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| Review of the Real Number System | |
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| Basic Concepts | |
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| Operations on Real Numbers | |
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| Exponents, Roots, and Order of Operations | |
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| Properties of Real Numbers | |
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| Linear Equations, Inequalities, and Applications | |
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| Linear Equations in One Variable Formulas | |
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| Applications of Linear Equations | |
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| Further Applications of Linear Equations | |
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| Summary Exercises on Solving Applied Problems | |
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| Linear Inequalities in One Variable | |
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| Set Operations and Compound Inequalities | |
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| Absolute Value Equations and Inequalities | |
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| Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities | |
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| Graphs, Linear Equations, and Functions | |
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| The Rectangular Coordinate System | |
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| The Slope of a Line | |
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| Linear Equations in Two Variables | |
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| Linear Inequalities in Two Variables to Functions Variation | |
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| Systems of Linear Equations of Linear Equations in Two Variables | |
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| Systems of Linear Equations in Three Variables Applications of Systems of Linear Equations | |
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| Solving Systems of Linear Equations by Matrix Methods | |
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| Determinants and Cramer's Rule | |
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| Exponents, Polynomials, and Polynomial Functions | |
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| Integer Exponents and Scientific Notation | |
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| Adding and Subtracting Polynomials | |
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| Polynomial Functions | |
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| Multiplying Polynomials | |
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| Dividing Polynomials | |
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| Factoring | |
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| Greatest Common Factors; Factoring by Grouping Factoring Trinomials | |
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| Special Factoring | |
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| A General Approach to Factoring | |
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| Solving Equations by Factoring | |
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| Rational Expressions and Functions | |
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| Rational Expressions and Functions; Multiplying and Dividing | |
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| Adding and Subtracting Rational Expressions | |
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| Complex Fractions | |
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| Equations with Rational Expressions and Graphs | |
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| Summary Exercises on Operations and Equations with Rational Expressions | |
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| Applications of Rational Expressions | |
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| Roots, Radicals, and Root Functions | |
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| Radical Expressions and Graphs | |
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| Rational Exponents | |
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| Simplifying Radical Expressions | |
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| Adding and Subtracting Radical Expressions | |
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| Multiplying and Dividing Radical Expressions | |
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| Summary Exercises on Operations with Radicals | |
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| Solving Equations with Radicals | |
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| Complex Numbers | |
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| Quadratic Equations and Inequalities | |
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| The Square Root Property and Completing the Square | |
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| The Quadratic Formula | |
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| Equations Quadratic in Form | |
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| Summary Exercises on Solving Quadratic Equations | |
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| Formulas and Further Applications | |
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| Quadratic and Rational Inequalities | |