# Algebra 2 Common Core Regents Exam - June 2023

High School Math based on the topics required for the Regents Exam conducted by NYSED.
The following are the worked solutions for the Algebra 2(Common Core) Regents High School Examination June 2023.

### Algebra 2 Common Core Regents New York State Exam - June 2023, Questions 1 - 37

The following are questions from the past paper
Regents High School Algebra 2, June 2023 Exam (pdf).

Algebra 2 - June 2023 Regents - Solutions for Questions 1 - 24

1. The population of Austin, Texas from 1850 to 2010 is summarized in the table below
2. Which expression is not equivalent to 36x6 - 25y4?
3. What are the zeros of s(x) = x4 - 9x2 + 3x3 - 27x - 10x2 + 90?
4. If θ is an angle in standard position whose terminal side passes through the point (22,23), what is the numerical value of tan θ?
5. The average monthly temperature, T(m), in degrees Fahrenheit, over a 12 month period, can be modeled by T(m)
6. Which expression is an equivalent form of
7. The expression 3i(ai - 6i2) is equivalent to
8. Which equation best represents the graph below?
9. Which function has the characteristic a
10. The expression (x2 + 3)2 - 2(x2 + 3) - 24 is equivalent to
11. What is the solution for the system of equations below?
12. The roots of the equation x2 - 4x = -13 are
13. Which expression is equivalent to
14. A popular celebrity tracks the number of people, in thousands, who have followed her on social media since January 1, 2015. A summary of the data she recorded is shown in the table below:
15. Luminescence is the emission of light that is not caused by heat. A luminescent substance decays according to the function below.
16. The heights of the students at Central High School can be modeled by a normal distribution with a mean of 68.1 and a standard deviation of 3.4 inches. According to this model, approximately what percent of the students would have a height less than 60 inches or greater than 75 inches?
17. Marissa and Sydney are trying to determine if there is enough interest in their school to put on a senior musical. They randomly surveyed 100 members of the senior class and 43% of them said they would be interested in being in a senior musical. Marissa and Sydney then conducted a simulation of 500 more surveys, each of 100 seniors, assuming that 43% of the senior class would be interested in being in the musical. The output of the simulation is shown below.
18. For f(x) = cos x, which statement is true?
19. The solution set of
20. Given x and y are positive, which expressions are equivalent to
21. Given the inverse function
22. How many equations below are identities?
23. If the focus of a parabola is (0, 6) and the directrix is y = 4, what is an equation for the parabola?
24. John and Margaret deposit \$500 into a savings account for their son on his first birthday. They continue to make a deposit of \$500 on the child’s birthday, with the last deposit being made on the child’s 21st birthday. If the account pays 4% annual interest, which equation represents the amount of money in the account after the last deposit is made?

1. The business office of a local college wishes to determine the methods of payment that will be used by students when buying books at the beginning of a semester. Explain how the office can gather an appropriate sample that minimizes bias.
2. Determine the solution of
3. The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function P(t) = 37e0.0532t. Determine whether the population is increasing or decreasing over time. Explain your reasoning.
4. The polynomial function g(x) = x3 + ax2 - 5x + 6 has a factor of (x - 3). Determine the value of a.
5. Write a recursive formula for the sequence 189, 63, 21, 7, … .
6. Solve algebraically for x to the nearest thousandth:
7. For all values of x for which the expression is defined, write the expression below in simplest form.
8. An app design company believes that the proportion of high school students who have purchased apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students was run based on this proportion and the results are shown below.
9. Patricia creates a cubic polynomial function, p(x), with a leading coefficient of 1. The zeros of the function are 2, 3, and 2-6. Write an equation for p(x).
10. A public radio station held a fund-raiser. The table below summarizes the donor category and method of donation.
11. Algebraically solve the system:
12. On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the palm tree population is decreasing at an annual rate of 3% per year and the flamingo population is growing at a continuous rate of 2% per year. Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this island, respectively, x years from now. State the solution to the equation P(x) = F(x), rounded to the nearest year. Interpret the meaning of this value within the given context
13. The volume of air in an average lung during breathing can be modeled by the graph below.

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