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Summary
For Intermediate Algebra courses including lecture-based, self-paced, discussion oriented, and modular classes.This clear, accessible treatment of mathematics features a building-block approach toward problem solving and realistic, diverse applications. Students practice problem solving and decision making with interesting applications throughout the text. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present students with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life.The problem solving strategy, highlighted by *A Mathematics Blueprint for Problem Solving, helps students determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. Chapter organizers help students focus their study on the concepts and examples. Developing Your Study Skills boxes throughout the text give students tips to help them improve their study skills. These features, together with the applications and emphasis on problem solving, help students to become effective and confident problem solvers.*Please note: A Mathematics Blueprint for Problem Solving is not a feature of Intermediate Algebra.
Table of Contents
1. Basic Concepts.
The Real Number System. Operations with Real Numbers. Powers, Square Roots, and the Order of Operations. Integer Exponents and Scientific Notation. Operations with Variables and Grouping Symbols. Evaluating Variable Expressions and Formulas.
2. Linear Equations and Inequalities.
First-Degree Equations with One Unknown. Literal Equations and Formulas. Absolute Value Equations. Using Equations to Solve Word Problems. Solving More Involved Word Problems. Linear Inequalities. Compound Inequalities. Absolute Value Inequalities.
3. Equations and Inequalities in Two Variables and Functions.
Graphing Linear Equations with Two Unknowns. Slope of a Line. Graphs and the Equations of a Line. Linear Inequalities in Two Variables. Concept of a Function. Graphing Functions from Equations and Tables of Data.
4. Systems of Linear Equations and Inequalities.
Systems of Equations in Two Variables. Systems of Equations in Three Variables. Applications of Systems of Linear Equations. Systems of Linear Inequalities.
5. Polynomials.
Introduction to Polynomials and Polynomial Functions: Addition, Subtraction and Multiplication. Division of Polynomials. Synthetic Division. Removing Common Factors: Factoring by Grouping. Factoring Trinomials. Special Cases of Factoring. Factoring a Polynomial Completely. Solving Equations and Exercises Using Polynomials.
6. Rational Expressions and Equations.
Rational Expressions and Functions: Simplifying, Multiplying, and Dividing. Addition and Subtraction of Rational Expressions. Complex Rational Expressions. Rational Equations. Applications: Formulas and Advanced Ratio Exercises.
7. Rational Exponents and Radicals.
Rational Exponents. Radical Expressions and Functions. Simplifying, Adding, and Subtracting Radicals. Multiplication and Division of Radicals. Radical Equations. Complex Numbers. Variation.
8. Quadratic Equations and Inequalities.
Quadratic Equations. The Quadratic Formula and Solutions to Quadratic Equations. Equations That Can Be Transformed to Quadratic Form. Formulas and Applications. Quadratic Functions. Quadratic Inequalities in One Variable.
9. The Conic Sections.
The Distance Formula and the Circle. The Parabola. The Ellipse. The Hyperbola. Nonlinear Systems of Equations.
10. Additional Properties of Functions.
Function Notation. General Graphing Procedures for Functions. Algebraic Operations on Functions. Inverse of a Function.
11. Logarithmic and Exponential Functions.
The Exponential Function. The Logarithmic Function. Properties of Logarithms. Finding Logarithmic Function Values on a Calculator. Exponential and Logarithmic Equations.