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).

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

- Solutions for Questions 25 - 37

- The population of Austin, Texas from 1850 to 2010 is summarized inthe table below
- Which expression is not equivalent to 36x
^{6}- 25y^{4}? - What are the zeros of s(x) = x
^{4}- 9x^{2}+ 3x^{3}- 27x - 10x2 + 90? - If θ is an angle in standard position whose terminal side passes throughthe point (22,23), what is the numerical value of tan θ?
- The average monthly temperature, T(m), in degrees Fahrenheit, overa 12 month period, can be modeled by T(m)
- Which expression is an equivalent form of
- The expression 3i(ai - 6i
^{2}) is equivalent to - Which equation best represents the graph below?
- Which function has the characteristic a
- The expression (x
^{2}+ 3)^{2}- 2(x^{2}+ 3) - 24 is equivalent to - What is the solution for the system of equations below?
- The roots of the equation x
^{2}- 4x = -13 are - Which expression is equivalent to
- A popular celebrity tracks the number of people, in thousands, whohave followed her on social media since January 1, 2015. A summaryof the data she recorded is shown in the table below:
- Luminescence is the emission of light that is not caused by heat. Aluminescent substance decays according to the function below.
- The heights of the students at Central High School can be modeledby a normal distribution with a mean of 68.1 and a standard deviationof 3.4 inches. According to this model, approximately what percent ofthe students would have a height less than 60 inches or greater than75 inches?
- Marissa and Sydney are trying to determine if there is enough interestin their school to put on a senior musical. They randomly surveyed100 members of the senior class and 43% of them said they wouldbe interested in being in a senior musical. Marissa and Sydney thenconducted a simulation of 500 more surveys, each of 100 seniors,assuming that 43% of the senior class would be interested in being inthe musical. The output of the simulation is shown below.
- For f(x) = cos x, which statement is true?
- The solution set of
- Given x and y are positive, which expressions are equivalent to
- Given the inverse function
- How many equations below are identities?
- If the focus of a parabola is (0, 6) and the directrix is y = 4, what is anequation for the parabola?
- John and Margaret deposit $500 into a savings account for their sonon his first birthday. They continue to make a deposit of $500 on thechild’s birthday, with the last deposit being made on the child’s 21stbirthday. If the account pays 4% annual interest, which equationrepresents the amount of money in the account after the last depositis made?

- The business office of a local college wishes to determine the methods of payment that will beused by students when buying books at the beginning of a semester. Explain how the office cangather an appropriate sample that minimizes bias.
- Determine the solution of
- The population of bacteria, P(t), in hundreds, after t hours can be modeled by the functionP(t) = 37e
^{0.0532t}. Determine whether the population is increasing or decreasing over time. Explainyour reasoning. - The polynomial function g(x) = x
^{3}+ ax^{2}- 5x + 6 has a factor of (x - 3). Determine thevalue of a. - Write a recursive formula for the sequence 189, 63, 21, 7, … .
- Solve algebraically for x to the nearest thousandth:
- For all values of x for which the expression is defined, write the expression below in simplest form.
- An app design company believes that the proportion of high school students who have purchasedapps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 studentswas run based on this proportion and the results are shown below.
- Patricia creates a cubic polynomial function, p(x), with a leading coefficient of 1. The zeros of thefunction are 2, 3, and 2-6. Write an equation for p(x).
- A public radio station held a fund-raiser. The table below summarizes the donor category andmethod of donation.
- Algebraically solve the system:
- On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose thepalm tree population is decreasing at an annual rate of 3% per year and the flamingo populationis 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 thisisland, respectively, x years from now.State the solution to the equation P(x) = F(x), rounded to the nearest year. Interpret the meaningof this value within the given context
- The volume of air in an average lung during breathing can be modeled by the graph below.

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