Week 1: Introduction to Algebra
- What is Algebra?
- Variables, Constants, and Expressions
- Order of Operations (PEMDAS)
- Algebraic Notation and Terminology
Week 2: Real Numbers and Their Properties
- Integers, Rational, and Irrational Numbers
- Absolute Value and Opposites
- Properties of Real Numbers: Commutative, Associative, Distributive
- Simplifying Expressions
Week 3: Solving Linear Equations
- One-Step and Two-Step Equations
- Solving Multi-Step Equations with Variables on Both Sides
- Applications of Linear Equations in Real Life
- Introduction to Word Problems
Week 4: Inequalities and Their Solutions
- Graphing Inequalities on the Number Line
- Solving Linear Inequalities
- Compound Inequalities
- Absolute Value Equations and Inequalities
Week 5: Graphing Linear Equations and Functions
- Cartesian Plane and Plotting Points
- Graphing Linear Equations in Two Variables
- Slope-Intercept Form and Point-Slope Form
- Graphing Linear Inequalities
Week 6: Systems of Linear Equations
- Introduction to Systems of Equations
- Solving Systems by Substitution and Elimination
- Graphical Solutions of Systems
- Applications of Systems of Equations
Week 7: Polynomials
- Definition and Classification of Polynomials
- Adding, Subtracting, and Multiplying Polynomials
- Special Products (Difference of Squares, Perfect Squares)
- Division of Polynomials
Week 8: Factoring Polynomials
- Common Factors and Factoring by Grouping
- Factoring Trinomials and Special Binomials
- Solving Quadratic Equations by Factoring
- Applications of Factoring
Week 9: Rational Expressions and Equations
- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Solving Rational Equations
Week 10: Quadratic Equations and Functions
- Solving Quadratic Equations by Factoring
- Completing the Square
- Using the Quadratic Formula
- Graphing Quadratic Functions
Week 11: Radical Expressions and Equations
- Simplifying Radicals
- Operations with Radical Expressions
- Solving Radical Equations
- Introduction to Complex Numbers
Week 12: Exponents and Exponential Functions
- Laws of Exponents
- Scientific Notation
- Exponential Growth and Decay
- Solving Exponential Equations
Week 13: Introduction to Functions
- Definition of a Function
- Domain and Range
- Evaluating Functions
- Linear vs. Non-Linear Functions
Week 14: Review and Practice
- Review of Key Concepts
- Practice Problems and Group Exercises
- Review of Past Assessments
- Preparation for Final Exam
Week 15: Final Exam and Course Wrap-up
- Final Exam (Cumulative)
- Course Feedback and Reflection
- Discussion of Next Steps in Mathematics
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