ModelCourses/BeginningAlgebra

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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

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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

1. • 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

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

radicals

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

quadratic equations

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

functions

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

exponents and logarithms

1. • 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.

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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