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# Beginning and Intermediate Algebra

**by**Messersmith, Sherri

3rd

### 9780073384375

0073384372

Hardcover

1/6/2011

McGraw-Hill Education

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## Summary

Building a Better Path to Success! Connecting Knowledge Sherri prepares her students for success by refreshing their knowledge of arithmetic. By helping students see the connection between arithmetic and algebra, Sherri found that her students were more confident in their abilities as they progressed through the course. This classroom tested practice was integrated into the texts so that both instructors and students could benefit. Messersmith accomplishes this by including arithmetic examples for most sections before the use of algebraic examples. Also, the author has developed through classroom use a series of Basic Skills Worksheets that can easily be integrated into the classroom. Presenting Concepts in "Bite Size" Pieces By breaking down the sections into manageable pieces, the author has identified the core places where students traditionally struggle and then assists them in understanding that material to be successful moving forward. Mastering Concepts- With the textbook and Connect Mathematics hosted by ALEKS, a new online homework and assessment tool, students can practice and master their understanding of algebraic concepts. Messersmith is rigorous enough to prepare students for the next level yet easy to read and understand. The exposition is written as if a professor is teaching in a lecture to be more accessible to students. The language is mathematically sound yet easy enough for students to understand.

## Table of Contents

** Chapter 1: The Real Number System and Geometry**

#### 1.1 Review of Fractions

#### 1.2 Exponents and Order of Operations

#### 1.3 Geometry Review

#### 1.4 Sets of Numbers and Absolute Value

#### 1.5 Addition and Subtraction of Real Numbers

#### 1.6 Multiplication and Division of Real Numbers

#### 1.7 Algebraic Expressions and Properties of Real Numbers

** Chapter 2: The Rules of Exponents**

#### 2.1 Basic Rules of Exponents

##### Part A The Product Rule and Power Rules

##### Part B Combining the Rules

#### 2.2 Integer Exponents

##### Part A Real-Number Bases

##### Part B Variable Bases

#### 2.3 The Quotient Rule

#### Putting It All Together

#### 2.4 Scientific Notation

** Chapter 3: Linear Equations and Inequalities**

#### 3.1 Solving Linear Equations Part I

#### 3.2 Solving Linear Equations Part II

#### 3.3 Applications of Linear Equations

#### 3.4 Applications Involving Percentages

#### 3.5 Geometry Applications and Solving Formulas

#### 3.6 Applications of Linear Equations to Proportions, Money Problems, and d=rt

#### 3.7 Solving Linear Inequalities in One Variable

#### 3.8 Solving Compound Inequalities

** Chapter 4: Linear Equations in Two Variables**

#### 4.1 Introduction to Linear Equations in Two Variables

#### 4.2 Graphing by Plotting Points and Finding Intercepts

#### 4.3 The Slope of a Line

#### 4.4 The Slope-Intercept Form of a Line

#### 4.5 Writing an Equation of a Line

#### 4.6 Introduction to Functions

** Chapter 5: Solving Systems of Linear Equations**

#### 5.1 Solving Systems by Graphing

#### 5.2 Solving Systems by Substitution

#### 5.3 Solving Systems by the Elimination Method

#### Putting It All Together

#### 5.4 Applications of Systems of Two Equations

#### 5.5 Systems of Three Equations and Applications

** Chapter 6: Polynomials**

#### 6.1 Review of the Rules of Exponents

#### 6.2 Addition and Subtraction of Polynomials

#### 6.3 Multiplication of Polynomials

#### 6.4 Division of Polynomials

** Chapter 7: Factoring Polynomials**

#### 7.1 The Greatest Common Factor and Factoring by Grouping

#### 7.2 Factoring Trinomials of the Form x2+bx+c

#### 7.3 Factoring Trinomials of the Form ax2+bx+c (a≠1)

#### 7.4 Factoring Special Trinomials and Binomials

#### Putting It All Together

#### 7.5 Solving Quadratic Equations by Factoring

#### 7.6 Applications of Quadratic Equations

** Chapter 8: Rational Expressions**

#### 8.1 Simplifying Rational Expressions

#### 8.2 Multiplying and Dividing Rational Expressions

#### 8.3 Finding the Least Common Denominator

#### 8.4 Adding and Subtracting Rational Expressions

#### Putting It All Together

#### 8.5 Simplifying Complex Fractions

#### 8.6 Solving Rational