2022 (Aug.): NY Regents - Algebra 2 - Sara Cowley | Library

Instructions

From the New York State Education Department. The University of the State of New York Regents High School Examination Algebra 2 August 2022. Internet. Available from https://www.nysedregents.org/algebratwo/822/algtwo82022-exam.pdf; accessed 3, May, 2023.

2

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

2

The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours.

H(t)=4.8\mathrm{sin}\big(\frac{\pi}{6}(t+3)\big)+5.1

Using this function, the amplitude of the tide is

2

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.

The study Liem conducted would be best described as

2

In the diagram of a unit circle below, point A, \big(-\frac{\sqrt{3}}{2},\frac{1}{2}\big), represents the point where the terminal side of \theta intersects the unit circle.

What is \mathrm{m}\angle{\theta}?

2

Consider the function f(x)=2x^{3}+x^{2}-18x-9. Which statement is true?

2

Which sketch could represent the function m(x)=-\log_{100}(x-2)?

2

Which equation has roots of 3+i and 3-i?

2

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?

2

What is the total number of points of intersection of the graphs of the equations y=e^x and xy=20?

2

The amount of a substance, A(t), in grams, remaining after t days is modeled by A(t)=50(0.5)^\frac{t}{3}. Which statement is false?

2

A parabola that has a vertex at (2,1) and a focus of (2,-3) has an equation of

2

The expression \big(a\sqrt[3]{2b^{2}}\big)\big(\sqrt[3]{4a^{2}b}\big) is equivalent to

2

Given f(x)=3^{x-1}+2, as x \rightarrow -\infin

2

For all values of x for which the expression is defined, \frac{x^{2}+3x}{x^{2}+5x+6} is equivalent to

2

A recursive formula for the sequence 64, 48, 36, ... is

2

Which expression is equivalent to \frac{x^{3}-2}{x-2}?

2

What is the solution set of the equation \frac{4}{k^{2}-8k+12}=\frac{k}{k-2}+\frac{1}{k-6}?

2

Given the polynomial identity x^{6}+y^{6}=(x^{2}+y^{2})(x^{4}-x^{2}y^{2}+y^{4}), which equation must also be true for all values of x and y?

2

Given p(\theta)=3\mathrm{sin}(\frac{1}{2}\theta) on the interval -\pi<\theta<\pi, the function p

2

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.
Which expression determines the total amount of money saved by the company over 5 years?

2

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%?

2

Given f(x)=-\frac{2}{5}x+4, which statement is true of the inverse function f^{-1}(x)?

2

The amount of a substance, A(t), that remains after t days can be given by the equation A(t)=A_{0}(0.5)^\frac{t}{0.0803}, where A_0 represents the initial amount of the substance. An equivalent form of this equation is

2

Determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below.

2

Factor the expression x^{3}-2x^{2}-9x+18 completely.

2

Solve algebraically for all values of x:

\sqrt{4x+1}=11-x

2

Given that \Bigg(\frac{y^{\frac{17}{8}}}{y^{\frac{5}{4}}}\Bigg)^{-4}=y^{n}, where y>0, determine the value of n.

2

Given \mathrm{cos} A=\frac{3}{\sqrt{10}} and \mathrm{cot} A=-3, determine the value of \mathrm{sin} A in radical form.

2

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.

2

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.

2

Algebraically determine the solution set for the system of equations below.

y=2x^{2}-7x+4
y=11-2x

4

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.

Part 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:
_______ 

Part 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:
_______ 

4

The function v(x)=x(3-x)(x+4) models the volume, in cubic inches, of a rectangular solid for 0\leq{x}\leq{3}.

Part A
Graph y=v(x) over the domain 0\leq{x}\leq{3} in the Show Your Work space.

Part B
To the nearest tenth of a cubic inch, what is the maximum volume of the rectangular solid?
_______ 

4

Given f(x)=3x^{3}-4x^{2}+2x-1 and g(x)=x-4, state the quotient and remainder of \frac{f(x)}{g(x)}, in the form q(x)+\frac{r(x)}{g(x)}:
_______ 

Is x=4 a root of f(x)? Explain your answer.
_______ 

4

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.

