# Major topics of the Algebra

Each topic may be addressed either in a concrete situation
or as pure mathematics

problem.

1. Solution of systems of linear equations.

2. Graphs of linear equations

3. What does it mean to have no or infinitely many solutions

4. Solution of systems of linear inequalities (in one unknown)

5. Solution of systems of linear inequalities (in two unknowns)

6. absolute value including solutions of inequalities and
equations in one or

two variables

7. Finding exact solutions; finding approximate solutions graphically

8. Normal forms

9. Properties of quadratic functions and their graphs

10. Solutions of quadratic equations (factoring,
completing the square, quadratic

formula)

11. representing functions by formulas, graph, table

12. Transformation of quadratics and the effect on the graph

13. understanding the logic of equation/inequality solutions

14. the zero product property and other properties of the real numbers

15. minimizing or maximizing quadratic functions

16. the function notion

A good study technique would be to find at least one
problem from the

homework or from the CME text that addresses each of these topics and solve

it. Some of the topics are broad enough so that you should look at several

different problems. Look for connections between the various topics. Often the

same concrete situation can be mathematized in several different ways. Look

for examples.