module 2.1) | 0:09:35 | 20 | |
| Algebra of Functions (Module 2.2) | 0:08:17 | 13 | |
| Domain and Range of Function (Module 2.3) | 0:13:24 | 16 | |
| Inverse Functions (Module 2.4) | 0:11:18 | 13 | |
| Module 3: Trigonometry 01:48:19 total video length 400 total reading pages |
Introduction (Module 3) | 0:01:16 | – |
| Introduction to Trigonometry (Module 3.1) | 0:01:07 | – | |
| Idea of Trigonometry (Module 3.1.1) | 0:04:51 | 29 | |
| Trigonometric Functions (Module 3.1.2) | 0:09:00 | 41 | |
| Trigonometric Examples (Module 3.2) | 0:07:16 | 12 | |
| Radians (Module 3.3) | 0:05:19 | 17 | |
| Periodicity and Plotting Trigonometric Functions (Module 3.4) | 0:08:32 | 36 | |
| Major Trigonometric Identities (Modules 3.5) | 0:07:51 | 75 | |
| Inverse Trigonometric Functions (Module 3.6) | 0:10:12 | 11 | |
| Domain and Range of Trigonometric Functions (Module 3.7) | 0:01:21 | – | |
| Domain and Range of Trigonometric Functions (Module 3.7.1) | 0:17:20 | 84 | |
|
Domain and Range of Inverse Trigonometric Functions (Module 3.7.2)
|
0:13:31 | 11 | |
| Law of Sines and Cosines (Module 3.8) | 0:08:25 | 26 | |
| Trigonometric Equations (Module 3.9) | 0:12:18 | 58 | |
| Module 4: Function Representations 00:41:02 total video length 85 total reading pages |
Introduction (Module 4) | 0:01:08 | – |
| Plotting Functions (Module 4.1) | 0:01:13 | – | |
|
Plotting Functions with Symmetry and Transformations (Module 4.1.1)
|
0:16:21 | 25 | |
| Plotting Functions with Asymptotes and Extrema (Module 4.1.2) | 0:08:24 | 13 | |
| Return to Function Algebra (Module 4.2) | 0:06:32 | 13 | |
| Tabular Representations (Module 4.3) | 0:07:24 | 34 | |
| Module 5: Modeling with Functions 00:49:15 total video length 45 total reading pages |
Introduction to Modeling with Functions (Module 5) | 0:01:50 | – |
| Linear Growth (Module 5.1) | 0:08:44 | 13 | |
| Exponential Growth (Module 5.2) | 0:21:26 | 15 | |
| Trigonometric Models (Module 5.3) | 0:17:15 | 17 | |
| Module 6: Analytic Geometry 00:59:41 total video length 93 total reading pages |
Introduction to Analytic Geometry (Module 6) | 0:01:25 | – |
| Lines (Module 6.1) | 0:09:01 | 19 | |
| Idea of Conic Sections (Module 6.2) | 0:04:13 | 15 | |
| Circles (Module 6.3) | 0:11:17 | 13 | |
| Ellipses (Module 6.4) | 0:14:02 | 16 | |
| Parabolas (Module 6.5) | 0:09:19 | 13 | |
| Hyperbolas (Module 6.6) | 0:10:24 | 17 |
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Student Stories
“It was totally free. I got college credit for all of the CLEP exams and passed all of them on the first try. I loved being able to learn at my own pace. Modern States is amazing.”
“I'm using Modern States to complete my engineering degree in the shortest amount of time possible”
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“All of my undergraduate courses, which I can CLEP out of, will go towards my nursing degree and probably save me close to $15,000.”
“Modern States made it possible to do a five-year degree in four years. It's helping dreams come true.”
“I'd like to thank Modern States for even making this possible to students.”
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