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# Algebra 1 and 2

### Overview

Dive into a comprehensive 6-hour video series covering essential topics in Algebra 1 and 2. Learn to manipulate variables, solve equations and inequalities, work with polynomials, graph functions, and explore advanced concepts like conic sections, logarithms, and complex numbers. Master fundamental algebraic skills through clear explanations of topics ranging from basic number properties to theoretical probability, preparing you for success in your algebra studies and beyond.

### Syllabus

Introduction to Algebra: Using Variables.
Basic Number Properties for Algebra.
Algebraic Equations and Their Solutions.
Algebraic Equations With Variables on Both Sides.
Algebraic Word Problems.
Solving Algebraic Inequalities.
Square Roots, Cube Roots, and Other Roots.
Simplifying Expressions With Roots and Exponents.
Solving Algebraic Equations With Roots and Exponents.
Introduction to Polynomials.
Multiplying Binomials by the FOIL Method.
Solving Quadratics by Completing the Square.
Solving Higher-Degree Polynomials by Synthetic Division and the Rational Roots Test.
Manipulating Rational Expressions: Simplification and Operations.
Graphing in Algebra: Ordered Pairs and the Coordinate Plane.
Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts.
Graphing Lines in Slope-Intercept Form (y = mx + b).
Graphing Lines in Standard Form (ax + by = c).
Graphing Parallel and Perpendicular Lines.
Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination.
Absolute Values: Defining, Calculating, and Graphing.
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational.
Back to Algebra: What are Functions?.
Manipulating Functions Algebraically and Evaluating Composite Functions.
Graphing Algebraic Functions: Domain and Range, Maxima and Minima.
Transforming Algebraic Functions: Shifting, Stretching, and Reflecting.
Continuous, Discontinuous, and Piecewise Functions.
Inverse Functions.
The Distance Formula: Finding the Distance Between Two Points.
Graphing Conic Sections Part 1: Circles.
Graphing Conic Sections Part 2: Ellipses.
Graphing Conic Sections Part 3: Parabolas in Standard Form.
Graphing Conic Sections Part 4: Hyperbolas.
Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros.
Graphing Rational Functions and Their Asymptotes.
Solving and Graphing Polynomial and Rational Inequalities.
Evaluating and Graphing Exponential Functions.
Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions.
Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property.
Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions.
Solving Exponential and Logarithmic Equations.
Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem.
Set Theory: Types of Sets, Unions and Intersections.
Sequences, Factorials, and Summation Notation.
Theoretical Probability, Permutations and Combinations.

### Taught by

Professor Dave Explains

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