Difference between revisions of "ModelCourses/BeginningAlgebra"

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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/phrases are the keys in a 3-level 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 under arithmetic as:
 +
basic set theory problems would be indexed under arithmetic as: <br\>
−
+
'''BeginningAlgebra'''->'''arithmetic'''->'''sets'''
−
'''BeginningAlgebra''':'''arithmetic''':'''sets'''
  
   
 
----
  
----
   
−
===Arithmetic (review)===
 +
===Arithmetic===
−
* '''Set 1.1 Integers'''
 +
====Review====
−
* '''Set 1.2 Fractions'''
 +
* '''Set 1.1 Integers'''<br> 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'''<br> 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 1.3 Integer exponents'''
−
* '''Set 1.4 Percentages'''
 +
* '''Set 1.4 Percentages'''<br> 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 1.5 Square roots'''
 
* '''Set 1.6 Decimals'''
  
* '''Set 1.6 Decimals'''
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* '''Set 1.8 Variables and variable expressions'''
  
* '''Set 1.8 Variables and variable expressions'''
 
* '''Set 1.9 Sets'''
  
* '''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===
  
===Linear Equations===
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* '''Set 5.5 Systems of linear inequalities'''
  
* '''Set 5.5 Systems of linear inequalities'''
   
−
===polynomials===
 +
===Polynomials===
−
#* exponents and '''simplifying'''
 +
* '''Set 6.1 Exponents and simplifying polynomials'''
−
#* '''evaluation'''
 +
* '''Set 6.2 Evaluation of polynomials'''
−
#* '''multiplication'''
 +
* '''Set 6.3 Multiplication of polynomials'''
−
#* '''division'''
 +
* '''Set 6.4 Polynomial division'''
−
#* factoring out the greatest common factor ('''factoring out GCF''')
 +
* '''Set 6.5 Factoring out the greatest common factor'''
−
#* factoring <math>x^2 + bx + x</math> ('''easy factoring''')
 +
* '''Set 6.6 Factoring polynomials of the type <math>ax^2 + bx + x</math> '''
−
#* factoring <math>ax^2 + bx + x</math> ('''harder factoring''')
 +
* '''Set 6.7 Special products and factoring'''
−
#* special products and factoring ('''special factoring''')
 +
* '''Set 6.8 Polynomial equations (<math> p(x) = 0 </math>)'''
−
#* '''zero product rule'''
 
−  
−
===rational expressions===
  
−
#* '''multiplication and division'''
  
−
#* '''addition and subtraction'''
  
−
#* complex fractions ('''complicated''')
  
−
#* rational '''equations'''
  
−
#* '''variation'''
  
   
−
===radicals===
  
  +
===Rational expressions===
−
#* fractional '''exponents and radicals'''
  
  +
* '''Set 7.1 Multiplication and division'''
−
#* '''radical operations'''
  
  +
* '''Set 7.2 Addition and subtraction'''
−
#* '''radical equations'''
  
  +
* '''Set 7.3 Complex fractions''' (''complicated'')
−
#* '''complex numbers'''
  
  +
* '''Set 7.4 Rational equations'''
  +
* '''Set 7.5 Variation'''
   
−
===quadratic equations===
 +
===Quadratic equations===
−
#* '''solving by factoring'''
 +
* '''Set 8.1 Solving by factoring'''
−
#* '''solving by taking roots'''
 +
* '''Set 8.2 Solving by taking roots'''
−
#* '''completing the square'''
 +
* '''Set 8.3 Completing the square'''
−
#* '''quadratic formula'''
 +
* '''Set 8.4 Quadratic formula'''
−
#* equations '''quadratic in form'''
 +
* '''Set 8.5 Equations that are quadratic in form'''
−
#* quadratic '''inequalities'''
 +
* '''Set 8.6 Quadratic inequalities'''
−
#* '''applications'''
 +
* '''Set 8.7 Applications of quadratic functions'''
   
−
===functions===
 +
===Functions===
−
#* '''quadratic''' functions
 +
* '''Set 9.1 Quadratic functions'''
−
#* '''graphs''' of functions
 +
* '''Set 9.2 Graphs of functions'''
−
#* '''algebra''' of functions
 +
* '''Set 9.3 Algebra of functions'''
−
#* '''1-1 and inverse''' functions
 +
* '''Set 9.4 1-1 functions'''
  +
* '''Set 9.5 Inverse functions'''
   
 
===exponents and logarithms===
  
===exponents and logarithms===
−
#* '''exponential functions'''
 +
* '''Set 10.1 Exponential functions'''
−
#* '''logarithms'''
 +
* '''Set 10.2 Logarithms'''
−
#* '''rules of logarithms'''
 +
* '''Set 10.3 Rules of logarithms'''
−
#* exponential and logarithmic '''equations'''
 +
* '''Set 10.4 Exponential and logarithmic equations'''
−
#* '''applications'''
 +
* '''Set 10.5 Applications of exponential and logarithmic functions'''
   
 
==Notes==
  
==Notes==

Latest revision as of 15:10, 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: <br\> 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.

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 @ Fond du Lac Tribal & Community College, 8/1/2012

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