Difference between revisions of "ModelCourses/BeginningAlgebra"

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== Beginning Algebra ==
  
== Beginning Algebra ==
   
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textbooks.
  
textbooks.
   
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# '''arithmetic''' (review)
  
  +
The outline below is meant to help index beginning algebra model course
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#* '''integers'''
  
  +
problems. The bold words/phrases are the keys in a 3-level hierarchy. For example,
−
#* rational numbers ('''fractions''')
  
  +
basic set theory problems would be indexed under arithmetic as:
−
#* '''integer exponents'''
  
  +
−
#* '''percent'''
  
  +
'''BeginningAlgebra'''->'''arithmetic'''->'''sets'''
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#* '''square roots'''
  
  +
−
#* '''decimals'''
  
  +
----
−
#* '''order of operations'''
  
  +
−
#* '''variables''' and variable expressions
  
  +
===Arithmetic===
−
#* '''sets'''
  
  +
====Review====
−
# '''linear Equations'''
  
  +
* '''Set 1.1 Integers'''<br> Students will be able to:
−
#* introduction: '''basic''' linear equations
  
  +
** Add and subtract integers
−
#* '''general''' linear equations
  
  +
** Add multiple numbers mentally
−
#* translating '''sentences into equations'''
  
  +
** Compute fractions of integers
−
#* '''applications''' of linear equations
  
  +
** Do a word problem using integers
−
#* '''linear inequalities'''
  
  +
−
#* '''absolute value equations'''
  
  +
* '''Set 1.2 Fractions'''<br> Students will be able to:
−
#* '''absolute value inequalities'''
  
  +
** Change expressions to a reduced fraction
−
# '''geometry'''
  
  +
** Change expressions to mixed numbers.
−
#* '''points, lines, and angles'''
  
  +
** Reduce fractions
−
#* '''plane figures'''
  
  +
** Divide two fractions
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#* '''solids'''
  
  +
** Take a textual description of a fraction, and write it as a decimal.
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# '''graphing linear equations'''
  
  +
−
#* The Cartesian Plane ('''the plane''')
  
  +
* '''Set 1.3 Integer exponents'''
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#* linear functions ('''slope-intercept form''')
  
  +
* '''Set 1.4 Percentages'''<br> Students will be able to:
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#* '''slope''' of a line
  
  +
** Write a decimal as a percent
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#* equation of a line ( '''point-slope form''')
  
  +
** Write a fraction as a percent
−
#* '''linear inequalities''' in two variables
  
  +
** Given a data set, compute the percentage for a given data characteristic
−
# '''systems of linear equations'''
  
  +
** Compute percentage change
−
#* 2x2 linear systems: '''introduction and graphing'''
  
  +
−
#* solving 2x2 linear systems: '''substitution'''
  
  +
* '''Set 1.5 Square roots'''
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#* solving 2x2 linear systems: '''elimination'''
  
  +
* '''Set 1.6 Decimals'''
−
#* '''determinants and Cramer's rule'''
  
  +
* '''Set 1.7 Order of operations'''
−
#* '''applications''' of linear systems
  
  +
* '''Set 1.8 Variables and variable expressions'''
−
#* systems of '''linear inequalities'''
  
  +
* '''Set 1.9 Sets'''
−
# '''polynomials'''
  
  +
−
#* exponents and '''simplifying'''
  
  +
====Additional====
−
#* '''evaluation'''
  
  +
* '''Set 1.10 fractional exponents and radicals'''
−
#* '''multiplication'''
  
  +
* '''Set 1.11 radical operations'''
−
#* '''division'''
  
  +
* '''Set 1.12 radical equations'''
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#* factoring out the greatest common factor ('''factoring out GCF''')
  
  +
* '''Set 1.13 complex numbers'''
−
#* factoring <math>x^2 + bx + x</math> '''easy factoring'''
  
  +
−
#* factoring <math>ax^2 + bx + x</math> '''harder factoring'''
  
