Intermediate Algebra (softcover)

© 2015
by Julie Miller, Molly O'neill, Nancy Hyde

3rd Edition 928 Pages Paperback / softback
9780073384429 0073384429
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  • Table of Contents
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Get Better Results with high quality content, exercise sets, and step-by-step pedagogy! 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.

Intermediate Algebra, 3rd Edition

R Review of Basic Algebraic Concepts


R.1 Study Skills
Group Activity: Becoming a Successful Student
R.2 Sets of Numbers and Interval Notation
R.3 Operations on Real Numbers
R.4 Simplifying Expressions

1 Linear Equations and Inequalities in One Variable


1.1 Linear Equations in One Variable
PRE: Equations versus Expressions
1.2 Application of Linear Equations in One Variable
1.3 Applications to Geometry and Literal Equations
1.4 Linear Inequalities in One Variable
1.5 Compound Inequalities
1.6 Absolute Value Equations
1.7 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 Variables
2.2 Slope of a Line and Rate of Change
2.3 Equations of a Line
PRE: Characteristics of Linear Equations
2.4 Application of Linear Equations and Modeling
Group Activity: Using Linear Equations to Construct Images

3 Relations and Functions


3.1 Relations and Applications
3.2 Introduction to Functions
3.3 Graphs of Basic Functions
PRE: Characteristics of Relations
3.4 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 Method
4.2 Solving Systems of Linear Equations by Using the Substitution Method
4.3 Solving Systems of Linear Equations by Using the Addition Method
PRE: Solving Systems of Linear Equations
4.4 Applications of Systems of Linear Equations in Two Variables
4.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables
4.6 Systems of Linear Equations in Three Variables and Applications
4.7 Solving Systems of Linear Equations by Using Matrices
Group Activity: Creating a Quadratic Model of the Form y = at^2 +bt + c

5 Polynomials


5.1 Properties of Integer Exponents and Scientific Notation
5.2 Addition and Subtraction of Polynomials and Polynomial Functions
5.3 Multiplication of Polynomials
5.4 Division of Polynomaisl
PRE: Operations on Polynomials
5.5 Greatest Common Factor and Factoring by Grouping
5.6 Factoring Trinomials and Perfect Square Trinomials
5.7 Factoring Binomials Including Sum and Difference of Cubes
PRE: Factoring Summary
5.8 Solving Equations and Applications by Factoring Group Activity: Investigating Pascal's Triangle

6 Rational Expressions and Rational Equations


6.1 Rational Expressions and Rational Functions
6.2 Multiplication and Division of Rational Expressions
6.3 Addition and Subtraction of Rational Expressions
6.4 Complex Fractions
PRE: Operations on Rational Expressions
6.5 Solving Rational Equations
PRE: Rational Equations versus Expressions
6.6 Applications of Rational Equations and Proportions
6.7 Variation
Group Activity: Computing the Future Value of an Investment

7 Radicals and Complex Numbers


7.1 Definition of an nth-Root
7.2 Rational Exponents
7.3 Simplifying Radical Expressions
7.4 Addition and Subtraction of Radicals
7.5 Multiplication of Radicals
PRE: Simplifying Radical Expressions
7.6 Division of Radicals and Rationalisation
7.7 Radical Equations and Applications
7.8 Complex Numbers
Group Activity: Margin of Error of Survey Results

8 Quadratic Equations, Functions, and Inequalities


8.1 Square Root Property and Completing the Square
8.2 Quadratic Formula and Applications
8.3 Equations in Quadratic Form
PRE: Equations in Quadratic Form
8.4 Graphs of Quadratic Functions
8.5 Vertex of a Parabola: Applications and Modeling
8.6 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 Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
PRE: Identifying Graphs of Functions
9.4 Properties of Logarithms
9.5 The Irrational Number e
PRE: Logarithmic and Exponential Forms
9.6 Exponential Equations and Applications
9.7 Logarithmic Equations and Applications
Group Activity: Creating a Population Model

10 Conic Sections


10.1 Distance Formula, Midpoint, and Circles
10.2 More of the Parabola
10.3 The Ellipse and Hyperbola
PRE: Formulas for Conic Sections
10.4 Nonlinear Systems of Equations in Two Variables
10.5 Nonlinear Inequalities and Systems of Inequalities
Group Activity: Investigating the Graphs of Conic Sections on a Calculator

