Difference between revisions of "ModelCourses/CollegeAlgebra"

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[[PREP_2011|Prep Main Page]] > [[ModelCourses|Model Courses]] > College Algebra Model Course
  
[[PREP_2011|Prep Main Page]] > [[ModelCourses|Model Courses]] > College Algebra Model Course
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==Description==
  
  +
== [https://test.webwork.maa.org/webwork2/College_Algebra/ Try it out] ==
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Starting with one particular textbook we created a set of topics that are covered in a typical college algebra course. We have not organized these by chapters so that any person teaching from any textbook could use these in any order they needed. We then used the NPL to populate those topics with problems that exist. This led us to trying to decide how to combine some of those groups so that they would be more user friendly. We also started to write some problems to cover areas that are not covered or thinly covered by the NPL, as well as trying to get some sort of order of difficulty in the numbering.
 
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This will be an ongoing and evolving project as we have already had to revamp some of our original ideas.
  
   
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==ToDo List==
  
  +
==General Description==
  +
* Freshman level college algebra course
  +
* Pre-requisite: Intermediate algebra or 2 years of high school algebra.
   
   
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==College Algebra Topics (Alex)==
  
  +
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.
   
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= Review =
  
  +
==Topics Covered==
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=== Unit 1 - [[ModelCourses/CollegeAlgebra/Review/RealNumbers|Real numbers; essential algebra rules ]] ===
  
  +
* Lines and Circles and their graphs
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:[[file01|Problem set for this unit]]
  
  +
* 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
   
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* evaluate algebraic expressions
  
  +
==Problem sets==
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* domain of a variable
  
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* laws of exponents
  
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* square roots
  
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* scientific notation
  
   
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=== Unit 2 - [[ModelCourses/CollegeAlgebra/Review/Formulas|Formulas]] ===
  
  +
=== Review ===
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:[[File:college_algebra05.tar.gz|Problem set for this unit]]
  
  +
* '''Set 01 Real numbers, essential algebra rules''' <br>
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** :[[File:college_algebra_0_1.tar.gz|Problem set for this unit]]
   
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* Formulas
  
  +
Students will be able to <br>
  +
** evaluate algebraic expressions
  +
** domain of a variable
  +
** laws of exponents
  +
** square roots
  +
** scientific notation
   
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=== Unit 3 - [[ModelCourses/CollegeAlgebra/Review/Polynomials|Polynomials ]] ===
  
  +
* '''Set 02 Formulas''' <br>
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:[[file03|Problem set for this unit]]
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** :[[File:college_algebra_0_2.tar.gz|Problem set for this unit]]
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* Polynomials
  
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* Multiplication formulas
  
   
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=== Unit 4 - [[ModelCourses/CollegeAlgebra/Review/FactoringPolynomials|Factoring polynomials]] ===
  
  +
Students will be able to <br>
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:[[file04|Problem set for this unit]]
  
  +
** Formulas
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* Factoring polynomials
  
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* Long division
  
   
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=== Unit 5 - [[ModelCourses/CollegeAlgebra/Review/SyntheticDivision|Synthetic Division]] ===
  
  +
* '''Set 03 Polynomials''' <br>
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:[[file05|Problem set for this unit]]
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** :[[File:college_algebra_0_3.tar.gz|Problem set for this unit]]
  +
  +
Students will be able to <br>
  +
** Polynomials
  +
** Multiplication formulas
  +
  +
* '''Set 04 Factoring polynomials''' <br>
  +
** :[[file04|Problem set for this unit]]
  +
** Factoring polynomials
  +
** Long division
  +
  +
* '''Set 05 Synthetic Division''' <br>
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** :[[File:college_algebra_0_4.tar.gz|Problem set for this unit]]
 
* Synthetic Division
  
* Synthetic Division
   
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=== Unit 6 - [[ModelCourses/CollegeAlgebra/Review/RationalExpressions|Rational Expressions]] ===
  
  +
* '''Set 06 Rational Expressions''' <br>
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:[[file06|Problem set for this unit]]
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** :[[file06|Problem set for this unit]]
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* Rational Expressions
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** Rational Expressions
  +
  +
* '''Set 07 Roots and rational exponents''' <br>
  +
** :[[File:college_algebra_0_5.tar.gz|Problem set for this unit]]
  +
** Roots and rational exponents
  +
  +
=== College algebra problem sets ===
   
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=== Unit 7 - [[ModelCourses/CollegeAlgebra/Review/RootsRationalExponents|Roots and rational exponents]] ===
  
