Difference between revisions of "ModelCourses/BeginningAlgebra"

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# '''arithmetic''' (review)
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==Arithmetic (review)==
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#* '''integers'''
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* '''Set 1.1 Integers'''
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#* rational numbers ('''fractions''')
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* '''Set 1.2 Fractions'''
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#* '''integer exponents'''
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* '''Set 1.3 Integer exponents'''
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#* '''percent'''
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* '''Set 1.4 Percentages'''
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#* '''square roots'''
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* '''Set 1.5 Square roots'''
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#* '''decimals'''
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* '''Set 1.6 Decimals'''
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#* '''order of operations'''
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* '''Set 1.7 Order of operations'''
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#* '''variables''' and variable expressions
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* '''Set 1.8 Variables and variable expressions'''
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#* '''sets'''
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* '''Set 1.9 Sets'''
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# '''linear Equations'''
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−
#* introduction: '''basic''' linear equations
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==Linear Equations==
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#* '''general''' linear equations
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* '''Set 2.1 Introduction to linear equations'''
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#* translating '''sentences into equations'''
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* '''Set 2.2 From sentences into equations'''
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#* '''applications''' of linear equations
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* '''Set 2.3 Applications of linear equations'''
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#* '''linear inequalities'''
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* '''Set 2.4 Linear inequalities'''
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#* '''absolute value equations'''
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* '''Set 2.5 Absolute value equations'''
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#* '''absolute value inequalities'''
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* '''Set 2.6 Absolute value inequalities'''
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# '''geometry'''
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#* '''points, lines, and angles'''
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==Geometry==
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#* '''plane figures'''
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* '''Set 3.1 Points, lines, and angles'''
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#* '''solids'''
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* '''Set 3.2 Plane figures'''
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# '''graphing linear equations'''
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* '''Set 3.3 Solids'''
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#* The Cartesian Plane ('''the plane''')
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#* linear functions ('''slope-intercept form''')
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==Graphing linear equations==
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#* '''slope''' of a line
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* '''Set 5.1 The Cartesian Plane'''
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#* equation of a line ( '''point-slope form''')
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* '''Set 5.2 Equations of lines in slope-intercept form'''
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#* '''linear inequalities''' in two variables
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* '''Set 5.3 The slope of a line
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# '''systems of linear equations'''
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* '''Set 5.4 Equations of lines in point-slope form'''
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#* 2x2 linear systems: '''introduction and graphing'''
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* '''Set 5.5 Linear inequalities in two variables'''
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#* solving 2x2 linear systems: '''substitution'''
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#* solving 2x2 linear systems: '''elimination'''
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==Systems of linear equations==
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#* '''determinants and Cramer's rule'''
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* '''Set 5.1 2x2 linear systems: introduction and graphing'''
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#* '''applications''' of linear systems
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* '''Set 5.2 Solving linear systems by substitution'''
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#* systems of '''linear inequalities'''
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* '''Set 5.3 Solving 2x2 linear systems by elimination'''
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# '''polynomials'''
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* '''Set 5.4 Determinants and Cramer's rule'''
  +
* '''Set 5.5 Applications of linear systems'''
  +
* '''Set 5.5 Systems of linear inequalities'''
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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'''
  
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  +
==radicals==
 
#* fractional '''exponents and radicals'''
  
#* fractional '''exponents and radicals'''
 
#* '''radical operations'''
  
#* '''radical operations'''
 
#* '''radical equations'''
  
#* '''radical equations'''
 
#* '''complex numbers'''
  
#* '''complex numbers'''
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# '''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'''
  
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  +
==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 15:09, 28 June 2013

Construction.png This article is under construction. Use the information herein with caution until this message is removed.

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/phrases are the keys in a 3-level hierarchy. For example, basic set theory problems would be indexed under arithmetic as:

BeginningAlgebra:arithmetic:sets

Arithmetic (review)

  • Set 1.1 Integers
  • Set 1.2 Fractions
  • Set 1.3 Integer exponents
  • Set 1.4 Percentages
  • Set 1.5 Square roots
  • Set 1.6 Decimals
  • Set 1.7 Order of operations
  • Set 1.8 Variables and variable expressions
  • Set 1.9 Sets

Linear Equations

  • Set 2.1 Introduction to linear equations
  • Set 2.2 From sentences into equations
  • Set 2.3 Applications of linear equations
  • Set 2.4 Linear inequalities
  • Set 2.5 Absolute value equations
  • Set 2.6 Absolute value inequalities

Geometry

  • Set 3.1 Points, lines, and angles
  • Set 3.2 Plane figures
  • Set 3.3 Solids

Graphing linear equations

  • Set 5.1 The Cartesian Plane
  • Set 5.2 Equations of lines in slope-intercept form
  • Set 5.3 The slope of a line
  • Set 5.4 Equations of lines in point-slope form
  • Set 5.5 Linear inequalities in two variables

Systems of linear equations

  • Set 5.1 2x2 linear systems: introduction and graphing
  • Set 5.2 Solving linear systems by substitution
  • Set 5.3 Solving 2x2 linear systems by elimination
  • Set 5.4 Determinants and Cramer's rule
  • Set 5.5 Applications of linear systems
  • Set 5.5 Systems of linear inequalities

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

rational expressions

    • multiplication and division
    • addition and subtraction
    • complex fractions (complicated)
    • rational equations
    • variation

radicals

    • fractional exponents and radicals
    • radical operations
    • radical equations
    • complex numbers

quadratic equations

    • solving by factoring
    • solving by taking roots
    • completing the square
    • quadratic formula
    • equations quadratic in form
    • quadratic inequalities
    • applications

functions

    • quadratic functions
    • graphs of functions
    • algebra of functions
    • 1-1 and inverse functions

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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