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 | |

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