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College AlgebraOnline College Course
The gateway math course — functions, equations, and graphs, taught so the reasoning actually sticks.
What You'll Learn
A full semester of college algebra — completed at your own pace, with no deadlines or fixed class times.
What You'll Be Able to Do
- Perform operations on real numbers, polynomials, and rational expressions, and apply properties of exponents and radicals to simplify algebraic expressions
- Solve linear, quadratic, polynomial, rational, radical, and absolute value equations and inequalities, and model real-world problems using these equation types
- Solve systems of linear equations in two and three variables using graphical, substitution, and elimination methods, and interpret solutions in context
- Analyze functions using proper notation — including domain, range, composition, transformations, and inverses — and graph linear, quadratic, absolute value, and piecewise-defined functions
- Graph and interpret polynomial and rational functions, identifying zeros, end behavior, asymptotes, and holes
- Solve and graph exponential and logarithmic equations, apply properties of logarithms, and model growth, decay, and compound interest scenarios
- Identify and evaluate arithmetic and geometric sequences and series, including finite sums and, where applicable, infinite geometric series
Major Course Topics
Course chapters and lessons
College Algebra has 10 chapters across 58 instructional hours, as listed in the course syllabus. Expand any chapter to see the lessons inside it.
- Chapters
- 10
- Lessons
- 50
- Instructional hours
- 58 hrs
- Semester hours
- 3
Chapter 1
Algebraic Foundations
- 1.1 Real Numbers and Their Properties number sets, absolute value, order of operations, properties of real numbers
- 1.2 Integer Exponents and Scientific Notation product, quotient, power, zero, and negative exponent rules; scientific notation
- 1.3 Radicals and Rational Exponents nth roots, simplifying radicals, rationalizing denominators, converting between radical and rational exponent notation
- 1.4 Simplifying Radical Expressions product and quotient rules for radicals, adding and subtracting radicals, multiplying radical expressions
Chapter 2
Polynomials & Factoring
- 2.1 Operations on Polynomials addition, subtraction, multiplication, special products (FOIL, difference of squares, perfect square trinomials)
- 2.2 Factoring: GCF and Grouping greatest common factor, factoring by grouping
- 2.3 Factoring Trinomials leading coefficient of 1 and a ≠ 1, trial-and-error and AC methods
- 2.4 Special Factoring Formulas difference of squares, sum and difference of cubes
- 2.5 Factoring Strategy choosing the appropriate factoring technique; factoring completely
Chapter 3
Rational & Radical Expressions
- 3.1 Simplifying Rational Expressions identifying excluded values, reducing to lowest terms
- 3.2 Multiplying and Dividing Rational Expressions factoring to cancel common factors
- 3.3 Adding and Subtracting Rational Expressions finding the LCD, combining fractions
- 3.4 Complex Fractions simplifying by LCD method and division method
- 3.5 Radical Expressions operations: multiplying, dividing, adding, subtracting radical expressions; conjugates
Chapter 4
Linear Equations & Inequalities
- 4.1 Linear Equations in One Variable solving, checking solutions, equations with fractions
- 4.2 Formulas and Applications literal equations, solving for a variable; applied word problems (distance, rate, mixture, geometry)
- 4.3 Linear Inequalities solving, graphing on a number line, interval notation
- 4.4 Compound Inequalities AND (intersection) and OR (union) compound inequalities
- 4.5 Absolute Value Equations and Inequalities solving |ax + b| = c, |ax + b| < c, |ax + b| > c
Chapter 5
Systems of Linear Equations
- 5.1 Systems of Two Linear Equations graphing method, substitution method, elimination method; consistent, inconsistent, dependent systems
- 5.2 Applications of 2×2 Systems mixture, rate, investment, and geometry word problems
- 5.3 Systems of Three Linear Equations solving 3×3 systems by elimination and back-substitution
- 5.4 Systems of Linear Inequalities graphing feasible regions, identifying vertices
Chapter 6
Quadratic Equations & Functions
