Intermediate Algebra

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.

Chapter 1: Real Numbers and Basic Geometry Concepts

1.1 Sets of Numbers

1.2 Operations on Real Numbers

1.3 Algebraic Expressions and Properties of Real Numbers

Chapter 2: Linear Equations and Inequalities in One Variable

2.1 Solving Linear Equations in One Variable

2.2 Applications of Linear Equations

2.3 Geometry Applications and Solving Formulas

2.4 More Applications of Linear Equations

2.5 Linear Inequalities in One Variable

2.6 Compound Inequalities in One Variable

2.7 Absolute Value Equations and Inequalities

Chapter 3: Linear Equations in Two Variables and Functions

3.1 Introduction to Linear Equations in Two Variables

3.2 Slope of a Line and Slope-Intercept Form

3.3 Writing an Equation of a Line

3.4 Linear and Compound Linear Inequalities in Two Variables

3.5 Introduction to Functions

Chapter 4: Solving Systems of Linear Equations

4.1 Solving Systems of Linear Equations in Two Variables

4.2 Solving Systems of Linear Equations in Three Variables

4.3 Applications of Systems of Linear Equations

4.4 Solving Systems of Linear Equations Using Matrices

Chapter 5: Polynomials and Polynomial Functions

5.1 The Rules of Exponents

5.2 More on Exponents and Scientific Notation

5.3 Addition and Subtraction of Polynomials and Polynomial Functions

5.4 Multiplication of Polynomials and Polynomial Functions

5.5 Division of Polynomials and Polynomial Functions

Chapter 6: Factoring Polynomials

6.1 The Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring Techniques

Putting It All Together

6.4 Solving Quadratic Equations by Factoring

6.5 Applications of Quadratic Equations

Chapter 7: Rational Expressions, Equations, and Functions

7.1 Simplifying, Multiplying, and Dividing Rational Expressions and Functions

7.2 Adding and Subtracting Rational Expressions

7.3 Simplifying Complex Fractions

7.4 Solving Rational Equations

Putting It All Together

7.5 Applications of Rational Equations

7.6 Variation

Chapter 8: Radicals and Rational Exponents

8.1 Radical Expressions and Functions

8.2 Rational Exponents

8.3 Simplifying Expressions Containing Square Roots

8.4 Simplifying Expressions Containing Higher Roots

8.5 Adding, Subtracting, and Multiplying Radicals

8.6 Dividing Radicals

Putting It All Together

8.7 Solving Radical Equations

8.8 Complex Numbers

Chapter 9: Quadratic Equations and Functions

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

Putting It All Together

9.3 Equations in Quadratic Form

9.4 Formulas and Applications

9.5 Quadratic Functions and Their Graphs

9.6 Applications of Quadratic Functions and Graphing Other Parabolas

9.7 Quadratic and Rational Inequalities

Chapter 10: Exponential, and Logarithmic Functions

10.1 Composite and Inverse Functions

10.2 Exponential Functions

10.3 Logarithmic Functions

10.4 Properties of Logarithms

10.5 Common and Natural Logarithms and Change of Base

10.6 Solving Exponential and Logarithmic Equation

Chapter 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

11.1 Graphs of Other Useful Functions

11.2 The Distance Formula, Midpoint, and Circle

11.3 The Ellipse

11.4 The Hyperbola

Putting It All Together

11.5 Nonlinear Systems of Equations

11.6 Second-Degree Inequalities and Systems of Inequalities

Chapter 12: Sequences and Series (Online Only)

12.1 Sequences and Series

12.2 Arithmetic Sequences and Series

12.3 Geometric Sequences and Series

12.4 The Binomial Theorem

A Appendix

A.1 Geometry Review

A.2 Determinants and Cramer’s Rule

A.3 Graphing Polynomial Functions

A.4 Synthetic Division and the Remainder Theorem