College Algebra

Math Lesson

A REVIEW OF BASIC ALGEBRA. Sets of Real Numbers. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Polynomials. Factoring Polynomials. Algebraic Fractions.

1. EQUATIONS AND INEQUALITIES. Equations. Applications of Linear Equations. Quadratic Equations. Applications of Quadratic Equations. Complex Numbers. Polynomial and Radical Equations. Inequalities. Absolute Value.

2. THE RECTANGULAR COORDINATE SYSTEM AND GRAPHS OF EQUATIONS. The Rectangular Coordinate System. The Slope of a Nonvertical Line. Writing Equations of Lines. Graphs of Equations. Proportion and Variation.

3. FUNCTIONS. Functions and Function Notation. Quadratic Functions. Polynomial and Other Functions. Translating and Stretching Graphs. Rational Functions. Operations on Functions. Inverse Functions.

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Applications of Exponential Functions. Logarithmic Functions and Their Graphs. Applications of Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations.

5. SOLVING POLYNOMIAL EQUATIONS. The Remainder and Factor Theorems; Synthetic Division. Descartes’ Rule of Signs and Bounds on Roots. Rational Roots of Polynomial Equations. Irrational Roots of Polynomial Equations.

6. LINEAR SYSTEMS. Systems of Linear Equations. Gaussian Eliminations and Matrix Methods. Matrix Algebra. Matrix Inversion. Determinants. Partial Fractions. Graphs of Linear Inequalities. Linear Programming.

7. CONIC SECTIONS AND QUADRATIC SYSTEMS. The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Simultaneous Second-Degree Equations.

8. NATURAL NUMBER FUNCTIONS AND PROBABILITY. The Binomial Theorem. Sequences, Series, and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. Permutations and Combinations. Probability. Computation of Compound Probabilities. Odds and Mathematical Expectation.

9. THE MATHEMATICS OF FINANCE. Interest. Annuities and Future Value. Present Value of an Annuit