Class Notes (Pre-Calc)
Chapter 1 - Fundamentals
Lesson 1.1 KEY - Exponents and Polynomial Operations
Lesson 1.2 KEY - Factoring Polynomials
Lesson 1.3 KEY - Rational Expressions
Lesson 1.4 KEY - Radicals & Rational Exponets
Lesson 1.5 KEY - Complex Numbers
Lesson 1.6 KEY - Linear Equations & Absolute Value Equations
Lesson 1.7 KEY - Quadratic Equations
Lesson 1.8 KEY - Radical Equations
Lesson 1.9 KEY - Rational Equations
Chapter 2 - Functions and Their Graphs
Lesson 2.1 KEY - Functions Review
Lesson 2.2 KEY - Intercepts, Zeros, & Critical Points
Lesson 2.3 KEY - Continuity & End Behavior
Lesson 2.4 KEY - Test for Symmetry & Even and Odd Functions
Lesson 2.5 KEY - Average Rate of Change
Lesson 2.6 KEY - Parent Functions and Transformations
Lesson 2.7 KEY - Graphing Functions
Lesson 2.8 KEY - Piecewise Functions
Lesson 2.9 KEY - Function Operations & Compositions of Functions
Chapter 3 - Polynomial and Rational Functions
Lesson 3.1 KEY - Graphing Power Functions
Lesson 3.2 KEY - Graphing Power Functions with Rational Exponets
Lesson 3.3 KEY - Graphing Polynomial Fucntions
Lesson 3.4 KEY - Zeros of Polynomials, Linear Factors, and Multiplicity
Lesson 3.5 KEY - Dividing Polynomials
Lesson 3.6 KEY - Remainder and Factor Theorems
Lesson 3.7 KEY - Rational Zero Theorem, Find Rational Zeros
Lesson 3.8 KEY - Irrational Zeros, Descartes Rule of Signs
Lesson 3.9 KEY - Complex Zeros, Fundamental Theorem of Algebra
Lesson 3.10 KEY - Using Zeros to Write Polynomial Functions
Lesson 3.11 KEY - Graphing Rotational Functions
Lesson 3.12 KEY - Rational Functions with Slant Asymptotes
Lesson 3.13 KEY - Nonlinear Inequalities, Polynomial Inequalities
Chapter 4 - Exponential & Logarithmic Functions
Lesson 4.1 KEY - Graphing Exponential Functions and the Natural Base
Lesson 4.2 KEY - Exponential Growth and Decay Application
Lesson 4.3 KEY - Compounding & Continouous Interest
Lesson 4.5 KEY - Properities of Logarithms
Lesson 4.6 KEY - Graphing Logarithms
Lesson 4.7 KEY - Solving Exponential Equations
Lesson 4.8 KEY- Solving Logarithmic Equations
Lesson 4.9 KEY - Solving Exponentials using Logs
Lesson 4.10 KEY - Review Logarithmic and Exponential Equations
Lesson 4.11 KEY - Application with Solving Equations
Chapter 5 - Trigonometric Functions
Lesson 5.1 KEY - Standard Form of an Angle
Lesson 5.2 KEY - Arc Length and Area of Sectors
Lesson 5.3 KEY - Circular Motion Linear and Angular Speed
Lesson 5.4 KEY- Six Trigonometric Functions
Lesson 5.5 KEY - Finding Side and Angle Measures
Lesson 5.6 KEY - Trigonometric Functions for Any Angle
Lesson 5.8 KEY- Law of Cosines
Lesson 5.9 KEY - Mixed Law of Sines & Law of Cosines Area of Triangles
Lesson 5.10 KEY - Graphing Sine, Cosine, and Tangent Functions
Lesson 5.11 KEY - Translating Sine, Cosine, and Tangent Functions
Lesson 5.12 KEY - Graphing Reciprocal Functions
Lesson 5.13 KEY - Graphing Trigonometric Functions Review
Lesson 5.14 KEY - Inverse Trigonometric Functions
Chapter 6 - Trigonometric Identities & Equations
Lesson 6.1 KEY - Basic Trigonometric Identities
Lesson 6.2 KEY - Simplify and Rewrite Trigonometric Expressions
Lesson 6.3 KEY - Proving Trigonometric Identities
Lesson 6.4 KEY - Sum and Difference of Angle Identities
Lesson 6.5 KEY - Double Andlge and Half Angle Identities
Lesson 6.6 KEY - Product SUm and Power Reducing Identities
Lesson 6.7 KEY - Proving Identities
Lesson 6.8 KEY - Solving Trigonometric Equations Part 1 and Part 2
