College Algebra
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engagement activities

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College Algebra Course Outline

What are the prerequisites to College Algebra?

Concepts Covered:

  • What are real numbers, why are they used, and how do we use them?
  • How are exponents and scientific notation used?
  • What is the difference between radicals and rational exponents?
  • How can polynomials be used?
  • How do we factor polynomials?
  • How do we use rational expressions?

How are equations and inequalities used?

Concepts Covered:

  • How are rectangular coordinate systems used in graphs?
  • How do we find linear equations in one variable?
  • How do linear equations apply to real-world applications?
  • How can complex numbers be used in various equations?
  • What are different ways to solve quadratic equations?
  • What are other types of equations?
  • What is the difference between linear inequalities and absolute value inequalities?

What are functions?

Concepts Covered:

  • How are functions related to function notation?
  • What is the difference between domain and range?
  • How does the rate of change affect the behavior of graphs?
  • How do you find the composition of functions?
  • How can functions be transformed?
  • How do you find absolute value functions?
  • What are inverse functions?

What are linear functions?

Concepts Covered:

  • How do we use linear functions?
  • How do we model linear functions?
  • How do we fit linear models to data?

How are polynomials related to rational functions?

Concepts Covered:

  • How are quadratic functions applied in parabolas?
  • What is the difference between power functions and polynomial functions?
  • Why do we graph polynomial functions?
  • How do we divide polynomials?
  • How do we find zeros in polynomial functions?
  • Why are rational functions important?
  • What is the difference between inverses and radical functions?
  • How do we model using variations?

What are exponential and logarithmic functions?

Concepts Covered:

  • How are exponential functions used?
  • How do we graph exponential functions?
  • How do we find logarithmic functions?
  • How do we graph logarithmic functions?
  • What are logarithmic properties?
  • What is difference between exponential and logarithmic equations?
  • How do we use exponential and logarithmic models?
  • How do we use data to fit exponential models?

How do the systems of equations and inequalities operate?

Concepts Covered:

  • How do you use the systems of linear equations using two variables?
  • How do you use the systems of linear equations using three variables?
  • What are the two variables in the systems of nonlinear equations and inequalities?
  • Why do we get partial fractions?
  • What is the difference between the matrices and matrix operations?
  • How do we solve different systems with the Gaussian elimination?
  • How do we solve different systems with inverses?
  • How do we solve different systems using Cramer’s rule?

What is analytic geometry?

Concepts Covered:

  • How is an ellipse formed?
  • What is a hyperbola?
  • How do we form parabolas?
  • What are the rotation of axes?
  • Where are the conic sections in the polar coordinates?

How do sequences, probability, and counting theory relate to each other?

Concepts Covered:

  • How do we find sequences and their notations?
  • How do we find arithmetic sequences?
  • How do we find geometric sequences?
  • How do we find series and their notations?
  • How do we count problems with principles?
  • What is binomial theorem?
  • What is probability?

About the book

College Algebra

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve

About the authors:

Senior Contributing Authors

Jay Abramson, Arizona State University

Contributing Authors

Valeree Falduto, Palm Beach State College
Rachael Gross, Towson University
Rick Norwood, East Tennessee State University
Nicholas Belloit, Florida State College at Jacksonville
Jean-Marie Magnier, Springfield Technical Community College
Harold Whipple, Formerly of Columbia College
Christina Fernandez
David Lippman, Pierce College
Melonie Rasmussen, Pierce College

Assessment Question Author

William C. Fanning
Adjunct Mathematics Professor
Central Virginia Community College

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