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PrecalculusOnline College Course
Everything you need before calculus — functions, trigonometry, and analytic geometry in one course.
What You'll Learn
A full semester of precalculus — completed at your own pace, with no deadlines or fixed class times.
What You'll Be Able to Do
- Solve and graph linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric equations and inequalities, including real-world applications
- Analyze and interpret the behavior of functions — including domain, range, transformations, composition, and inverses — using algebraic and graphical methods
- Model real-world scenarios with linear, polynomial, exponential, logarithmic, and trigonometric functions, selecting appropriate types and interpreting results
- Apply degree and radian measure, the unit circle, and all six trigonometric functions to solve right triangles, oblique triangles (Law of Sines and Cosines), and applied problems
- Evaluate and simplify trigonometric expressions using fundamental identities, sum/difference, double-angle, and half-angle formulas
- Represent and interpret data in Cartesian, polar, and vector forms and connect representations across function types
- Solve linear and nonlinear systems of equations using substitution, elimination, and matrix methods including Gaussian elimination
- Compute the nth term and sum of arithmetic and geometric sequences and series, and apply the binomial theorem and basic probability concepts
Major Course Topics
Course chapters and lessons
Precalculus has 11 chapters across 75 instructional hours, as listed in the course syllabus. Expand any chapter to see the lessons inside it.
- Chapters
- 11
- Lessons
- 67
- Instructional hours
- 75 hrs
- Semester hours
- 3
Chapter 1
Algebraic Foundations & Prerequisites
- 1.1 Real Numbers, Order, and Absolute Value
- 1.2 Exponents, Radicals, and Rational Exponents
- 1.3 Polynomials: Operations and Factoring
- 1.4 Rational Expressions
- 1.5 Linear Inequalities and Absolute Value Inequalities
- 1.6 Polynomial and Rational Inequalities
- 1.7 Coordinate Geometry: Distance Formula, Midpoint Formula, and Circles
Chapter 2
Functions & Their Behavior
- 2.1 Understanding Functions and Notation
- 2.2 Domain and Range of Functions
- 2.3 Graphs, Rates of Change, and Graph Behavior
- 2.4 Piecewise-Defined Functions
- 2.5 Combining Functions: Arithmetic Operations and Composition
- 2.6 Transformations of Graphs
- 2.7 Inverse Functions and Their Properties
Chapter 3
Linear & Quadratic Functions
- 3.1 Linear Functions and Their Representations
- 3.2 Graphing and Interpreting Linear Models
- 3.3 Applications of Linear Functions
- 3.4 Absolute Value Functions and Applications
- 3.5 Quadratic Functions and Their Graphs
- 3.6 Solving Quadratic Equations and Inequalities
- 3.7 Data Modeling with Linear Regression
Chapter 4
Polynomial & Rational Functions
- 4.1 Complex Numbers and Operations
- 4.2 Power Functions and Higher-Degree Polynomials
- 4.3 Analyzing Graphs of Polynomial Functions
- 4.4 Polynomial Division Techniques
- 4.5 Zeros and Factors of Polynomial Functions
- 4.6 Solving Polynomial Inequalities
- 4.7 Rational Functions and Their Graphs
- 4.8 Solving Rational Equations and Inequalities
- 4.9 Radical Functions and Inverse Relationships
Chapter 5
Exponential & Logarithmic Functions
- 5.1 Exponential Functions and Growth/Decay Models
- 5.2 Graphs and Transformations of Exponential Functions
- 5.3 Logarithmic Functions and Their Meaning
- 5.4 Graphs and Transformations of Logarithmic Functions
- 5.5 Properties of Logarithms
- 5.6 Solving Exponential and Logarithmic Equations
- 5.7 Applications and Data Modeling
Chapter 6
Trigonometric Foundations
- 6.1 Angle Measurement in Degrees and Radians
- 6.2 The Unit Circle and the Sine and Cosine Functions
- 6.3 The Six Trigonometric Functions
- 6.4 Right Triangle Trigonometry and Applications
- 6.5 Modeling with Periodic Functions
Chapter 7
Graphs of Trigonometric Functions
- 7.1 Graphs and Transformations of Sine and Cosine
- 7.2 Graphs of Tangent, Cotangent, Secant, and Cosecant
- 7.3 Inverse Trigonometric Functions
Chapter 8
Trigonometric Identities & Equations
- 8.1 Fundamental Trigonometric Identities