  +
===Linear Equations===
−
#* special products and factoring '''special factoring'''
  
  +
* '''Set 2.1 Introduction to linear equations'''
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#* '''zero product rule'''
 
  +
* '''Set 2.2 From sentences into equations'''
−
# '''rational expressions'''
  
  +
* '''Set 2.3 Applications of linear equations'''
−
#* '''multiplication and division'''
  
  +
* '''Set 2.4 Linear inequalities'''
−
#* '''addition and subtraction'''
  
  +
* '''Set 2.5 Absolute value equations'''
−
#* complex fractions ('''complicated''')
  
  +
* '''Set 2.6 Absolute value inequalities'''
−
#* rational '''equations'''
  
  +
−
#* '''variation'''
  
  +
===Geometry===
−
# '''radicals'''
  
  +
* '''Set 3.1 Points, lines, and angles'''
−
#* fractional '''exponents and radicals'''
  
  +
* '''Set 3.2 Plane figures'''
−
#* '''radical operations'''
 +
* '''Set 3.3 Solids'''
−
#* '''radical equations'''
 +
−
#* '''complex numbers'''
 +
===Graphing linear equations===
−
# '''quadratic equations'''
 +
* '''Set 4.1 The Cartesian Plane'''
−
#* solving by factoring or taking roots
 +
* '''Set 4.2 Equations of lines in slope-intercept form'''
−
#* completing the square
 +
* '''Set 4.3 The slope of a line
−
#* quadratic formula
 +
* '''Set 4.4 Equations of lines in point-slope form'''
−
#* equations quadratic in form
 +
* '''Set 4.5 Linear inequalities in two variables'''
−
#* quadratic inequalities
 +
−
#* applications
 +
===Systems of linear equations===
−
# Functions
 +
* '''Set 5.1 2x2 linear systems: introduction and graphing'''
−
#* quadratic functions
 +
* '''Set 5.2 Solving linear systems by substitution'''
−
#* graphs of functions
 +
* '''Set 5.3 Solving 2x2 linear systems by elimination'''
−
#* algebra of functions
 +
* '''Set 5.4 Determinants and Cramer's rule'''
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#* 1-1 and inverse functions
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* '''Set 5.5 Applications of linear systems'''
−
# Exponents and Logarithms
 +
* '''Set 5.5 Systems of linear inequalities'''
−
#* exponential functions
 +
−
#* logarithms
 +
===Polynomials===
−
#* rules of logarithms
 +
* '''Set 6.1 Exponents and simplifying polynomials'''
−
#* exponential and logarithmic equations
 +
* '''Set 6.2 Evaluation of polynomials'''
−
#* applications
 +
* '''Set 6.3 Multiplication of polynomials'''
  +
* '''Set 6.4 Polynomial division'''
  +
* '''Set 6.5 Factoring out the greatest common factor'''
  +
* '''Set 6.6 Factoring polynomials of the type <math>ax^2 + bx + x</math> '''
  +
* '''Set 6.7 Special products and factoring'''
  +
* '''Set 6.8 Polynomial equations (<math> p(x) = 0 </math>)'''
  +
  +
===Rational expressions===
  +
* '''Set 7.1 Multiplication and division'''
  +
* '''Set 7.2 Addition and subtraction'''
  +
* '''Set 7.3 Complex fractions''' (''complicated'')
  +
* '''Set 7.4 Rational equations'''
  +
* '''Set 7.5 Variation'''
  +
  +
===Quadratic equations===
  +
* '''Set 8.1 Solving by factoring'''
  +
* '''Set 8.2 Solving by taking roots'''
  +
* '''Set 8.3 Completing the square'''
  +
* '''Set 8.4 Quadratic formula'''
  +
* '''Set 8.5 Equations that are quadratic in form'''
  +
* '''Set 8.6 Quadratic inequalities'''
  +
* '''Set 8.7 Applications of quadratic functions'''
  +
  +
===Functions===
  +
* '''Set 9.1 Quadratic functions'''
  +
* '''Set 9.2 Graphs of functions'''
  +
* '''Set 9.3 Algebra of functions'''
  +
* '''Set 9.4 1-1 functions'''
  +
* '''Set 9.5 Inverse functions'''
  +
  +
===exponents and logarithms===
  +
* '''Set 10.1 Exponential functions'''
  +
* '''Set 10.2 Logarithms'''
  +
* '''Set 10.3 Rules of logarithms'''
  +
* '''Set 10.4 Exponential and logarithmic equations'''
  +
* '''Set 10.5 Applications of exponential and logarithmic functions'''
   
