College Algebra

College Algebra is a rigorous, college-level course that revisits topics from Algebra 2 at greater depth and introduces new material — matrices, conic sections, combinatorics, and formal polynomial theory. It is the standard prerequisite for precalculus and calculus at most community colleges and universities.

Who Is This For?

College Algebra is designed for:

• Community college students taking the required math course (this course has a 30–40% national failure rate — we aim to change that)
• Placement test prep — college math placement exams draw heavily from these topics
• Advanced high school students preparing for dual enrollment or AP courses
• Career changers needing college-level math for STEM, business, or healthcare programs

You should be comfortable with Algebra 2 topics — exponential and logarithmic functions, polynomial operations, and function analysis — before starting here.

What You Will Learn

College Algebra covers eight areas:

1. Functions in Depth — rigorous treatment of notation, domain/range, transformations, composition, inverses, and symmetry
2. Polynomial Functions — optimization, detailed graph analysis, the Rational Root Theorem, Descartes’ Rule, and bounds on zeros
3. Rational Functions — asymptote analysis (vertical, horizontal, oblique), advanced graphing, and partial fraction decomposition
4. Exponential and Logarithmic Applications — modeling, compound interest, Newton’s Law of Cooling, and logistic growth
5. Systems and Matrices — Gaussian elimination, matrix operations, determinants, inverses, and Cramer’s Rule
6. Conic Sections — circles, parabolas (focus/directrix), ellipses, and hyperbolas
7. Sequences and Combinatorics — the Binomial Theorem, mathematical induction, permutations, combinations, and probability
8. Advanced Equations — polynomial inequalities, rational inequalities, and equations reducible to quadratic form

Where to Start

If you are reviewing for a placement test, start with Functions in Depth — functions are the organizing principle of the entire course, and placement exams test function fluency heavily. If you are working through the course sequentially, follow the clusters in order.

What Comes Next

After College Algebra, you are ready for Precalculus (coming soon) or Trigonometry if you have not covered it yet. Together, College Algebra and Trigonometry form the complete foundation for Calculus.