Learning Objectives
5 objectives- Understand and apply fundamental algebraic concepts including variables, constants, coefficients, and terms.
- Solve various types of linear and quadratic equations using algebraic and graphical methods.
- Graph linear equations, inequalities, and interpret their key features such as slope and intercepts.
- Manipulate polynomials, exponents, radicals, and rational expressions accurately.
- Translate real-world problems into algebraic expressions and solve them using appropriate strategies.
Content Outline
PreviewUnit 2935: Comprehensive Algebra
1. Introduction to Algebra
- Definition and importance of algebra
- Variables, constants, coefficients, and terms
- Algebraic expressions
- Writing expressions from real-world scenarios
- Combining like terms
2. Solving Linear Equations
- One-step equations
- Using inverse operations
- Two-step equations
- Multi-step equations
- Combining like terms
- Applying the distributive property
- Checking solutions
3. Graphing Linear Equations
- Coordinate plane basics
- Forms of linear equations
- Slope-intercept form (y = mx + b)
- Point-slope form
- Standard form (Ax + By = C)
- Plotting points and drawing the line
- Understanding slope and y-intercept
- Applications of graphing
4. Systems of Equations
- Definition and types of systems
- Methods of solving systems
- Substitution method
- Elimination method
- Graphical method
- Interpreting solutions
- One solution
- No solution
- Infinite solutions
- Real-life applications of systems of equations
5. Quadratic Equations
- Definition and standard form (ax² + bx + c = 0)
- Methods of solving
- Factoring
- Quadratic formula
- Completing the square
- Graphing quadratic functions
- Parabolas
- Vertex, axis of symmetry, and intercepts
6. Inequalities
- Linear inequalities in one variable
- Solving and graphing on number lines
- Linear inequalities in two variables
- Graphing on coordinate plane
- Compound inequalities
- And, or statements
- Solution sets
7. Exponents and Radicals
- Properties of exponents
- Product rule
- Quotient rule
- Power of a power
- Simplifying expressions with exponents
- Introduction to radicals
- Simplifying radicals
- Rational exponents
8. Polynomials
- Definition and terminology
- Terms, degree, leading coefficient
- Operations on polynomials
- Addition and subtraction
- Multiplication
- Division (long division and synthetic division)
9. Rational Expressions
- Definition and examples
- Simplifying rational expressions
- Factoring numerator and denominator
- Finding common denominators
- Reducing to lowest terms
- Solving equations involving rational expressions
10. Word Problems in Algebra
- Translating word problems into algebraic expressions
- Setting up equations and inequalities
- Strategies for solving
- Practice with diverse real-world problems
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