  +
* '''Set 01 Linear Equations''' <br>
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:[[file07|Problem set for this unit]]
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** :[[File:college_algebra_1_1.tar.gz|Problem set for this unit]]
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* Roots and rational exponents
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** Linear equations <span style="color:blue">(populated)</span>
   
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= College Algebra =
  
  +
* '''Set 02 Quadratic Equations''' <br>
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** :[[File:college_algebra_1_2.tar.gz|Problem set for this unit]]
  +
** Quadratic Equations <span style="color:blue">(populated)</span>
   
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=== Unit 1 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
  +
* '''Set 03 Quadratic Equations with Complex Roots''' <br>
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:[[file11|Problem set for this unit]]
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** :[[File:college_algebra_1_3.tar.gz|Problem set for this unit]]
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* Linear equations <span style="color:blue">(populated)</span>
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** Complex numbers and quadratic equations <span style="color:blue">(populated)</span>
   
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=== Unit 2 - [[ModelCourses/CollegeAlgebra/QuadraticEquations |Quadratic Equations ]] ===
  
  +
* '''Set 04 Equations with Quadratic form and Radicals''' <br>
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:[[file12|Problem set for this unit]]
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** :[[File:college_algebra_1_4.tar.gz|Problem set for this unit]]
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* Quadratic Equations <span style="color:blue">(populated)</span>
  
   
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=== Unit 3 - [[ModelCourses/CollegeAlgebra/ComplexRoots|Quadratic Equations with Complex Roots]] ===
  
  +
Students will be able to <br>
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:[[file13|Problem set for this unit]]
  
  +
** Use Quadratic form equations
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* Complex numbers and quadratic equations <span style="color:blue">(populated)</span>
  
  +
** Solve Factorable equations
  +
** Solve Equations with radicals <span style="color:blue">(populated)</span>
   
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=== Unit 4 - [[ModelCourses/CollegeAlgebra/BeyondQuadratics|equations with Quadratic form and Radicals]] ===
  
  +
* '''Set 05 Inequalities''' <br>
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:[[file14|Problem set for this unit]]
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** :[[File:college_algebra_1_5.tar.gz|Problem set for this unit]]
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* Quadratic in form equations
  
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* Factorable equations
  
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* Equations with radicals <span style="color:blue">(populated)</span>
  
   
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=== Unit 5 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
  +
Students will be able to <br>
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:[[file15|Problem set for this unit]]
  
  +
** Solve very simple inequalities
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* Very simple inequalities, compound inequalities <span style="color:red">(populated, needs more)</span>
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** Solve compound inequalities <span style="color:red">(populated, needs more)</span>
   
 
=== Unit 6 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 6 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file16|Problem set for this unit]]
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:[[File:college_algebra_1_6.tar.gz|Problem set for this unit]]
 
* Absolute value equations and inequalities <span style="color:blue">(populated)</span>
  
* Absolute value equations and inequalities <span style="color:blue">(populated)</span>
   
 
=== Unit 7 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 7 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file17|Problem set for this unit]]
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:[[File:college_algebra_1_7.tar.gz|Problem set for this unit]]
 
* Word problems: interest, mixture, motion, constant rate jobs <span style="color:blue">(populated)</span>
  
* Word problems: interest, mixture, motion, constant rate jobs <span style="color:blue">(populated)</span>
   
 
=== Unit 8 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 8 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file18|Problem set for this unit]]
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:[[File:college_algebra_1_8.tar.gz|Problem set for this unit]]
 
* Coordinate system. Distance and midpoint formula <span style="color:blue">(populated)</span>
  
* Coordinate system. Distance and midpoint formula <span style="color:blue">(populated)</span>
   
 
=== Unit 9 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 9 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file19|Problem set for this unit]]
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:[[File:college_algebra_1_9.tar.gz|Problem set for this unit]]
 
* Graphs of equations in two variables, intercepts, symmetry <span style="color:blue">(populated)</span>
  
* Graphs of equations in two variables, intercepts, symmetry <span style="color:blue">(populated)</span>
   
 
=== Unit 10 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 10 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file110|Problem set for this unit]]
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:[[File:college_algebra_1_10.tar.gz|Problem set for this unit]]
 
* Lines
  
* Lines
   
 
=== Unit 11 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 11 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file111|Problem set for this unit]]
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:[[File:college_algebra_1_11.tar.gz|Problem set for this unit]]
 
