Intermediate Algebra: A Guided Approach

1. A REVIEW OF BASIC ALGEBRA. Reach for Success. The Real Number System. Arithmetic and Properties of Real Numbers. Exponents. Scientific Notation. Solving Linear Equations in One Variable. Using Linear Equations to Solve Applications. More Applications of Linear Equations in One Variable. Projects. Reach for Success Extension. Chapter Review. Chapter Test. 2. GRAPHS, EQUATIONS OF LINES, AND FUNCTIONS. Reach for Success. Graphing Linear Equations. Slope of a Line. Writing Equations of Lines. Introduction to Functions. Graphing Other Functions. Projects. Reach for Success Extension. Chapter Review. Chapter Test. Cumulative Review for Chapters 1-2. 3. SYSTEMS OF LINEAR EQUATIONS. Reach for Success. Solving Systems of Two Linear Equations in Two Variables by Graphing. Solving Systems of Two Linear Equations in Two Variables by Substitution and Elimination (Addition). Solving Systems of Three Linear Equations in Three Variables. Solving Systems of Linear Equations Using Matrices. Solving Systems of Linear Equations Using Determinants. Projects. Reach for Success Extension. Chapter Review. Chapter Test. 4. INEQUALITIES. Reach for Success. Solving Linear Inequalities in One Variable. Solving Absolute Value Equations and Inequalities in One Variable. Solving Linear Inequalities in Two Variables. Solving Systems if Linear and Quadratic Inequalities in Two Variables by Graphing. Solving Systems Using Linear Programming. Projects. Reach for Success Extension. Chapter Review. Chapter Test. Cumulative Review for Chapters 1-4. 5. POLYNOMIALS, POLYNOMIAL FUNCTIONS, AND EQUATIONS. Reach for Success. Polynomial and Polynomial Functions. Adding and Subtracting Polynomials. Multiplying Polynomials. The Greatest Common Factor and Factoring by Grouping. The Difference of Two Squares; the Sum and Difference of Two Cubes. Factoring Trinomials. Summary of Factoring Techniques. Solving Equations by Factoring. Projects. Reach for Success Extension. Chapter Review. Chapter Test. 6. RATIONAL EXPRESSIONS. Reach for Success. Finding the Domain of Rational Functions and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Simplifying Complex Fractions. Solving Equations Containing Rational Expressions. Dividing Polynomials. Synthetic Division. Proportion and Variation. Projects. Reach for Success Extension. Chapter Review. Chapter Test. Cumulative Review for Chapters 1-6. 7. RADICAL EXPRESSIONS AND EQUATIONS. Reach for Success. Radical Expressions. Applications of the Pythagorean Theorem and the Distance Formula. Rational Exponents. Simplifying and Combining Radical Expressions. Multiplying Radical Expressions and Rationalizing. Radical Equations. Complex Numbers. Projects. Reach for Success Extension. Chapter Review. Chapter Test. 8. QUADRATIC EQUATIONS AND FUNCTIONS; INEQUALITIES; AND ALGEBRA, COMPOSITION, AND INVERSES OF FUNCTIONS. Reach for Success. Solving Quadratic Equations Using the Square-Root Property and by Completing the Square. Solving Quadratic Equations Using the Quadratic Formula. The Discriminant and Equations That Can Be Written in Quadratic Form. Graphs of Quadratic Functions. Quadratic and Other Nonlinear Inequalities. Algebra and Composition of Functions. Inverses of Functions. Projects. Reach for Success Extension. Chapter Review. Chapter Test. Cumulative Review for Chapters 1-8. 9. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Reach for Success. Exponential Functions. Base-e Exponential Functions. Logarithmic Functions. Natural Logarithms. Properties of Logarithms. Exponential and Logarithmic Equations. Projects. Reach for Success Extension. Chapter Review. Chapter Test. 10. CONIC SECTIONS AND MORE GRAPHING. Reach for Success. The Circle and the Parabola. The Ellipse. The Hyperbola. Systems Containing Second-Degree Equations. Piecewise-Defined Functions and the Greatest Integer Function. Projects. Reach for Success Extension. Chapter Review. Chapter Test. Cumulative Review for Chapters 1-10. 11. MISCELLANEOUS TOPICS. Reach for Success. The Binomial Theorem. Arithmetic Sequences and Series. Geometric Sequences and Series. Infinite Geometric Sequences and Series. Permutations and Combination. Probability. Projects. Reach for Success Extension. Chapter Review. Chapter Test. Cumulative Review for Chapters 1-11. APPENDIX 1: SYMMETRIES OF GRAPHS. APPENDIX 2: SAMPLE FINAL EXAMINATION. APPENDIX 3: TABLES. APPENDIX 4: ANSWERS TO SELECTED EXERCISES.