Algebra 1 Review Study Guide - Online Course / Basic Overview – EOC & Regents – Common Core

Introduction

This tutorial serves as a comprehensive review of Algebra 1 concepts, essential for high school students preparing for exams like the EOC and Regents. It synthesizes key lessons, formulas, and practice problems to help you understand and apply algebraic principles effectively.

Step 1: Understand Basic Algebraic Concepts

• Variables and Expressions: Familiarize yourself with variables (e.g., x, y) and how to manipulate expressions.
• Order of Operations: Remember the order of operations (PEMDAS/BODMAS):
  1. Parentheses/Brackets
  2. Exponents/Orders
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)
• Equations: Learn how to solve linear equations and understand equality.

Step 2: Master Linear Functions

• Function Definition: Understand what a function is and how to identify the domain and range.
• Graphing Linear Equations: Practice plotting points and drawing the line for equations in the form y = mx + b, where:
  • m is the slope
  • b is the y-intercept
• Slope Calculation: Use the formula:
  • Slope (m) = (y2 - y1) / (x2 - x1)

Step 3: Explore Systems of Equations

• Graphical Method: Solve systems by graphing the equations and finding their intersection point.
• Substitution Method: Substitute one equation into another to find variable values.
• Elimination Method: Add or subtract equations to eliminate a variable.

Step 4: Learn About Polynomials

• Definition and Types: Understand what polynomials are, including terms like monomials, binomials, and trinomials.
• Operations: Practice adding, subtracting, and multiplying polynomials.
• Factoring: Learn how to factor polynomials using techniques like grouping, the distributive property, and special products (e.g., difference of squares).

Step 5: Delve into Quadratic Functions

• Standard Form: Recognize the standard form of a quadratic equation, ax² + bx + c = 0.
• Graphing Quadratics: Understand the shape of parabola graphs and how to find the vertex and axis of symmetry.
• Quadratic Formula: Use the quadratic formula to find the roots:

  x = (-b ± √(b² - 4ac)) / (2a)
  

• Completing the Square: Learn this method for solving quadratics and converting to vertex form.

Step 6: Practice with Inequalities

• Solving Inequalities: Understand how to solve linear inequalities and represent solutions on a number line.
• Graphing: Know how to graph inequalities on a coordinate plane.

Step 7: Work on Word Problems

• Translating Words to Equations: Practice converting word problems into algebraic equations.
• Strategies: Use strategies such as identifying keywords and creating a step-by-step plan to solve.

Conclusion

This Algebra 1 review covers essential concepts, including functions, systems of equations, polynomials, quadratics, and inequalities. To reinforce your understanding, practice problems regularly and review any topic you find challenging. For further learning, consider watching the complete video tutorial on YouTube or accessing additional resources through the provided links. Happy studying!