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Intermediate Algebra

ISBN-10: 0321645944
ISBN-13: 9780321645944
Edition: 2011 (Student Manual, Study Guide, etc.)
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Book details

Copyright year: 2011
Publisher: Prentice Hall PTR
Publication date: 1/3/2010
Binding: Print, Other 
Pages: 1400
Size: 7.00" wide x 9.00" long x 0.50" tall
Weight: 0.308
Language: English

Kirk Trigsted teaches mathematics at the University of Idaho and has been Director of the Polya Mathematics Center since its inception in 2001. Kirk has taught with MyMathLab for many years, and has contributed to the videos for several Pearson books. Kirk is also actively involved with the National Center for Academic Transformation (NCAT).

Normal 0 false false false Kirk Trigstedteaches mathematics at the University of Idaho and has been Director of the Polya Mathematics Center since its inception in 2001. Kirk has taught with MyMathLab for many years, and has contributed to the videos for several Pearson books. Kirk is also actively involved with the National Center for Academic Transformation (NCAT). nbsp; Randy Gallaheris a professor of mathematics at Lewis & Clark Community College where he has taught since 1997. Prior to this position, Randy taught high school and middle school mathematics for five years in Missouri. He holds a masters degree in mathematics from Southeast Missouri State University and has completed additional graduate coursework at both Missouri State University and the University of Illinois at Urbana-Champaign. He has coauthored ancillary materials for numerous math and statistics textbooks and has worked as a math author on several grant projects for the Illinois Community College Board. Randy is married with three children and spends most evenings actively involved in their activities. In his limited free time, he loves to fish the small rivers and streams of Southern Missouri. nbsp; Kevin Boddenis a professor of mathematics at Lewis & Clark Community College where he has taught since 1999. He holds a masters degree in mathematics from Southern Illinois University at Edwardsville and a masters degree in engineering from Purdue University. He has authored or co-authored ancillary material for numerous textbooks ranging from basic college math to calculus and statistics. Kevin is married with three children and is actively involved in their school and extracurricular activities. In his spare time, he enjoys reading, camping, and geocaching. nbsp;