Based on the simulation, determine an interval containing the middle 95% of plausible proportions. Round your answer to the nearest thousandth. _______ 

The community organization conducted its own sample survey of 60 people and found 70% supported the repeal. Based on the results of the simulation, explain why the organization should question the State officials’ claim. _______ 

6

A technology company is comparing two plans for speeding up its technical support time. Plan A can be modeled by the function A(x)=15.7(0.98)^x and plan B can be modeled by the function B(x)=11(0.99)^x where x is the number of customer service representatives employed by the company and A(x) and B(x) represent the average wait time, in minutes, of each customer.

Part A
Graph A(x) and B(x) in the interval 0\leq{x}\leq100 on the set of axes in the Show Your Work space.

Part B
To the nearest integer, solve the equation A(x)=B(x).
_______ 

Part C
Determine, to the nearest minute, B(100)-A(100). 
_______ 
Explain what this value represents in the given context.
_______ 

2022 (Aug.): NY Regents - Algebra 2

2022 (Aug.): NY Regents - Algebra 2

Given that i is the imaginary unit, the expression (x-2i)^2 is equivalent to

The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours.H(t)=4.8\mathrm{sin}\big(\frac{\pi}{6}(t+3)\big)+5.1Using this function, the amplitude of the tide is

In the diagram of a unit circle below, point A, \big(-\frac{\sqrt{3}}{2},\frac{1}{2}\big), represents the point where the terminal side of \theta intersects the unit circle.What is \mathrm{m}\angle{\theta}?

Consider the function f(x)=2x^{3}+x^{2}-18x-9. Which statement is true?

Which sketch could represent the function m(x)=-\log_{100}(x-2)?

Which equation has roots of 3+i and 3-i?

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?

What is the total number of points of intersection of the graphs of the equations y=e^x and xy=20?

The amount of a substance, A(t), in grams, remaining after t days is modeled by A(t)=50(0.5)^\frac{t}{3}. Which statement is false?

A parabola that has a vertex at (2,1) and a focus of (2,-3) has an equation of

The expression \big(a\sqrt[3]{2b^{2}}\big)\big(\sqrt[3]{4a^{2}b}\big) is equivalent to

Given f(x)=3^{x-1}+2, as x \rightarrow -\infin

For all values of x for which the expression is defined, \frac{x^{2}+3x}{x^{2}+5x+6} is equivalent to

A recursive formula for the sequence 64, 48, 36, ... is

Which expression is equivalent to \frac{x^{3}-2}{x-2}?

What is the solution set of the equation \frac{4}{k^{2}-8k+12}=\frac{k}{k-2}+\frac{1}{k-6}?

Given the polynomial identity x^{6}+y^{6}=(x^{2}+y^{2})(x^{4}-x^{2}y^{2}+y^{4}), which equation must also be true for all values of x and y?

Given p(\theta)=3\mathrm{sin}(\frac{1}{2}\theta) on the interval -\pi<\theta<\pi, the function p

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.Which expression determines the total amount of money saved by the company over 5 years?

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%?

Given f(x)=-\frac{2}{5}x+4, which statement is true of the inverse function f^{-1}(x)?

The amount of a substance, A(t), that remains after t days can be given by the equation A(t)=A_{0}(0.5)^\frac{t}{0.0803}, where A_0 represents the initial amount of the substance. An equivalent form of this equation is

Determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below.

Factor the expression x^{3}-2x^{2}-9x+18 completely.

Solve algebraically for all values of x:\sqrt{4x+1}=11-x

Given that \Bigg(\frac{y^{\frac{17}{8}}}{y^{\frac{5}{4}}}\Bigg)^{-4}=y^{n}, where y>0, determine the value of n.

Given \mathrm{cos} A=\frac{3}{\sqrt{10}} and \mathrm{cot} A=-3, determine the value of \mathrm{sin} A in radical form.

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.

