College Algebra for High School Students

College Algebra: Reasoning, Functions, and Applications

Build the algebraic fluency, mathematical reasoning, and modeling habits needed for advanced high school mathematics. This independent Computing4All course supports students studying college algebra, including OnRamps students. It develops 11 connected topics through original instruction, visual explanations, and practice.

Across 33 lessons, you will connect formulas with graphs and situations, explain why methods work, check assumptions, and communicate complete solutions. The course includes 264 practice exercises with worked solutions, 11 synthesis investigations, and 22 practice quizzes containing 220 questions with explanations.

What you will learn

• Construct arguments, test conjectures, use counterexamples, and maintain valid algebraic steps.
• Analyze functions through domains, graphs, transformations, composition, and inverses.
• Solve systems and use matrices to organize equations and transformations.
• Work with quadratic, polynomial, rational, radical, exponential, and logarithmic functions.
• Use complex numbers to solve equations and interpret nonreal roots.
• Select and assess models using data, residuals, and meaningful restrictions.
• Describe sequences, calculate series, and explain binomial coefficients.

How to study

1. Read each lesson with pencil and paper. Pause at an example and predict the next step.
2. Attempt all eight practice exercises before reading their worked solutions.
3. Use the figures actively: identify axes, points, restrictions, and the relationship described by each caption.
4. Take the two practice quizzes in each unit. Study the explanation even when your answer is correct, then retry as often as needed.
5. Complete the unit synthesis investigation and explain the result in your own words.
6. Keep an error journal containing the mistaken idea, its correction, and a new example.

Practice quizzes allow unlimited attempts with no time limit. Aim for at least 80%, then continue until you can explain every answer. Use calculators to explore and check; retain exact fractions and radicals when the problem calls for an exact result.

Prerequisites and materials

Bring familiarity with signed numbers, fractions, basic equations, exponents, coordinate graphs, and elementary geometry. Have paper, a pencil, and access to a scientific or graphing calculator. Review a missing prerequisite when it appears rather than guessing past it.

These materials supplement a student’s school course. They are not official University of Texas at Austin assignments or assessments.