SETS
A set is a collection of objects. The objects are called elements or members. In mathematics
our focus is on numbers, therefore, we deal with sets of numbers. In this course we mainly will
be dealing with six sets of numbers. As you can see by the di
FORMULAS
The word "formula" seems to frighten many students. If you are one, please understand that a
formula is merely a mathematical sentence or expression. It tells us how the variables and/or
numbers relate to on another. A = l * w is a familiar formu
APPLICATION PROBLEMS
We have reached the point in the course where we can apply the concept of
solving equations to real life situations. These problems are referred to as word,
story, or application problems. BE AWARE: There is NO ONE SOLUTION
METHOD for
APPLICATION PROBLEMS Unknown Numerical Quantity
Using the seven step plan for solving application problems, find the three consecutive odd
integer numbers whose sum is 105.
1. Read the problem. Repeat until you fully understand it.
Know the meaning of int
APPLICATION PROBLEMS  Mixtures
How much water must be added to 20 L of 50% liquid plant fertilizer solution to reduce it to
40% liquid plant fertilizer?
Use the seven step plan for solving application problems to answer this question.
1. Read the problem
APPLICATION PROBLEMS Investments
John has $34.000 to invest. He invests some at 17% and the balance at 20%.
His total annual interest income is $6245. Find the amount invested at each rate.
Use the seven step plan for solving application problems to find
APPLICATION PROBLEMS Percentages
In 1996, the number of participants in the ACT exam was 925,000. Earlier in
1990, a total of 817,000 took the exam. What percent increase was this? What
percent of increase was this? (Source: The American College Testing P
LINEAR INEQUALITIES IN ONE VARIABLE
A linear inequality is very similar to a linear equation. The difference the two
expressions are not equal to each other. One expression will have a greater
value than the other. Instead of solving to find one value tha
UNION AND INTERSECTION OF SETS
Recall sets are collections of elements. The union and intersection operations
allow us to join sets together. As you might guess the union operation unites all
elements in different sets together. The intersection operation
ABSOLUTE VALUE EQUATIONS
Recall that absolute values are always positive, so keeping that in mind: If x = 2,
then x = 2, 2; both values are two units from zero.
x = cfw_2, 2
Both values are two units from zero.

6
4
2
0
2
4
6
If x > 2, then x
RECTANGULAR COORDINATE SYSTEM
The number line can be used for graphing equations of one variable. For
equations with two variables we need the twodimensional plane. It has a
horizontal line, with the same properties as the number line, called the xaxis.
LINEAR EQUATIONS IN ONE VARIABLE
Before we embark on the task of solving linear equations lets make sure we understand the
difference between an expression and an equation. Visually we can determine we have an
equation when we see the equal sign, =. If th
EVALUATING ALGEBRAIC EXPRESSIONS
An expression can be a single word or phrase. A mathematical expression is
referred to as algebraic expression. It is comprised of a combination of
numbers, variables, and operations. A numerical expression is comprised of
PROPERTIES OF REAL NUMBERS
Just like people, number sets have characteristics. We refer to them as
properties. Given a set of conditions we find number sets will consistently
behave in a certain manner. When this happens, we can derive a general rule
abou
NUMBER LINE
Thinking back to basic geometry we know that a line is defined by two points. The number
line we use to represent the set of Real Numbers is made by combining two rays. A ray is a
straight line that extends into infinity from a fixed point. Th
ABSOLUTE VALUE
When asked to find a point on the number line two units from zero you would intuitively say 2.
You would be correct, but you would not be complete. Negative two is also two units away
from zero. Irregardless of the direction traveled two un
INEQUALITIES and INTERVAL NOTATION
When we looked at the number line earlier we noted moving to the right, the values of the
coordinates increase. In mathematics we use the terms greater than or less than to describe a
value on the number line in relation
ADDITION
You have been doing these operations for years, so why bother? We need to review the rules
of why the algorithms (procedures used to solve problems) you have been using really work.
In doing so, you will prepare yourself for using those rules on
SUBTRACTION
What addition puts together subtraction takes apart. This operation reverses the action of
addition. If you have three apples and you get two more you now have five apples. Thats
addition. If you give two of your apples to friends, you now hav
MULTIPLICATION
This operation is a result of repetitive addition. If we have numerous addends in an addition
problem that are all the same, we do not want to keep repeating our efforts adding each
addend into the running total. We shortcut the repetitive
DIVISION
Division of real numbers is to multiplication of real numbers as addition of real
numbers is to subtraction of real numbers. This operation reverses the action of
multiplication. As multiplication grew out of repetitive addition, division grew ou
EXPONENTIAL EXPRESSIONS
Just as multiplication is a result of repeated adding, an exponential expression is
a result of repeated multiplication. If we have several factors in a multiplication
problem that are all the same, we do not want to keep writing e
ROOTS
Recall how subtraction reversed the addition operation and division reversed the
multiplication operation? Finding the root of a number reverses operation of
evaluating an exponential expression. The process is written as a radical
expression. The n
ORDER OF OPERATIONS
Simplify this expression: 18 6 3 . Did you simplify it to 9 or 1?
If you divided 18 by 6 to get 3, then multiplied that 3 by the last 3 in the
expression, your answer to the question is 9.
If you began by multiplying the 6 and 3 togeth
SOLVING AND GRAPHING EQUATIONS OF TWO
VARIABLES
When we find a solution to a two variable equation we will have an x value and a
y value. Together they are called an ordered pair. The x value comes first
followed by the y value, and is written like this:
SLOPE
Steepness; grade; pitch, all of these terms refer to slope, which is the ratio of the
vertical change to the horizontal change over a certain distance. Many times this
is called "rise over run." The formula, the mathematical statement describing the
RATIONAL EXPRESSIONS
What are rational expressions? In arithmetic class we called putting numbers
in this form, fractions. The numerator and denominator in rational expressions
now contain polynomials. All the rules we used for fractions apply to rational
INVERSE FUNCTIONS
We began our mathematics journey this term with operations  addition and its
opposite, subtraction; multiplication and its opposite, division; exponents and
their opposites, roots. Our last concept for this course discusses inverse
func
SYSTEMS OF EQUATIONS
In the discussion of graphing a line for an equation we learned the line
represents all the infinitely possible solutions for the equation. So, if two graphed
lines intersect, the exact point of intersection must be a solution for bot
COMPLEX NUMBERS
The concept of the complex number system grew from the desire to have a
solution to a simple equation. The equation x2 + 1 = 0 could not be factored so
the zerofactor property could not be applied. When the equation was rewritten
and the