# Algebra 2 Common Core Regents Exam - January 2024

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 January 2024.

### Algebra 2 Common Core Regents New York State Exam - January 2024, Questions 1 - 37

The following are questions from the past paper
Regents High School Algebra 2, January 2024 Exam (pdf).

Algebra 2 - January 2024 Regents - Solutions for Questions 1 - 24

1. A cafeteria food manager studied the lunchtime eating habits of a group of employees in their office building. The purpose of the study was to determine the proportion of employees who purchased lunch in the cafeteria, brought their lunch from home, or purchased lunch from an outside vendor. This collection of data would best be classified as
2. Which graph has imaginary roots?
3. Given
4. Which graph best represents the graph of f(x) = (x + a)2(x - b), where a and b are positive real numbers?
5. The graph of a quadratic function is shown below.
6. The equations y = 3t + 6 and y = (1.82)t approximately model the growth of two separate populations where t > 0. What is the best approximation of the time, t, at which the populations are the same?
7. Given y = -2x and x2 + y2 = 5, the point of intersection in Quadrant II is
8. The rational expression
9. The equation of the parabola that has its focus at the point (-3, 2) and directrix at y = 0 is
10. The seventh term of the geometric sequence
11. A company wishes to determine the cooking time for one pound of spaghetti. The company’s technicians cooked one pound of spaghetti and recorded the time needed for the spaghetti to be ready to eat. Repeating this process 35 times resulted in an approximately normal distribution, with a mean of 9.82 minutes and a standard deviation of 1.4 minutes. In which interval should the middle 95% of cooking times fall?
12. Given
13. Which equation is equivalent to P
14. The average cost of a gallon of milk in the United States between the years of 1995 and 2018 can be modeled by the equation P(t) = 20.0004t3 + 0.0114t2 - 0.0150t + 2.6602, where P(t) represents the cost, in dollars, and t is time in years since January 1995. During this time period, in what year did P(t) reach its maximum?
15. The temperature, F, in degrees Fahrenheit, after t hours of a roast put into an oven is given by the equation F = 325 - 185e-0.4t. What was the temperature of the roast when it was put into the oven?
16. The roots of the equation 0 = x2 + 6x + 10 in simplest a + bi form are
17. Which equation does not represent an identity?
18. Two surveys were conducted to estimate the proportion of teens who use social media at least once per day.
19. Given
20. Robert is buying a car that costs \$22,000. After a down payment of \$4000, he borrows the remainder from a bank, a six year loan at 6.24% annual interest rate. The following formula can be used to calculate his monthly loan payment.
21. Given
22. To solve the equation
23. Beginning July 1, 2019, Michelle deposited \$250 into an account that yields 0.15% each month. She continued to make \$250 deposits into this account on the first of each month for 3 years. Which expression represents the amount of money that was in the account after her last deposit was made on June 1, 2022?
24. A study of the red tailed hawk population in a given area shows the population, H(t), can be represented by the function H(t) = 50(1.19)t where t represents the number of years since the study began. In terms of the monthly rate of growth, the population can be best approximated by the function

1. Factor x3 + 4x2 - 9x - 36, completely.
2. Determine if x + 4 is a factor of 2x3 + 10x2 + 4x - 16. Explain your answer.
3. An initial investment of \$1000 reaches a value, V(t), according to the model V(t) = 1000(1.01)4t, where t is the time in years. Determine the average rate of change, to the nearest dollar per year, of this investment from year 2 to year 7.
4. When
5. The heights of the members of a ski club are normally distributed. The average height is 64.7 inches with a standard deviation of 4.3 inches. Determine the percentage of club members, to the nearest percent, who are between 67 inches and 72 inches tall.
6. The explicit formula an = 6 + 6n represents the number of seats in each row in a movie theater, where n represents the row number. Rewrite this formula in recursive form.
7. Express (2xi3 - 3y)2 in simplest form
8. A survey was given to 1250 randomly selected high school students at the end of their junior year. The survey offered four post-graduation options: two-year college, four-year college, military, or work. Of the 1250 responses, 475 chose a four-year college. State one possible conclusion that can be made about the population of high school juniors, based on this survey.
9. A researcher wants to determine if nut allergies and milk allergies are related to each other. The researcher surveyed 1500 people and asked them if they are allergic to nuts or milk. The survey results are summarized in the table below.
10. Algebraically solve for x:
11. During the summer, Adam saved \$4000 and Betty saved \$3500. Adam deposited his money in Bank A at an annual rate of 2.4% compounded monthly. Betty deposited her money in Bank B at an annual rate of 4% compounded quarterly. Write two functions that represent the value of each account after t years if no other deposits or withdrawals are made, where Adam’s account value is represented by A(t), and Betty’s by B(t).
12. On the graph below, draw at least one complete cycle of a sine graph passing through point (0,2) that has an amplitude of 3, a period of π, and a midline at y = 2.
13. A manufacturer of sweatshirts finds that profits and costs fluctuate depending on the number of products created. Creating more products doesn’t always increase profits because it requires additional costs, such as building a larger facility or hiring more workers. The manufacturer determines the profit, p(x), in thousands of dollars, as a function of the number of sweatshirts sold, x, in thousands. This function, p, is given below.

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