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Contents
Table of Contents
R. Prealgebra Review
R.1 Fractions
R.2 Decimals and Percents
Study Skills Using Your Math Text
The Real Number System
1.1 Exponents, Order of Operations, and Inequality
Study Skills Taking Lecture Notes
1.2 Variables, Expressions, and Equations
Study Skills Reading Your Math Text
1.3 Real Numbers and the Number Line
Study Skills Using Study Cards
1.4 Adding Real Numbers
1.5 Subtracting Real Numbers
Study Skills Completing Your Homework
1.6 Multiplying and Dividing Real Numbers
Summary Exercises Performing Operations with Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying Expressions
Study Skills Reviewing a Chapter
Equations, Inequalities, and Applications
2.1 The Addition Property of Equality
Study Skills Managing Your Time
2.2 The Multiplication Property of Equality
2.3 More on Solving Linear Equations
Study Skills Using Study Cards Revisited
Summary Exercises Applying Methods for Solving Linear Equations
2.4 An Introduction to Applications of Linear Equations
2.5 Formulas and Additional Applications from Geometry
2.6 Ratio, Proportion, and Percent
Summary Exercises Applying Problem-Solving Techniques
2.7 Solving Linear Inequalities
Study Skills Taking Math Tests
Graphs of Linear Equations and Inequalities in Two Variables
3.1 Linear Equations and Rectangular Coordinates
Study Skills Analyzing Your Test Results
3.2 Graphing Linear Equations in Two Variables
3.3 The Slope of a Line
3.4 Slope-Intercept Form of a Linear Equation
3.5 Point-Slope Form of a Linear Equation and Modeling
Summary Exercises Applying Graphing and
Equation-Writing Techniques for Lines
Study Skills Preparing for Your Math Final Exam
3.6 Graphing Linear Inequalities in Two Variables
Systems of Linear Equations and Inequalities
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Elimination
Summary Exercises Applying Techniques for Solving Systems of Linear Equations
4.4 Applications of Linear Systems
4.5 Solving Systems of Linear Inequalities
Exponents and Polynomials
5.1 The Product Rule and Power Rules for Exponents
5.2 Integer Exponents and the Quotient Rule
Summary Exercises Applying the Rules for Exponents
5.3 An Application of Exponents: Scientific Notation
5.4 Adding and Subtracting Polynomials
5.5 Multiplying Polynomials
5.6 Special Products
5.7 Dividing a Polynomial by a Monomial
5.8 Dividing a Polynomial by a Polynomial
Factoring and Applications
6.1 Greatest Common Factors; Factor by Grouping
6.2 Factoring Trinomials
6.3 Factoring Trinomials by Grouping
6.4 Factoring Trinomials Using the FOIL Method
6.5 Special Factoring Techniques
6.6 A General Approach to Factoring
6.7 Solving Quadratic Equations Using the Zero-Factor Property
6.8 Applications of Quadratic Equations
Rational Expressions and Applications
7.1 The Fundamental Property of Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Least Common Denominators
7.4 Adding and Subtracting Rational Expressions
7.5 Complex Fractions
7.6 Solving Equations with Rational Expressions
Summary Exercises Simplifying Rational Expressions vs. Solving Rational Equations
7.7 Applications of Rational Expressions
7.8 Variation
Equations, Inequalities, Graphs, and Systems Revisited
8.1 Review of Solving Linear Equations and Inequalities in one Variable
8.2 Set Operations and Compound Inequalities
8.3 Absolute Value Equations and Inequalities
Summary Exercises Solving Linear and Absolute Value Equations and Inequalities
8.4 Review of Graphing Linear Equations in Two Variables; Slope
8.6 Systems of Linear Equations in Three Variables; Applications
Relations and Functions
9.1 Introduction to Relations and Functions
9.2 Function Notation and Linear Functions
9.3 Polynomial Functions, Operations, and Graphs
9.4 Variation
Roots, Radicals, and Root Functions
10.1 Radical Expressions and Graphs
10.2 Rational Exponents
10.3 Simplifying Radical Expressions
10.4 Adding and Subtracting Radical Expressions
10.5 Multiplying and Dividing Radical Expressions
Summary Exercises Performing Operations with Radicals and Rational Exponents
10.6 Solving Equations with Radicals
10.7 Complex Numbers
Quadratic Equations, Inequalities, and Functions
11.1 Solving Quadratic Equations by the Square Root Property
11.2 Solving Quadratic Equations by Completing the Square
11.3 Solving Quadratic Equations by the Quadratic Formula
11.4 Equations Quadratic in Form
Summary Exercises Applying Methods for Solving Quadratic Equations
11.5 Formulas and Further Applications
11.6 Graphs of Quadratic Functions
11.7 More about Parabolas and Their Applications
11.8 Polynomial and Rational Inequalities
Inverse, Exponential, and Logarithmic Functions
12.1 Composition of Functions
12.2 Inverse Functions
12.3 Exponential Functions
12.4 Logarithmic Functions
12.5 Properties of Logarithms
12.6 Common and Natural Logarithms
12.7 Exponential and Logarithmic Equations and Their Applications
Nonlinear Functions, Conic Sections, and Nonlinear Systems
13.1 Additional Graphs of Functions
13.2 Circles and Ellipses
13.3 Hyperbolas and Functions Defined by Radicals
13.4 Nonlinear Systems of Equations
13.5 Second-Degree Inequalities and Systems of Inequalities
Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra) Appendix B: Synthetic Division Appendix C: Solving Systems of Linear Equations by Matrix Methods Answers to Selected Exercises Index