Review
Sets of Numbers
Identify sets
Classify real numbers
Plot real numbers on a number line
Use inequality symbols to order real numbers
Compute the absolute value of a real number
Order of Operations and Properties of Real Numbers
Perform operations on real numbers
Simplify numeric expressions containing exponents and radicals
Identify and use the properties of real numbers
Use order of operations to evaluate numeric expressions
Algebraic Expressions
Evaluate algebraic expressions
Simplify algebraic expressions
Write verbal descriptions as algebraic expressions
Equations and Inequalities in One Variable
Linear Equations in One Variable
Determine if a given value is a solution to an equation
Solve linear equations in one variable
Identify equations that are contradictions and those that are identities
Use linear equations to solve application problems
Linear Inequalities in One Variable
Determine if a given value is a solution to an inequality
Graph the solution set of an inequality on a number line
Use interval notation to express the solution set of an inequality
Solve linear inequalities in one variable
Use linear inequalities to solve application problems
Compound Inequalities; Absolute Value Equations and Inequalities
Find the union and intersection of two sets
Solve compound linear inequalities in one variable
Solve absolute value equations
Solve absolute value inequalities
Formulas and Problem Solving
Solve a formula for a given variable
Use formulas to solve application problems
Graphs and Functions
The Rectangular Coordinate System and Graphing
Plot ordered pairs in the rectangular coordinate system
Determine if an ordered pair is a solution to an equation
Find unknown coordinates
Graph equations by plotting points
Find x- and y-intercepts
Relations and Functions
Identify independent and dependent variables
Find the domain and range of a relation
Determine if relations are functions
Determine if graphs are functions
Solve application problems involving relations and functions
Function Notation and Applications
Express equations of functions using function notation
Evaluate functions
Graph simple functions by plotting points
Interpret graphs of functions
Solve application problems involving functions
Graphs of Linear Functions
Graph linear functions by plotting points
Graph linear functions by using intercepts
Graph vertical and horizontal lines
Linear Equations in Two Variables
Find the slope of a line
Graph a line using the slope and a point
Determine the relationship between two lines
Write the equation of a line from given information
Write equations of parallel and perpendicular lines
Use linear models to solve application problems; direct variation
Linear Inequalities in Two Variables
Determine if an ordered pair is a solution to a linear inequality in two variables
Graph a linear inequality in two variables
Systems of Linear Equations and Inequalities
Systems of Linear Equations in Two Variables
Determine if an ordered pair is a solution to a system of linear equations in two variables
Solve systems of linear equations in two variables by graphing
Solve systems of linear equations in two variables by substitution
Solve systems of linear equations in two variables by elimination
Solve inconsistent and dependent systems
Use systems of linear equations in two variables to solve application problems
Systems of Linear Equations in Three Variables
Determine if an ordered triple is a solution to a system of linear equations in three variables
Solve systems of linear equations in three variables
Use systems of linear equations in three variables to solve application problems
More Problem Solving with Systems of Linear Equations
Use systems of linear equations to solve uniform motion problems
Use systems of linear equations to solve geometry problems
Use systems of linear equations to solve mixture problems
Systems of Linear Inequalities in Two Variables
Determine if an ordered pair is a solution to a system of linear inequalities in two variables
Graph systems of linear inequalities in two variables
Polynomial Expressions and Functions
Rules for Exponents
Simplify exponential expressions using the product rule
Simplify exponential expressions using the quotient rule
Use the zero-power rule
Use the negative-power rule
Use the power-to-power rule
Use the product-to-power and quotient-to-power rules
Simplify exponential expressions using a combination of rules
Use rules for exponents with scientific notation
Introduction to Polynomial Functions
Find the coefficient and degree of a monomial
Find the leading coefficient and degree of a polynomial
Evaluate a polynomial function for a given value
Add polynomials
Subtract polynomials
Add and subtract polynomial functions
Multiplying Polynomials
Multiply monomials
Multiply a polynomial by a monomial
Multiply two binomials
Multiply two binomials using special product rules
Multiply two or more polynomials
Multiply polynomial functions
Dividing Polynomials
Divide a polynomial by a monomial
Divide polynomials using long division
Divide polynomials using synthetic division
Divide polynomial functions
Use the Remainder and Factor theorems
Factoring
Greatest Common Factor and Factoring by Grouping
Factor out the greatest common factor from a polynomial
Factor by grouping
Factoring Trinomials
Factor trinomials of the form x2+ bx + c
Factor trinomials of the form ax2+ bx + c using trial-and-error
Factor trinomials of the form ax2+ bx + c using the ac method
Factor trinomials using substitution
Special-Case Factoring; A General Factoring Strategy
Factor the difference of two squares
Factor perfect square trinomials
Factor the sum or difference of two cubes
Factor polynomials completely
Polynomial Equations and Models
Solve polynomial equations by factoring
Find the zeros of a polynomial function
Use polynomial equations and models to solve application problems
Rational Expressions, Equations, and Functions
Introduction to Rational Expressions and Functions
Find the domain of a rational function
Evaluate rational functions
Simplify rational expressions
Multiplying and Dividing Rational Expressions
Multiply rational expressions
Divide rational expressions
Adding and Subtracting Rational Expressions
Add and subtract rational expressions with common denominators
Find the least common denominator of rational expressions
Add and subtract rational expressions with unlike denominators
Complex Rational Expressions
Simplify complex rational expressions by first simplifying the numerator and denominator
Simplify complex rational expressions by multiplying by a common denominator
Rational Equations and Models
Identify rational equations
Solve rational equations
Find the zeros of a rational function
Use rational equations to solve application problems
Variation
Solve application problems involving direct variation
Solve application problems involving inverse variation
Solve application problems involving combined variation
