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 INTERMEDIATE ALGEBRA
 Course Syllabus for Algebra I
 MidPlains Community College
 FRACTION OF A WHOLE NUMBER
 Systems of Linear Equations
 MATH FIELD DAY
 Course Outline for Finite Mathematics
 Calculus
 Algebra Final Examination
 Math 310 Exam #2
 Review of Trigonometric Functions
 Math 118 Practice test
 Precalculus Review
 Section 12
 Literal Equations
 Calculus Term Definitions
 Math 327A Exercise 2
 Public Key Algorithms II
 Maximizing Triangle Area
 Precalculus I Review for Midterm
 REVIEW OF A FIRST COURSE IN LINEAR ALGEBRA
 Math 6310 Homework 5
 Some Proofs of the Existence of Irrational Numbers
 ALGEBRAIC PROPERTIES OF MATRIX OPERATIONS
 Math 142  Chapter 2 Lecture Notes
 Math 112 syllabus
 Math 371 Problem Set
 Complex Numbers,Complex Functions and Contour Integrals
 APPLICATIONS OF LINEAR EQUATIONS
 Week 4 Math
 Fractions
 Investigating Liner Equations Using Graphing Calculator
 MATH 23 FINAL EXAM REVIEW
 Algebra 1
 PYTHAGOREAN THEOREM AND DISTANCE FORMULA
 Georgia Performance Standards Framework for Mathematics  Grade 6
 Intermediate Algebra
 Introduction to Fractions
 FACTORINGS OF QUADRATIC FUNCTIONS
 Elementary Algebra Syllabus
 Description of Mathematics
 Integration Review Solutions
 College Algebra  Applications
 A Tip Sheet on GREATEST COMMON FACTOR
 Syllabus for Elementary Algebra
 College Algebra II and Analytic Geometry
 Functions
 BASIC MATHEMATICS
 Quadratic Equations
 Language Arts, Math, Science, Social Studies, Char
 Fractions and Decimals
 ON SOLUTIONS OF LINEAR EQUATIONS
 Math 35 Practice Final
 Solving Equations
 Introduction to Symbolic Computation
 Course Syllabus for Math 935
 Fractions
 Fabulous Fractions
 Archimedean Property and Distribution of Q in R
 Algebra for Calculus
 Math112 Practice Test #2
 College Algebra and Trigonometry
 ALGEBRA 1A TASKS
 Description of Mathematics
 Simplifying Expressions
 Imaginary and Complex Numbers
 Building and Teaching a Math Enhancement
 Math Problems
 Algebra of Matrices Systems of Linear Equations
 Survey of Algebra
 Approximation of irrational numbers
 More about Quadratic Functions
 Long Division
 Algebraic Properties of Matrix Operation
 MATH 101 Intermediate Algebra
 Rational Number Project
 Departmental Syllabus for Finite Mathematics
 WRITTEN HOMEWORK ASSIGNMENT
 Description of Mathematics
 Rationalize Denominators
 Math Proficiency Placement Exam
 linear Equations
 Description of Mathematics & Statistics
 Systems of Linear Equations
 Algebraic Thinking
 Study Sheets  Decimals
 An Overview of Babylonian Mathematics
 Mathematics 115  College Algebra
 Complex Numbers,Complex Functions and Contour Integrals
 Growing Circles
 Algebra II Course Curriculum
 The Natural Logarithmic Function: Integration
 Rational Expressions
 QUANTITATIVE METHODS
 Basic Facts about Rational Funct
 Statistics
 MAT 1033 FINAL WORKSHOP REVIEW
 Measurements Significant figures
 PreCalculus 1
 Compositions and Inverses of Functions
Algebraic Thinking
Outline
1 What is Algebra?
2 Algebra and Graphs
3 Algebraic Manipulations
4 Conclusion
Examples of Algebra
Many people find the thought of algebra, equations, and variables
intimidating. But it is just generalized arithmetic.
Algebraic Examples
Consider the following common uses of algebra.
•Formulas – (C = πd)
Relation between two or more variables
•Equations – (5x = 30)
Finding an unknown value
•Identities – (sin^{2}x + cos^{2}x = 1)
An expression true for any x
•Property – (a + b = b + a)
Expression of a general rule
•Function – (f (x) = 3x + 1)
An input (independent) and output (dependent) variable
Examples of Using Algebra
Let’s look at a few examples from this list.
Formulas 
The formula
relates temperatures in Farenheit to temperatures in Celsius. Use this formula to convert 20 degrees cesius to farenheit and 41 degrees farenheit to celsius. 
Equations 
Fill in the blank.

Properties 
Use symbols to express the fact that every number
has an additive inverse. 
Algebra as a Study of Structure
There are many different ways to view algebra.
Study of Structure  
Algebra can be seen as a study of structure. That
is, what is the structure of arithmetic? How does it work? 

Example  
For all real numbers a, b and c the following
laws hold:

Algebra as a Study of Relationships
Another way to view algebra is a method to express relationships.
Relationships Between Quantities 
Algebra can be seen as a study of the
relationship between quantities. The concept of a function is important here as there is usually an “input” quantity and an “output” quantity. 
Example 
A phone card has a connection fee of $0.25 plus a
$0.05/minute charge for the actual time of the call. Describe the price of the call as a function of the number of minutes spent on the call. 
Use the following methods to express the relationship above 
•a table •a graph •a function rule 
Using Graphs to Visualize Algebraic Relationships
As we saw in the previous example, graphs can be an
important
way to visualize a relationship between quantities which can be
expressed algebraically.
Example 
A beautician charges $15 for haircuts. Each week
she has fixed expenses of $150. Express her profit as a function of teh number of haircuts she gives. Use a graph to describe this function. 
Question 
Are the table, graph, and formula we used to
answer the previous question really accurate? In particular, is it possible to give haircuts? How is this problem seen in the graph? 
Interpreting Graphs
Many times a graph is enough to describe a relationship.
Example 
Below are descriptions of three runners in a
race. Match each description to the correct graph and explain your choice.
•Alex started slowly, then ran a bit faster, and then
ran even faster at the end of the race. 
Recalling Algebraic Rules
There are several symbolic rules to working with algebra
which you
have learned in the past. Let’s review some of these rules.
Adding Polynomials 
When adding polynomials group like terms together
and use the distributive property (a(b + c) = ab + ac) to combine like terms. 
Example 
Add the following polynomials.

Multiplication and Factoring
Finally, we will briefly review multiplying and factoring.
Example 
Multiply the following polynomials.

Example 
Factor the following polynomials completely.

Important Concepts
Things to Remember from Section 2.2 
1 Various uses of algebra 2 Solving equations 3 Representing relationships using fuctions and graphs 4 Adding, multiplying, and factorying polynomials 