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The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Intermediate Algebra. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students. Throughout the text, the authors communicate to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. Also included are Problem Recognition Exercises, designed to help students recognise which solution strategies are most appropriate for a given exercise. These types of exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor.
Table of Contents
Intermediate Algebra, 3rd Edition
R Review of Basic Algebraic Concepts
R.1 Study Skills Group Activity: Becoming a Successful StudentR.2 Sets of Numbers and Interval NotationR.3 Operations on Real NumbersR.4 Simplifying Expressions
1 Linear Equations and Inequalities in One Variable
1.1 Linear Equations in One Variable PRE: Equations versus Expressions1.2 Application of Linear Equations in One Variable1.3 Applications to Geometry and Literal Equations1.4 Linear Inequalities in One Variable1.5 Compound Inequalities1.6 Absolute Value Equations1.7 Absolute Value Inequalities PRE: Identifying Equations and Inequalities Group Activity: Understanding the Symbolism of Mathematics
2 Linear Equations in Two Variables
2.1 Linear Equations in Two Variables2.2 Slope of a Line and Rate of Change2.3 Equations of a Line PRE: Characteristics of Linear Equations2.4 Application of Linear Equations and Modeling Group Activity: Using Linear Equations to Construct Images
3 Relations and Functions
3.1 Relations and Applications3.2 Introduction to Functions3.3 Graphs of Basic Functions PRE: Characteristics of Relations3.4 Algebra of Functions, Composition, and Applications Group Activity: Deciphering a Coded Message
4 Systems of Linear Equations
4.1 Solving Systems of Linear Equations by the Graphing Method4.2 Solving Systems of Linear Equations by Using the Substitution Method4.3 Solving Systems of Linear Equations by Using the Addition Method PRE: Solving Systems of Linear Equations4.4 Applications of Systems of Linear Equations in Two Variables4.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables4.6 Systems of Linear Equations in Three Variables and Applications4.7 Solving Systems of Linear Equations by Using Matrices Group Activity: Creating a Quadratic Model of the Form y = at^2 +bt + c
5.1 Properties of Integer Exponents and Scientific Notation5.2 Addition and Subtraction of Polynomials and Polynomial Functions5.3 Multiplication of Polynomials5.4 Division of Polynomaisl PRE: Operations on Polynomials5.5 Greatest Common Factor and Factoring by Grouping5.6 Factoring Trinomials and Perfect Square Trinomials5.7 Factoring Binomials Including Sum and Difference of Cubes PRE: Factoring Summary5.8 Solving Equations and Applications by Factoring Group Activity: Investigating Pascal's Triangle
6 Rational Expressions and Rational Equations
6.1 Rational Expressions and Rational Functions6.2 Multiplication and Division of Rational Expressions6.3 Addition and Subtraction of Rational Expressions6.4 Complex Fractions PRE: Operations on Rational Expressions6.5 Solving Rational Equations PRE: Rational Equations versus Expressions6.6 Applications of Rational Equations and Proportions6.7 Variation Group Activity: Computing the Future Value of an Investment
7 Radicals and Complex Numbers
7.1 Definition of an nth-Root7.2 Rational Exponents7.3 Simplifying Radical Expressions7.4 Addition and Subtraction of Radicals7.5 Multiplication of Radicals PRE: Simplifying Radical Expressions7.6 Division of Radicals and Rationalization7.7 Radical Equations and Applications7.8 Complex Numbers Group Activity: Margin of Error of Survey Results
8 Quadratic Equations, Functions, and Inequalities
8.1 Square Root Property and Completing the Square8.2 Quadratic Formula and Applications8.3 Equations in Quadratic Form PRE: Equations in Quadratic Form8.4 Graphs of Quadratic Functions8.5 Vertex of a Parabola: Applications and Modeling8.6 Polynomials and Rational Inequalities PRE: Recognizing Equations and Inequalities Group Activity: Creating a Quadratic Model of the Form y = a(x - h)^2 + k
9 Exponential and Logarithmic Functions
9.1 Inverse Functions9.2 Exponential Functions9.3 Logarithmic Functions PRE: Identifying Graphs of Functions9.4 Properties of Logarithms9.5 The Irrational Number e PRE: Logarithmic and Exponential Forms9.6 Exponential Equations and Applications9.7 Logarithmic Equations and Applications Group Activity: Creating a Population Model
10 Conic Sections
10.1 Distance Formula, Midpoint, and Circles10.2 More of the Parabola10.3 The Ellipse and Hyperbola PRE: Formulas for Conic Sections10.4 Nonlinear Systems of Equations in Two Variables10.5 Nonlinear Inequalities and Systems of Inequalities Group Activity: Investigating the Graphs of Conic Sections on a Calculator
Additional Topics Appendix
A.1 Binomial ExpansionsA.2 Determinants and Cramer's RuleA.3 Sequences and SeriesA.4 Arithmetic and Geometric Sequences and Series