Real Numbers and Their Basic Properties | |

Real numbers and their graphs | |

Fractions | |

Exponents and order of operations | |

Adding and subtracting real numbers | |

Multiplying and dividing real numbers | |

Algebraic expressions | |

Properties of real numbers | |

Projects | |

Chapter summary | |

Test | |

Equations and Inequalities | |

Solving basic linear equations in one variable | |

Solving more linear equations in one variable | |

Simplifying expressions to solve linear equations in one variable | |

Formulas | |

Introduction to problem solving | |

Motion and mixed problems | |

Solving linear inequalities in one variable | |

Projects | |

Chapter summary | |

Chapter test Cumulative review exercises | |

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

The rectangular coordinate system | |

Graphing linear equations | |

Solving systems of linear equations by graphing | |

Solving systems of linear equations by substitution | |

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

Applications of systems of linear equations | |

Solving Systems of linear inequalities | |

Projects | |

Chapter summary | |

Chapter test | |

Polynomials | |

Natural-number exponents | |

Zero and negative-integral exponents | |

Scientific notation | |

Polynomials and Polynomial Functions | |

Adding and subtracting polynomials | |

Multiplying polynomials | |

Dividing polynomials by monomials | |

Dividing polynomials by polynomials | |

Projects | |

Chapter summary | |

Chapter test Cumulative review exercises | |

Factoring Polynomials | |

Factoring out the greatest common factor | |

Factoring by grouping | |

Factoring the difference of two squares | |

Factoring trinomials with leading coefficients of | |

Factoring general trinomials | |

Factoring the sum and difference of two cubes | |

Summary of factoring techniques | |

Solving equations by factoring | |

Problem solving | |

Projects | |

Chapter summary | |

Chapter test | |

Proportions and Rational Expressions | |

Simplifying rational expressions | |

Multiplying and dividing rational expressions | |

Adding and subtracting rational expressions | |

Complex fractions | |

Solving equations that contain rational expressions | |

Applications of equations that contain rational expressions | |

Ratios | |

Proportions and similar triangles | |

Projects | |

Chapter summary | |

Chapter test Cumulative review exercises | |

More Equations, Inequalities, and Factoring | |

Review of equations and inequalities | |

Equations containing absolute value | |

Inequalities containing absolute values | |

Review of factoring | |

Review of rational expressions | |

Synthetic division | |

Projects | |

Chapter summary | |

Test | |

Writing Equations of Lines, Functions, and Variation | |

A review of the rectangular coordinate system | |

Slope of a nonvertical line | |

Writing equations of lines | |

A review of functions | |

Graphs of nonlinear functions | |

Variation | |

Projects | |

Chapter summary | |

Test Cumulative review exercises | |

Radicals and Rational Exponents | |

Radical expressions | |

Applications of radicals | |

Rational exponents | |

Simplifying and combining radical expressions | |

Multiplying and dividing radical expressions | |

Radical equations | |

Complex numbers | |

Projects | |

Chapter summary | |

Chapter test | |

Quadratic Functions, Inequalities and Algebra of Functions | |

Solving quadratic equations by completing the square | |

Solving quadratic equations by the quadratic formula | |

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

Graphs of quadratic functions | |

Quadratic and other nonlinear inequalities | |

Algebra and composition of functions | |

Inverses of functions | |

Projects | |

Chapter summary | |

Chapter test Cumulative review exercises | |

Exponential and Logarithmic Functions | |

Exponential functions | |

Base- exponential functions | |

Logarithmic functions | |

Base- logarithms | |

Properties of logarithms | |

Exponential and logarithmic equations | |

Projects | |

Chapter summary | |

Chapter test | |

Conic Sections and More Graphing | |

The circle and the parabola | |

The ellipse | |

The hyperbola | |

Piecewise-defined functions and the greatest integer function | |

Projects | |

Chapter summary | |

Chapter test Cumulative review exercises | |

More on Systems of Equations and Inequalities | |

Solutions of two equations in two variables | |

Solutions of three equations in three variables | |

Solution by matrices | |

Solution by determinants | |

Solving simultaneous second-degree equations and inequalities | |

Projects | |

Chapter summary | |

Chapter test | |

Miscellaneous Topics | |

The binomial theorem | |

The nth term of a binomial expansion | |

Arithmetic sequences | |

Geometric sequences | |

Infinite geometric sequences | |

Permutations and combinations | |

Probability | |

Projects | |

Chapter summary | |

Chapter test Cumulative review exercises | |

Symmetries of graphs | |

Tables | |

Powers and roots | |

Base-10 logarithms | |

Base-e logarithms | |

Answers to Selected Exercises | |

Index | |

Index of Applications | |

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