ModelCourses/CollegeAlgebra

Model Courses > College Algebra Model Course

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General Description

• Freshman level college algebra course
• Pre-requisite: Intermediate algebra or 2 years of high school algebra or high enough mathematics placement.

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

• Linear Equations
• Qaudratic Equations
• Equations Quadratic In Form
• Radical Equations
• 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 Equations
• Logarithmic Equations
• Systems of Equations and Inequalities

(2013 Edition) Problem Sets

Download Options

• Download the set-definition files and any local problems used by the course (you would be able to use File Manager to upload the file to Templates (default) directory, and then import the set-definition files)
  • Archive with set-definition files and local problems
  • Instructions on how to use the file -- to be posted
• Download complete archive of the model course (you webwork administrator would have to place the archive in the corect place on your webwork server)
  • Full archive of the course
  • Instructions on how to use the file -- to be posted

Problem Sets

• HW Set 1a – Review of Polynomials: Addition and Multiplication
  • Students will be able to:
    • Add and Subtract Polynomials
    • Multiply Polynomials

• HW Set 1b - Review of Polynomials: Factoring
  • Students will be able to:
    • Factor Polynomials

• HW Set 2 – Linear and Rational equations
  • Students will be able to:
    • Solve Basic Linear Equations
    • Solve Basic Rational Equations

• HW Set 3 - Quadratic Equations in the Field of Real Numbers
  • Students will be able to:
    • Solve Quadratic Equations in the Real Domain

• HW Set 4a – Review of Complex Numbers
  • Students will be able to:
    • Add and Subtract Complex Numbers
    • Multiply and Divide Complex Numbers

• HW Set 4b – Quadratic Equations in the Field of Complex Numbers (can use more problems)
  • Students will be able to:
    • Solve Quadratic Equations in the Complex Domain

• HW Set 5a – Rational Equations equivalent to Quadratic Equations
  • Students will be able to:
    • Solve Quadratic Equations with Rational Expressions

• HW Set 5b - Radical Equations
  • Students will be able to:
    • Solve Radical Equations

• HW Set 5c - Other Quadratic in Form Equations
  • Students will be able to:
    • Solve Equations (Degree Greater than 2) Quadratic in Form

• HW Set 5d - Factorable Equations; Misc Equations
  • Students will be able to:
    • Solve Factorable Equations
    • Solve Miscellaneous Equations

• HW Set 6 – Linear Inequalities
  • Students will be able to:
    • Solve Linear Inequalities

• HW Set 7a – Absolute Value Equations
  • Students will be able to:
    • Solve Absolute Value Equations

• HW Set 7b - Absolute Value Inequalities
  • Students will be able to:
    • Solve Absolute Value Inequalities

• HW Set 8 – Word Problems – Total Value, Interest, Uniform Motion, Work Rate, Geometry Problems
  • Students will be able to:
    • Solve Basic Number/Money and Geometric Application Problems
    • Solve Uniform Motion Application Problems
    • Solve Simple Interest Application Problems
    • Solve Mixture Application Problems
    • Solve Work Rate Application Problems

• HW Set 9 – Coordinate System, Distance Formula, Midpoints
  • Students will be able to:
    • Determine Distance Between Two Points
    • Use Midpoint Formula
    • Solve Applications Using Midpoint and Distance Formula

• HW Set 10 – Graphs, Intercepts, Symmetry
  • Students will be able to:
    • Determine x-intercepts of Graph
    • Determine y-intercepts of Graph
    • Determine Symmetry of Graph

• HW Set 11 – Lines and Slopes; Perpendicular and Parallel Lines
  • Students will be able to:

• HW Set 12 – Circles
  • Students will be able to:

• HW Set 13 – Variation
  • Students will be able to:

• HW Set 14a – Concept of a Function; Evaluation of a Function at a point
  • Students will be able to:

• HW Set 14b - Concept of a Function; Domain of a Function
  • Students will be able to:

• HW Set 15 – Graphs of Basic Functions (can use more problems)
  • Students will be able to:

• HW Set 16 – Properties of Functions: Even and Odd Functions (can use more problems)
  • Students will be able to:

• HW Set 17 – Library of Functions (can use more problems)
  • Students will be able to:

• HW Set 18 – Graphing Transformations
  • Students will be able to:

• HW Set 19 – Math Models (can use more problems)
  • Students will be able to:

• HW Set 20 – Linear Functions
  • Students will be able to:

• HW Set 21 – Linear Models and Scatterplots
  • Students will be able to:

• HW Set 22 – Quadratic Functions
  • Students will be able to:

• HW Set 23 – Quadratic Models (Max/Min Problems) and Scatterplots (can use more problems)
  • Students will be able to:

• HW Set 24 – Quadratic Inequalities
  • Students will be able to:

• HW Set 25 – Polynomial Functions and Properties
  • Students will be able to:

• HW Set 26 – Graph of Polynomial and Power Function
  • Students will be able to:

• HW Set 27 – Rational Function and Properties
  • Students will be able to:

• HW Set 28 – Graph of Rational Function
  • Students will be able to:

• HW Set 29 – Polynomial and Rational Inequalities
  • Students will be able to:

• HW Set 30 – Polynomial Real Zeros
  • Students will be able to:

• HW Set 31 – Polynomial Complex Zeros
  • Students will be able to:

• HW Set 32 – Composite Functions
  • Students will be able to:

• HW Set 33 – One-to-one and Inverse Functions
  • Students will be able to:

• HW Set 34 – Exponential Functions (Properties and Graph)
  • Students will be able to:

• HW Set 35 – Log Functions (Basic Properties and Graph)
  • Students will be able to:

• HW Set 36 – Properties of Logs
  • Students will be able to:

• HW Set 37 – Exponential Equations
  • Students will be able to:

• HW Set 38 – Log Equations
  • Students will be able to:

• HW Set 39a - Systems of Linear Equations 2 variables
  • Students will be able to:

• HW Set 39b - Systems of Linear Equations 3 and more variables
  • Students will be able to:

(2011 Edition) 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