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Chapter 1 Foundations of Algebra

1.1 Number Sets and the Structure of Algebra

1.2 Fractions

1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers

1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers

1.5 Exponents, Roots, and Order of Operations

1.6 Translating Word Phrases to Expressions

1.7 Evaluating and Rewriting Expressions

Chapter 2 Solving Linear Equations and

Inequalities

2.1 Equations, Formulas, and the Problem-Solving Process

2.2 The Addition Principle

2.3 The Multiplication Principle

2.4 Applying the Principles to Formulas

2.5 Translating Word Sentences to Equations

2.6 Solving Linear Inequalities

Chapter 3 Problem Solving

3.1 Ratios and Proportions

3.2 Percents

3.3 Problems with Two or More Unknowns

3.4 Rates

3.5 Investment and Mixture

Chapter 4 Graphing Linear Equations and

Inequalities

4.1 The Rectangular Coordinate System

4.2 Graphing Linear Equations

4.3 Graphing Using Intercepts

4.4 Slope-Intercept Form

4.5 Point-Slope Form

4.6 Graphing Linear Inequalities

4.7 Introduction to Functions and Function

Notation

Chapter 5 Polynomials

5.1 Exponents and Scientific Notation

5.2 Introduction to Polynomials

5.3 Adding and Subtracting Polynomials

5.4 Exponent Rules and Multiplying

Monomials

5.5 Multiplying Polynomials; Special Products

5.6 Exponent Rules and Dividing Polynomials

Chapter 6 Factoring

6.1 Greatest Common Factor and Factoring by

Grouping

6.2 Factoring Trinomials of the Form

x2 + bx + c

6.3 Factoring Trinomials of the Form

ax2 + bx + c, where a ≠ 1

6.4 Factoring Special Products

6.5 Strategies for Factoring

6.6 Solving Quadratic Equations by Factoring

6.7 Graphs of Quadratic Equations and

Functions

Chapter 7 Rational Expressions and

Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational

Expressions

7.3 Adding and Subtracting Rational

Expressions with the Same Denominator

7.4 Adding and Subtracting Rational

Expressions with Different Denominators

7.5 Complex Rational Expressions

7.6 Solving Equations Containing Rational

Expressions

7.7 Applications with Rational Expressions

Chapter 8 More on Inequalities, Absolute

Value and Functions

8.1 Compound Inequalities

8.2 Equations Involving Absolute Value

8.3 Inequalities Involving Absolute Value

8.4 Functions and Graphing

8.5 Function Operations

Chapter 9 Systems of Equations

9.1 Solving Systems of Linear Equations

Graphically

9.2 Solving Systems of Linear Equations by

Substitution

9.3 Solving Systems of Linear Equations by

Elimination

9.4 Solving Systems of Linear Equations in

Three Variables

9.5 Solving Systems of Linear Equations

Using Matrices

9.6 Solving Systems of Linear Equations

Using Cramer’s Rule

9.7 Solving Systems of Linear Inequalities

Chapter 10 Rational Exponents, Radicals,

and Complex Numbers

10.1 Radical Expressions and Functions

10.2 Rational Exponents

10.3 Multiplying, Dividing, and Simplifying

Radicals

10.4 Adding, Subtracting, and Multiplying

Radical Expressions

10.5 Rationalizing Numerators and

Denominators of Radical Expressions

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

Chapter 11 Quadratic Equations

11.1 Completing the Square

11.2 Solving Quadratic Equations Using the

Quadratic Formula

11.3 Solving Equations That Are Quadratic in

Form

11.4 Graphing Quadratic Functions

11.5 Solving Nonlinear Inequalities

Chapter 12 Exponential and Logarithmic

Functions

12.1 Composite and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithms

12.5 Common and Natural Logarithms

12.6 Exponential and Logarithmic Equations

with Applications

Chapter 13 Conic Sections

13.1 The Parabola and the Circle

13.2 Ellipses and Hyperbolas

13.3 Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of

Inequalities