Unit 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