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, having an x and a y coordinate is called an ordered pai
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 +23 =0
(2) Find the Standard Form of the equation of the
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 independent equations,
If the system has no solution (as in the
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.
2. Write a linear absolute value equation in one varia
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. Its the same thing.
Greatest Common Factor - GCF
The firs
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 of 2; there is an equal symbol;
there is only one vari
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 last type (the
ax 2 +c =0 where there is no bx or no l
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 completing the square and decided to shortcut this repetitive
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 these. The first type is rational equations.
RATIONAL EQUA
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 equations where the exponent with the variable is greater
than
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) There is an equal symbol in the original problem
(3) The
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 unit is a more detailed study of this important topic. Le
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 arithmetic if we were asked to factor
12, we could say 4 3 . I
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 graph is a line.
Now we are going to graph linear inequal
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 . At that time, we said that this was not a real
number it
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 sets rather than simplified expressions.
Remember that
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 much as we simplify (rewrite) them.
Dealing with radic
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 (fractions) especially when it comes to the operations
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 root.
This rule says we cannot leave a radical expressio
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, C =5
Slope-Intercept Form
y =mx +b or y =- 2 x - 5
Wher
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 the 2 rational or irrational? Its Irrational and canno
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 natural number such as cfw_ 1, 2,3K
n - times
Definition 2:
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 one
2. There are two expressions linked by an equal symb
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 + 4 - 4 2x 2x - 6 -4
x -10
Interval notation [-10, ) So
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/equation must be solved for y. In Intermediate Algebra, most
MAT 108 Intermediate Algebra
Unit 2 Part 1 Introduction to Functions
Graphing Cartesian Coordinates
We see graphs all the time today newspapers ads, TV commercials.
Graphing of mathematical equations can reveal a large amount of information by
visual insp
Homework Answers Unit 2 Part 1
Page 132-133
(2)
D = cfw_4, -4, 2, 10
R = cfw_9, 3, -5 Function
(4)
D = cfw_6, 5, 7
R = cfw_6, -2
(6)
D = cfw_1 2, 3, 4
R = cfw_1
(8)
D = cfw_, 0, -2, 4
R = cfw_0, , -2, 4 Function
(12)
D = cfw_-1, 0, 1, 2
R = cfw_1,0,-1,2)