1. Variables, Real Numbers, and Mathematical Models
1.1 Introduction to Algebra: Variables and Mathematical Models
1.2 Fractions in Algebra
1.3 The Real Numbers
1.4 Basic Rules of Algebra
Mid-Chapter Check Point
1.5 Addition of Real Numbers
1.6 Subtraction of Real Numbers
1.7 Multiplication and Division of Real Numbers
1.8 Exponents and Order of Operations
2. Linear Equations and Inequalities in One Variable
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Solving Linear Equations
2.4 Formulas and Percents
Mid-Chapter Check Point
2.5 An Introduction to Problem Solving
2.6 Problem Solving in Geometry
2.7 Solving Linear Inequalities
3. Linear Equations in Two Variables
3.1 Graphing Linear Equations in Two Variables
3.2 Graphing Linear Equations Using Intercepts
3.3 Slope
3.4 The Slope-Intercept Form of the Equation of a Line
Mid-Chapter Check Point
3.5 The Point-Slope Form of the Equation of a Line
4. Systems of Linear Equations
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by the Substitution Method
4.3 Solving Systems of Linear Equations by the Addition Method
Mid-Chapter Check Point
4.4 Problem Solving Using Systems of Equations
4.5 Systems of Linear Equations in Three Variables
5. Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.2 Multiplying Polynomials
5.3 Special Products
5.4 Polynomials in Several Variables
Mid-Chapter Check Point
5.5 Dividing Polynomials
5.6 Long Division of Polynomials; Synthetic Division
5.7 Negative Exponents and Scientific Notation
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials Whose Leading Coefficient is 1
6.3 Factoring Trinomials Whose Leading Coefficient is Not 1
Mid-Chapter Check Point
6.4 Factoring Special Forms
6.5 A General Factoring Strategy
6.6 Solving Quadratic Equations by Factoring
7. Rational Expressions
7.1 Rational Expressions and Their Simplification
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
Mid-Chapter Check Point
7.5 Complex Rational Expressions
7.6 Solving Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Modeling Using Variation
8. Basics of Functions
8.1 Introduction to Functions
8.2 Graphs of Functions
8.3 The Algebra of Functions
Mid-Chapter Check Point
8.4 Composite and Inverse Functions
9. Inequalities and Problem Solving
9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications
9.2 Compound Inequalities
9.3 Equations and Inequalities Involving Absolute Value
Mid-Chapter Check Point
9.4 Linear Inequalities in Two Variables
10. Radicals, Radical Functions, and Rational Exponents
10.1 Radical Expressions and Functions
10.2 Rational Exponents
10.3 Multiplying and Simplifying Radical Expressions
10.4 Adding, Subtracting, and Dividing Radical Expressions
Mid-Chapter Check Point
10.5 Multiplying with More Than One Term and Rationalizing Denominators
10.6 Radical Equations
10.7 Complex Numbers
11. Quadratic Equations and Functions
11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formula
11.2 The Quadratic Formula
11.3 Quadratic Functions and Their Graphs
Mid-Chapter Check Point
11.4 Equations Quadratic in Form
11.5 Polynomial and Rational Inequalities
12. Exponential and Logarithmic Functions
12.1 Exponential Functions
12.2 Logarithmic Functions
12.3 Properties of Logarithms
Mid-Chapter Check Point
12.4 Exponential and Logarithmic Equations
12.5 Exponential Growth and Decay; Modeling Data
13. Conic Sections and Systems of Nonlinear Equations
13.1 The Circle
13.2 The Ellipse
13.3 The Hyperbola
Mid-Chapter Check Point
13.4 The Parabola; Identifying Conic Sections
13.5 Systems of Nonlinear Equations in Two Variables
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences and Summation Notation
14.2 Arithmetic Sequences
14.3 Geometric Sequences
Mid-Chapter Check Point
14.4 The Binomial Theorem
