Intermediate Algebra: The Language and Symbolism of Mathematics

1 REVIEW OF BEGINNING ALGEBRA

1.1 Preparing for an Algebra Class

1.2 The Real Number Line and Algebraic Expressions

1.3 Operations with Real Numbers

1.4 Exponents and Order of Operations

1.5 Properties of Exponents and Scientific Notation

1.6 Solving Linear Equations in One Variable

1.7 Ratios, Proportions, and Direct Variation

1.8 Using and Rearranging Formulas

2 AN INTRODUCTION TO FUNCTIONS AND LINEAR MODELING

2.1 The Rectangular Coordinate System, Tables, and Graphs

2.2 Functions and Representations of Functions

2.3Linear Functions

2.4 Slope of a Line and Applications of Slope

2.5 Special Forms of Linear Equations In Two Variables

2.6 Properties of the Graphs of Linear and Absolute Value Functions

2.7 Curve Fitting - Selecting the Line of Best Fit

3 LINEAR EQUATIONS AND SYSTEMS OF LINEAR EQUATIONS

3.1 Applications of Linear Equations

3.2 Solving Systems of Linear Equations In Two Variables Graphically and Numerically

3.3 Solving Systems of Linear Systems In Two Variables by the Substitution Method

3.4 Solving Systems of Linear Systems In Two Variables by the Addition Method

3.5 More Applications of Linear Systems

3.6 Solving Systems of Linear Equations Using Augmented Matrices

3.7 Systems of Linear equations in Three Variables

4 LINEAR INEQUALITIES AND SYSTEMS OF LINEAR INEQUALITIES

4.1 Solving Linear Inequalities in One Variable

4.2 Solving Compound Inequalities

4.3 Solving Absolute Value Equations and Inequalities

4.4 Graphing Systems of Linear Inequalities in Two Variables

5 POLYNOMIALS AND POLYNOMIAL FUNCTIONS

5.1 Polynomials and Properties of the Graphs of Polynomial Functions

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials and Special Products

5.4 An Introduction to Factoring

5.5 Factoring Trinomials of the Form ax²+bx+c

5.6 A General Strategy for Factoring Polynomials

5.7 Solving Equations by Factoring

6 QUADRATIC FUNCTIONS

6.1 Quadratic Functions, Parabolas, and Modeling Using Quadratic Equations

6.2 Solving Quadratic Equations by Inequalities by Factoring

6.3 Using the Quadratic Formula to Find Real Solutions

6.4 More Applications of Quadratic Equations

6.5 Complex Numbers

6.6 Solving Quadratic Equations with Complex Solutions

7 RATIONAL FUNCTIONS

7.1 Properties of the Graphs of Rational Functions and Reducing Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions

7.4 Combining Operations and Simplifying Complex Rational Expressions

7.5 Dividing Polynomials

7.6 Solving Equations Containing Rational Expressions

7.7 Inverse and Joint Variation and Other Applications Yielding Equations with Fractions

8 SQUARE ROOT AND CUBE ROOT FUNCTIONS AND RATIONAL EXPONENTS

8.1 Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

8.2 Adding and Subtracting Radical Expressions

8.3 Multiplying and Dividing Radical Expressions

8.4 Solving Equations Containing Radical Expressions

8.5 Rational Exponents and Radicals

9 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

9.1 Geometric Sequences and Properties of the Graphs of Exponential Functions

9.2 Inverse Functions

9.3 Logarithmic Functions

9.4 Evaluating Logarithms

9.5 Properties of Logarithms

9.6 Solving Exponential and Logarithmic Equations

9.7 Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations

10 A PREVIEW OF COLLEGE ALGEBRA

10.1 Horizontal and Vertical Translations of the Graphs of Functions

10.2 Stretching, Shrinking, and Reflecting Graphs of Functions

10.3 Algebra of Functions

10.4 Sequences, Series, and Summation Notation

10.5 Conic Sections