Introductory Algebra

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

3rd Edition 784 Pages Paperback / softback
9780073384542 0073384542
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  • Description
  • 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 Introductory 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 recognize 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.

Introductory Algebra, 3rd Edition


R Reference


R.1 Study Tips
R.2 Fractions
R.3 Decimals and Percents
R.4 Introduction to Geometry

1 The Set of Real Numbers


1.1 Introduction to Algebra and the Set of Real Numbers
1.2 Exponents, Square Roots, and the Order of Operations
1.3 Addition of Real Numbers
1.4 Subtraction of Real Numbers
PRE: Addition and Subtraction of Real Numbers
1.5 Multiplication and Division of Real Numbers
1.6 Properties of Real Numbers and Simplifying Expressions
Group Activity: Evaluating Formulas Using a Calculator

2 Linear Equations and Inequalities


2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality
2.2 Solving Linear Equations
2.3 Linear Equations: Clearing Fractions and Decimals
PRE: Equations and Expressions
2.4 Applications of Linear Equations:Introduction to Problem Solving
2.5 Applications Involving Percents
2.6 Literal Equations and Applications of Geometry
2.7 Mixture Applications and Uniform Motion
2.8 Linear Inequalities
Group Activity: Computing Body Mass Index (BMI)

3 Graphing Linear Equations in Two Variables


3.1 Rectangular Coordinate System
3.2 Linear Equations in Two Variables
3.3 Slope of a Line and Rate of Change
3.4 Slope-Intercept Form of a Linear Equation
PRE: Linear Equations in Two Variables 3.5 Point-Slope Formula
3.6 Applications of Linear Equations and Modeling
Group Activity: Modeling a Linear Equation

4 Systems of Linear Equations in Two Variables


4.1 Solving Systems of Equations by the Graphing Method
4.2 Solving Systems of Equations by the Substitution Method
4.3 Solving Systems of Equations by the Addition Method
PRE: Systems of Equations
4.4 Applications of Linear Inequalities in Two Variables
4.5 Linear Inequalities and Systems of Inequalities in Two Variables
Group Activity: Creating Linear Models from Data

5 Polynomials and Properties of Exponents


5.1 Multiplying and Dividing Expressions with Common Bases
5.2 More Properties of Exponents
5.3 Definitions of b^0 and b^-n
PRE: Properties of Exponents
5.4 Scientific Notation
5.5 Addition and Subtraction of Polynomials
5.6 Multiplication of Polynomials and Special Products
5.7 Division of Polynomials
PRE: Operations on Polynomials
Group Activity: The Pythagorean Theorem and a Geometric 'Proof'

6 Factoring Polynomials


6.1 Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x^2 + bx + c
6.3 Factoring Trinomials: Trial and Error Method
6.4 Factoring Trinomials: A-C Method
6.5 Difference of Squares and Perfect Square Trinomials
6.6 Sum and Difference of Cubes
PRE: Factoring Strategy
6.7 Solving Equations Using the Zero Product Rule
PRE: Polynomial Expressions versus Polynomial Equations
6.8 Applications of Quadratic Equations
Group Activity: Building a Factoring Test

7 Rational Expressions and Equations


7.1 Introduction to Rational Expressions
7.2 Multiplication and Division of Rational Expressions
7.3 Least Common Denominator
7.4 Addition and Subtraction of Rational Expressions
PRE: Operations on Rational Expressions
7.5 Complex Fractions
7.6 Rational Equations
PRE: Comparing Rational Equations and Rational Expressions
7.7 Applications of Rational Equations and Proportions 7.8 Variation
Group Activity: Computing Monthly Mortgage Payments

8 Radicals


8.1 Introduction to Roots and Radicals
8.2 Simplifying Radicals
8.3 Addition and Subtraction of Radicals
8.4 Multiplication of Radicals
8.5 Division of Radicals and Rationalisation
PRE: Operations on Radicals
8.6 Radicals Equations
8.7 Rational Exponents
Group Activity: Calculating Standard Deviation

9 More Quadratic Equations


9.1 The Square Root Property
9.2 Completing the Square
9.3 Quadratic Formula
PRE: Solving Different Types of Equations
9.4 Graphing Quadratic Equations
9.5 Introduction to Functions
Group Activity: Maximising Volume

Additional Topics Appendix


A.1 Converting Units of Measurement
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.


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 individualised 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.

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.

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 puzzle 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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