ModelCourses/BeginningAlgebra
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Contents
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
