# Algebra 2 Common Core Regents Exam - August 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 August 2023.

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

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

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

1. A group of high school students wanted to collect information on how many times per week students exercised. If they want the least biased results they should survey every fifth student at the school who is
2. Given x ≠ -3, which expression is equivalent to
3. The table below shows the food preferences of sports fans whose favorite sport is football or baseball.
4. If f(x) = 12x - 4, then the inverse function f-1(x) is
5. The graph of a quadratic function is shown below.
6. What is the solution of 2(3x + 4) = 56?
7. In a survey of people who recently bought a laptop, 45% said they were looking for a large screen, 31% said they were looking for a fast processor, and 58% said they wanted a large screen or a fast processor. If a survey respondent is selected at random, what is the probability that the respondent wanted both a large screen and a fast processor?
8. In the quadratic formula, b2 - 4ac is called the discriminant. The function f(x) has a discriminant value of 8, and g(x) has a discriminant value of -16. The quadratic graphs, h(x) and j(x), are shown below
9. The element Americium has a half-life of 25 minutes. Given an initial amount, A0, which expression could be used to determine the amount of Americium remaining after t minutes?
10. Which function has the greatest y-intercept?
11. According to the USGS, an agency within the Department of Interior of the United States, the frog population in the U.S. is decreasing at the rate of 3.79% per year. A student created a model, P 5 12,150(0.962)t, to estimate the population in a pond after t years. The student then created a model that would predict the population after d decades. This model is best represented by
12. What is the value of tan θ when sin θ = -2/5 and θ is in quadrant II?
13. A population is normally distributed with a mean of 23 and a standard deviation of 1.2. The percentage of the population that falls below 21, to the nearest hundredth, is
14. Audra is interested in studying the number of students entering kindergarten in the Ahlville Central School District over the next several years. Using data dating back to 2015, she determines that the number of kindergarteners is decreasing at an exponential rate. She creates a formula to model this situation y = a(b)x, where x is the number of years since 2015 and y is the number of students entering kindergarten. If there were 105 students entering kindergarten in Ahlville in 2015, which statement about Audra’s formula is true?
15. The solution set for the equation
16. The George family would like to borrow \$45,000 to purchase a new boat. They qualified for a loan with an annual interest rate of 6.75%. The monthly loan payment can be found using the formula below.
17. A retailer advertises that items will be discounted by 10% every Monday until they are sold. In how many weeks will an item costing \$50 first be sold for under half price?
18. The graph of the function f(x) is shown below.
19. If f(x) = (x2 + 3x + 2)(x2 - 4x + 3) and g(x) = x2 - 9, then how many real solutions are there to the equation f(x) = g(x)?
20. Which expression is a factor of x4 - x3 - 11x2 + 5x + 30?
21. The expression
22. Stone Manufacturing has developed a cost model,
23. Which function is even?
24. The graph of a cubic polynomial function p(x) is shown below.

1. Factor the expression 2x3 - 3x2 - 18x + 27 completely.
2. Algebraically determine the values of x that satisfy the system of equations shown below:
3. Solve the equation 3x2 + 5x + 8 = 0. Write your solution in a + bi form
4. On the coordinate plane below, sketch at least one cycle of a cosine function with a midline at y = -2, an amplitude of 3, and a period of π/2.
5. Given i is the imaginary unit, simplify (5xi3 - 4i)2 as a polynomial in standard form.
6. Consider the parabola given by y = 1/4 x2 + x + 8 with vertex (-2,7) and focus (-2,8). Use this information to explain how to determine the equation of the directrix.
7. Write as a single term in simplest form, with a rational exponent.
8. A fruit fly population can be modeled by the equation P = 10(1.27)t, where P represents the number of fruit flies after t days. What is the average rate of change of the population, rounded to the nearest hundredth, over the interval [0,10.5]? Include appropriate units in your answer.
9. Sketch p(x) = -log2(x + 3) + 2 on the axes below.
10. Solve for x algebraically:
11. Solve the following system of equations algebraically for x, y, and z.
12. Two classes of students were entered into an experiment to see whether using an interactive whiteboard leads to better grades. It was observed that the mean grade of students in the class with the interactive whiteboard was 0.6 points higher than the class without it. To determine if the observed difference is statistically significant, the classes were rerandomized 5000 times to study these random differences in the mean grades. The output of the simulation is summarized in the histogram below.
13. The Manford family started savings accounts for their twins, Abby and Brett, on the day they were born. They invested \$8000 in an account for each child. Abby’s account pays 4.2% annual interest compounded quarterly. Brett’s account pays 3.9% annual interest compounded continuously. Write a function, A(t), for Abby’s account and a function, B(t), for Brett’s account that calculates the value of each account after t years.
Determine who will have more money in their account when the twins turn 18 years old, and find the difference in the amounts in the accounts to the nearest cent.

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