Difference between revisions of "ModelCourses/BeginningAlgebra"

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basic set theory problems would be indexed as:
  
basic set theory problems would be indexed as:
   
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'''BeginningAlgebra''':''''arithmetic'''':'''sets'''
 +
'''BeginningAlgebra''':'''arithmetic''':'''sets'''
   
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# ''''arithmetic'''' (review)
  
  +
==BeginningAlgebra==
  +
# '''arithmetic''' (review)
 
#* '''integers'''
  
#* '''integers'''
 
#* rational numbers ('''fractions''')
  
#* rational numbers ('''fractions''')
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#* '''variables''' and variable expressions
  
#* '''variables''' and variable expressions
 
#* '''sets'''
  
#* '''sets'''
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# ''''linear Equations''''
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# '''linear Equations'''
 
#* introduction: '''basic''' linear equations
  
#* introduction: '''basic''' linear equations
 
#* '''general''' linear equations
  
#* '''general''' linear equations
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#* '''absolute value equations'''
  
#* '''absolute value equations'''
 
#* '''absolute value inequalities'''
  
#* '''absolute value inequalities'''
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# ''''geometry''''
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# '''geometry'''
 
#* '''points, lines, and angles'''
  
#* '''points, lines, and angles'''
 
#* '''plane figures'''
  
#* '''plane figures'''
 
#* '''solids'''
  
#* '''solids'''
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# ''''graphing linear equations''''
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# '''graphing linear equations'''
 
#* The Cartesian Plane ('''the plane''')
  
#* The Cartesian Plane ('''the plane''')
 
#* linear functions ('''slope-intercept form''')
  
#* linear functions ('''slope-intercept form''')
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#* equation of a line ( '''point-slope form''')
  
#* equation of a line ( '''point-slope form''')
 
#* '''linear inequalities''' in two variables
  
#* '''linear inequalities''' in two variables
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# ''''systems of linear equations''''
 +
# '''systems of linear equations'''
 
#* 2x2 linear systems: '''introduction and graphing'''
  
#* 2x2 linear systems: '''introduction and graphing'''
 
#* solving 2x2 linear systems: '''substitution'''
  
#* solving 2x2 linear systems: '''substitution'''
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#* '''applications''' of linear systems
  
#* '''applications''' of linear systems
 
#* systems of '''linear inequalities'''
  
#* systems of '''linear inequalities'''
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# ''''polynomials''''
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# '''polynomials'''
 
#* exponents and '''simplifying'''
  
#* exponents and '''simplifying'''
 
#* '''evaluation'''
  
#* '''evaluation'''
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#* special products and factoring ('''special factoring''')
  
#* special products and factoring ('''special factoring''')
 
#* '''zero product rule'''
 
#* '''zero product rule'''
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# ''''rational expressions''''
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# '''rational expressions'''
 
#* '''multiplication and division'''
  
#* '''multiplication and division'''
 
#* '''addition and subtraction'''
  
#* '''addition and subtraction'''
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#* rational '''equations'''
  
#* rational '''equations'''
 
#* '''variation'''
  
#* '''variation'''
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# ''''radicals''''
 +
# '''radicals'''
 
#* fractional '''exponents and radicals'''
  
#* fractional '''exponents and radicals'''
 
#* '''radical operations'''
  
#* '''radical operations'''
 
#* '''radical equations'''
  
#* '''radical equations'''
 
#* '''complex numbers'''
  
#* '''complex numbers'''
−
# ''''quadratic equations''''
 +
# '''quadratic equations'''
 
#* '''solving by factoring'''
  
#* '''solving by factoring'''
 
#* '''solving by taking roots'''
  
#* '''solving by taking roots'''
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#* quadratic '''inequalities'''
  
#* quadratic '''inequalities'''
 
#* '''applications'''
  
#* '''applications'''
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# ''''functions''''
 +
# '''functions'''
 
#* '''quadratic''' functions
  
#* '''quadratic''' functions
 
#* '''graphs''' of functions
  
#* '''graphs''' of functions
 
#* '''algebra''' of functions
  
#* '''algebra''' of functions
 
#* '''1-1 and inverse''' functions
  
#* '''1-1 and inverse''' functions
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# ''''exponents and logarithms''''
 +
# '''exponents and logarithms'''
 
#* '''exponential functions'''
  
#* '''exponential functions'''
 
#* '''logarithms'''
  
#* '''logarithms'''

Revision as of 21:16, 5 August 2012

Beginning Algebra

The beginning algebra model course spans "developmental" algebra between Arithmetic/Pre-algebra and College Algebra/Pre-calculus. There are many ways to arrange this material, and it is usual for the material to overlap with College Algebra.

A common two-course sequence (with two separate books) is Beginning Algebra followed by Higher/Intermediate Algebra. There are also combined Beginning and Intermediate Algebra textbooks.

The outline below is meant to help index beginning algebra model course problems. The bold words are the keys in a 3-word hierarchy. For example, basic set theory problems would be indexed as:

BeginningAlgebra:arithmetic:sets

BeginningAlgebra

  1. arithmetic (review)
    • integers
    • rational numbers (fractions)
    • integer exponents
    • percent
    • square roots
    • decimals
    • order of operations
    • variables and variable expressions
    • sets
  2. linear Equations
    • introduction: basic linear equations
    • general linear equations
    • translating sentences into equations
    • applications of linear equations
    • linear inequalities
    • absolute value equations
    • absolute value inequalities
  3. geometry
    • points, lines, and angles
    • plane figures
    • solids
  4. graphing linear equations
    • The Cartesian Plane (the plane)
    • linear functions (slope-intercept form)
    • slope of a line
    • equation of a line ( point-slope form)
    • linear inequalities in two variables
  5. systems of linear equations
    • 2x2 linear systems: introduction and graphing
    • solving 2x2 linear systems: substitution
    • solving 2x2 linear systems: elimination
    • determinants and Cramer's rule
    • applications of linear systems
    • systems of linear inequalities
  6. polynomials
    • exponents and simplifying
    • evaluation
    • multiplication
    • division
    • factoring out the greatest common factor (factoring out GCF)
    • factoring [math]x^2 + bx + x[/math] (easy factoring)
    • factoring [math]ax^2 + bx + x[/math] (harder factoring)
    • special products and factoring (special factoring)
    • zero product rule
  7. rational expressions
    • multiplication and division
    • addition and subtraction
    • complex fractions (complicated)
    • rational equations
    • variation
  8. radicals
    • fractional exponents and radicals
    • radical operations
    • radical equations
    • complex numbers
  9. quadratic equations
    • solving by factoring
    • solving by taking roots
    • completing the square
    • quadratic formula
    • equations quadratic in form
    • quadratic inequalities
    • applications
  10. functions
    • quadratic functions
    • graphs of functions
    • algebra of functions
    • 1-1 and inverse functions
  11. exponents and logarithms
    • exponential functions
    • logarithms
    • rules of logarithms
    • exponential and logarithmic equations
    • applications

Notes

Some Higher/Intermediate Algebra textbooks include conic sections, series and sequences, probability, and statistics. These topics are in the College Algebra model course.

Geometry problems are usually mixed among algebra sections as application problems. The geometry section here covers basic plane geometry along with common formulas and applications with area and volume.

Below is a link to some WebWork problem sets for a Beginning Algebra course. Login as guest.

http://webwork.fdltcc.edu/webwork2/Math0020_Beginning_Algebra/

- Wetherbee @ FDLTCC, 8/1/2012

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