ModelCourses/CollegeAlgebra
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College Algebra Topics:
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
