I am teaching intermediate algebra this spring and I wanted to post the syllabus and give a bit of a comment here. You can find the syllabus on my math education page.

The course catalog gives a description:

A study of problem-solving techniques in intermediate-level algebra. The goal is to demonstrate number sense and estimation skills; interpret mathematical ideas using appropriate terminology; manipulate, evaluate, and simplify real-number and algebraic expressions; and translate, solve, and interpret applied problems. Emphasis is on numbers and algebraic properties, graphing skills, and applications drawn from a variety of areas (such as finance, science, and the physical world). Topics include polynomials; factoring; exponents and their notation; rational expressions and equations; rational exponents and radical expressions; linear, quadratic, and other equations; and inequalities.

As we can see, this corresponds to what high school students normally call Algebra II. Let that sink in.

*Image by Wokandapix via Pixabay. One day I will run out of generic free math pictures. But that day is not today.*