Algebraically determine the solution set for the system of equations below.y=2x^{2}-7x+4y=11-2x

Given that i is the imaginary unit, the expression (x-2i)^2 is equivalent to

The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours.H(t)=4.8\mathrm{sin}\big(\frac{\pi}{6}(t+3)\big)+5.1Using this function, the amplitude of the tide is

In the diagram of a unit circle below, point A, \big(-\frac{\sqrt{3}}{2},\frac{1}{2}\big), represents the point where the terminal side of \theta intersects the unit circle.What is \mathrm{m}\angle{\theta}?

Consider the function f(x)=2x^{3}+x^{2}-18x-9. Which statement is true?

Which sketch could represent the function m(x)=-\log_{100}(x-2)?

Which equation has roots of 3+i and 3-i?

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?

What is the total number of points of intersection of the graphs of the equations y=e^x and xy=20?

The amount of a substance, A(t), in grams, remaining after t days is modeled by A(t)=50(0.5)^\frac{t}{3}. Which statement is false?

A parabola that has a vertex at (2,1) and a focus of (2,-3) has an equation of

The expression \big(a\sqrt[3]{2b^{2}}\big)\big(\sqrt[3]{4a^{2}b}\big) is equivalent to

Given f(x)=3^{x-1}+2, as x \rightarrow -\infin

For all values of x for which the expression is defined, \frac{x^{2}+3x}{x^{2}+5x+6} is equivalent to

A recursive formula for the sequence 64, 48, 36, ... is

Which expression is equivalent to \frac{x^{3}-2}{x-2}?

What is the solution set of the equation \frac{4}{k^{2}-8k+12}=\frac{k}{k-2}+\frac{1}{k-6}?

Given the polynomial identity x^{6}+y^{6}=(x^{2}+y^{2})(x^{4}-x^{2}y^{2}+y^{4}), which equation must also be true for all values of x and y?

Given p(\theta)=3\mathrm{sin}(\frac{1}{2}\theta) on the interval -\pi<\theta<\pi, the function p

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.Which expression determines the total amount of money saved by the company over 5 years?

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%?

Given f(x)=-\frac{2}{5}x+4, which statement is true of the inverse function f^{-1}(x)?

The amount of a substance, A(t), that remains after t days can be given by the equation A(t)=A_{0}(0.5)^\frac{t}{0.0803}, where A_0 represents the initial amount of the substance. An equivalent form of this equation is

Determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below.

Factor the expression x^{3}-2x^{2}-9x+18 completely.

Solve algebraically for all values of x:\sqrt{4x+1}=11-x

Given that \Bigg(\frac{y^{\frac{17}{8}}}{y^{\frac{5}{4}}}\Bigg)^{-4}=y^{n}, where y>0, determine the value of n.

Given \mathrm{cos} A=\frac{3}{\sqrt{10}} and \mathrm{cot} A=-3, determine the value of \mathrm{sin} A in radical form.

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.

Algebraically determine the solution set for the system of equations below.y=2x^{2}-7x+4y=11-2x

The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours.

H(t)=4.8\mathrm{sin}\big(\frac{\pi}{6}(t+3)\big)+5.1

Using this function, the amplitude of the tide is

In the diagram of a unit circle below, point A, \big(-\frac{\sqrt{3}}{2},\frac{1}{2}\big), represents the point where the terminal side of \theta intersects the unit circle.

What is \mathrm{m}\angle{\theta}?

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.
Which expression determines the total amount of money saved by the company over 5 years?

Solve algebraically for all values of x:

\sqrt{4x+1}=11-x

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.

Algebraically determine the solution set for the system of equations below.

y=2x^{2}-7x+4
y=11-2x

The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours.

H(t)=4.8\mathrm{sin}\big(\frac{\pi}{6}(t+3)\big)+5.1

Using this function, the amplitude of the tide is

In the diagram of a unit circle below, point A, \big(-\frac{\sqrt{3}}{2},\frac{1}{2}\big), represents the point where the terminal side of \theta intersects the unit circle.

What is \mathrm{m}\angle{\theta}?

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.
Which expression determines the total amount of money saved by the company over 5 years?

Solve algebraically for all values of x:

\sqrt{4x+1}=11-x

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.

Algebraically determine the solution set for the system of equations below.

y=2x^{2}-7x+4
y=11-2x