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Real Numbers and Their Basic Properties | |

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Real numbers and their graphs | |

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Fractions | |

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Exponents and order of operations | |

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Adding and subtracting real numbers | |

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Multiplying and dividing real numbers | |

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Algebraic expressions | |

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Properties of real numbers | |

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Projects | |

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Chapter summary | |

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Test | |

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Equations and Inequalities | |

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Solving basic linear equations in one variable | |

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Solving more linear equations in one variable | |

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Simplifying expressions to solve linear equations in one variable | |

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Formulas | |

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Introduction to problem solving | |

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Motion and mixed problems | |

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Solving linear inequalities in one variable | |

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Projects | |

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Chapter summary | |

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Chapter test Cumulative review exercises | |

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Graphing and Solving Systems of Linear Equations and Linear Inequalities | |

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The rectangular coordinate system | |

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Graphing linear equations | |

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Solving systems of linear equations by graphing | |

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Solving systems of linear equations by substitution | |

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Solving systems of linear equations by elimination (addition) | |

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Applications of systems of linear equations | |

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Solving Systems of linear inequalities | |

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Projects | |

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Chapter summary | |

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Chapter test | |

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Polynomials | |

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Natural-number exponents | |

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Zero and negative-integral exponents | |

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Scientific notation | |

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Polynomials and Polynomial Functions | |

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Adding and subtracting polynomials | |

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Multiplying polynomials | |

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Dividing polynomials by monomials | |

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Dividing polynomials by polynomials | |

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Projects | |

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Chapter summary | |

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Chapter test Cumulative review exercises | |

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Factoring Polynomials | |

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Factoring out the greatest common factor | |

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Factoring by grouping | |

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Factoring the difference of two squares | |

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Factoring trinomials with leading coefficients of | |

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Factoring general trinomials | |

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Factoring the sum and difference of two cubes | |

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Summary of factoring techniques | |

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Solving equations by factoring | |

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Problem solving | |

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Projects | |

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Chapter summary | |

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Chapter test | |

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Proportions and Rational Expressions | |

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Simplifying rational expressions | |

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Multiplying and dividing rational expressions | |

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Adding and subtracting rational expressions | |

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Complex fractions | |

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Solving equations that contain rational expressions | |

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Applications of equations that contain rational expressions | |

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Ratios | |

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Proportions and similar triangles | |

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Projects | |

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Chapter summary | |

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Chapter test Cumulative review exercises | |

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More Equations, Inequalities, and Factoring | |

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Review of equations and inequalities | |

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Equations containing absolute value | |

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Inequalities containing absolute values | |

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Review of factoring | |

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Review of rational expressions | |

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Synthetic division | |

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Projects | |

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Chapter summary | |

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Test | |

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Writing Equations of Lines, Functions, and Variation | |

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A review of the rectangular coordinate system | |

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Slope of a nonvertical line | |

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Writing equations of lines | |

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A review of functions | |

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Graphs of nonlinear functions | |

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Variation | |

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Projects | |

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Chapter summary | |

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Test Cumulative review exercises | |

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Radicals and Rational Exponents | |

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Radical expressions | |

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Applications of radicals | |

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Rational exponents | |

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Simplifying and combining radical expressions | |

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Multiplying and dividing radical expressions | |

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Radical equations | |

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Complex numbers | |

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Projects | |

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Chapter summary | |

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Chapter test | |

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Quadratic Functions, Inequalities and Algebra of Functions | |

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Solving quadratic equations by completing the square | |

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Solving quadratic equations by the quadratic formula | |

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The discriminant and equations that can be written in quadratic form | |

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Graphs of quadratic functions | |

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Quadratic and other nonlinear inequalities | |

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Algebra and composition of functions | |

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Inverses of functions | |

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Projects | |

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Chapter summary | |

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Chapter test Cumulative review exercises | |

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Exponential and Logarithmic Functions | |

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Exponential functions | |

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Base- exponential functions | |

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Logarithmic functions | |

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Base- logarithms | |

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Properties of logarithms | |

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Exponential and logarithmic equations | |

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Projects | |

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Chapter summary | |

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Chapter test | |

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Conic Sections and More Graphing | |

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The circle and the parabola | |

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The ellipse | |

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The hyperbola | |

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Piecewise-defined functions and the greatest integer function | |

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Projects | |

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Chapter summary | |

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Chapter test Cumulative review exercises | |

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More on Systems of Equations and Inequalities | |

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Solutions of two equations in two variables | |

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Solutions of three equations in three variables | |

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Solution by matrices | |

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Solution by determinants | |

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Solving simultaneous second-degree equations and inequalities | |

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Projects | |

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Chapter summary | |

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Chapter test | |

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Miscellaneous Topics | |

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The binomial theorem | |

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The nth term of a binomial expansion | |

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Arithmetic sequences | |

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Geometric sequences | |

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Infinite geometric sequences | |

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Permutations and combinations | |

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Probability | |

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Projects | |

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Chapter summary | |

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Chapter test Cumulative review exercises | |

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Symmetries of graphs | |

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Tables | |

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Powers and roots | |

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Base-10 logarithms | |

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Base-e logarithms | |

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Answers to Selected Exercises | |

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Index | |

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Index of Applications | |