Beginning and Intermediate Algebra

1. REAL NUMBERS AND THEIR BASIC PROPERTIES. Real Numbers and Their Graphs. Fractions. Exponents and Order of Operations. Adding and Subtracting Real Numbers. Multiplying and Dividing Real Numbers. Algebraic Expressions. Properties of Real Numbers. Projects. Chapter 1 Review. Chapter 1 Test. 2. EQUATIONS AND INEQUALITIES. Solving Basic Linear Equations in One Variable. Solving More Linear Equations in One Variable. Simplifying Expressions to Solve Linear Equations in One Variable. Formulas. Introduction to Problem Solving. Motion and Mixture Problems. Solving Linear Inequalities in One Variable. Projects. Chapter 2 Review. Chapter 2 Test. Cumulative Review for Chapters 1-2. 3. GRAPHING; WRITING EQUATIONS OF LINES; FUNCTIONS. The Rectangular Coordinate System. Graphing Linear Equations. Slope of a Line. Point-Slope Form. Slope-Intercept Form. Functions. Solving Linear Inequalities in One or Two Variables. Projects. Chapter 3 Review. Chapter 3 Test. 4. POLYNOMIALS. Natural-Number Exponents. Zero and Negative-Integer Exponents. Scientific Notation. Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Dividing Polynomials by Monomials. Dividing Polynomials by Polynomials. Synthetic Division. Projects. Chapter 4 Review. Chapter 4 Test. Cumulative Review Exercises for Chapters 1-4. 5. FACTORING POLYNOMIALS. Factoring Out the Greatest Common Factor; Factoring by Grouping. Factoring the Difference of Two Squares. Factoring Trinomials with a Leading Coefficient of 1. Factoring General Trinomials. Factoring the Sum and Difference of Two Cubes. Summary of Factoring Techniques. Solving Equations by Factoring. Problem Solving. Projects. Chapter 5 Review. Chapter 5 Test. 6. RATIONAL EXPRESSIONS AND EQUATIONS; PROPORTION AND VARIATION. Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Simplifying Complex Fractions. Solving Equations That Contain Rational Expressions. Solving Applications That Contain Rational Expressions. Proportion and Variation. Projects. Chapter 6 Review. Chapter 6 Test. Cumulative Review Exercises for Chapters 1-6. 7. TRANSITIONING TO INTERMEDIATE ALGEBRA. Review of Solving Linear Equations and Inequalities in One Variable. Review of Graphing, Slope, and Writing Equations of Lines. Review of Functions. Review of Factoring. Review of Rational Expressions. Solving Equations in One Variable Containing Absolute Values. Solving Inequalities in One Variable Containing an Absolute-Value Term. Projects. Chapter 7 Review. Chapter 7 Test. 8. SOLVING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES. Solving Systems of Linear Equations by Graphing. Solving Systems of Linear Equations by Substitution and Elimination. Solving Applications of Systems of Linear Equations in Two Variables. Solving Systems of Three Linear Equations in Three Variables. Solving Systems if Linear Equations Using Matrices. Solving Systems of Linear Equations Using Determinants. Solving Systems of Linear Inequalities in Two Variables. Solving Systems Using Linear Programming. Projects. Chapter 8 Review. Chapter 8 Test. Cumulative Review Exercises for Chapters 1-8. 9. RADICALS AND RATIONAL EXPONENTS. Radical Expressions. Applications of the Pythagorean Theorem and the Distance Formula. Rational Exponents. Simplifying and Combining Rational Expressions. Multiplying and Dividing Radical Expressions. Radical Equations. Complex Numbers. Projects. Chapter 9 Review. Chapter 9 Test. 10. QUADRATIC FUNCTIONS AND INEQUALITIES. Solving Quadratic Equations Using the Square-Root Property and by Completing the Square. Solving Quadratic Equations by the Quadratic Formula. The Discriminant and Equations That Can be Written in Quadratic Form. Graphs of Quadratic Functions. Graphs of Nonlinear Functions. Quadratic and Other Nonlinear Inequalities. Projects. Chapter 10 Review. Chapter 10 Test. Cumulative Review Exercises for Chapters 1-10. 11. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Algebra and Composition of Functions. Inverse of Functions.