Difference between revisions of "ModelCourses/CollegeAlgebra"
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Revision as of 09:59, 10 March 2013
Prep Main Page > Model Courses > College Algebra Model Course
Contents
Try it out
General Description
- Freshman level college algebra course
- Pre-requisite: Intermediate algebra or 2 years of high school algebra.
Possible textbooks include, but are not limited to:
- Michael Sullivan and Michael Sullivan III. College Algebra—Enhanced with Graphing Utilities, Fifth Edition. Upper Saddle River, NJ: Prentice-Hall, Inc., 2009.
Topics Covered
- Lines and Circles and their graphs
- Functions and Their Graphs
- Inverse Functions
- Linear Functions, Their Properties, and Linear Models
- Quadratic Functions and Their Properties
- Inequalities Involving Quadratic Functions
- Polynomial and Rational Functions
- Exponential Functions
- Logarithmic Functions
- Exponential Growth and Decay Models
- Conics: Parabola, Ellipse and Hyperbola
- Systems of Equations and Inequalities
Problem sets
Review
- Set 01 Real numbers, essential algebra rules
- Problem set for this unit
- Students will be able to
- evaluate algebraic expressions
- domain of a variable
- laws of exponents
- square roots
- scientific notation
- Set 02 Formulas
- Problem set for this unit
- Students will be able to
- Use Formulas
- Problem set for this unit
- Set 03 Polynomials
- Problem set for this unit
- Students will be able to
- Use Polynomials
- Use Multiplication formulas
- Set 04 Factoring polynomials
- Problem set for this unit
- Students will be able to
- Factor polynomials
- Do Long division
- Set 05 Synthetic Division
- Problem set for this unit
- Students will be able to
- Do Synthetic Division
- Set 06 Rational Expressions
- Problem set for this unit
- Students will be able to
- Solve Rational Expressions
- Set 07 Roots and rational exponents
- Problem set for this unit
- Students will be able to
- Solve for roots
- Solve rational exponents
College algebra problem sets
- Set 01 Linear Equations
- Problem set for this unit
- Students will be able to
- Solve linear equations (populated)
- Set 02 Quadratic Equations
- Problem set for this unit
- Students will be able to
- Solve Quadratic Equations (populated)
- Set 03 Quadratic Equations with Complex Roots
- Problem set for this unit
- Students will be able to
- Solve quadratic equations with complex roots (populated)
- Set 04 Equations with Quadratic form and Radicals
- Problem set for this unit
- Students will be able to
- Use Quadratic form equations
- Solve Factorable equations
- Solve Equations with radicals (populated)
- Set 05 Inequalities
- Problem set for this unit
- Students will be able to
- Solve very simple inequalities
- Solve compound inequalities (populated, needs more)
- Set 06 Absolute value
- Problem set for this unit
- Students will be able to
- Solve equations involving absolute values
- Solve inequalities involving absolute values (populated)
- Set 07 Applications
- Problem set for this unit
- Students will be able to
- Solve word problems about interest
- Solve mixture problems
- Solve word problems about motion
- Solve word problems about constant rate jobs (populated)
- Set 08 Coordinate system
- Problem set for this unit
- Students will be able to
- Solve problems using the distance formula
- Solve problems using the midpoint formula (populated)
- Set 09 Graphs of equations in two variables
- Problem set for this unit
- Students will be able to
- Find graphs of equations in two variables
- Find intercepts
- Analyze symmetry of graphs (populated)
- Set 10 Lines
- Problem set for this unit
- Students will be able to
- Find graphs of lines
- Set 11 Lines
- Problem set for this unit
- Students will be able to
- Find graphs of circles
- Set 12 Variation
- Problem set for this unit
- Students will be able to
- Do problems involving variation
- Apply formulas to science laws
- Set 13 Functions
- Problem set for this unit
- Students will be able to
- Determine if an equation is a function
- Evaluate functions
- Set 14 Graph of functions
- Problem set for this unit
- Students will be able to
- Find graphs of functions
- Set 15 Properties of functions
- Problem set for this unit
- Students will be able to
- Use properties of functions
- Set 16 Library of functions
- Problem set for this unit
- Students will be able to
- Use several of a library of functions
- Graph piecewise-defined functions
- Evaluate piecewise-defined functions
- Set 17 Transformations of functions
- Problem set for this unit
- Students will be able to
- Use graphing techniques
- Use transformations to graph composite functions
- Set 18 Math models
- Problem set for this unit
- Students will be able to
- Build functions
- Set 19 Properties of Linear Functions
- Problem set for this unit
- Students will be able to
- Recognize linear functions (populated)
- Set 20 Linear models
- Problem set for this unit
- Students will be able to
- Use Linear models
- Set 21 Properties of Quadratic functions
- Problem set for this unit
- Students will be able to
- Use Quadratic functions
- Set 22 Applications of Quadratic functions
- Problem set for this unit
- Students will be able to
- Solve word problems using quadratic functions
- Set 23 Inequalities with Quadratic functions
- Problem set for this unit
- Students will be able to
- Solve inequalities with quadratic functions
- Set 24 Polynomial functions and models
- Problem set for this unit
- Students will be able to
- Solve problems using Polynomial functions and models
- Set 25 Properties of Rational Functions
- Problem set for this unit
- Students will be able to
- Solve problems related to properties of rational functions
- Set 26 Graphs of a Rational Functions
- Problem set for this unit
- Students will be able to
- Find vertical asymptotes
- Find horizontal asymptotes
- Find the domain and range of a rational function.
- Graph rational functions
- Set 27 Graphs of a Rational Functions
- Problem set for this unit
- Students will be able to
- Solve Polynomial Inequalities
- Solve Rational Inequalities
- Set 28 Real zeros of polynomials
- Problem set for this unit
- Students will be able to
- Find real zeros of polynomials
- Set 29 Complex zeros
- Problem set for this unit
- Students will be able to
- Find complex zeros
- Apply the fundamental theorem of algebra
- Set 30 Composite functions
- Problem set for this unit
- Students will be able to
- Evaluate composite functions
- Set 31 Inverse functions
- Problem set for this unit
- Students will be able to
- Determine if a function is one-to-one
- Find the inverse of a function
- Set 32 Conic sections
- Problem set for this unit
- Students will be able to
- Find equations for circles
- Find equations for ellipses
- Find equations for parabolas