Additional Topics Appendix


A.1 Binomial Expansions
A.2 Determinants and Cramer's Rule
A.3 Sequences and Series
A.4 Arithmetic and Geometric Sequences and Series
New to this Edition

SmartBook is the first and only adaptive reading experience available for the higher education market. Powered by an intelligent diagnostic and adaptive engine, SmartBook facilitates the reading process by identifying what content a student knows and doesn't know through adaptive assessments. As the student reads, the reading material constantly adapts to ensure the student is focused on the content he or she needs the most to close any knowledge gaps.

LearnSmart is an adaptive self-study technology that provides students with a seamless combination of practice, assessment, and remediation for every concept in the textbook. LearnSmart's intelligent software adapts to every student response and automatically delivers concepts that advance students' understanding while reducing time devoted to the concepts already mastered. The result for every student is the fastest path to mastery of the chapter concepts.

The Student Resource Manual (SRM), created by the authors, is a printable, electronic supplement available to students through Connect Math hosted by ALEKS. Instructors can also choose to customize this manual and package with their course materials. With increasing demands on faculty schedules, this resource offers a convenient means for both full-time and adjunct faculty to promote active learning and success strategies in the classroom. The SRM has NEW group activities, guided lecture notes, and problem recognition exercise worksheets.


Retained Features

Connect Math hosted by ALEKS is an exciting new assignment and assessment eHomework platform. Instructors can assign an AI-driven ALEKS Assessment to identify the strengths and weaknesses of each student at the beginning of the term rather than after the first exam. Assignment creation and navigation is efficient and intuitive. The gradebook, based on instructor feedback, has a straightforward design and allows flexibility to import and export additional grades.

ALEKS is a unique online program that significantly raises student proficiency and success rats in mathematics, while reducing faculty workload and office-hour lines. ALEKS uses artificial intelligence and adaptive questioning to assess precisely a student's knowledge and deliver individualized learning tailored to the student's needs. With a comprehensive library of math courses, ALEKS delivers an unparalleled adaptive learning system that has helped millions of students achieve math success.

Julie Miller constructed a series of Flash animations to illustrate difficult concepts where static images and text fall short. The animations leverage the use of on-screen movement and morphing shapes to give students an interactive approach to conceptual learning. Some provide a virtual laboratory for which an application is simulated and where students can collect data points for analysis and modeling. Others provide interactive question-and-answer sessions to test conceptual learning.

Problem Recognition exercise sets are designed to help students recognise the difference between types of problems that appear to be similar but are indeed different and require different approaches. Because teachers usually cover only one process at a time, often the students will see a combination of topics for the first time on a test. These Problem Recognition Exercises combine similar topics to give students practice in identifying what to do as well as how to do it. We've included one or more Problem Recognition Exercise sets in each chapter.

Each chapter concludes with a Group Activity selected by objective to promote classroom discussion and collaboration, helping students not only to solve problems but to explain their solutions for better mathematical mastery. Group Activities are great for instructors and adjuncts - bringing a more interactive approach to teaching mathematics!

Worked examples in the text offer a clear, concise methodology that replicates the mathematical processes used in the authors' classroom lectures. Many multi-part sets and examples have been split up to make viewing the solutions easier.

Real-world applications have been developed to include focus on current events. The authors have broadened the scope of the applications by enlisting the help of the Board of Advisors to seek out new and interesting applications.

For each example in the text, we reference an even-numbered exercise from the end-of-section exercises, to be used as a Classroom Example. These exercises are highlighted in the practice set at the end of each section and mirror the related example. If an instructor presents all of the highlighted exercises in class as examples, then every objective of that section will be covered. This is especially helpful for new instructors, adjunct instructors, and graduate assistants. By using exercises in the text, students will not waste valuable class time copying down complicated classroom examples from the board.

The Chapter openers are engaging puzzles that require students to review the skills needed to be successful in the chapter.

Avoiding Mistakes boxes are integrated throughout the text to alert students to common errors and how to avoid them.

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