Beginning and Intermediate Algebra: The Language & Symbolism of Mathematics

1 Operations with Real Numbers and a Review of Geome

1.1 Preparing for an Algebra Class

1.2 The Real Number Line

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

1.5 Multiplication of Real Numbers and Natural Number Exponents

1.6 Division of Real Numbers

1.7 Order of Operations

2 Linear Equations and Patterns

2.1 The Rectangular Coordinate System and Arithmetic Sequences

2.2 Function Notation and Linear Functions

2.3 Graphs of Linear Equations in Two Variables

2.4 Solving Linear Equations in One Variable by Using the Addition-Subtraction Principle

2.5 Solving Linear Equations in One Variable by Using the Multiplication-Division Principle

2.6 Using and Rearranging Formulas

2.7 Proportions and Direct Variation

2.8 More Applications of Linear Equations

3 Lines and Systems of Linear Equations in Two Variables

3.1 Slope of a Line and Applications of Slope

3.2 Special Forms of Linear Equations in Two Variables

3.3 Solving Systems of Linear Equations in Two Variables Graphically and Numerically

3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method

3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method

3.6 More Applications of Linear Systems

4 Linear Inequalities and Systems of Linear Inequalities

4.1 Solving Linear Inequalities by Using the Addition-Subtraction Principle

4.2 Solving Linear Inequalities by Using the Multiplication-Divison Principle

4.3 Solving Compound Inequalities

4.4 Solving Absolute Value Equations and Inequalities

4.5 Graphing Systems of Linear Inequalities in Two Variables

5 Exponents and Operations with Polynomials

5.1 Product and Power Rules for Exponents

5.2 Quotient Rule and Zero Exponents

5.3 Negative Exponents and Scientific Notation

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6 Special Products of Binomials

5.7 Dividing Polynomials

6 Factoring Polynomials

6.1 An Introduction to Factoring Polynomials

6.2 Factoring Trinomials of the Form x2 + bxy + cy2

6.3 Factoring Trinomials of the Form ax2 + bxy + cy2

6.4 Factoring Special Forms

6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials

6.6 Solving Equations by Factoring

7 Solving Quadratic Equations

8 Functions: Linear, Absolute Value, and Quadratic

8.1 Functions and Representations of Functions

8.2 Linear and Absolute Value Functions

8.3 Linear and Quadratic Functions and Curve Fitting

8.4 Using the Quadratic Formula to find Real Solutions

8.5 The Vertex of a Parabola and Max-Min Applications

8.6 More Applications of Quadratic Equations

8.7 Complex Numbers and Solving Quadratic Equations with Complex Solutions

9 Rational Functions

9.1 Graphs of Rational Functions and Reducing Rational Expressions

9.2 Multiplying and Dividing Rational Expressions

9.3 Adding and Subtracting Rational Expressions

9.4 Combining Operations and Simplifying Complex Rational Expressions

9.5 Solving Equations Containing Rational Expressions

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

10 Square Root and Cube Root Functions and Rational Exponents

10.1 Evaluating Radical Expressions and Graphs of Square Root and Cube Root Functions

10.2 Adding and Subtracting Radical Expressions

10.3 Multiplying and Dividing Radical Expressions

10.4 Solving Equations Containing Radical Expressions

10.5 Rational Exponents and Radicals

11 Exponential and Logarithmic Functions

11.1 Geometric Sequences Graphs of Exponential Functions

11.2 Inverse Functions

11.3 Logarithmic Functions

11.4 Evaluating Logarithms

11.5 Properties of Logarithms

11.6 Solving Exponential and Logarithmic Equations

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

12 A Preview of College Algebra

12.1 Solving Systems of Linear Equations by Using Augmented Matrices

12.2 Systems of Linear Equations in Three Variables

12.3 Horizontal and Vertical Translations of the Graphs of Functions

12.4 Stretching, Shrinking and Reflecting Graphs of Functions

12.5 Algebra of Functions

12.6 Sequences, Series and Summation Notation

12.7 Conic Sections

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