Algebra 2 Regents June 2023: Key Concepts and Problem Solving

Vin guides viewers through the Algebra 2 June 2023 Regents exam, covering parts two, three, and four. The video includes solving algebraic equations, analyzing exponential functions, finding polynomial roots, writing recursive sequences, solving logarithmic equations, simplifying expressions, calculating probabilities, creating polynomial functions, solving systems of equations, and modeling population changes. Each section provides detailed explanations and problem-solving strategies to help students understand and apply mathematical concepts effectively.

What is one method to minimize bias when gathering a sample for a survey?

• Survey only students in the library

• Survey every student entering the campus

• Ask students to volunteer for the survey

• Pick random names from a list of students

When solving the equation algebraically, what is the first step after identifying a square root?

• Add the same value to both sides

• Take the natural log of both sides

• Square both sides of the equation

• Subtract the same value from both sides

How can you determine if a population modeled by an exponential function is increasing?

• Check if the base of the exponent is greater than 1

• Check if the coefficient is negative

• Check if the base of the exponent is between 0 and 1

• Check if the exponent is a negative number

What is the recursive formula for a geometric sequence where each term is one-third of the previous term?

• a_n = a_1 * (1/3)^(n-1)

• a_n = a_(n-1) / 3

• a_n = a_1 + (n-1) * (1/3)

• a_n = a_(n-1) * 3

In a confidence interval calculation, what does it mean if a sample proportion falls within the interval?

• The sample proportion is too low

• The sample proportion is too high

• The sample proportion is reasonable

• The sample proportion is likely incorrect

What is the probability that a randomly selected donor was categorized as a supporter given that the donation was made online?

• 0.250

• 0.600

• 0.500

• 0.373

How can you verify if being a supporter is independent of donating online?

• By calculating the average donation amount.

• By checking if the probability of being a supporter given donating online equals the probability of being a supporter.

• By checking if the total number of supporters is greater than the total number of donors.

• By comparing the number of online donations to offline donations.

What is the most straightforward method to solve a system of equations involving a circle and a line?

• Matrix method

• Graphing

• Substitution

• Elimination

Which formula is used for continuous growth in population modeling?

• A = P(1 + r)^T

• A = P(1 - r)^T

• A = Pe^(rt)

• A = P(1 + rt)

How many times do the functions n(t) and e(t) intersect during the five-second interval?

• 4 times

• 3 times

• 2 times

• 5 times