ModelCourses/CollegeAlgebra

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
• Quadratic Equations
• Complex numbers and quadratic equations
• Quadratic in form equations, factorable equations, equations with radicals
• Very simple inequalities, compound inequalities
• Absolute value equations and inequalities
• Word problems: interest, mixture, motion, constant rate jobs
• Coordinate system. Distance and midpoint formula
• Graphs of equations in two variables, intercepts, symmetry
• 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
• Linear models
• Quadratic functions and their properties
• Quadratic models from ‘word problems’
• Inequalities with quadratic functions
• Polynomial functions and models
• Properties of rational functions?
• Graph of a rational function?
• Polynomial and Rational Inequalities
• Real zeros of polynomials
• Complex zeros, fundamental theorem of algebra
• Composite functions
• One-to-one functions; inverse functions