Pre-Calculus
P. Prerequisites: Fundamental Concepts of Algebra
- P.1. Real Numbers
- P.2. Exponents
- P.3. Scientific Notation
- P.4. Radicals and Rational Exponents
- P.5. Polynomials
- P.6. Polynomial Arithmetic
- P.7. Factoring Polynomials
- P.8. Rational Expressions
- P.9. Linear Equations
- P.10. Quadratic Equations
- P.11. Linear Inequalities
1. Graphs, Functions, and Models
- 1.1. Graphs and Graphing Utilities
- 1.2. Lines and Slopes
- 1.3. Distance and Midpoint Formulas
- 1.4. Circles
- 1.5. Basics of Functions
- 1.6. Graphs of Functions
- 1.7. Transformations of Functions
- 1.8. Combinations of Functions
- 1.9. Inverse Functions
- 1.10. Modeling with Functions
2. Polynomial and Rational Functions
- 2.1. Complex Numbers
- 2.2. Complex Arithmetic
- 2.3. Quadratic Functions and Their Graphs
- 2.4. Polynomial Functions and Their Graphs
- 2.5. Dividing Polynomials
- 2.6. Zeros of Polynomial Functions
- 2.7. Rational Functions and Their Graphs
- 2.8. Polynomial and Rational Inequalitites
3. Exponential and Logarithmic Functions
- 3.1. Exponential Functions
- 3.2. Logarithmic Functions
- 3.3. Properties of Logarithms
- 3.4. Exponential and Logarithmic Equations
- 3.5. Modeling with Exponential and Logarithmic Functions
- 4.1. Angles and Their Measure
- 4.2. Trigonometric Functions: The Unit Circle
- 4.3. Right Triangle Trigonometry
- 4.4. Trigonometric Functions of Any Angle
- 4.5. Graphs of Sine and Cosine Functions
- 4.6. Graphs of Other Trigonometric Functions
- 4.7. Inverse Trigonometric Functions
- 4.8. Applications of Trigonometric Functions
- 5.1. Verifying Trigonometric Identities
- 5.2. Sum and Difference Formulas
- 5.3. Double-Angle and Half-Angle Formulas
- 5.4. Product-to-Sum and Sum-to-Product Formulas
- 5.5. Trigonometric Equations
6. Additional Topics in Trigonometry
- 6.1. The Law of Sines
- 6.2. The Law of Cosines
- 6.3. Polar Coordinates
- 6.4. Graphs of Polar Equations
- 6.5. Complex Numbers in Polar Form
- 6.6. De Moivre's Theorem
- 6.7. Vectors
- 6.8. The Dot Product
7. Systems of Equations and Inequalities
- 7.1. Systems of Linear Equations in Two Variables
- 7.2. Systems of Linear Equations in Three Variables
- 7.3. Partial Fractions
- 7.4. Systems of Noninear Equations in Two Variables
- 7.5. Systems of Inequalities in Two Variables
- 8.1. Matrices
- 8.2. Determinants and Inverses
- 8.3. Row Reduction
- 8.4. Cramer's Rule
- 8.5. Coordinate Transformation Matrices
9. Conic Sections and Analytic Geometry
- 9.1. The Ellipse
- 9.2. The Hyperbola
- 9.3. The Parabola
- 9.4. Rotation of Axes
- 9.5. Parametric Equations
- 9.6. Conic Sections in Polar Coordinates
