Algebra for College Students

1. BASIC CONCEPTS AND PROPERTIES. 1.0 Review of Fractions. 1.1 Sets, Real Numbers, and Numerical Expressions. 1.2 Operations with Real Numbers. 1.3 Properties of Real Numbers and the Use of Exponents. 1.4 Algebraic Expressions. Chapter 1 Summary. Chapter 1 Review Problem Set. Chapter 1 Test. 2. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING. 2.1 Solving First-Degree Equations. 2.2 Equations Involving Fractional Forms. 2.3 Equations Involving Decimals and Problem Solving. 2.4 Formulas. 2.5 Inequalities. 2.6 More on Inequalities and Problem Solving. 2.7 Equations and Inequalities Involving Absolute Value. Chapter 2 Summary. Chapter 2 Review Problem Set. Chapter 2 Test. Chapters 1-2 Cumulative Test. 3. POLYNOMIALS. 3.1 Polynomials: Sums and Differences. 3.2 Products and Quotients of Monomials. 3.3 Multiplying Polynomials. 3.4 Factoring: Greatest Common Factor and Common Binomial Factor. 3.5 Factoring: Difference of Two Squares and Sum or Difference of Two Cubes. 3.6 Factoring Trinomials. 3.7 Equations and Problem Solving. Chapter 3 Summary. Chapter 3 Review Problem Set. Chapter 3 Test. 4. RATIONAL EXPRESSIONS. 4.1 Simplifying Rational Expressions. 4.2 Multiplying and Dividing Rational Expressions. 4.3 Adding and Subtracting Rational Expressions. 4.4 More on Rational Expressions and Complex Fractions. 4.5 Dividing Polynomials. 4.6 Fractional Equations. 4.7 More Fractional Equations and Applications. Chapter 4 Summary. Chapter 4 Review Problem Set. Chapter 4 Test. Chapters 1-4 Cumulative Review Problem Set. 5. EXPONENTS AND RADICALS. 5.1 Using Integers as Exponents. 5.2 Roots and Radicals. 5.3 Combining Radicals and Simplifying Radicals That Contain Variables. 5.4 Products and Quotients Involving Radicals. 5.5 Equations Involving Radicals. 5.6 Merging Exponents and Roots. 5.7 Scientific Notation. Chapter 5 Summary. Chapter 5 Review Problem Set. Chapter 5 Test. 6. QUADRATIC EQUATIONS AND INEQUALITIES. 6.1 Complex Numbers. 6.2 Quadratic Equations. 6.3 Completing the Square. 6.4 Quadratic Formula. 6.5 More Quadratic Equations and Applications. 6.6 Quadratic and Other Nonlinear Inequalities. Chapter 6 Summary. Chapter 6 Review Problem Set. Chapter 6 Test. Chapters 1-6 Cumulative Review Problem Set. 7. EQUATIONS AND INEQUALITIES IN TWO VARIABLES. 7.1 Rectangular Coordinate System and Linear Equations. 7.2 Linear Inequalities in Two Variables. 7.3 Distance and Slope. 7.4 Determining the Equation of a Line. 7.5 Graphing Nonlinear Equations. Chapter 7 Summary. Chapter 7 Review Problem Set. Chapter 7 Test. 8. FUNCTIONS. 8.1 Concept of a Function. 8.2 Linear Functions and Applications. 8.3 Quadratic Functions. 8.4 More Quadratic Functions and Applications. 8.5 Transformations and Some Basic Curves. 8.6 Combining Functions. 8.7 Direct and Inverse Variation. Chapter 8 Summary. Chapter 8 Review Problem Set. Chapter 8 Test. Chapters 1-8 Cumulative Review Problem Set. 9. POLYNOMIAL AND RATIONAL FUNCTIONS. 9.1 Synthetic Division. 9.2 Remainder and Factor Theorems. 9.3 Polynomial Equations. 9.4 Graphing Polynomial Functions. 9.5 Graphing Rational Functions. 9.6 More on Graphing Rational Functions. Chapter 9 Summary. Chapter 9 Review Problem Set. Chapter 9 Test. 10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. 10.1 Exponents and Exponential Functions. 10.2 Applications of Exponential Functions. 10.3 Inverse Functions. 10.4 Logarithms. 10.5 Logarithmic Functions. 10.6 Exponential Equations, Logarithmic Equations, and Problem Solving. Chapter 10 Summary. Chapter 10 Review Problem Set. Chapter 10 Test. Chapters 1-10 Cumulative Review Problem Set. 11. SYSTEMS OF EQUATIONS. 11.1 Systems of Two Linear Equations in Two Variables. 11.2 Systems of Three Linear Equations in Three Variables. 11.3 Matrix Approach to Solving Linear Systems. 11.4 Determinants. 11.5 Cramer's Rule. 11.6 Partial Fractions (Optional). Chapter 11 Summary. Chapter 11 Review Problem Set. Chapter 11 Test. 12. ALGEBRA OF MATRICES. 12.1 Algebra of 2 X 2 Matrices. 12.2 Multiplicative Inverses. 12.3 _m_ X _n_ Matrices. 12.4 Systems of Linear Inequalities: Linear Programming. Chapter 12 Summary. Chapter 12 Review Problem Set. Chapter 12 Test. Chapters 1-12 Cumulative Review Problem Set. 13. CONIC SECTIONS. 13.1 Circles. 13.2 Parabolas. 13.3 Ellipses. 13.4 Hyperbolas. 13.5 Systems Involving Nonlinear Equations. Chapter 13 Summary. Chapter 13 Review Problem Set. Chapter 13 Test. 14. SEQUENCES AND MATHEMATICAL INDUCTION. 14.1 Arithmetic Sequences. 14.2 Geometric Sequences. 14.3 Another Look at Problem Solving. 14.4 Mathematical Induction. Chapter 14 Summary. Chapter 14 Review Problem Set. Chapter 14 Test. Appendix A: Prime Numbers and Operations with Fractions. Appendix B: Binomial Theorem.