College Algebra

P. PREREQUISITES. Modeling the Real World with Algebra. Real Numbers and Their Properties. The Real Number Line and Order. Integer Exponents. Rational Exponents and Radicals. Algebraic Expressions. Discovery Project Visualizing a Formula. Factoring. Rational Expressions. Chapter P Review. Chapter P Test. Focus on Problem Solving General Principles. 1. EQUATIONS AND INEQUALIITIES. Basic Equations. Modeling with Equations. Discovery Project Equations Through the Ages. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. Absolute Value Equations and Inequalities. Chapter 1 Review. Chapter 1 Test. Focus on Modeling Making the Best Decisions. 2. COORDINATES AND GRAPHS. The Coordinate Plane. Discovery Project Visualizing Data. Graphs of Equations in Two Variables. Graphing Calculators: Solving Equations and Inequalities Graphically. Lines. Making Models Using Variation. Chapter 2 Review. Chapter 2 Test. Cumulative Review Test: Chapters 1 and 2. Focus on Modeling Fitting Lines to Data. 3. FUNCTIONS. What is a Function? Graphs of Functions. Discovery Project Relations and Functions. Getting Information from the Graph of a Function. Average Rate of Change of a Function. Transformations of Functions. Combining Functions. Discovery Project Iteration and Chaos. One-to-One Functions and Their Inverses. Chapter 3 Review. Chapter 3 Test. Focus on Modeling with Functions. 4. POLYNOMIALS AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Discovery Project Zeroing in on a Zero. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Chapter 4 Review. Chapter 4 Test. Focus on Modeling Fitting Polynomial Curves to Data. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Discovery Project Exponential Explosion. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Chapter 5 Review. Chapter 5 Test. Cumulative Review Test: Chapters 3, 4, and 5. Focus on Modeling Fitting Exponential and Power Curves to Data. 6. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. DISCOVERY PROJECT Best Fit Versus Exact Fit. Partial Fractions. Systems of Inequalities. Chapter 6 Review. Chapter 6 Test. Focus on Modeling Linear Programming. 7. MATRICES AND DETERMINANTS. Matrices and Systems of Linear Equations. The Algebra of Matrices. Discovery Project Will the Species Survive? Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rule. Chapter 7 Review. Chapter 7 Test. Focus on Modeling Computer Graphics. 8. CONIC SECTIONS. Parabolas. Discovery Project Rolling Down a Ramp. Ellipses. Hyperbolas. Shifted Conics. Chapter 8 Review. Chapter 8 Test. Cumulative Review Test: Chapters 6, 7, and 8. Focus on Modeling Conics in Architecture. 9. SEQUENCES AND SERIES. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Discovery Project Finding Patterns. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Chapter 9 Review. Chapter 9 Test. Focus on Modeling with Recursive Sequences.