Algebra 1 Regents Exam Review: Part 1

Overview

• Focus: January 2025 Algebra 1 Regents Exam, Part 1 (First 24 Multiple Choice Questions)
• Additional resources and full series links available in video description.
• Covers understanding and solving algebraic expressions, sequences, functions, inequalities, and more.

Key Concepts and Problems

Question 1: Factoring

• Expression: x^3 + 36x
• Factor by taking out common term x:
  • Result: x(x^2 + 36)
• Recognize difference of perfect squares:
  • Formula: a^2 - b^2 = (a + b)(a - b)
  • Result: x(x + 6)(x - 6)
• Correct Answer: Choice 3

Question 2: Equation of a Line

• Points: (-1, 8) and (4, -2)
• Equation: y = mx + b
• Find slope (m):
  • Formula: m = (y2 - y1) / (x2 - x1)
  • Slope: m = -2
• Calculate b (y-intercept):
  • Use one of the points to solve for b
  • Final equation: y = -2x + 6
• Correct Answer: Choice 1

Question 3: Geometric Sequence

• Find common ratio of sequence
• Method: Divide last term by the previous term
• Example: 32/8 = 4
• Correct Answer: 4

Question 4: Constant Term

• Polynomial: 2x^3 - x + 5 + 4x^2
• Identify term without x: 5
• Correct Answer: Choice 1

Question 5: Interpreting Linear Functions

• Function: C(x) = 55x + 80
• Identify components:
  • 55 is the hourly labor rate m
  • 80 is the set fee b
• Correct Answer: 55 represents hourly labor rate

Question 6: Simplifying Expressions

• Expression: 5x^2 - 2x + 4 - (3x^2 + 3x - 1)
• Distribute negative:
  • Result: 5x^2 - 2x + 4 - 3x^2 - 3x + 1
• Combine like terms:
  • Final: 2x^2 - 5x + 5
• Correct Answer: Choice 2

Question 7: Systems of Inequalities

• Identify overlapping shaded region as the solution
• Exclude points on dashed lines
• Correct answer: Points within the overlap

Question 8: Arithmetic Sequence

• Sequence begins at 25 and decreases by 5 each term
• 10th term: -20
• Correct Answer: -20

Question 9: Solving for W

• Formula: P = 2L + 2W
• Solve W:
  • W = (P - 2L) / 2
• Correct Answer: Choice 2

Question 10: Percentage Calculation

• Calculate percent of plain deep dish pizzas
• Formula: part (200) / whole (1000) * 100
• Result: 20%
• Correct Answer: 20%

Question 11: Solving an Equation

• Solve: -2(3x - 5) = 9/2x - 2
• Steps: Distribute, simplify, solve for x
• Solution: 8/7
• Correct Answer: Choice 1

Question 12: Exponentiation Rules

• Expression: x^(2a + b)
• Use rule: x^a * x^b = x^(a+b)
• Rewriting: x^a * x^(a+b)
• Correct Answer: Choice 3

Question 13: Function Identification

• Table of values analyzed
• Determine non-linear due to variable rate of change
• Correct Answer: Exponential function

Question 14: Properties of Equality

• Solve equation by removing -8
• Addition property of equality
• Correct Answer: Addition property

Question 15: Simplifying Radicals

• Problem: 8sqrt(3) + sqrt(3)
• Approach: Like terms, result in 9sqrt(3)
• Correct Answer: 9sqrt(3)

Question 16: Analyzing a Dot Plot

• Mode: Most frequent value
• Median: Middle value after sorting
• Correct plot reflects these characteristics

Question 17: Domain of a Function

• Analyze given graph
• Domain based on x values from -2 to infinity
• Use open/closed circles to determine inclusion
• Correct Answer: Choice 1

Question 18: Equation Solutions via Ordered Pairs

• Verify solutions by substituting pairs in equation
• Simplify and check equality
• Correct Answer: Matching pair that satisfies equation

Question 19: Unit Conversion

• Convert speed from meters/second to inches/minute
• Set up fractions to cancel units appropriately
• Correct Answer: Choice 4

Question 20: Interquartile Range

• Use calculator to find Q3 and Q1
• Calculate IQR: Q3 - Q1
• Correct Answer: 11

Question 21: Effects of Multiplying Quadratics

• Parabola shifts with negative multiplication
• Results in a reflected, narrower graph
• Correct Answer: Choice 4

Question 22: Solving Inequalities

• Solve inequality and draw number line
• Understand open/closed circles and direction
• Correct Answer: Choice 4

Question 23: Creating Inequality from Word Problem

• Establish relationship between fish and frogs
• Set inequality for total number exceeding 20
• Correct Answer: Choice 4

Question 24: Identifying Decreasing Functions

• Focus on restricted interval
• Determine which graph is decreasing
• Read graph from left to right
• Correct Answer: Choice 4

Conclusion

• Completion of part 1 of the Algebra 1 Regents Exam review.
• Links to further video parts and additional topics are in the description.
• Encouragement to ask questions and seek clarification in the comments section.