Equations

#### 8.7 Applications of Rational Equations

** Chapter 9: More Equations and Inequalities**#### 9.1 Solving Absolute Value Equations

#### 9.2 Solving Absolute Value Inequalities

#### 9.3 Solving Linear and Compound Linear Inequalities in Two Variables

#### 9.4 Solving Systems of Linear Equations Using Matrices

** Chapter 10: Radicals and Rational Exponents**

#### 10.1 Finding Roots

#### 10.2 Rational Exponents

#### 10.3 Simplifying Expressions Containing Square Roots

#### 10.4 Simplifying Expressions Containing Higher Roots

#### 10.5 Adding, Subtracting, and Multiplying Radicals

#### 10.6 Dividing Radicals

#### Putting It All Together

#### 10.7 Solving Radical Equations

#### 10.8 Complex Numbers

** Chapter 11: Quadratic Equations**

#### 11.1 Review of Solving Equations by Factoring

#### 11.2 The Square Root Property and Completing the Square

#### 11.3 The Quadratic Formula

#### Putting It All Together

#### 11.6 Equations in Quadratic Form

#### 11.7 Formulas and Applications

** Chapter 12: Functions and their Graphs**

#### 12.1 Relations and Functions

#### 12.2 Graphs of Functions and Transformations

#### 12.3 Quadratic Functions and Their Graphs

#### 12.4 Applications of Quadratic Functions and Graphing Other Parabolas

#### 12.5 The Algebra of Functions

#### 12.6 Variation

** Chapter 13: Exponential, and Logarithmic Functions **

#### 13.1 Inverse Functions

#### 13.2 Exponential Functions

#### 13.3 Logarithmic Functions

#### 13.4 Properties of Logarithms

#### 13.5 Common and Natural Logarithms and Change of Base

#### 13.6 Solving Exponential and Logarithmic Equations

** Chapter 14: Conic Sections, Nonlinear Inequalities, and Nonlinear Systems**

#### 14.1 The Circle

#### 14.2 The Ellipse and the Hyperbola

#### Putting It All Together

#### 14.3 Nonlinear Systems of Equations

#### 14.4 Quadratic and Rational Inequalities

** Chapter 15: Sequences and Series (Online Only)**

#### 15.1 Sequences and Series

#### 15.2 Arithmetic Sequences and Series

#### 15.3 Geometric Sequences and Series

#### 15.4 The Binomial Theorem

** Appendix: Beginning Algebra Review**

#### A1 The Real Number System and Geometry

#### A2 Variables and Exponents

#### A3 Linear Equations and Inequalities

#### A4 Linear Equations in Two Variables and Functions

#### A5 Solving Systems of Linear Equations

#### A6 Polynomials

#### A7 Factoring Polynomials

#### A8 Rational Expressions

#### 9.1 Solving Absolute Value Equations

#### 9.2 Solving Absolute Value Inequalities

#### 9.3 Solving Linear and Compound Linear Inequalities in Two Variables

#### 9.4 Solving Systems of Linear Equations Using Matrices

** Chapter 10: Radicals and Rational Exponents**

#### 10.1 Finding Roots

#### 10.2 Rational Exponents

#### 10.3 Simplifying Expressions Containing Square Roots

#### 10.4 Simplifying Expressions Containing Higher Roots

#### 10.5 Adding, Subtracting, and Multiplying Radicals

#### 10.6 Dividing Radicals

#### Putting It All Together

#### 10.7 Solving Radical Equations

#### 10.8 Complex Numbers

** Chapter 11: Quadratic Equations**

#### 11.1 Review of Solving Equations by Factoring

#### 11.2 The Square Root Property and Completing the Square

#### 11.3 The Quadratic Formula

#### Putting It All Together

#### 11.6 Equations in Quadratic Form

#### 11.7 Formulas and Applications

** Chapter 12: Functions and their Graphs**

#### 12.1 Relations and Functions

#### 12.2 Graphs of Functions and Transformations

#### 12.3 Quadratic Functions and Their Graphs

#### 12.4 Applications of Quadratic Functions and Graphing Other Parabolas

#### 12.5 The Algebra of Functions

#### 12.6 Variation

** Chapter 13: Exponential, and Logarithmic Functions **

#### 13.1 Inverse Functions

#### 13.2 Exponential Functions

#### 13.3 Logarithmic Functions

#### 13.4 Properties of Logarithms

#### 13.5 Common and Natural Logarithms and Change of Base

#### 13.6 Solving Exponential and Logarithmic Equations

** Chapter 14: Conic Sections, Nonlinear Inequalities, and Nonlinear Systems**

#### 14.1 The Circle

#### 14.2 The Ellipse and the Hyperbola

#### Putting It All Together

#### 14.3 Nonlinear Systems of Equations

#### 14.4 Quadratic and Rational Inequalities

** Chapter 15: Sequences and Series (Online Only)**

#### 15.1 Sequences and Series

#### 15.2 Arithmetic Sequences and Series

#### 15.3 Geometric Sequences and Series

#### 15.4 The Binomial Theorem