 
==Notes==
  
==Notes==
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basic plane geometry along with common formulas and
 
basic plane geometry along with common formulas and
 
applications with area and volume.
  
applications with area and volume.
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−
----
  
−  
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Below is a link to some WebWork problem sets for a Beginning Algebra course. Login as
  
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guest.
  
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http://webwork.fdltcc.edu/webwork2/Math0020_Beginning_Algebra/
  
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- Wetherbee @ FDLTCC, 8/1/2012
  
   
 
[[Category:Model_Courses]]
  
[[Category:Model_Courses]]

Latest revision as of 12:54, 20 June 2025

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
    Students will be able to:
    • Add and subtract integers
    • Add multiple numbers mentally
    • Compute fractions of integers
    • Do a word problem using integers
  • Set 1.2 Fractions
    Students will be able to:
    • Change expressions to a reduced fraction
    • Change expressions to mixed numbers.
    • Reduce fractions
    • Divide two fractions
    • Take a textual description of a fraction, and write it as a decimal.
  • Set 1.3 Integer exponents
  • Set 1.4 Percentages
    Students will be able to:
    • Write a decimal as a percent
    • Write a fraction as a percent
    • Given a data set, compute the percentage for a given data characteristic
    • Compute percentage change
  • 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

Additional

  • Set 1.10 fractional exponents and radicals
  • Set 1.11 radical operations
  • Set 1.12 radical equations
  • Set 1.13 complex numbers

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 4.1 The Cartesian Plane
  • Set 4.2 Equations of lines in slope-intercept form
  • Set 4.3 The slope of a line
  • Set 4.4 Equations of lines in point-slope form
  • Set 4.5 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

  • Set 6.1 Exponents and simplifying polynomials
  • Set 6.2 Evaluation of polynomials
  • Set 6.3 Multiplication of polynomials
  • Set 6.4 Polynomial division
  • Set 6.5 Factoring out the greatest common factor
  • Set 6.6 Factoring polynomials of the type [math]ax^2 + bx + x[/math]
  • Set 6.7 Special products and factoring
  • Set 6.8 Polynomial equations ([math] p(x) = 0 [/math])

Rational expressions

  • Set 7.1 Multiplication and division
  • Set 7.2 Addition and subtraction
  • Set 7.3 Complex fractions (complicated)
  • Set 7.4 Rational equations
  • Set 7.5 Variation

Quadratic equations

  • Set 8.1 Solving by factoring
  • Set 8.2 Solving by taking roots
  • Set 8.3 Completing the square
  • Set 8.4 Quadratic formula
  • Set 8.5 Equations that are quadratic in form
  • Set 8.6 Quadratic inequalities
  • Set 8.7 Applications of quadratic functions

Functions

  • Set 9.1 Quadratic functions
  • Set 9.2 Graphs of functions
  • Set 9.3 Algebra of functions
  • Set 9.4 1-1 functions
  • Set 9.5 Inverse functions

exponents and logarithms

  • Set 10.1 Exponential functions
  • Set 10.2 Logarithms
  • Set 10.3 Rules of logarithms
  • Set 10.4 Exponential and logarithmic equations
  • Set 10.5 Applications of exponential and logarithmic functions

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.

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