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).

Download the questions and try them, then look at the following videos to check your answers with the step by step solutions.

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

- Solutions for Questions 25 - 37

- A cafeteria food manager studied the lunchtime eating habits of agroup of employees in their office building. The purpose of the studywas to determine the proportion of employees who purchased lunchin the cafeteria, brought their lunch from home, or purchased lunchfrom an outside vendor. This collection of data would best be classifiedas
- Which graph has imaginary roots?
- Given
- Which graph best represents the graph of f(x) = (x + a)
^{2}(x - b),where a and b are positive real numbers? - The graph of a quadratic function is shown below.
- The equations y = 3t + 6 and y = (1.82)
^{t}approximately model thegrowth of two separate populations where t > 0. What is the bestapproximation of the time, t, at which the populations are the same? - Given y = -2x and x
^{2}+ y^{2}= 5, the point of intersection inQuadrant II is - The rational expression
- The equation of the parabola that has its focus at the point (-3, 2) anddirectrix at y = 0 is
- The seventh term of the geometric sequence
- A company wishes to determine the cooking time for one pound ofspaghetti. The company’s technicians cooked one pound of spaghettiand recorded the time needed for the spaghetti to be ready to eat.Repeating this process 35 times resulted in an approximately normaldistribution, with a mean of 9.82 minutes and a standard deviationof 1.4 minutes. In which interval should the middle 95% of cookingtimes fall?
- Given
- Which equation is equivalent to P
- The average cost of a gallon of milk in the United States betweenthe years of 1995 and 2018 can be modeled by the equationP(t) = 20.0004t
^{3}+ 0.0114t^{2}- 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? - The temperature, F, in degrees Fahrenheit, after t hours of a roast putinto an oven is given by the equation F = 325 - 185e
^{-0.4t}. What wasthe temperature of the roast when it was put into the oven? - The roots of the equation 0 = x
^{2}+ 6x + 10 in simplest a + bi formare - Which equation does not represent an identity?
- Two surveys were conducted to estimate the proportion of teens whouse social media at least once per day.
- Given
- 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 calculatehis monthly loan payment.
- Given
- To solve the equation
- Beginning July 1, 2019, Michelle deposited $250 into an account thatyields 0.15% each month. She continued to make $250 deposits intothis account on the first of each month for 3 years. Which expressionrepresents the amount of money that was in the account after her lastdeposit was made on June 1, 2022?
- A study of the red tailed hawk population in a given area shows thepopulation, 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. Interms of the monthly rate of growth, the population can be bestapproximated by the function

- Factor x
^{3}+ 4x^{2}- 9x - 36, completely. - Determine if x + 4 is a factor of 2x
^{3}+ 10x^{2}+ 4x - 16. Explain your answer. - 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 year2 to year 7. - When
- The heights of the members of a ski club are normally distributed. The average height is 64.7inches with a standard deviation of 4.3 inches. Determine the percentage of club members, to thenearest percent, who are between 67 inches and 72 inches tall.
- The explicit formula a
_{n}= 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. - Express (2xi
^{3}- 3y)^{2}in simplest form - 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, orwork. Of the 1250 responses, 475 chose a four-year college. State one possible conclusion that canbe made about the population of high school juniors, based on this survey.
- A researcher wants to determine if nut allergies and milk allergies are related to each other. Theresearcher surveyed 1500 people and asked them if they are allergic to nuts or milk. The surveyresults are summarized in the table below.
- Algebraically solve for x:
- During the summer, Adam saved $4000 and Betty saved $3500. Adam deposited his money inBank A at an annual rate of 2.4% compounded monthly. Betty deposited her money in Bank B atan annual rate of 4% compounded quarterly. Write two functions that represent the value of eachaccount after t years if no other deposits or withdrawals are made, where Adam’s account value isrepresented by A(t), and Betty’s by B(t).
- 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.
- A manufacturer of sweatshirts finds that profits and costs fluctuate depending on the numberof products created. Creating more products doesn’t always increase profits because it requiresadditional costs, such as building a larger facility or hiring more workers. The manufacturerdetermines the profit, p(x), in thousands of dollars, as a function of the number of sweatshirtssold, x, in thousands. This function, p, is given below.

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