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Intermediate Algebra 4e

Reference: Review of Basic Algebraic Concepts

R.1 Study Skills

R.2 Sets of Numbers and Interval Notation

R.3 Operations of Real Numbers

R.4 Simplifying Algebraic Expressions

Chapter 1: Linear Equations and Inequalities in One Variable

1.1 Linear Equations in One Variable

Problem Recognition Exercises-Equations versus Expressions

1.2 Applications of Linear Equations in One Variable

1.3 Applications of Geometry and Literal Equations

1.4 Linear Inequalities in One Variable

1.5 Compound Inequalities

1.6 Absolute Value Equations

1.7 Absolute Value Inequalities

Problem Recognition Exercises-Identifying Equations and Inequalities

Chapter 2: Linear Equations in Two Variables and Functions

2.1 Linear Equations in Two Variables

2.2 Slope of a Line and Rate of Change

2.3 Equations of a Line

Problem Recognition Exercises-Characteristics of Linear Equations

2.4 Applications of Linear Equations and Modeling

2.5 Introduction to Relations

2.6 Introduction to Functions

2.7 Graphs of Functions

Problem Recognition Exercises-Characteristics of Relations

Chapter 3: Systems of Linear Equations and Inequalities

3.1 Solving Systems of Linear Equations by the Graphing Method

3.2 Solving Systems of Linear Equations by the Substitution Method

3.3 Solving Systems of Linear Equations by the Addition Method

Problem Recognition Exercises-Solving Systems of Linear Equations

3.4 Applications of Systems of Linear Equations in Two Variables

3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

3.6 Systems of Linear Equations in Three Variables and Applications

3.7 Solving Systems of Linear Equations by Using Matrices

Chapter 4: Polynomials

4.1 Properties of Integer Exponents and Scientific Notation

4.2 Addition and Subtraction of Polynomials and Polynomials Functions

4.3 Multiplication of Polynomials

4.4 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

4.5 Greatest Common Factor and Factoring by Grouping

4.6 Factoring Trinomials

4.7 Factoring Binomials

Problem Recognition Exercises-Factoring Summary

4.8 Solving Equations by Using the Zero Product Rule

Chapter 5: Rational Expressions and Rational Equations

5.1 Rational Expressions and Rational Functions

5.2 Multiplication and Division of Rational Expressions

5.3 Addition and Subtraction of Rational Expressions

5.4 Complex Fractions

Problem Recognition Exercises-Operations on Rational Expressions

5.5 Solving Rational Equations

Problem Recognition Exercises-Rational Equations versus Expressions

5.6 Applications of Rational Equations and Proportions


Chapter 6: Radicals and Complex Numbers

6.1 Definition of an nth Root

6.2 Rational Exponents

6.3 Simplifying Radical Expressions

6.4 Addition and Subtraction of Radicals

6.5 Multiplication of Radicals

Problem Recognition Exercises-Simplifying Radical Expressions

6.6 Division of Radicals and Rationalization

6.7 Solving Radical Equations

6.8 Complex Numbers

Chapter 7: Quadratic Equations, Functions and Inequalities

7.1 Square Root Property and Completing the Square

7.2 Quadratic Formula

7.3 Equations in Quadratic Form

Problem Recognition Exercises-Quadratic and Quadratic Type Equations

7.4 Graphs of Quadratic Functions

7.5 Vertex of a Parabola: Applications and Modeling

7.6 Polynomial and Rational Inequalities

Problem Recognition Exercises-Recognizing Equations and Inequalities

Chapter 8: Exponential and Logarithmic Functions and Applications

8.1 Algebra of Functions and Composition

8.2 Inverse Functions

8.3 Exponential Functions

8.4 Logarithmic Functions

Problem Recognition Exercises-Identifying Graphs of Functions

8.5 Properties of Logarithms

8.6 The Irrational Number e and Change of Base

Problem Recognition Exercises-Logarithmic and Exponential Forms

8.7 Logarithmic and Exponential Equations and Applications

Chapter 9: Conic Sections

9.1 Distance Formula, Midpoint Formula, and Circles

9.2 More on the Parabola

9.3 The Ellipse and Hyperbola

Problem Recognition Exercises-Formulas and Conic Sections

9.4 Nonlinear systems of Equations in Two Variables

9.5 Nonlinear Inequalities and Systems of Inequalities

Chapter 10: Binomial Expansions, Sequences, and Series

10.1 Binomial Expansions

10.2 Sequences and Series

10.3 Arithmetic Sequences and Series

10.4 Geometric Sequences and Series

Problem Recognition Exercises-Identifying Arithmetic and Geometric Series

Additional Topics Appendix

A.1 Determinants and Cramer’s Rule