# Algebra 2 Common Core Regents Exam - August 2022

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 2022.

### Algebra 2 Common Core Regents New York State Exam - August 2022, Questions 1 - 37

The following are questions from the past paper
Regents High School Algebra 2, August 2022 Exam (pdf).

Algebra 2 - August 2022 Regents - Solutions for Questions 1 - 24

1. The Hot and Tasty Coffee chain conducts a survey of its customers at its location at the Staten Island ferry terminal. After the survey is completed, the statistical consultant states that 70% of customers who took the survey said the most important factor in choosing where to get their coffee is how fast they are served. Based on this result, Hot and Tasty Coffee can infer that
2. Given that i is the imaginary unit, the expression (x - 2i)2 is equivalent to
3. The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours
4. In watching auditions for lead singer in a band, Liem became curious as to whether there is an association between how animated the lead singer is and the amount of applause from the audience. He decided to watch each singer and rate the singer on a scale of 1 to 5, where 1 is the least animated and 5 is the most animated. He did this for all 5 nights of auditions and found that the more animated singers did receive louder applause.
5. In the diagram of a unit circle below, point A,
6. Consider the function f(x) = 2x3 + x2 - 18x - 9. Which statement is true?
7. Which sketch could represent the function m(x) = -log100(x - 2)?
8. Which equation has roots of 3 + i and 3 - i ?
9. A local university has a current enrollment of 12,000 students. The enrollment is increasing continuously at a rate of 2.5% each year. Which logarithm is equal to the number of years it will take for the population to increase to 15,000 students?
10. What is the total number of points of intersection of the graphs of the equations y = ex and xy = 20 ?
11. The amount of a substance, A(t), in grams, remaining after t days is modeled by A(t) = 50(0.5)t/3. Which statement is false?
12. Consider the graph of g and the table representing t below
13. The expression
14. Given f(x) = 3x-1 + 2,
15. For all values of x for which the expression is defined,
16. A recursive formula for the sequence 64, 48, 36, … is
17. Which expression is equivalent to
18. What is the solution set of the equation
19. Given the polynomial identity
20. Given p(θ) = 3sin(1/2 θ) on the interval -π < θ < π the function p
21. A company fired several employees in order to save money. The amount of money the company saved per year over five years following the loss of employees is shown in the table below.
22. A rush-hour commuter train has arrived on time 64 of its first 80 days. As arrivals continue, which equation can be used to find x, the number of consecutive days that the train must arrive on schedule to raise its on-time performance rate to 90%?
23. Given f(x) = - 2/5x + 4 ,
24. The amount of a substance, A(t), that remains after t days can be given by the equation

1. Determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below
2. Factor the expression x3 - 2x2 - 9x + 18 completely.
3. Solve algebraically for n:
4. Given that
5. Given cos A
6. According to a study done at a hospital, the average weight of a newborn baby is 3.39 kg, with a standard deviation of 0.55 kg. The weights of all the newborns in this hospital closely follow a normal distribution. Last year, 9256 babies were born at this hospital. Determine, to the nearest integer, approximately how many babies weighed more than 4 kg.
7. The table below shows the results of gender and music preference. Based on these data, determine if the events “the person is female” and “the person prefers classic rock” are independent of each other. Justify your answer.
8. Algebraically determine the solution set for the system of equations below.
9. When observed by researchers under a microscope, a smartphone screen contained approximately 11,000 bacteria per square inch. Bacteria, under normal conditions, double in population every 20 minutes.
a) Assuming an initial value of 11,000 bacteria, write a function, p(t), that can be used to model the population of bacteria, p, on a smartphone screen, where t represents the time in minutes after it is first observed under a microscope.
b) Using p(t) from part a, determine algebraically, to the nearest hundredth of a minute, the amount of time it would take for a smartphone screen that was not touched or cleaned to have a population of 1,000,000 bacteria per square inch.
10. The function v(x) = x(3 - x)(x + 4) models the volume, in cubic inches, of a rectangular solid
11. Given f(x) = 3x3 - 4x2 + 2x - 1 and g(x) = x - 4, state the quotient and remainder
12. State officials claim 82% of a community want to repeal the 30 mph speed limit on an expressway. A community organization devises a simulation based on the claim that 82% of the community supports the repeal. Each dot on the graph below represents the proportion of community members who support the repeal. The graph shows 200 simulated surveys, each of sample size 60.
13. A technology company is comparing two plans for speeding up its technical support time.

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