ModelCourses/CollegeAlgebra

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Description

Starting with one particular textbook we created a set of topics that are covered in a typical college algebra course. We have not organized these by chapters so that any person teaching from any textbook could use these in any order they needed. We then used the NPL to populate those topics with problems that exist. This led us to trying to decide how to combine some of those groups so that they would be more user friendly. We also started to write some problems to cover areas that are not covered or thinly covered by the NPL, as well as trying to get some sort of order of difficulty in the numbering. This will be an ongoing and evolving project as we have already had to revamp some of our original ideas.

College Algebra Topics (Alex)

Review part:

• Real numbers; essential algebra rules (evaluate algebraic expressions, domain of a variable, laws of exponents, square roots, scientific notation)
• Geometry essentials (formulas)
• Polynomials (multiplication formulas)
• Factoring polynomials; Long division
• Synthetic Division
• Rational Expressions
• Roots and rational exponents

Main part:

• Linear equations (populated)
• Quadratic Equations (populated)
• Complex numbers and quadratic equations (populated)
• Quadratic in form equations, factorable equations, equations with radicals (populated)
• Very simple inequalities, compound inequalities (populated, needs more)
• Absolute value equations and inequalities (populated)
• Word problems: interest, mixture, motion, constant rate jobs (populated)
• Coordinate system. Distance and midpoint formula (populated)
• Graphs of equations in two variables, intercepts, symmetry (populated)
• Lines
• Circles
• Variation (formulas for science laws, say)
• Functions
• Graph of functions
• Properties of functions
• Library of functions, piecewise-defined functions
• Graphing techniques, transformations
• Math models: building functions
• Linear functions and their properties (populated)
• Linear models
• Quadratic functions and their properties
• Quadratic models from ‘word problems’
• Inequalities with quadratic functions Audrey
• Polynomial functions and models
• Properties of rational functions?
• Graph of a rational function?
• Polynomial and Rational Inequalities: Audrey
• Real zeros of polynomials
• Complex zeros, fundamental theorem of algebra
• Composite functions
• One-to-one functions; inverse functions
• Conic sections