Course Title: Fundamentals of Algebra
Course Description: This course covers the fundamental concepts and techniques of algebra, including operations with algebraic expressions, equations, inequalities, functions, and graphing. Students will develop problem-solving skills and gain a solid foundation in algebraic reasoning.
Course Outline:
- Week 1: Introduction to Algebra
- Definition of algebra and its applications
- Basic algebraic operations (addition, subtraction, multiplication, division)
- Properties of real numbers
- Week 2: Algebraic Expressions
- Simplifying algebraic expressions
- Combining like terms
- Distributive property and factoring
- Week 3: Solving Linear Equations
- One-step and two-step equations
- Multi-step equations
- Equations with variables on both sides
- Week 4: Solving Linear Inequalities
- Solving inequalities and graphing solutions on a number line
- Compound inequalities and interval notation
- Systems of linear inequalities
- Week 5: Functions and Function Notation
- Definition of functions
- Function notation (f(x), g(x))
- Evaluating functions and function composition
- Week 6: Graphing Linear Equations
- Slope-intercept form (y = mx + b)
- Point-slope form and standard form
- Graphing lines and finding intercepts
- Week 7: Systems of Linear Equations
- Solving systems of equations by graphing
- Solving systems of equations by substitution and elimination
- Applications of systems of equations
- Week 8: Exponents and Exponential Functions
- Laws of exponents
- Exponential growth and decay
- Graphing exponential functions
- Week 9: Quadratic Equations and Functions
- Solving quadratic equations by factoring
- Quadratic formula and completing the square
- Graphing quadratic functions
- Week 10: Rational Expressions and Equations
- Simplifying and multiplying rational expressions
- Dividing rational expressions and solving rational equations
- Applications of rational functions
Course Assignments:
- Weekly problem sets and quizzes
- Equation-solving and inequality-solving exercises
- Function evaluation and graphing assignments
- Systems of equations and applications problems
- Quadratic equation and rational expression problems
- Final project: Algebraic problem-solving and application
Course Materials:
- Textbook: “Algebra Essentials” by Robert F. Blitzer
- Online tutorials and resources for algebra concepts
- Graphing calculator or graphing software
- Practice worksheets and exercises
- Real-world applications of algebra in various fields
Assessment:
- Quizzes and exams covering algebraic concepts and techniques
- Problem-solving assignments and projects
- Function evaluation and graphing proficiency assessment
- Final project evaluation based on problem-solving skills and application of algebraic concepts
- Class participation and engagement in discussions and activities
Prerequisites: Basic arithmetic skills and familiarity with elementary algebra concepts (e.g., solving simple equations, basic operations with fractions) would be helpful but not required.