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Basic Concepts and Properties | |
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Sets, Real Numbers, and Numerical Expressions | |
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Operations with Real Numbers | |
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Properties of Real Numbers and the Use of Exponents | |
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Algebraic Expressions | |
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Summary | |
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Review Problem Set | |
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Test | |
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Equations, Inequalities, and Problem Solving | |
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Solving First-Degree Equations | |
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Equations Involving Fractional Forms | |
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Equations Involving Decimals and Problem Solving | |
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Formulas | |
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Inequalities | |
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More on Inequalities and Problem Solving | |
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Equations and Inequalities Involving Absolute Value | |
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Summary | |
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Review Problem Set | |
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Test | |
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Polynomials | |
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Polynomials: Sums and Differences | |
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Products and Quotients of Monomials | |
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Multiplying Polynomials | |
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Factoring: Use of the Distributive Property | |
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Factoring: Difference of Two Squares and Sum or Difference of Two Cubes | |
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Factoring Trinomials | |
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Equations and Problem Solving | |
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Summary | |
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Review Problem Set | |
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Test | |
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Cumulative Review Problem Set (Chapters 1-3) | |
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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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More on Rational Expressions and Complex Fractions | |
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Dividing Polynomials | |
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Fractional Equations | |
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More Fractional Equations and Applications | |
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Summary | |
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Review Problem Set | |
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Test | |
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Exponents and Radicals | |
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Using Integers as Exponents | |
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Roots and Radicals | |
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Combining Radicals and Simplifying Radicals That Contain Variables | |
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Products and Quotients Involving Radicals | |
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Equations Involving Radicals | |
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Merging Exponents and Roots | |
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Scientific Notation | |
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Summary | |
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Review Problems Set | |
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Test | |
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Quadratic Equations and Inequalities | |
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Complex Numbers | |
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Quadratic Equations | |
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Completing the Square | |
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Quadratic Formula | |
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More Quadratic Equations and Applications | |
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Quadratic and Other Nonlinear Inequalities | |
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Summary | |
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Review Problem Set | |
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Test | |
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Cumulative Review Problem Set (Chapters 1-6) | |
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Linear Equations and Inequalities in two Variables | |
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Rectangular Coordinate System and Linear Equations | |
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Graphing Nonlinear Equations Linear Inequalities in Two Variables | |
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Distance and Slope | |
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Determining the Equation of a Line | |
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Summary | |
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Review Problem Set | |
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Test | |
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Functions | |
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Concept of a Function | |
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Linear Functions and Applications | |
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Quadratic Functions | |
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More Quadratic Functions and Applications | |
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Transformations of Some Basic Curves | |
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Combining Functions | |
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Direct and Inverse Variation | |
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Summary | |
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Review Problem Set | |
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Test | |
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Polynomial and Rational Functions | |
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Synthetic Division | |
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Remainder and Factor Theorems | |
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Polynomial Equations | |
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Graphing Polynomial Functions | |
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Graphing Rational Functions | |
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More on Graphing Rational Functions | |
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Summary | |
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Review Problem Set | |
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Test | |
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Exponential and Logarithmic Functions | |
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Exponents and Exponential Functions | |
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Applications of Exponential Functions | |
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Inverse Functions | |
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Logarithms | |
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Logarithmic Functions | |
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Exponential Equations, Logarithmic Equations, and Problem Solving | |
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Summary | |
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Review Problem Set | |
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Test | |
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Cumulative Review Problem Set (Chapter 1-10) | |
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Systems of Equations | |
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Systems of Two Linear Equations in Two Variables | |
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Systems of Three Linear Equations in Three Variables | |
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Matrix Approach to Solving Linear Systems | |
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Determinants | |
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Cramer's Rule | |
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Partial Fractions | |
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Summary | |
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Review Problem Set | |
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Test | |
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Algebra of Matrices | |
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Algebra of 2 X 2 Matrices | |
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Multiplicative Inverses | |
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m x n Matrices | |
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Systems of Linear Inequalities: Linear Programming | |
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Summary | |
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Review Problem Set | |
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Test | |
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Conic Sections | |
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Circles | |
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Parabolas | |
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Ellipses | |
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Hyperbolas | |
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System Involving Nonlinear Equations | |
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Summary | |
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Review Problem Set | |
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Test | |
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Sequences and Mathematical Induction | |
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Arithmetic Sequences | |
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Geometric Sequences | |
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Another Look at Problem Solving | |
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Mathematical Induction | |
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Summary | |
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Review Problem Set | |
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Test | |
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Counting Techniques, Probability, and the Binomial Theorem | |
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Fundamental Principle of Counting | |
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Permutations and Combinations | |
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Probability | |
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Some Properties of Probability: Expected Values | |
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Conditional Probability: Dependent and Independent Events | |
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Binomial Theorem | |
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Summary | |
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Review Problem Set | |
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Test | |
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Common Logarithms | |