* Circles
  
* Circles
   
 
=== Unit 12 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 12 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file112|Problem set for this unit]]
 +
:[[File:college_algebra_1_12.tar.gz|Problem set for this unit]]
 
* Variation (formulas for science laws, say)
  
* Variation (formulas for science laws, say)
   
 
=== Unit 13 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 13 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file113|Problem set for this unit]]
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:[[File:college_algebra_1_13.tar.gz|Problem set for this unit]]
 
* Functions
  
* Functions
   
 
=== Unit 14 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 14 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file114|Problem set for this unit]]
 +
:[[File:college_algebra_1_14.tar.gz|Problem set for this unit]]
 
* Graph of functions
  
* Graph of functions
   
 
=== Unit 15 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 15 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
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:[[file115|Problem set for this unit]]
 +
:[[File:college_algebra_1_15.tar.gz|Problem set for this unit]]
 
* Properties of functions
  
* Properties of functions
   
 
=== Unit 16 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 16 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file116|Problem set for this unit]]
 +
:[[File:college_algebra_1_16.tar.gz|Problem set for this unit]]
 
* Library of functions, piecewise-defined functions
  
* Library of functions, piecewise-defined functions
   
 
=== Unit 17 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 17 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file117|Problem set for this unit]]
 +
:[[File:college_algebra_1_17.tar.gz|Problem set for this unit]]
 
* Graphing techniques, transformations
  
* Graphing techniques, transformations
   
 
=== Unit 18 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 18 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file118|Problem set for this unit]]
 +
:[[File:college_algebra_1_18.tar.gz|Problem set for this unit]]
 
* Math models: building functions
  
* Math models: building functions
   
 
=== Unit 19 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 19 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file119|Problem set for this unit]]
 +
:[[File:college_algebra_1_19.tar.gz|Problem set for this unit]]
 
* Linear functions and their properties <span style="color:blue">(populated)</span>
  
* Linear functions and their properties <span style="color:blue">(populated)</span>
   
 
=== Unit 20 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 20 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file120|Problem set for this unit]]
 +
:[[File:college_algebra_1_20.tar.gz|Problem set for this unit]]
 
* Linear models
  
* Linear models
   
 
=== Unit 21 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 21 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file121|Problem set for this unit]]
 +
:[[File:college_algebra_1_21.tar.gz|Problem set for this unit]]
 
* Quadratic functions and their properties
  
* Quadratic functions and their properties
   
 
=== Unit 22 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 22 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file122|Problem set for this unit]]
 +
:[[File:college_algebra_1_22.tar.gz|Problem set for this unit]]
 
* Quadratic models from ‘word problems’
  
* Quadratic models from ‘word problems’
   
 
=== Unit 23 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 23 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file123|Problem set for this unit]]
 +
:[[File:college_algebra_1_23.tar.gz|Problem set for this unit]]
 
* Inequalities with quadratic functions Audrey
  
* Inequalities with quadratic functions Audrey
   
 
=== Unit 24 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 24 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file124|Problem set for this unit]]
 +
:[[File:college_algebra_1_24.tar.gz|Problem set for this unit]]
 
* Polynomial functions and models
  
* Polynomial functions and models
   
 
=== Unit 25 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 25 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file125|Problem set for this unit]]
 +
:[[File:college_algebra_1_25.tar.gz|Problem set for this unit]]
 
* Properties of rational functions?
  
* Properties of rational functions?
   
 
=== Unit 26 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 26 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file126|Problem set for this unit]]
 +
:[[File:college_algebra_1_26.tar.gz|Problem set for this unit]]
 
* Graph of a rational function?
  
* Graph of a rational function?
   
 
=== Unit 27 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 27 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file127|Problem set for this unit]]
 +
:[[File:college_algebra_1_27.tar.gz|Problem set for this unit]]
 
* Polynomial and Rational Inequalities: Audrey
  
* Polynomial and Rational Inequalities: Audrey
   
 
=== Unit 28 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 28 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file128|Problem set for this unit]]
 +
:[[File:college_algebra_1_28.tar.gz|Problem set for this unit]]
 
* Real zeros of polynomials
  
* Real zeros of polynomials
   
 
=== Unit 29 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 29 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file129|Problem set for this unit]]
 +
:[[File:college_algebra_1_29.tar.gz|Problem set for this unit]]
 
