# Ma 090 Math Preparatory Modules

These are the modules that you will have to demonstrate proficiency in:

**Ma 091 – Number systems – ***review of foundational properties of numbers with an emphasis on the real numbers*

A quick review of how real numbers work (integers, fractions, decimals, order of operations, simple linear equations, etc.)

**Ma 092 – Power Functions – ***development and use of exponents, both integer and fractional, and polynomials*

What does the exponent in x^{2} mean? How does it work? What if the exponent is negative? Or even a fraction? Fraction exponents actually mean the same as √ (a radical expression), so we will spend some time on radicals here as well. What makes a radical expression be in simplest form? How do you add, subtract, multiply, and divide radical expressions? Can you solve equations that include radicals? What makes an expression a polynomial? How do you add/subtract/multiply/divide polynomials?

**Ma 093 – Inequalities – ***solving inequality relationships with radicals and polynomials*

By now you should be used to solving linear equations like 2*x* + 3 = 7 for *x*, but what if it is an inequality instead? For instance, 2*x* + 3 < 7. You are finding *all *of the *x*s that make that a true statement. How do you do that? And how would you graph it?

*Students taking Ma 103 or 180 do 094 and 095* and stop.* Students taking Ma 220 or BA/Ma 320 skip to 096 and 097.*

**Ma 094 – Factoring – ***basic factoring techniques including factoring common terms and special forms*

Factoring is SO important. In a lot of problems that you will see in college-level math classes, the first step will be to factor the polynomial. You need to be at a point where factoring over the integers is second nature to you--you barely have to think about it. This will free your mind to concentrate on what you are supposed to do with the factors that you find. This module provides you with *lots* of opportunity to practice. Of course, some quadratic equations are not factorable over the integers, so for those you need something a little more powerful--the quadratic formula! And when you use the quadratic formula, you find that some equations can't even be solved with real numbers so we have to go a little way into the realm of imaginary numbers. (Which I think is so amazing! God gave us an insight into numbers that can't even exist, and there is a whole algebra including practical applications of those numbers. Wow!)

**Ma 095 – Rational Expressions – ***simplifying rational expressions, including addition, subtraction, multiplication, and complex fractions *

In this module, you will be working with rational expressions, which are basically polynomials as numerators and denominators of fractions. You will have to draw on all you know about calculating with fractions (When do you need a common denominator? How do you get a common denominator? What do you do with fractions on top of fractions?), and combine it with what you know about polynomials (lots of factoring!) This kind of problem-solving will prepare you for multi-step problems that you will encounter in the future. You have to work every step carefully, or the whole thing will probably be unsolvable.

**Ma 096 – Systems of Equations – ***solving equations with two or more unknowns*

You got really good at solving for *x* in a problem in module 085, but what do you do if there is an *x* and a *y* - or even a *z* and you don't know what *any* of them are? For one thing, you should have as many equations as you have unknowns, and we have three ways to tackle the problem - graphing, substitution, and elimination.

**Ma 097 – Probability and Statistics – ***builds on ideas in Ma 085, including combinations and permutations, correlation, frequency distribution, quartiles, and more graphs*

A few things in this module will be a review from module 085, but we are going to go deeper. How many possible outcomes are there? How likely is it that I will get the outcome that I want? Can I predict one outcome knowing another? These are some of the questions that Probability and Statistics can help us answer. (And get you ready for Applied Statistics!)

*All modules offered for 0 credits. Ma 086 must be completed before Ma 091. Then the modules must be completed in a linear progression--091 before 092, 092 before 093, etc.*