SOLVING SECOND DEGREE POLYNOMIAL EQUATIONS
Equations with an exponent of one (usually not written) will have one solution
(unless you have a variable inside an absolute value). They are referred to as
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
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
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 t
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 inc
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 se
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 applicatio
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
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
RECTANGULAR COORDINATE SYSTEM
The number line can be used for graphing equations of one variable. For
equations with two variables we need the two-dimensional plane. It has a
horizontal line, with the
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 fi
INTEGER EXPONENT PROPERTIES
Recall that exponential expressions are shortcut writing of multiplication of
repeated factors. If we have five factors of three, we put that in an exponential
expression o
POLYNOMIALS
A polynomial is a mathematical expression that is a finite sum of terms, each
term being a product of a constant and a variable, or variables, with whole
number exponents, and with no vari
POLYNOMIALS - Addition and Subtraction
It is important to use parentheses around polynomial expressions when applying
operations on them. It keeps the terms of each polynomial grouped together until
t
POLYNOMIALS - Multiplication
When multiplying two polynomials together we are required to multiply every term
of the first polynomial by every term of the second polynomial. We can use the
associative
POLYNOMIALS Division
Are you seeing a pattern to how we learn algebra? First we learn the properties
of the concept we are studying, followed by learning how to simplify it. Then we
start learning how
FUNCTIONS
Now that we feel comfortable with using ordered pairs (x, y), lets look at them a
little closer. When the value of one of the numbers in an ordered pair is
controlled by the other we say the
LINEAR INEQUALITIES IN TWO VARIABLES
We can solve linear inequalities in two variables in a similar fashion to the linear
inequalities in one variable that we solved earlier in the term. Instead of an
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."
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
numb
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 w
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,
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
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 dea
Factoring trinomials
#7. Here is a way to tell if a polynomial is factorable. Given the form ax^2 + by + c,
multiply a and c. In this case it is 10*4=40. Next ask yourself, "Are there two
numbers that
Math 107
Quiz 2
Solution
(April 2014)
(60 Points)
1. Find the mid-point and the length of the line segment with endpoints: (2,3), (-3,2)
Solution: d ( P1 , P2 )
x2 x1 2 y2 y1 2
2 32 3 22
25 1 5.1
x
Name:
University of Maryland University College
European Division
MATH 107 DE: College Algebra
Lecturer: Gunter Neubert
Group 2, Exam 2
April 2014
[There are 20 problems worth 10 points each for a tot
Name:
University of Maryland University College
April 2014
European Division
MATH 107: College Algebra
Lecturer: Gunter Neubert
Exam 1 (Group 2)
[There are 20 problems worth 10 points each, plus a bon
May 2014
Exam conditions:
Time limit: 48 Hours
Outside help: None-Honor
System
MATH 107 (College Algebra)
Group 2, FINAL EXAMINATION
Name:
This is a hybrid Final consisting of 15 Multiple Choice probl