- 6.1 Solving Quadratic Equations by Factoring zero product property, checking solutions
- 6.2 Square Root Property and Completing the Square solving equations of the form x² = k; completing the square method
- 6.3 The Quadratic Formula and Discriminant deriving and applying the quadratic formula; using discriminant to determine number and type of solutions
- 6.4 Quadratic Functions and Parabolas standard form y = ax² + bx + c; vertex form y = a(x−h)² + k; vertex, axis of symmetry, direction of opening, intercepts
- 6.5 Quadratic Inequalities solving using sign charts; expressing solutions in interval notation
Chapter 7
Functions & Their Graphs
- 7.1 Relations, Functions, and Function Notation definition, vertical line test, evaluating f(x), difference quotient
- 7.2 Domain and Range finding algebraically and from graphs; interval notation
- 7.3 Graphs of Basic Functions linear, absolute value, square root, cube root, quadratic; identifying and sketching
- 7.4 Piecewise-Defined Functions evaluating and graphing
- 7.5 Transformations of Functions vertical/horizontal shifts, reflections, stretches, and compressions
- 7.6 Combining Functions sum, difference, product, quotient of functions; composite functions (f ∘ g)(x); domain of combined functions
- 7.7 Inverse Functions one-to-one functions, horizontal line test, finding f⁻¹(x), verifying via composition
Chapter 8
Polynomial & Rational Functions
- 8.1 Polynomial Functions and End Behavior degree, leading coefficient, end behavior, turning points
- 8.2 Zeros of Polynomial Functions real zeros, multiplicity, graphs touching vs. crossing the x-axis
- 8.3 Polynomial Division and the Remainder Theorem long division, synthetic division, Remainder and Factor Theorems
- 8.4 Rational Functions and Their Graphs vertical asymptotes, horizontal asymptotes, oblique asymptotes, holes, graphing strategy
- 8.5 Polynomial and Rational Inequalities sign chart method; interval notation solutions
Chapter 9
Exponential & Logarithmic Functions
- 9.1 Exponential Functions definition, base restrictions, graphs and transformations, natural base e, compound interest formula
- 9.2 Logarithmic Functions definition as inverse of exponential, converting between forms, evaluating log and ln
- 9.3 Properties of Logarithms product, quotient, power rules; change-of-base formula; expanding and condensing
- 9.4 Solving Exponential and Logarithmic Equations algebraic methods, checking extraneous solutions
- 9.5 Applications exponential growth and decay, half-life, population models, compound and continuous interest
Chapter 10
Sequences & Series
- 10.1 Sequences and Recursive Definitions explicit and recursive formulas, generating terms
- 10.2 Arithmetic Sequences and Series common difference, nth term, sum of first n terms
- 10.3 Geometric Sequences and Series common ratio, nth term, sum of finite geometric series
- 10.4 Infinite Geometric Series condition for convergence (|r| < 1), sum formula, applications
- 10.5 Sigma Notation writing and evaluating series using sigma notation
These chapters come straight from the official course syllabus, which also sets out the graded assignment and the proctored final exam.
Course Details
| Course | College Algebra (MATH 111) |
|---|---|
| Format | 100% online |
| Learning Style | Self-paced — no deadlines or class times |
| Credits | 3 College Credits |
| Lab | Not required |
| Prerequisites | High-school algebra |
| 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 |
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The gateway math course — functions, equations, and graphs, taught so the reasoning actually sticks.
🎯 Why It Matters
- College Algebra is the most common math prerequisite across U.S. degree programs
- Required gateway to Precalculus, Statistics, Calculus, and most STEM and business majors
- Quantitative reasoning is a general-education requirement at nearly every institution
- Function modeling underpins finance, data analysis, and the sciences
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- 58 contact hours, fully self-paced
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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 College Algebra college-level course.
Official Transcript
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