Throughout this text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format, pairing each example with a corresponding practice exercise, encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section. Mindstretchers incorporate related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and cultural connections. To show how mathematics has evolved over the centuries, in many cultures, and throughout the world, each chapter features a compelling Cultural Note that investigates and illustrates the origins of mathematical concepts. Diverse topics include art, music, the evolution of digit notation, and the ancient practice of using a scale to find an unknown weight.
R. Prealgebra Review
R.1 Exponents and Order of Operations
R.2 Factors, Primes, and Least Common Multiples
R.3 Fractions
R.4 Decimals
R.5 Percents
1. Real Numbers and Algebraic Expressions
1.1 Real Numbers and the Real Number Line
1.2 Addition of Real Numbers
1.3 Subtraction of Real Numbers
1.4 Multiplication and Division of Real Numbers
1.5 Properties of Real Numbers
1.6 Algebraic Expressions, Translations, and Exponents
1.7 Simplifying Algebraic Expressions
1.8 Translating and Evaluating Algebraic Expressions
2. Solving Linear Equations and Inequalities
2.1 Solving Linear Equations: the Addition Property
2.2 Solving Linear Equations: the Multiplication Property
2.3 Solving Linear Equations by Combining Properties
2.4 Applications of Linear Equations: Formulas
2.6 Solving Linear Inequalities
3. Graphing Linear Equations and Inequalities; Functions
3.1 The Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 Slope of a Line
3.4 Linear Equations and their Graphs
3.5 Graphing Linear Inequalities
3.6 Introduction to Functions
4. Systems of 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
4.4 Solving Systems of Linear Inequalities
5. Exponents and Polynomials
5.1 Laws of Exponents
5.2 Negative Exponents and Scientific Notation
5.3 Addition and Subtraction of Polynomials
5.4 Multiplication of Polynomials
5.5 Special Products
5.6 Division of Polynomials
6. Factoring Polynomials
6.1 Common Factors and Factoring by Grouping
6.2 Factoring Trinomials Whose Leading Coefficient is One
6.3 Factoring Trinomials Whose Leading Coefficient is not One
6.4 Special Factoring
6.5 More on Factoring and Factoring Strategies
6.6 Solving Quadratic Equations by Factoring
7. Rational Expressions and Equations
7.1 Rational Expressions and Functions
7.2 Multiplication and Division of Rational Expressions
7.3 Addition and Subtraction of Rational Expressions
7.4 Complex Rational Expressions
7.5 Solving Rational equations
7.6 Ratio and Proportion; Variation
8. Radical Expressions and Equations
8.1 Rational Exponents
8.2 Radical Expressions and Functions
8.3 Simplifying Radical Expressions
8.4 Addition and Subtraction of Radical Expressions
8.5 Multiplication and Division of Radical Expressions
8.6 Solving Radical Equations
8.7 Complex Numbers
9. Quadratic Equations, Functions, and Inequalities
9.1 Solving Quadratic Equations: Square Root Property and Completing the Square
9.2 Solving Quadratic Equations: Quadratic Formula
9.3 More on Quadratic Equations
9.4 Graphing Quadratic Functions
9.5 Compound Inequalities and Solving Quadratic and Rational Inequalities
10. Exponential and Logarithmic Functions
10.1 More on Functions; the Algebra of Functions
10.2 Inverse Functions
10.3 Exponential Functions
10.4 Logarithmic Functions
10.5 Properties of Logarithms
10.6 Common Logarithms, Natural Logarithms, and Change of Bases
10.7 Exponential and Logarithmic Equations
11. Conic Sections and Nonlinear Systems
11.1 Introduction to Conics; the Parabola
11.2 The Circle
11.3 The Ellipse and the Hyperbola
11.4 Solving Nonlinear Systems of Equations
11.5 Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities
Appendix A
A.1 Review Solving Linear Equations and Inequalities
A.2 Absolute Value Equations and Inequalities
A.3 More on Systems of Linear Equations
A.4 Solving Systems of Linear Equations by Using Matrices
Appendix B
B.1 Determinants / Cramer’s Rule
B.2 Synthetic Division and the Remainder Theorem
B.3 Sequences (Arithmetic and Geometric)
B.4 Series