Mat 108 Intermediate Algebra
Review for Exam 2
Part 1
Cartesian Coordinate System
Be familiar with Cartesian coordinate system. Know how to plot points on
coordinate system.
Ordered Pairs
Each point,
Additional Review Problems for Unit 2 Exam
Find the equations of the following lines.
(1) Find the General Form of the equation of the line passing through
( - 9,1) and ( - 1, - 5 )
Answer:
3 x +4 y +
Comments on Solutions for Systems of Equations
Look at the chart below.
If a system of equations has one solution, as shown in the left diagram, the system is
considered to be consistent with independ
Additional Problems for Unit 1 Review
1. Write a linear equation in one variable that has
(a)
A solution set of cfw_ or
(b)
A solution set of (or all real numbers)
(c)
A solution set with one value.
MAT 108 Intermediate Algebra
Review for Exam 4
Summary of Factoring
In algebra, the instruction is usually not written as find the prime factorization of an
expression; we ask to factor completely. It
Mat 108 Intermediate Algebra
Unit 4
Summary of Quadratic Equations in One Variable
(1) What does a quadratic equation in one variable look like?
An equation where the variable appears with an exponent
Mat 108 Intermediate Algebra
Unit 4 Part 3
The Square Root Method and Completing the Square
(Repeating some of the Notes from Part 2)
A long time ago, mathematicians solved quadratic equations of this
Mat 108 Intermediate Algebra
Unit 4 Part 4
Quadratic Equations and the Quadratic Formula
Apparently, a mathematician (maybe Bombelli in the 16th century) tired of solving
quadratic equations by comple
Mat 108 Intermediate Algebra
Unit 4 Part 5
Equations that Lead to Quadratic Equations
There are numerous examples of equations in mathematics that lead to quadratic
equations; we will study two of the
Mat 108 Intermediate Algebra
Unit 4 Part 6
Higher Degree Equations in One Variable
The last topic for this unit is that of higher degree equations in one variable.
By our definition, these are equatio
Mat - 108 Intermediate Algebra
Unit 2 Part 3
LINEAR EQUATIONS IN TWO VARIABLES
EXAMPLES:
2 x 3 y 4
2 x 3 y 6 0
2 x 7 0
RECOGNITION:
(1) The highest exponent with either variable is one (implied)
(2) T
Mat 108 Intermediate Algebra
Unit 4 - Part 2
Quadratic Equations in One Variable
Although solving quadratic equations in one variable was discussed in the last unit (in
the radical equations), this un
MAT 108 Intermediate Algebra
Unit 4 Part 1
Factoring
Factoring is the skill of finding numbers or expressions that, when multiplied, give you
the original number or expression. For example, in arithme
Mat 108 Intermediate Algebra
Unit 2 Part 5
Graphing Linear Inequalities
The graph of a linear equation in two variables is the graph of all ordered pairs that
satisfy the equation and the resulting gr
Mat 108 Intermediate Algebra
Unit 3 Part 7
Imaginary and Complex Numbers
If you remember, we encountered the square root of a negative number in the first section
of this unit specifically the - 9 . A
Mat 108 Intermediate Algebra
Unit3 Part 6
Radical Equations in One Variable
This topic involves solving algebraic sentences and not manipulating algebraic
expressions; therefore, we will find solution
Mat 108 Intermediate Algebra
Unit 3 Part 5
Combining Radical Expressions with Division
As you will see with the notes for this assignment, we do not really combine radical
expressions with division so
Mat 108 Intermediate Algebra
Unit 3 Part 4
Combining Radical Expressions with Addition/Subtraction
There are numerous similarities between radicals (some of which are irrational) and
rational numbers
MAT 108 Intermediate Algebra
Unit 3 Part 3
Simplifying Radicals
Do you remember Rule I for simplifying radicals?
Thou shalt not leave a radical expression as a radical, if the radicand
has a perfect r
Mat 108 Intermediate Algebra
Unit 2 Part 4
Forms of Straight Lines
Standard Form of Line Dx +Ey =F
2x +y =- 5
Where D =2, E =1, F =- 5
General Form of Line
Ax +By +C =0 2x + y +5 =0
Where A =2, B =1,
MAT 108 Intermediate Algebra
Unit 3 Part 1
Radicals
Remember that
is the radical and the expression inside (under) the radical is called the
radicand.
Definition 1:
2
a = b if and only if ( b ) = a
Is
Mat 108 Intermediate Algebra
Unit 3 Part 2
Rational Exponents
Do you remember the three definitions, five laws, and two theorems of exponents?
Definition 1:
a n =a a
a aK
14 2 43 provided n is a natur
Mat 108 Intermediate Algebra
Unit 2 - Part 6
Linear Equations in Three Variables
Example of linear equation in three variables.
x - 2 y +2 z =5
RECOGNITIION
1. The only exponent with any variable is o
Mat 108 Intermediate Algebra
Unit 1 Part 4
Compound Linear Inequalities
Up to now we have looked at inequalities with only 1 inequality sign.
Such as, 3x + 4 2x 6, and the solution for this is
3x -2x
MAT 108 Intermediate Algebra
Unit 2 Part 2
Finding the Domain of a Relation from a Rule/Equation
To determine the domain of a relation in rule/equation form, the first criterion is that the
rule/equat