- 8.2 Sum and Difference Identities
- 8.3 Double-Angle and Half-Angle Formulas
- 8.4 Solving Trigonometric Equations
Chapter 9
Applications of Trigonometry
- 9.1 Solving Oblique Triangles: Law of Sines
- 9.2 Solving Oblique Triangles: Law of Cosines
- 9.3 Polar Coordinate Systems
- 9.4 Graphing Polar Equations
- 9.5 Complex Numbers in Polar Form
- 9.6 Introduction to Vectors
Chapter 10
Systems of Equations & Matrices
- 10.1 Solving Linear Systems in Two Variables
- 10.2 Solving Linear Systems in Three Variables
- 10.3 Nonlinear Systems and Inequalities
- 10.4 Partial Fraction Decomposition
- 10.5 Matrices and Matrix Operations
- 10.6 Gaussian Elimination
Chapter 11
Sequences, Series & Counting
- 11.1 Sequences and Recursive Definitions
- 11.2 Arithmetic Sequences
- 11.3 Geometric Sequences
- 11.4 Series and Sigma Notation
- 11.5 The Binomial Theorem
- 11.6 Basic Counting Principles and Probability
These chapters come straight from the official course syllabus, which also sets out the graded assignment and the proctored final exam.
Course Details
| Course | Precalculus (MATH 115) |
|---|---|
| Format | 100% online |
| Learning Style | Self-paced — no deadlines or class times |
| Credits | 3 College Credits |
| Lab | Not required |
| Prerequisites | Solid algebra foundation |
| Assessment | 25% Attendance · 25% Quizzes · 25% Assignments · 25% Final Exam |
| Estimated Completion | Self-paced · no deadlines |
| Credit Recommendation | NCCRS Credit Recommended |
| Transfer Information | Transferable via the credit recommendation above — your registrar can confirm your school's policy |
Pick What Fits You
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- Lifetime access — no subscription, no expiration
- Official transcript on completion
- Best if you only need this one prerequisite
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- Ideal if you're planning to complete several prerequisites
- Same NCCRS-recommended credit and official transcript
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Master precalculus and build a foundation for your degree — and your future.
Everything you need before calculus — functions, trigonometry, and analytic geometry in one course.
🎯 Why It Matters
- Precalculus is the required bridge into Calculus I for STEM, engineering, and economics majors
- Trigonometry is essential for physics, engineering, architecture, and surveying
- Removes the most common blocker between students and a calculus sequence
- Satisfies quantitative-reasoning requirements at most institutions
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🚀 How This Sets You Up
- Complete 11 chapters from functions through trigonometry and analytic geometry
- Quiz per subchapter, one assignment, 100-question final exam
- 75 contact hours, fully self-paced
- Direct preparation for Calculus I
- Follows naturally from College Algebra
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A 54-second look at Precalculus.
Common Questions Answered.
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Save time and reduce tuition costs. Many students complete prerequisites faster and shorten their time to graduation — at a fraction of the cost.
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This course is NCCRS-recommended for 3 semester credit hours. Transfer as many credits as your university allows — students have transferred anywhere from 3 to 90+ credits depending on their school's policy.
Everything You Need to Succeed
Video-Based Lessons
HD video lectures broken into short, focused modules. Watch at your own pace — pause, rewind, replay any time.
Quizzes & Final Exam
Evaluate your understanding after every section with quizzes and a comprehensive final exam that mirrors real college assessment.
Structured College-Level Course
Structured lessons covering every topic — designed as a standard Precalculus college-level course.
Official Transcript
Complete the course, request your transcript, and transfer 3 credit hours to cooperating universities. No separate exam required.
Earn 3 College Credits
for $250.
Self-paced. No deadlines. NCCRS-recommended, recognized by various NCCRS cooperating universities. Join 135,000+ learners on the UPI Study platform.