* Complex zeros, fundamental theorem of algebra
  
* Complex zeros, fundamental theorem of algebra
   
 
=== Unit 30 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
  
=== Unit 30 - [[ModelCourses/CollegeAlgebra/LinearEquations|Linear Equations]] ===
−
:[[file130|Problem set for this unit]]
 +
:[[File:college_algebra_1_30.tar.gz|Problem set for this unit]]
 
* Composite functions
  
* Composite functions
   
 
=== Unit 31 - [[ModelCourses/CollegeAlgebra/MoreFunctions|More about Functions]] ===
  
=== Unit 31 - [[ModelCourses/CollegeAlgebra/MoreFunctions|More about Functions]] ===
−
:[[file131|Problem set for this unit]]
 +
:[[File:college_algebra_1_31.tar.gz|Problem set for this unit]]
 
* One-to-one functions
  
* One-to-one functions
 
* Inverse functions
  
* Inverse functions
   
 
=== Unit 32 - [[ModelCourses/CollegeAlgebra/ConicSections|Conic sections]] ===
  
=== Unit 32 - [[ModelCourses/CollegeAlgebra/ConicSections|Conic sections]] ===
−
:[[file132|Problem set for this unit]]
 +
:[[File:college_algebra_1_32.tar.gz|Problem set for this unit]]
 
* Conic sections
  
* Conic sections
   

Revision as of 10:16, 10 March 2013

Prep Main Page > Model Courses > College Algebra Model Course

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

Students will be able to

    • evaluate algebraic expressions
    • domain of a variable
    • laws of exponents
    • square roots
    • scientific notation

Students will be able to

    • Formulas

Students will be able to

    • Polynomials
    • Multiplication formulas

College algebra problem sets

  • Set 03 Quadratic Equations with Complex Roots

Students will be able to

    • Use Quadratic form equations
    • Solve Factorable equations
    • Solve Equations with radicals (populated)

Students will be able to

    • Solve very simple inequalities
    • Solve compound inequalities (populated, needs more)

Unit 6 - Linear Equations

Problem set for this unit
  • Absolute value equations and inequalities (populated)

Unit 7 - Linear Equations

Problem set for this unit
  • Word problems: interest, mixture, motion, constant rate jobs (populated)

Unit 8 - Linear Equations

Problem set for this unit
  • Coordinate system. Distance and midpoint formula (populated)

Unit 9 - Linear Equations

Problem set for this unit
  • Graphs of equations in two variables, intercepts, symmetry (populated)

Unit 10 - Linear Equations

Problem set for this unit
  • Lines

Unit 11 - Linear Equations

Problem set for this unit
  • Circles

Unit 12 - Linear Equations

Problem set for this unit
  • Variation (formulas for science laws, say)

Unit 13 - Linear Equations

Problem set for this unit
  • Functions

Unit 14 - Linear Equations

Problem set for this unit
  • Graph of functions

Unit 15 - Linear Equations

Problem set for this unit
  • Properties of functions

Unit 16 - Linear Equations

Problem set for this unit
  • Library of functions, piecewise-defined functions

Unit 17 - Linear Equations

Problem set for this unit
  • Graphing techniques, transformations

Unit 18 - Linear Equations

Problem set for this unit
  • Math models: building functions

Unit 19 - Linear Equations

Problem set for this unit
  • Linear functions and their properties (populated)

Unit 20 - Linear Equations

Problem set for this unit
  • Linear models

Unit 21 - Linear Equations

Problem set for this unit
  • Quadratic functions and their properties

Unit 22 - Linear Equations

Problem set for this unit
  • Quadratic models from ‘word problems’

Unit 23 - Linear Equations

Problem set for this unit
  • Inequalities with quadratic functions Audrey

Unit 24 - Linear Equations

Problem set for this unit
  • Polynomial functions and models

Unit 25 - Linear Equations

Problem set for this unit
  • Properties of rational functions?

Unit 26 - Linear Equations

Problem set for this unit
  • Graph of a rational function?

Unit 27 - Linear Equations

Problem set for this unit
  • Polynomial and Rational Inequalities: Audrey

Unit 28 - Linear Equations

Problem set for this unit
  • Real zeros of polynomials

Unit 29 - Linear Equations

Problem set for this unit
  • Complex zeros, fundamental theorem of algebra

Unit 30 - Linear Equations

Problem set for this unit
  • Composite functions

Unit 31 - More about Functions

Problem set for this unit
  • One-to-one functions
  • Inverse functions

Unit 32 - Conic sections

Problem set for this unit
  • Conic sections

Other Model Courses

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