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
1. exponents: problems from Exponents and Radicals Handout #1-8, 10, 16, 20, 22, 25, 50-52
2. GCF, LCM of numbers (handouts from Holt book) and factored algebraic expressions (come back to this)
3. complex fractions
4. addition of numeric and algebraic simple fractions (no factoring of polynomials needed).

5. types of numbers: natural, whole, rational, irrational, and real
6. repeating decimals and other arithmetic topics as needed (check chapter 0 and 1 of Algebra book)
7. interval notation and solve simple inequalities including some with absolute value and others with negative coefficients on variable
8. order of operations: plug values into an expression and simplify
9. solve linear equations
10. sets: unions, intersections, set builder notation, interval notation
11. linear inequalities
12. absolute value and absolute value as a distance
13. absolute value inequalities
14. solve simple linear equations and more inequalitiy problems
15. Compound Inequalities

16. polynomial expressions and terminology: add, subtract and multiply
17. divide polynomials
18. polynomial expressions: factor
19. introduction to graphing
20. lines: slope intercept, parallel, perpendicular, graphs
21. Solve factorable polynomial equations.
22. graphs of factored polynomial expressions

23. Roots of numbers, square root, cube root etc.. Rationalize denominators including denominators like: √(2)+3.
24. complex fractions: add and subtract numeric expressions
25. complex fractions and add and subtract algebraic fractions
26. Roots of algebraic expressions.
27. rational expressions: factor and
    • add,
    • subt,
    • mult,
    • divide
28. revisit complex fractions with things that can be factored and simplified

29. function notation: domain and range, evaluate at values, read info from a graph as well as from a given equation
30. solve polynomial equations, and rational equations
31. solve polynomial and rational inequalities at least graphically
32. work with linear functions
33. quadratic functions
34. polynomial and rational functions and graphs
35. study systems of equations
36. 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

37. extention of ratio problems to right triangle trig
38. counting problems
39. transformations of functions
40. linear models
41. quadratic functions in terms of transformations
42. complex number arithmetic and plots
43. algebra of functions
44. inverse functions
45. piecewise defined functions
46. Sequences: Recursively and Explicitly defined, Arithmetic, and Geometric