ModelCourses/CollegeAlgebra

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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

• 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