Algebra EOC Review with Mr. Peters

Introduction

• Focus on algebra end-of-course (EOC) review
• Emphasis on process of elimination and properties of exponents

Key Problems Discussed

1. Properties of Exponents

• Problem involves multiplying with the same base:
  • Multiply coefficients: 8 * 3 = 24
  • Add exponents with the same base: x^4 * x^3 = x^7, y^2 * y^2 = y^4
• Correct Answer: 24x^7y^4
• Tip: Multiply exponents only when dealing with parentheses, e.g., (3x^4y^9)^2*

2. Combining Expressions

• Important trick: Subtraction changes the sign of every number after it.
• Example:
  • Start with: 2x^2 - 7x + 9
  • Adjust signs for the second expression: -5x^2 - 4x + 1
• Combine like terms: 2 - 5 = -3, -7 - 4 = -11, 9 + 1 = 10
• Correct Answer: -3x^2 - 11x + 10 (Answer Choice B)

3. Inequalities

• Solve and match with the correct graph:
  • Example: 6x - 14 ≤ 6x + 6 - 4x
  • Simplify to: 4x - 14 ≤ 6
  • Result: x ≤ 5
• Graphing Tip:
  • "Less than" or "greater than": Open circle on graph.
  • "Less than or equal to" or "greater than or equal to": Closed circle.
• Correct Answer: Graph with closed circle at x=5, arrow pointing left (Answer Choice A)

4. Rearranging Equations

• Solve for L:
  • Example: Given S = πrL + πr^2
  • Subtract πr^2 and divide by πr
  • Solution: L = (S - πr^2) / (πr) (Answer Choice A)
• Tip: Apply inverse operations for addition and multiplication to isolate variables.

5. Solving Equations

• Example: Distribute and combine like terms
  • Start with: 5x + 20 = -8x - 28 + 5x
  • Simplify to: 8x + 20 = -28
  • Final result: x = -6
• Note: Properly manipulate variables and constants to one side of the equation.

Conclusion

• Encouragement to engage with algebra resources
• Calls to action for liking, subscribing, and commenting for more content suggestions

General Tips

• Always remember to flip signs after subtraction.
• Use process of elimination to identify incorrect answer choices.
• Practice working through each step to ensure a clear understanding of algebraic principles.