Difference between revisions of "ModelCourses/BeginningAlgebra"

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