Radicals and Rational Exponents
Radical Expressions
Find square roots of perfect squares
Approximate square roots
Simplify radical expressions of the formv(a2)
Find cube roots
Find and approximatenth roots
Radical Functions
Evaluate radical functions
Find the domain of a radical function
Graph functions that contain square roots or cube roots
Rational Exponents and Simplifying Radical Expressions
Use the definition for rational exponents of the forma1/n
Use the definition for rational exponents of the form am/n
Simplify exponential expressions involving rational exponents
Use rational exponents to simplify radical expressions
Simplify radical expressions using the product rule
Simplify radical expressions using the quotient rule
Operations with Radicals
Add and subtract radical expressions
Multiply radical expressions
Rationalize denominators of radical expressions
Radical Equations and Models
Solve equations involving one radical expression
Solve equations involving two radical expressions
Use radical equations and models to solve application problems
Complex Numbers
Simplify powers of i
Add and subtract complex numbers
Multiply complex numbers
Divide complex numbers
Simplify radicals with negative radicands
Quadratic Equations and Functions; Circles
Solving Quadratic Equations
Solve quadratic equations using factoring
Solve quadratic equations using the square root property
Solve quadratic equations by completing the square
Solve quadratic equations using the quadratic formula
Use the discriminant to determine the number and type of solutions to a quadratic equation
Solve equations that are quadratic in form
Quadratic Functions and Their Graphs
Identify the characteristics of a quadratic function from its graph
Graph quadratic functions by using translations
Graph quadratic functions of the form f(x) = a(x-h)2+ k
Find the vertex of a parabola by completing the square
Graph quadratic functions of the form f(x) = ax2+ bx + c by completing the square
Find the vertex of a parabola by using the vertex formula
Graph quadratic functions of the form f(x) = ax2+ bx + c by using the vertex formula
Applications and Modeling of Quadratic Functions
Solve applications involving unknown numbers
Solve applications involving projectile motion
Solve applications involving geometric formulas
Solve applications involving distance, rate, and time
Solve applications involving work
Maximize quadratic functions to solve application problems
Minimize quadratic functions to solve application problems
Circles
Find the distance between two points
Find the midpoint of a line segment
Write the standard form of an equation of a circle
Sketch the graph of a circle
Find the center and radius of a circle
Polynomial and Rational Inequalities
Solve polynomial inequalities
Solve rational inequalities
Exponential and Logarithmic Functions and Equations
Transformations of Functions
Use vertical shifts to graph functions
Use horizontal shifts to graph functions
Use reflections to graph functions
Use vertical stretches and compressions to graph functions
Use horizontal stretches and compressions to graph functions
Use a combination of transformations to graph functions
Composite and Inverse Functions
Form and evaluate composite functions
Determine the domain of composite functions
Determine if a function is one-to-one using the horizontal line test
Verify inverse functions
Sketch the graphs of inverse functions
Find the inverse of a one-to-one function
Exponential Functions
Use the characteristics of exponential functions
Sketch the graph of exponential functions using transformations
Solve exponential equations by relating the bases
Solve applications of exponential functions
The Natural Exponential Function
Use the characteristics of the natural exponential function
Sketch the graph of natural exponential functions using transformations
Solve natural exponential equations by relating the bases
Solve applications of natural exponential functions
Logarithmic Functions
Use the definition of a logarithmic function
Evaluate logarithmic expressions
Use the properties of logarithms
Use the common and natural logarithms
Use the characteristics of logarithmic functions
Sketch the graph of logarithmic functions using transformations
Find the domain of logarithmic functions
Properties of Logarithms
Use the product rule, quotient rule, and power rule for logarithms
Expand and condense logarithmic expressions
Solve logarithmic equations by using the logarithm property of equality
Use the change-of-base formula
Exponential and Logarithmic Equations
Solve exponential equations
Solve logarithmic equations
Applications of Exponential and Logarithmic Functions
Solve compound interest applications
Solve exponential growth and decay applications
Solve logistic growth applications
Use Newton's Law of Cooling
Conic Sections
Introduction to Conic Sections
The Parabola
Work With the Equation of a Parabola with a Vertical Axis of Symmetry
Work With the Equation of a Parabola with a Horizontal Axis of Symmetry
Find the Equation of a Parabola Given Information about the Graph
Complete the Square to Find the Equation of a Parabola in Standard Form
Solve Applications Involving Parabolas
The Ellipse
Sketch the Graph of an Ellipse
Find the Equation of an Ellipse Given Information about the Graph
Complete the Square to Find the Equation of an Ellipse in Standard Form
Solve Applications Involving Ellipses
The Hyperbola
Sketch the Graph of a Hyperbola
Find the Equation of a Hyperbola in Standard Form
Complete the Square to Find the Equation of a Hyperbola in Standard Form
Solve Applications Involving Hyperbolas
Sequences and Series
Introduction to Sequences and Series
Write the terms of a sequence
Write the terms of a recursive sequence
Write the general term for a given sequence
Compute partial sums of a series
Determine the sum of a finite series written in summation notation
Write a series using summation notation
Arithmetic Sequences and Series
Determine if a sequence is arithmetic
Find the general term or specific term of an arithmetic sequence
Compute the nth partial sum of an arithmetic series
Solve applications of arithmetic sequences and series
Geometric Sequences and Series
Write the terms of a geometric sequence
Determine if a sequence is geometric
Find the general term or specific term of a geometric sequence
Compute the nth partial sum of a geometric series
Determine if an infinite geometric series converges or diverges
Solve applications of geometric sequences and series
The Binomial Theorem
Expand binomials raised to a power using Pascal's Triangle
Evaluate binomial coefficients
Expand binomials raised to a power using the Binomial Theorem
Find a particular term or a particular coefficient of a binomial expansion
Basic Math Review - Fractions, Decimals, Proportions, Percents
Fractions
Decimals
Proportions
Percents

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