Description: 1. Review of Real Numbers. Symbols. Sets of Numbers. Fractions. Exponents, Roots, and Order of Operations. Introduction to Variables and Equations. Adding and Subtracting Real Numbers. Multiplying and Dividing Real Numbers. Properties of Real Numbers. 2. Equations and Problem Solving. Simplifying Algebraic Expressions. The Addition and Multiplication Properties of Equality. Solving Linear Equations. Formulas. An Introduction to Problem Solving. Reading Graphs and Ordered Pairs. 3. Inequalities, Absolute Value, and Problem Solving. Ratio and Proportion. Percent and Problem Solving. Further Applications of Linear Equations. Absolute Value Equations. The Addition and Multiplication Properties of Inequality. Compound Inequalities. Absolute Value Inequalities. 4. Graphing. Graphing Equations. Introduction to Functions. Graphing Linear Functions. The Slope of a Line. Equations of Lines. Graphing Linear Inequalities. 5. Exponents and Polynomials. Exponents. Negative Exponents and Scientific Notation. Addition and Subtraction of Polynomials. Multiplication of Polynomials. Division of Polynomials. Synthetic Division and the Remainder Theorem. Algebra of Functions and Composition of Functions. 6. Factoring Polynomials. The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials of the Form x + bx + c . Factoring Trinomials of the Form ax + bx + c . Factoring Binomials. Factoring Polynomials Completely. Solving Equations by Factoring and Problem Solving. An Introduction to Graphing Polynomial Functions. 7. Rational Expressions. Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Complex Fractions. Solving Equations Containing Rational Expressions. Rational Expressions and Problem Solving. Variation and Problem Solving. 8. Roots and Radicals. Introduction to Radicals. Simplifying Radicals. Adding and Subtracting Radicals. Multiplying and Dividing Radicals. Rational Exponents. Solving Equations Containing Radicals. 9. Quadratic Equations and Inequalities. Solving Quadratic Equations by Completing the Square. Solving Quadratic Equations by the Quadratic Formula. Solving Equations in Quadratic Form. Nonlinear Inequalities in One Variable. Quadratic Functions and Their Graphs. Further Graphing of Quadratic Functions. The Parabola and the Circle. The Ellipse and the Hyperbola. 10. Systems of Equations and Inequalities. Solving the Systems of Linear Equations in Two Variables. Solving the Systems of Linear Equations in Three Variables. Applications of Linear Systems of Equations. Solving Systems of Equations by Determinates. Solving Systems of Equations by Matrices. Solving Nonlinear Systems of Equations. Nonlinear Inequalities and Systems of Inequalities. 11. Exponential and Logarithmic Functions. Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Common Logarithms, Natural Logarithms and Change of Base. Exponential and Logarithmic Functions and Problem Solving. 12. Sequences, Series, and the Binomial Theorem. Sequences. Arithmetic and Geometric Sequences. Series. Partial Sums of Arithmetic and Geometric Sequences. The Binomial Theorem. Appendix A. Operations on Decimals. Appendix B. Review of Angles, Lines, and Special Triangles. Appendix C. Review of Geometric Figures. Appendix D. Table of Squares and Square Roots. Appendix E. Answers to Selected Exercises. Index.

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