Introduction to Algebra TopicsLast Update: May 23, 2011
There may be other topics that we will run across, but these are the ones that I came up with for now.
Warm Up Topics
- exponents: problems from Exponents and Radicals Handout #1-8, 10, 16, 20, 22, 25, 50-52
- GCF, LCM of numbers (handouts from Holt book) and factored algebraic expressions (come back to this)
- complex fractions
- addition of numeric and algebraic simple fractions (no factoring of polynomials needed).
Unit 1
- types of numbers: natural, whole, rational, irrational, and real
- repeating decimals and other arithmetic topics as needed (check chapter 0 and 1 of Algebra book)
- interval notation and solve simple inequalities including some with absolute value and others with negative coefficients on variable
- order of operations: plug values into an expression and simplify
- solve linear equations
- sets: unions, intersections, set builder notation, interval notation
- linear inequalities
- absolute value and absolute value as a distance
- absolute value inequalities
- solve simple linear equations and more inequalitiy problems
- Compound Inequalities
Unit 2
- polynomial expressions and terminology: add, subtract and multiply
- divide polynomials
- polynomial expressions: factor
- introduction to graphing
- lines: slope intercept, parallel, perpendicular, graphs
- Solve factorable polynomial equations.
- graphs of factored polynomial expressions
Unit 3
- Roots of numbers, square root, cube root etc.. Rationalize denominators including denominators like: √(2)+3.
- complex fractions: add and subtract numeric expressions
- complex fractions and add and subtract algebraic fractions
- Roots of algebraic expressions.
- rational expressions: factor and
- revisit complex fractions with things that can be factored and simplified
Unit 4
- function notation: domain and range, evaluate at values, read info from a graph as well as from a given equation
- solve polynomial equations, and rational equations
- solve polynomial and rational inequalities at least graphically
- work with linear functions
- quadratic functions
- polynomial and rational functions and graphs
- study systems of equations
- application problems:
- translate words into sentences,
- problems involving percents,
- mixture problems,
- rate time distance problems,
- interest rate problems,
- rate of work problems,
- variation problems,
- ratio problems
Unit 5 and beyond
- extention of ratio problems to right triangle trig
- counting problems
- transformations of functions
- linear models
- quadratic functions in terms of transformations
- complex number arithmetic and plots
- algebra of functions
- inverse functions
- piecewise defined functions
- Sequences: Recursively and Explicitly defined, Arithmetic, and Geometric