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Linear Equations and Inequalities in One Variable | |

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Linear Equations in One Variable | |

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Problem Recognition Exercises: Equations versus Expressions | |

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Applications of Linear Equations in One Variable | |

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Applications to Geometry and Literal Equations | |

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Linear Inequalities in One Variable | |

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Compound Inequalities | |

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Absolute Value Equations | |

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Absolute Value Inequalities | |

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Problem Recognition Exercises: Identifying Equations and Inequalities | |

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Group Activity: Understanding the Symbolism of Mathematics | |

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Summary | |

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Review Exercises | |

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Test | |

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Linear Equations in Two Variables and Functions | |

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Linear Equations in Two Variables | |

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Slope of a Line and Rate of Change | |

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Equations of a Line | |

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Problem Recognition Exercises: Characteristics of Linear Equations | |

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Applications of Linear Equations and Modeling | |

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Introduction to Relations | |

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Introduction to Functions | |

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Graphs of Basic Functions | |

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Problem Recognition Exercises: Characteristics of Relations | |

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Group Activity: Deciphering a Coded Message | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Systems of Linear Equations and Inequalities | |

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Solving Systems of Linear Equations by the Graphing Method | |

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Solving Systems of Linear Equations by the Substitution Method | |

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Solving Systems of Linear Equations by the Addition Method | |

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Problem Recognition Exercises: Solving Systems of Linear Equations | |

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Applications of Systems of Linear Equations in Two Variables | |

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Linear Inequalities and Systems of Linear Inequalities in Two Variables | |

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Systems of Linear Equations in Three Variables and Applications | |

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Solving Systems of Linear Equations by Using Matrices | |

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Group Activity: Creating a Quadratic Model of the Form y = at2 + bt + c | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Polynomials | |

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Properties of Integer Exponents and Scientific Notation | |

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Addition and Subtraction of Polynomials and Polynomial Functions | |

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Multiplication of Polynomials | |

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Division of Polynomials | |

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Problem Recognition Exercises: Operations on Polynomials | |

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Greatest Common Factor and Factoring by Grouping | |

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Factoring Trinomials | |

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Factoring Binomials | |

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Problem Recognition Exercises: Factoring Summary | |

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Solving Equations by Using the Zero Product Rule | |

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Group Activity: Investigating Pascal’s Triangle | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Rational Expressions and Rational Equations | |

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Rational Expressions and Rational Functions | |

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Multiplication and Division of Rational Expressions | |

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Addition and Subtraction of Rational Expressions | |

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Complex Fractions | |

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Problem Recognition Exercises: Operations on Rational Expressions | |

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Solving Rational Equationsv | |

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Problem Recognition Exercises: Rational Equations vs. Expressions | |

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Applications of Rational Equations and Proportions | |

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Variation | |

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Group Activity: Computing the Future Value of an Investment | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Radicals and Complex Numbers | |

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Definition of an nth Root | |

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Rational Exponents | |

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Simplifying Radical Expressions | |

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Addition and Subtraction of Radicals | |

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Multiplication of Radicals | |

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Problem Recognition Exercises: Simplifying Radical Expressions | |

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Division of Radicals and Rationalization | |

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Solving Radical Equations | |

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Complex Numbers | |

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Group Activity: Margin of Error of Survey Results | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Quadratic Equations and Functions | |

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Square Root Property and Completing the Square | |

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Quadratic Formula | |

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Equations in Quadratic Form | |

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Problem Recognition Exercises: Quadratic and Quadratic Type Equations | |

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Graphs of Quadratic Functions | |

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Vertex of a Parabola: Applications and Modeling | |

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Nonlinear Inequalities | |

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Problem Recognition Exercises: Recognizing Equations and Inequalities | |

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Group Activity: Creating a Quadratic Model of the Form y = a(x - h)2 + k | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Exponential and Logarithmic Functions and Applications | |

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Algebra and Composition of Functions | |

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Inverse Functions | |

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Exponential Functions | |

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Logarithmic Functions | |

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Problem Recognition Exercises: Identifying Graphs of Functions | |

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Properties of Logarithms | |

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The Irrational Number and Change of Base | |

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Problem Recognition Exercises: Logarithmic and Exponential Forms | |

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Logarithmic and Exponential Equations and Applications | |

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Group Activity: Creating a Population Model | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Conic Sections | |

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Distance Formula, Midpoint Formula, and Circles | |

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More on the Parabola | |

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The Ellipse and Hyperbola | |

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Problem Recognition Exercises: Formulas and Conic Sections | |

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Nonlinear Systems of Equations in Two Variables | |

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Nonlinear Inequalities and Systems of Inequalities | |

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Group Activity: Investigating the Graphs of Conic Sections on a Calculator | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Binomial Expansions, Sequences, and Series | |

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Binomial Expansions | |

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Sequences and Series | |

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Arithmetic Sequences and Series | |

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Geometric Sequences and Series | |

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Problem Recognition Exercises: Identifying Arithmetic and Geometric Sequences | |

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Group Activity: Investigating Mean and Standard Deviation | |

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Summary | |

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Review Exercises | |

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Test | |

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Cumulative Review Exercises | |

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Additional Topics Appendix | |

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Determinants and Cramer’s Rule | |