**Course Description:**

A practical course in mathematics involving a wide range of topics: critical
thinking, problem

solving, set theory, logic, number theory, algebra, geometry, consumer math,
probability, and

statistics.

This course counts as a math elective towards graduation (but does not transfer
as a math course

to most 4 year colleges).

**Pre-Requisite/Co-Requisite:**

A grade of C- or better in MAT*095 Elementary Algebra Foundations or
satisfactory grade on

the Mathematics Placement Test (score of 58 or better on Accuplacer Elementary
Algebra test

within the past 6 months.

A knowledge of the following topics is indicated by completion of the above
prerequisites:

1. Number system development (natural numbers, integers, rational numbers,
irrational

numbers, and real

numbers)

2. Concepts of terms vs. factors, expressions vs. equations, prime factors,
greatest common

factor, and least common multiple

3. Computations with integers (including absolute value)

4. Simplifying algebraic expressions

5. Solving linear equations

6. Computations with algebraic fractional expressions

7. Solving algebraic fraction equations

8. Solving and graphing linear inequalities

9. Graphing linear equations (including “table of values” method)

10. Solving systems of linear equations in 2 variables

11. Computation with polynomials (including the “FOIL” method)

12. Factor polynomials (including greatest common factor, factoring by grouping,
“AC” method,

difference of 2 squares, sum and difference of 2 cubes)

13. Computations with integer exponents

14. Simply square roots

15. Solve quadratic equations (by factoring, “square root method”, and quadratic
formula)

**Goals:**

1. To further develop analytical reasoning and critical thinking skills that
will enhance more

advanced problem solving capabilities.

2. To complete a semester’s study of a variety of math topics at the college
level (as a

comparable alternative to the traditional Intermediate Algebra).

**Outcomes:**

Upon successful completion of this course, each student must have demonstrated

understanding and competency in each of the following topics and techniques
(through

in-class testing of each individual student independently):

1. Understanding word problem applications

2. Understanding concepts of set theory
(subset, universal set) and doing computations

with set operations (complement, intersection, union)

3. Constructing Venn diagrams with 2 and 3 sets (including word problem
applications)

4. Understanding, doing operations with, and constructing truth tables for,
logic

statements (negation, conjunction,
disjunction, conditional, biconditional)

5. Understanding and construction truth tables for equivalent statements and
symbolic

arguments

6. Understanding of number system development (natural numbers, integers,
rational

numbers, irrational numbers, real numbers)

7. Doing computations with integers

8. Simplify radicals

9. Simplifying and doing computations with integer exponents (including
scientific

notation)

10. Simplifying algebraic expressions

11. Solving linear equations (including word problem applications)

12. Solving and graphing linear inequalities in 1 variable

13. Graphing linear equations

14. Graphing linear inequalities in 2 variables

15. Solving quadratic equations (by factoring, “square root method”, and
quadratic

formula—in radical, non-decimal format)

16. Understanding function notation

17. Solving systems of equations in 2 variables (by substitution and
elimination)

18. Graphing systems of linear inequalities (including linear programming
applications)

19. Doing measurement conversions (English-metric)

20. Doing geometric computations (area, perimeter, volume)

21. Doing percent word problem applications

22. Understanding and doing computations with: probability (empirical,
theoretical,

conditional), odds, and expected value

23. Constructing tree diagrams

24. Construct frequency distributions and statistical graphs (histogram and
frequency

polygon)

Doing computations with statistical measures of: central tendency (mean, median,
mode) and

dispersion (range, standard deviation)