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| Review of Basic Algebraic Concepts | |
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| Sets of Number and Interval Notation | |
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| Operation on Real Numbers | |
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| Simplifying Expressions | |
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| Linear Equations in One Variable -- Problem Recognition Exercises: Expressions and Equations | |
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| Applications of Linear Equations in One Variable | |
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| Literal Equations and Applications to Geometry | |
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| Linear Inequalities in One Variable | |
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| Properties of Integer Exponents and Scientific Notation | |
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| Graphing Linear Equations and Functions | |
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| Linear Equations in Two Variables | |
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| Slope of a Line -- Problem Recognition Exercises: Intercepts and Slope | |
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| Equations of a Line | |
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| Application 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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| Systems of Linear Equations | |
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| Solving Systems of Linear Equations by Graphing | |
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| Solving Systems of Linear Equations by Using the Substitution Method | |
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| Solving Systems of Linear Equations by Using the Addition Method -- Problem Recognition Exercises: Method of Solving Systems of Equations | |
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| Applications of Systems of Linear Equations 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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| Polynomials | |
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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 -- 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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| Additional Factoring Strategies | |
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| Solving Equations by Using the Zero Product Rule | |
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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 -- Problem Recognition Exercises: Simplifying Rational Expressions | |
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| Solving Rational Equations -- Problem Recognition Exercises: Rational Expressions and Equations | |
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| Applications of Rational Equations and Proportions | |
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| Variation | |
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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 -- Problem Recognition Exercises: Operations on Radical Expressions | |
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| Rationalization | |
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| Solving Radical Equations | |
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| Complex Numbers | |
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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 -- Problem Recognition Exercises: Recognizing Equation Types | |
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| Graphs of Quadratic Functions | |
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| Applications of Quadratic Functions and Modeling | |
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| More Equations and Inequalities | |
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| Compound Inequalities | |
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| Polynomial and Rational Inequalities | |
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| Absolute Value Equations | |
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| Absolute Value Inequalities -- Problem Recognition Exercises: Equations and Inequalities | |
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| Linear Inequalities in Two Variables | |
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| Exponential and Logarithmic Functions | |
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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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| Properties of Logarithms | |
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| The Irrational Number e -- Problem Recognition Exercises: Logarithmic and Exponential Forms | |
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| Exponential and Logarithmic Equations | |
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| Conic Sections | |
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| Distance Formula, Midpoint, and Circles | |
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| More of the Parabola | |
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| The Ellipse and Hyperbola -- Problem Recognition Exercises: Identifying and Graphing Conic Sections | |
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| Nonlinear Systems of Equations in Two Variables | |
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| Nonlinear Inequalities and System if Inequalities | |
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| Additional Topics Appendix | |
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| Binomial Expansions | |
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| Determinants and Cramer's Rule | |
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| Sequences and Series | |
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| Arithmetic and Geometric Sequences and Series | |