This course covers a wide range of algebra topics from basic number properties to complex numbers and set theory. By the end of the course, students will be able to solve algebraic equations, graph functions, work with polynomials, understand logarithms, and apply probability concepts. The teaching method includes lectures, examples, and practice problems. This course is intended for students in Algebra 1 and Algebra 2 looking to strengthen their algebra skills and knowledge.
Overview
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.
Adding and Subtracting Polynomials.
Multiplying Binomials by the FOIL Method.
Solving Quadratics by Factoring.
Solving Quadratics by Completing the Square.
Solving Quadratics by Using the Quadratic Formula.
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
