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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
Precalculus Review
• Precalculus Review I
• Precalculus Review II
• The Cartesian Coordinate System
• Straight Lines
The Real Numbers
The real numbers can be ordered and
represented in order on a number line
Inequalities, graphs, and notations
Inequality  Graph  Interval 
) or ( means not included in the solution
] or [ means included in the solution
Intervals
Interval  Graph  Example 
Properties of Inequalities
If a, b, and c are any real numbers, then  Example  
Property 1  If a<b and b<c , then . a <c 
2 < 3 and 3 < 8, so 2 < 8. 
Property 2  If a<b then . a +c< b+c 
5<3,so 5+2<3 +2 that is,3<1 
Property 3  If a<b and c<0 then ac<bc 
5<3,and 2>0,we have (5)(2)<(3)(2);that is ,10< 6 
Property 4  If a<b and c<0 then ab>bc 
5<4,and 2<0,we have (5)(2)>(4)(2);that is,10>8 
Absolute Value
Absolute Value Properties
If a and b are any real numbers, then  Example  
Property 5  l−a l= lal  l−4l = −(−4) = 4 = l4l 
Property 6  la bl = lal lbl  l(2)(−3)l = l−6l = l2l l−3l 
Property 7  
Property 8 
Exponents
n,m positive integers 
Definition  Example 
n factors

Laws of Exponents
Law  Example 
Algebraic Expressions
• Polynomials
• Rational Expressions
• Other Algebraic Fractions
Polynomials
• Addition
• Subtraction
Polynomials
• Multiplication
Factoring Polynomials
•Greatest Common Factor
• Grouping
Factoring Polynomials
Difference of Two Squares:
• Sum/Difference of Two Cubes:
Factoring Polynomials
• Trinomials
Roots of Polynomials
• Finding roots by factoring
(find where the polynomial = 0)
Roots of Polynomials
• Finding roots by the Quadratic Formula
• The Quadratic Formula:
If ax^{2} + bx + c = 0 (a ≠ 0)
with a, b, and c real numbers,
then
Example
Using the Quadratic Formula:
Ex. Find the roots of 3x^{2} + 7x +1= 0
Rational Expressions
Operation  P, Q, R, and S are polynomials 
Addition  
Subtraction  
Multiplication  
Division 
Rational Expressions
Rational Expressions
• Adding/Subtracting
Other Algebraic Fractions
• Complex Fractions
Other Algebraic Fractions
Notice:
• Rationalizing a Denominator
Cartesian Coordinate System
Cartesian Coordinate System
The Distance Formula
The Distance Formula
Ex. Find the distance between (7, 5) and (3, 2)
The Equation of a Circle
A circle with center (h, k) and radius of
length r can be expressed in the form:
(x − h)^{2}+ ( y − k )^{2}= r^{2}
Ex. Find an equation of the circle with center at
(4, 0) and radius of length 3 
Straight Lines
• Slope
• PointSlope Form
• SlopeIntercept Form
Slope – the slope of a nonvertical line
that passes through the points
(x_{1},y_{1})and (x_{2},y_{2})is given by:
Ex. Find the slope of the line that passes
through the points (4,0) and (6, 3) 
Slope
Two lines are parallel if and only if their
slopes are equal or both undefined
Two lines are perpendicular if and only if
the product of their slopes is –1. That is,
one slope is the negative reciprocal of the
other slope (ex. 3/4 a n d 3/4 ).
PointSlope Form
An equation of a line that passes through
the point with slope m is given
by:
y − y_{1} = m x − x_{1}
Ex. Find an equation of the line that passes through (3,1)
and has slope m = 4.
SlopeIntercept Form
An equation of a line with slope m and
yintercept ( 0 , b ) is given by:
y = mx + b
Vertical Lines
Horizontal Lines
Example
Find an equation of the line that passes
through (2, 1) and is perpendicular to the line
y = 2x − 7.
Solution:
Step 1.Since the slope of the line y=2x  7 is 2,
we have the slope of the perpendicular line is m=1/2 .
Step 2.
Example
Find an equation of the line that passes through
(0, 1) and is parallel to the line 6x + 2 y = 5.
Solution:
Step 1.We need to find the slope of the line
6x + 2 y = 5.
The slope of the parallel line is also m=3.
Step 2.
Since m=3 and b=1,