| |
| |
| |
| Linear Equations and Inequalities in One Variable | |
| |
| |
| |
| Linear Equations in One Variable | |
| |
| |
| Problem Recognition Exercises: Equations versus Expressions | |
| |
| |
| |
| Applications of Linear Equations in One Variable | |
| |
| |
| |
| Applications to Geometry and Literal Equations | |
| |
| |
| |
| Linear Inequalities in One Variable | |
| |
| |
| |
| Compound Inequalities | |
| |
| |
| |
| Absolute Value Equations | |
| |
| |
| |
| Absolute Value Inequalities | |
| |
| |
| Problem Recognition Exercises: Identifying Equations and Inequalities | |
| |
| |
| Group Activity: Understanding the Symbolism of Mathematics | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Linear Equations in Two Variables and Functions | |
| |
| |
| |
| Linear Equations in Two Variables | |
| |
| |
| |
| Slope of a Line and Rate of Change | |
| |
| |
| |
| Equations of a Line | |
| |
| |
| Problem Recognition Exercises: Characteristics of Linear Equations | |
| |
| |
| |
| Applications of Linear Equations and Modeling | |
| |
| |
| |
| Introduction to Relations | |
| |
| |
| |
| Introduction to Functions | |
| |
| |
| |
| Graphs of Basic Functions | |
| |
| |
| Problem Recognition Exercises: Characteristics of Relations | |
| |
| |
| Group Activity: Deciphering a Coded Message | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Systems of Linear Equations and Inequalities | |
| |
| |
| |
| Solving Systems of Linear Equations by the Graphing Method | |
| |
| |
| |
| Solving Systems of Linear Equations by the Substitution Method | |
| |
| |
| |
| Solving Systems of Linear Equations by the Addition Method | |
| |
| |
| Problem Recognition Exercises: Solving Systems of Linear Equations | |
| |
| |
| |
| Applications of Systems of Linear Equations in Two Variables | |
| |
| |
| |
| Linear Inequalities and Systems of Linear Inequalities in Two Variables | |
| |
| |
| |
| Systems of Linear Equations in Three Variables and Applications | |
| |
| |
| |
| Solving Systems of Linear Equations by Using Matrices | |
| |
| |
| Group Activity: Creating a Quadratic Model of the Form y = at2 + bt + c | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Polynomials | |
| |
| |
| |
| Properties of Integer Exponents and Scientific Notation | |
| |
| |
| |
| Addition and Subtraction of Polynomials and Polynomial Functions | |
| |
| |
| |
| Multiplication of Polynomials | |
| |
| |
| |
| Division of Polynomials | |
| |
| |
| Problem Recognition Exercises: Operations on Polynomials | |
| |
| |
| |
| Greatest Common Factor and Factoring by Grouping | |
| |
| |
| |
| Factoring Trinomials | |
| |
| |
| |
| Factoring Binomials | |
| |
| |
| Problem Recognition Exercises: Factoring Summary | |
| |
| |
| |
| Solving Equations by Using the Zero Product Rule | |
| |
| |
| Group Activity: Investigating Pascal’s Triangle | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Rational Expressions and Rational Equations | |
| |
| |
| |
| Rational Expressions and Rational Functions | |
| |
| |
| |
| Multiplication and Division of Rational Expressions | |
| |
| |
| |
| Addition and Subtraction of Rational Expressions | |
| |
| |
| |
| Complex Fractions | |
| |
| |
| Problem Recognition Exercises: Operations on Rational Expressions | |
| |
| |
| |
| Solving Rational Equationsv | |
| |
| |
| Problem Recognition Exercises: Rational Equations vs. Expressions | |
| |
| |
| |
| Applications of Rational Equations and Proportions | |
| |
| |
| |
| Variation | |
| |
| |
| Group Activity: Computing the Future Value of an Investment | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Radicals and Complex Numbers | |
| |
| |
| |
| Definition of an nth Root | |
| |
| |
| |
| Rational Exponents | |
| |
| |
| |
| Simplifying Radical Expressions | |
| |
| |
| |
| Addition and Subtraction of Radicals | |
| |
| |
| |
| Multiplication of Radicals | |
| |
| |
| Problem Recognition Exercises: Simplifying Radical Expressions | |
| |
| |
| |
| Division of Radicals and Rationalization | |
| |
| |
| |
| Solving Radical Equations | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| Group Activity: Margin of Error of Survey Results | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Quadratic Equations and Functions | |
| |
| |
| |
| Square Root Property and Completing the Square | |
| |
| |
| |
| Quadratic Formula | |
| |
| |
| |
| Equations in Quadratic Form | |
| |
| |
| Problem Recognition Exercises: Quadratic and Quadratic Type Equations | |
| |
| |
| |
| Graphs of Quadratic Functions | |
| |
| |
| |
| Vertex of a Parabola: Applications and Modeling | |
| |
| |
| |
| Nonlinear Inequalities | |
| |
| |
| Problem Recognition Exercises: Recognizing Equations and Inequalities | |
| |
| |
| Group Activity: Creating a Quadratic Model of the Form y = a(x - h)2 + k | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Exponential and Logarithmic Functions and Applications | |
| |
| |
| |
| Algebra and Composition of Functions | |
| |
| |
| |
| Inverse Functions | |
| |
| |
| |
| Exponential Functions | |
| |
| |
| |
| Logarithmic Functions | |
| |
| |
| Problem Recognition Exercises: Identifying Graphs of Functions | |
| |
| |
| |
| Properties of Logarithms | |
| |
| |
| |
| The Irrational Number and Change of Base | |
| |
| |
| Problem Recognition Exercises: Logarithmic and Exponential Forms | |
| |
| |
| |
| Logarithmic and Exponential Equations and Applications | |
| |
| |
| Group Activity: Creating a Population Model | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Conic Sections | |
| |
| |
| |
| Distance Formula, Midpoint Formula, and Circles | |
| |
| |
| |
| More on the Parabola | |
| |
| |
| |
| The Ellipse and Hyperbola | |
| |
| |
| Problem Recognition Exercises: Formulas and Conic Sections | |
| |
| |
| |
| Nonlinear Systems of Equations in Two Variables | |
| |
| |
| |
| Nonlinear Inequalities and Systems of Inequalities | |
| |
| |
| Group Activity: Investigating the Graphs of Conic Sections on a Calculator | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| |
| Binomial Expansions, Sequences, and Series | |
| |
| |
| |
| Binomial Expansions | |
| |
| |
| |
| Sequences and Series | |
| |
| |
| |
| Arithmetic Sequences and Series | |
| |
| |
| |
| Geometric Sequences and Series | |
| |
| |
| Problem Recognition Exercises: Identifying Arithmetic and Geometric Sequences | |
| |
| |
| Group Activity: Investigating Mean and Standard Deviation | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Review Exercises | |
| |
| |
| |
| Test | |
| |
| |
| |
| Cumulative Review Exercises | |
| |
| |
| Additional Topics Appendix | |
| |
| |
| |
| Determinants and Cramer’s Rule | |