Intermediate Algebra
1. BASIC CONCEPTS AND PROPERTIES. Sets, Real Numbers, and Numerical Expressions. Operations with Real Numbers. Properties of Real Numbers and the Use of Exponents. Algebraic Expressions. Summary. Review Problem Set. Test. 2. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING. Solving First-Degree Equations. Equations Involving Fractional Forms. Equations Involving Decimals and Problem Solving. Formulas. Inequalities. More on Inequalities and Problem Solving. Equations and Inequalities Involving Absolute Value. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-2) 3. POLYNOMIALS. Polynomials: Sums and Differences. Products and Quotients of Monomials. Multiplying Polynomials. Factoring: Greatest Common Factor and Common Binomial Factor. Factoring: Difference of Two Squares and Sum or Difference of Two Cubes. Factoring Trinomials. Equations and Problem Solving. Summary. Review Problem Set. Test. 4. RATIONAL EXPRESSIONS. Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. More on Rational Expressions and Complex Fractions. Dividing Polynomials. Fractional Equations. More Fractional Equations and Applications. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-4) 5. EXPONENTS AND RADICALS. Using Integers as Exponents. Roots and Radicals. Combining Radicals and Simplifying Radicals That Contain Variables. Products and Quotients Involving Radicals. Equations Involving Radicals. Merging Exponents and Roots. Scientific Notation. Summary. Review Problems Set. Test. 6. QUADRATIC EQUATIONS AND INEQUALITIES. Complex Numbers. Quadratic Equations. Completing the Square. Quadratic Formula. More Quadratic Equations and Applications. Quadratic and Other Nonlinear Inequalities. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-6). 7. LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES. Rectangular Coordinate System and Linear Equations. Linear Inequalities in Two Variables. Distance and Slope. Determining the Equation of a Line. Graphing Nonlinear Equations. Summary. Review Problem Set. Test. 8. CONIC SECTIONS. Graphing Parabolas. More Parabolas and Some Circles. Graphing Ellipses. Graphing Hyperbolas. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-8). 9. FUNCTIONS. Relations and Functions. Functions: Their Graphs and Applications. Graphing Made Easy Via Transformations. Composition of Functions. Inverse Functions. Direct and Inverse Variations. Summary. Review Problem Set. Test. 10. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations and Linear Inequalities in Two Variables. Substitution Method. Elimination-by-Addition Method. Systems of Three Linear Equations in Three Variables. Matrix Approach to Solving Systems. Determinants. 3x3 Determinants and Systems of Three Linear Equations in Three Variables. Systems Involving Nonlinear Equations and Systems of Inequalities. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-10). 11. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponents and Exponential Functions. Applications of Exponential Functions. Logarithms. Logarithmic Functions. Exponential Equations, Logarithmic Equations, and Problem Solving. Summary. Review Problem Set. Test. Appendix A: Prime Numbers and Operations with Fractions. Appendix B: Binomial Expansions. Answers to Odd-Numbered Problems and All Chapter Review, Chapter Test, Cumulative. Review, Appendix A and Appendix B Problems. Answers to Selected Even-Numbered Problems. Index.