Keystone Exam Review - Day 1

Overview

• Instructor: M Sher
• Session: First day of a four-day review
• Focus: Module 1 of Keystone Exam
• Content: Released questions from Keystone exam administrators

Important Concepts

Greatest Common Factor (GCF) in Monomials

• Definition: The GCF for variables is the smallest power of the variable, not the largest.
• Example: Given monomials: (x^4 y^8) and (x^6 y^4)
  • Smallest power for (x): (x^4)
  • Smallest power for (y): (y^4)
  • GCF: (x^4 y^4)

Simplifying Expressions with Roots

• Index Rule: Divide the exponent by the index of the root.
• Example: Cube root and square root operations:
  • Mistake Identified: Divide by 3 for cube root, not by 2.
  • Correct Answer: Wyatt divided exponents in the numerator by 2 instead of 3.

Determining Number of Items from Total Cost

• Scenario: John buys fruit drinks priced between $2 and $4, pays $36.54.
• Solution: Calculate using extremes (all $2 or all $4 drinks).
  • Correct number of drinks: 12 (C).

Subtracting Polynomial Expressions

• Steps:
  • Rewrite second polynomial with opposite signs.
  • Add the resulting expressions.
• Example:
  • Result: (4x^2y - 7x + 14y^2)
  • Correct Answer: B

Equations for Savings Goals

• Scenario: Kaden wants $600 in 12 months, starts with $84.
• Equation: (12x + 84 = 600)
  • Correct Answer: A

Properties of Equations

• Commutative Property: Rearrange terms on one side.
• Example: -3x moves next to 4x, and 7 moves next to 10.
• Correct Property: Commutative Property

Interpreting Linear Equations

• Scenario: Fernando earns base pay plus commission.
• Equation: (y = 120 + 0.25x)
  • Base Pay: $120
  • Commission: 25% of sales
  • Ordered Pair Interpretation: Correct answer - C

Graph Interpretation

• Scenario: Ticket prices for school play
• Intersection Point: Represents the price of adult and student tickets.
  • Adult Ticket: $4
  • Student Ticket: $3
  • Correct Answer: D

Conclusion

• Next Steps: Continue review with more examples in subsequent sessions.