Elementary and Intermediate Algebra
1. AN INTRODUCTION TO ALGEBRA. Introducing the Language of Algebra. Fractions. The Real Numbers. Adding Real Numbers; Properties of Addition. Subtracting Real Numbers. Multiplying and Dividing Real Numbers; Multiplication and Division Properties. Exponents and Order of Operations. Algebraic Expressions. Simplifying Algebraic Expressions Using Properties of Real Numbers. Chapter Summary and Review. Chapter Test. Group Project. 2. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING. Solving Equations Using Properties of Equality. More about Solving Equations. Applications of Percent. Formulas. Problem Solving. More about Problem Solving. Solving Inequalities. Chapter Summary and Review. Chapter Test. Group Project. 3. GRAPHING LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES; FUNCTIONS. Graphing Using the Rectangular Coordinate System. Graphing Linear Equations. Intercepts. Slope and Rate of Change. Slope-Intercept Form. Point-Slope Form. Graphing Linear Inequalities. An Introduction to Functions. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 4. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES. Solving Systems of Equations by Graphing. Solving Systems of Equations by Substitution. Solving Systems of Equations by Elimination (Addition). Problem Solving Using Systems of Equations. Solving Systems of Linear Inequalities. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 5. EXPONENTS AND POLYNOMIALS. Rules for Exponents. Zero and Negative Exponents. Scientific Notation. Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Special Products. Polynomials. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 6. FACTORING AND QUADRATIC EQUATIONS. The Greatest Common Factor; Factoring by Grouping. Factoring Trinomials of the Form x2 + bx + c. Factoring Trinomials of the Form ax2 + bx + c. Factoring Perfect-Square Trinomials and the Difference of Two Squares. Factoring the Sum and Difference of Two Cubes. A Factoring Strategy. Solving Quadratic Equations by Factoring. Applications of Quadratic Equations. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 7. RATIONAL EXPRESSIONS AND EQUATIONS. Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting with Like Denominators; Least Common Denominators. Adding and Subtracting with Unlike Denominators. Simplifying Complex Fractions. Solving Rational Equations. Problem Solving Using Rational Equations. Proportions and Similar Triangles. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 8. TRANSITION TO INTERMEDIATE ALGEBRA. Review of Solving Linear Equations, Formulas, and Linear Inequalities; Applications. Functions. Graphs of Functions. Solving Compound Inequalities. Solving Absolute Value Equations and Inequalities. Review of Factoring Methods: GCF, Grouping, Trinomials. Review of Factoring Methods: The Difference of Two Squares; The Sum and Difference of Two Cubes. Review of Rational Expressions and Rational Equations; Rational Functions. Variation. Chapter Summary and Review. Chapter Test. Group Project. 9. RADICAL EXPRESSIONS AND EQUATIONS. Radical Expressions and Radical Functions. Rational Exponents. Simplifying and Combining Radical Expressions. Multiplying and Dividing Radical Expressions. Solving Radical Equations. Geometric Applications of Radicals. Complex Numbers. Chapter Summary and Review. Chapter Test. Group Project. 10. QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES. The Square Root Property and Completing the Square. The Quadratic Formula. The Discriminant and Equations That Can Be Written in Quadratic Form. Quadratic Functions and Their Graphs. Quadratic and Other Nonlinear Inequalities. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 11. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Algebra and Composition of Functions. Inverse Functions. Exponential Functions. Base-e Exponential Functions. Logarithmic Functions. Base-e Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary and Review. Chapter Test. Group Project. 12. MORE ON SYSTEMS OF EQUATIONS. Solving Systems of Equations in Two Variables; Applications. Solving Systems of Equations in Three Variables. Problem Solving Using Systems of Three Equations. Solving Systems of Equations Using Matrices. Solving Systems of Equations Using Determinants. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 13. CONIC SECTIONS; MORE GRAPHING. The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Nonlinear Systems of Equations. Chapter Summary and Review. Chapter Test. Group Project. 14. MISCELLANEOUS TOPICS. The Binomial Theorem. Arithmetic Sequences and Series. Geometric Sequences and Series. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. Appendix 1: Roots and Powers. Appendix 2: Synthetic Division. Appendix 3: Answers to Selected Problems.--This text refers to thePaperbackedition.