Algebra 1

  1. Introduction to Algebra

    • Understanding Variables and Expressions

    • The Role of Constants and Coefficients

    • Writing and Evaluating Expressions

    • Order of Operations (PEMDAS)

  2. Solving Linear Equations

    • Properties of Equality

    • One-Step Equations

      • Examples: (x + 5 = 12) and (x - 3 = 4)

    • Two-Step Equations

      • Examples: (2x + 3 = 11)

    • Multi-Step Equations

      • Examples: (3(x - 2) = 9)

    • Solving Equations with Variables on Both Sides

  3. Graphing Linear Equations

    • The Cartesian Coordinate System

    • Writing Linear Equations in Slope-Intercept Form ((y = mx + b))

    • Finding the Slope from a Graph

    • Graphing Linear Equations

    • Using a Table of Values

  4. Inequalities

    • Solving Linear Inequalities

    • Graphing Inequalities on a Number Line

    • Compound Inequalities

    • Systems of Inequalities

  5. Systems of Linear Equations

    • Solving Systems by Graphing

    • Solving Systems Using Substitution

    • Solving Systems Using Elimination

    • Applications of Systems of Equations

  6. Exponents and Polynomials

    • Laws of Exponents

    • Adding and Subtracting Polynomials

    • Multiplying Polynomials

    • Special Products

    • Factoring Polynomials

  7. Quadratic Functions

    • Introduction to Quadratic Equations

    • The Standard Form of Quadratics ((y = ax^2 + bx + c))

    • Graphing Quadratic Functions

    • Finding the Vertex and Axis of Symmetry

    • Applications of Quadratic Functions

  8. Data Analysis and Probability

    • Representing Data with Graphs

    • Measures of Central Tendency (Mean, Median, Mode)

    • Understanding Probability Basics

    • Theoretical vs. Experimental Probability

  9. Functions and Relations

    • Understanding Functions and Their Notation

    • Evaluating Functions

    • Domain and Range

    • Function Operations (Addition, Subtraction, etc.)

  10. Review and Practice

    • Practice Problems for Each Unit

    • Review Worksheets

    • Sample Tests and Quizzes

    • Study Tips and Resources

This study guide covers all essential topics in Algebra 1, ensuring thorough preparation for learning and assessments.