Algebra 2 Regents August 2023: Key Concepts and Problem Solving

Vin reviews the Algebra 2 Regents exam from August 2023, covering topics like survey bias, synthetic division, probability, inverse functions, graphing systems, exponential and logarithmic equations, Venn diagrams, discriminant and roots, half-life calculations, y-intercepts, exponential models, trigonometric functions, normal distribution, exponential decay, and polynomial division. Each question is explained in detail, with strategies for solving and verifying answers.

Which method would provide the least biased results when surveying high school students about their exercise habits?

• Surveying students entering the library

• Surveying every fifth student entering the building

• Surveying only the juniors

• Surveying students entering the gym

What is the result of the synthetic division of the polynomial 2x^3 + 3x^2 - 4x + 5 by x + 3?

• 2x^2 + 3x - 4 + 5/(x - 3)

• 2x^2 - 3x + 5 - 10/(x - 3)

• 2x^2 + 3x - 4 + 5/(x + 3)

• 2x^2 - 3x + 5 - 10/(x + 3)

Given the function f(x) = 12x - 4, what is the inverse function f^(-1)(x)?

• (x - 4)/12

• 12/(x - 4)

• (x + 4)/12

• 12/(x + 4)

In a survey, 45% of respondents wanted a large screen, 31% wanted a fast processor, and 58% wanted either. What is the probability that a respondent wanted both a large screen and a fast processor?

• 13%

• 31%

• 18%

• 27%

If sin(θ) = 2/5 and θ is in quadrant II, what is the value of tan(θ)?

• 2/√21

• -2/√21

• √21/2

• -√21/2

What is the mean value in the normal distribution problem discussed?

• 21

• 21.8

• 23

• 24.2

In the exponential decay model, what does the variable 'a' represent?

• The rate of decrease

• The final population

• The initial population

• The number of years

Why can't the value of 'b' be negative in the exponential decay model?

• Because it would result in a negative population

• Because it would result in a zero population

• Because it would result in an increasing population

• Because it would make the equation invalid

What is the solution to the equation when x = 6?

• x = 3

• x = 6

• x = 0

• x = -3

Which factor appears twice in the polynomial function P(x)?

• x + 3

• x - 3

• x - 2

• x + 2