Intermediate Algebra

1. A REVIEW OF BASIC ALGEBRA. The Language of Algebra. The Real Numbers. Operations with Real Numbers. Simplifying Algebraic Expressions Using Properties of Real Numbers. Solving Linear Equations Using Properties of Equality. Solving Formulas; Geometry. Using Equations to Solve Problems. More about Problem Solving. Chapter Summary and Review. Chapter Test. Group Project. 2. GRAPHS, EQUATIONS OF LINES, AND FUNCTIONS. Graphs. Graphing Linear Equations in Two Variables. Rate of Change and the Slope of a Line. Writing Equations of Lines. An Introduction to Functions. Graphs of Functions. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 3. SYSTEMS OF EQUATIONS. Solving Systems of Equations by Graphing. Solving Systems of Equations Algebraically. Solving Systems of Equation in Three Variables. Solving Systems of Equations Using Matrices. Solving Systems of Equations Using Determinants. Problem Solving Using Systems of Two Equations. Problem Solving Using Systems of Three Equations. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 4. INEQUALITIES. Solving Linear Inequalities in One Variable. Solving Compound Inequalities. Solving Absolute Value Equations and Inequalities. Linear Inequalities in Two Variables. Systems of Linear Inequalities. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 5. EXPONENTS, POLYNOMIALS, AND POLYNOMIAL FUNCTIONS. Exponents. Scientific Notation. Polynomials and Polynomial Functions. Multiplying Polynomials. The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials. The Difference of Two Squares; the Sum and Difference of Two Cubes. Summary of Factoring Techniques. Solving Equations by Factoring. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 6. RATIONAL EXPRESSIONS AND EQUATIONS. Rational Functions and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Simplifying Complex Fractions. Dividing Polynomials. Synthetic Division. Solving Rational Equations. Problem Solving Using Rational Equations. Proportion and Variation. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review 7. 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. Cumulative Review. 8. 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. 9. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Algebra and Composition of Functions. Inverse Functions. Exponential Functions. Logarithmic Functions. Base-e Exponential and Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review. 10. 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. 11. 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: Answers to Selected Problems.