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Summary
Miller/O'Neill Beginning Algebra is an insightful text written by instructors who have first-hand experience with students of developmental mathematics.The authors have placed an emphasis on graphing, by including special sections called, "Connections to Graphing" at the end of Chapters 1-5, before the formal presentation of Graphing appears in Chapter 6. The "Connections to Graphing" sections may be considered optional for those instructors who do not prefer an early introduction to graphing. For those who do prefer graphing early, instructors can use the "Connections to Graphing" sections together where they prefer to introduce graphing.A section on geometry appears in "Chapter R" for instructors who look for such content in Beginning Algebra. Applications that incorporate geometric concepts may also be found throughout the text.Chapter R also contains a section on study skills. This section provides easy to digest tips (in list format) for course success.The authors have crafted the exercise sets with the idea of infusing review. In each set of practice exercises, instructors will find a set of exercises that help students to review concepts previously learned, and in this way, students will retain more of what they have learned.The exercise sets also contain "translation" exercises which provide students with an opportunity to convert from English phrases to mathematical symbols and from mathematical symbols to English phrases, thus helping students to strengthen their command of mathematical language.Moreover, the applications found in the exercise sets are based on real-world data, which helps to promote students' interest in mathematics, and in turn, may serve to motivate and engage them more effectively.Other features include mid-chapter reviews and classroom activities. The classroom activities are of special value, in that through their use, students may begin to take greater ownership over their learning. The classroom activities were designed to be quick activities students could perform in class (either individually, or collaboratively in groups).In short, the Miller/O'Neill Beginning Algebra text offers enriching applications, a high level of readability, and excellent opportunities for students to become actively engaged in their exploration of mathematics.
Table of Contents
Reference: Fractions, Decimals, Percents, Geometry, and Study Skills
R.1 Fractions
R.2 Decimals and Percents
R.3 Introduction to Geometry
R.4 Study Skills
1 Set of Real Numbers
1.1 Sets of Numbers and the Real Number Line
1.2 Order of Operations
1.3 Addition of Real Numbers
1.4 Subtraction of Real Numbers
Midchapter Review
1.5 Multiplication and Division of Real Numbers
1.6 Properties of Real Numbers and Simplifying Expressions
1.7 Connections to Graphing: Rectangular Coordinate System
2 Linear Equations and Inequalities
2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality
2.2 Solving Linear Equations
2.3 Applications of Linear Equations: Introduction to Problem Solving
2.4 Linear Equations: Clearing Fractions and Decimals
Midchapter Review
2.5 Applications of Geometry
2.6 More Applications of Linear Equations
2.7 Linear Inequalities
2.8 Connections to Graphing: Linear Equations in Two Variables
3 Polynomials and Properties of Exponents
3.1 Exponents: Multiplying and Dividing Common Bases
3.2 More Properties of Exponents
3.3 Definitions of b0 and bn
3.4 Scientific Notation
Midchapter Review
3.5 Addition and Subtraction of Polynomials
3.6 Multiplication of Polynomials
3.7 Division of Polynomials
3.8 Connections to Graphing: Introduction to Nonlinear Graphs
4 Factoring Polynomials
4.1 Greatest Common Factor and Factoring by Grouping
4.2 Factoring Trinomials: Grouping Method
4.3 Factoring Trinomials: Trial-and-Error Method
4.4 Factoring Perfect Square Trinomials and the Difference of Squares
Midchapter Review: "Factoring Strategy"
4.5 Factoring the Sum and Difference of Cubes and General Factoring Summary
4.6 Solving Quadratic Equations Using the Zero Product Rule
4.7 Connections to Graphing: x- and y-Intercepts
5 Rational Expressions
5.1 Introduction to Rational Expressions
5.2 Multiplication and Division of Rational Expressions
5.3 Least Common Denominator
5.4 Addition and Subtraction of Rational Expressions
Midchapter Review
5.5 Complex Fractions
5.6 Rational Equations
5.7 Applications of Rational Equations and Proportions
6 Graphing Linear Equations in Two Variables
6.1 Linear Equations in Two Variables
6.2 Slope of a Line
6.3 Slope-Intercept Form of a Line
Midchapter Review
6.4 Point-Slope Formula
6.5 Connections to Graphing: Applications of Linear Equations
7 Systems of Linear Equations in Two Variables
7.1 Introduction to Systems of Linear Equations
7.2 Substitution Method
7.3 Addition Method
Midchapter Review
7.4 Applications of Linear Equations in Two Variables
7.5 Connections to Graphing: Linear Inequalities in Two Variables
8 Radicals
8.1 Introduction to Roots and Radicals
8.2 Properties of Radicals
8.3 Addition and Subtraction of Radicals
8.4 Multiplication of Radicals
Midchapter Review
8.5 Rationalization
8.6 Radical Equations
8.7 Rational Exponents
9 Functions, Complex Numbers, and Quadratic Equations
9.1 Introductions to Functions and Function Notation