Chapter 7 - Polar and Parametric Equations
Lesson 7.1 KEY - Polar Coordinates
Lesson 7.2 KEY - Symmetry of Polar Graphs
Lesson 7.3 KEY - Classifying & Graphing Classic Polar Curves
Lesson 7.4 KEY - Converting between Polar & Rectangular Forms
Lesson 7.5 KEY - Polar Forms of Complex Numbers
Lesson 7.6 KEY - Products, Quotients, Powers (DeMoivre's Theorem) and Roots of Complex Numbers
Lesson 7.7 KEY - Parametric Equations: Graphing and Writing in Rectangular Form
Lesson 7.8 KEY - Modeling with Parametric Equations (Projectile Motion)
Chapter 8 - Vectors
Lesson 8.1 KEY - Introduction to Vectors (Parts, Naming, Types)
Lesson 8.2 KEY - Operations with Vectors
Lesson 8.3 KEY - Vector Application; Horizontal and Vertical Componets
Lesson 8.4 KEY - Dot Product
Lesson 8.5 KEY Video - Vector Projections
Lesson 8.6 KEY - Vectors in 3D Space
Chapter 9 - Conic Sections
Lesson 9.1 KEY - Introduction to Conic Sections; Circles
Lesson 9.2 KEY - Ellipses (Day 1 - Graphing)
Lesson 9.3 KEY - Ellipses (Day 2 - Writing Equations)
Lesson 9.4 KEY - Hyperbolas (Day 1 - Graphing)
Lesson 9.5 KEY - Hyperbolas (Day 2 - Writing Equations)
Lesson 9.6 KEY - Parabolas (Day 1 - Graphing)
Lesson 9.7 KEY - Parabolas (Day 2 - Writing Equations)
Lesson 9.8 KEY - Applications of Conic Sections
Lesson 9.9 KEY - General Conic Form; Identifying Conic Sections
Lesson 9.10 KEY - Polar Equations of Conic Sections (Day 1 - Identifying & Graphing)
Lesson 9.11 KEY - Polar Equations of Conic Sections (Day 2 - Writing)
Chapter 10 - Systems of Equations and Matrices
Lesson 10.1 KEY - Two-Variable Systems of Equations Review
Lesson 10.2 Video - Nonlinear Systems of Equations
Lesson 10.3 KEY - Systems of Equations in three Variables
Lesson 10.4 KEY - Introduction to Matrices
Lesson 10.5 KEY - Multiplying Matrices
Lesson 10.6 KEY - Determinants and inverse Matrices
Lesson 10.7 KEY - Matrices and Graphing Calculator
Lesson 10.8 KEY - Solving Systems of Equations with Cramer's Rule
Lesson 10.9 KEY - Solving Systems of Equations with Inverse Matrices
Lesson 10.10 KEY - Solving Systems with Gaussian Elimination
Lesson 10.11 KEY - Solving Systems with Gauss-Jordan Elimination
Lesson 10.12 KEY - Partial Fractions (Day 1 - Proper Expressions)
Lesson 10.13 KEY - Partial Fractions (Day 2 - Improper Expressions)
Lesson 10.14 KEY - Partial Fractions (Day 3 - Special Case Factors)
Chapter 11 - Sequences and Series
Lesson 11.1 KEY - Explicit and Recursive Sequences
Lesson 11.2 KEY - Arithmetic Sequences
Lesson 11.3 KEY - Geometric Sequences
Lesson 11.4 KEY - Series & Sigma Notation; Arithmetic Series
Lesson 11.5 KEY - Geometric Series (Finite and Infinite)
Lesson 11.6 KEY - Arithmetic vs. Geometric Sequences and Series
Lesson 11.7 KEY - Mathematical Induction
Lesson 11.8 KEY - Binomial Expansion: Pascal's Triangle & Binomial Theorem
Unit 11 Study Guide (KEY)
Chapter 12 - Introduction to Calculus
Lesson 12.1 KEY - Limit Notation, Estimating Limits Graphicaaly, Limits that Fail to Exist
Lesson 12.2 KEY - One-Sided Limits
Lesson 12.3 KEY - Finding Limits Algebraically: Properties of Limits & Direct Substitution
Lesson 12.4 KEY - Finidng Limits Algebraically: Factoring & Rationalizing
Lesson 12.5 KEY - Limits at infinity; Limits of Sequences
Lesson 12.6 KEY - Tangent Lines
Lesson 12.7 KEY - Derivatives (using limits and rules)
Lesson 12.8 KEY - Application: Average vs Instantaneous Rate of Chance and Velocity