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Biblioteka

2023 (Jan.): NY Regents - Algebra 2

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From the New York State Education Department. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II. Internet. Available from https://www.nysedregents.org/algebratwo/123/algtwo12023-exam.pdf; accessed 23, June, 2023.

From the New York State Education Department. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II. Internet. Available from https://www.nysedregents.org/algebratwo/123/algtwo12023-exam.pdf; accessed 23, June, 2023.

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Part I

Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question.

Pitanje 1
1.

Which expression is equivalent to (x+2)^{2}-5(x+2)+6?

Pitanje 2
2.

To the nearest tenth, the solution to the equation 4300e^{0.07x}-123=5000 is

Pitanje 3
3.

The value of an automobile t years after it was purchased is given by the function V=38,000(0.84)^t . Which statement is true?

Pitanje 4
4.

Which function represents exponential decay?

Pitanje 5
5.

The expression \frac{x^4-5x^2+4x+14}{x+2} is equivalent to

Pitanje 6
6.

The sum of the first 20 terms of the series -2+6-18+54- ... is

Pitanje 7
7.

If f(x)=2x^{4}-x^3-16x+8, then f(\frac{1}{2})

Pitanje 8
8.

If (6-ki)^{2}=27-36i, the value of k is

Pitanje 9
9.

What is the solution set of the equation \frac{x+2}{x}+\frac{x}{3}=\frac{2x^{2}+6}{3x} ?

Pitanje 10
10.

How many real solutions exist for the system of equations below?

y=\frac{1}{4}x-8

y=\frac{1}{2}x^{2}+2x

Pitanje 11
11.

Which equation represents a polynomial identity?

Pitanje 12
12.

Given x>0, the expression \frac{x^{\frac{1}{5}}}{x^{\frac{1}{2}}} can be rewritten as

Pitanje 13
13.

A cyclist pedals a bike at a rate of 60 revolutions per minute. The height, h, of a pedal at time t, in seconds, is plotted below.

The graph can be modeled by the function h(t)=5\mathrm{sin}(kt), where k is equal to

Pitanje 14
14.

Which statement about data collection is most accurate?

Pitanje 15
15.

If f(x)=\frac{1}{2}x+2, then the inverse function is

Pitanje 16
16.

Given f(x)=x^{4}-x^3-6x^2, for what values of x will f(x)>0?

Pitanje 17
17.

For which approximate value(s) of x will \mathrm{log}(x+5)=\vert{x-1}-3?

Pitanje 18
18.

Consider a cubic polynomial with the characteristics below.

  • exactly one real root

  • as x\rightarrow\infin, f(x){\rightarrow}-\infin

Given a>0 and b>0, which equation represents a cubic polynomial with these characteristics?

Pitanje 19
19.

Betty conducted a survey of her class to see if they like pizza. She gathered 200 responses and 65% of the voters said they did like pizza. Betty then ran a simulation of 400 more surveys, each with 200 responses, assuming that 65% of the voters would like pizza. The output of the simulation is shown below.

Considering the middle 95% of the data, what is the margin of error for the simulation?

Pitanje 20
20.

If \mathrm{cos}A=\frac{\sqrt{5}}{3} and \mathrm{tan}A<0, what is the value of \mathrm{sin}A?

Pitanje 21
21.

A tree farm initially has 150 trees. Each year, 20\% of the trees are cut down and 80 seedlings are planted. Which recursive formula models the number of trees, a_n, after n years?

Pitanje 22
22.

Which equation represents a parabola with a focus of (4,-3) and directrix of y=1?

Pitanje 23
23.

Mia has a student loan that is in deferment, meaning that she does not need to make payments right now. The balance of her loan account during her deferment can be represented by the function f(x)=35000(1.0325)^{x}, where x is the number of years since the deferment began. If the bank decides to calculate her balance showing a monthly growth rate, an approximately equivalent function would be

Pitanje 24
24.

Which graph shows a quadratic function with two imaginary zeros?

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

Pitanje 25
25.
Pitanje 26
26.
Pitanje 27
27.
Pitanje 28
28.
Pitanje 29
29.
Pitanje 30
30.
Pitanje 31
31.
Pitanje 32
32.

Natalia's teacher has given her the following information about angle \theta.

  • \pi<\theta<2\pi

  • \mathrm{cos}\theta=\frac{\sqrt{3}}{4}

Explain how Natalia can determine if the value of \mathrm{tan}\theta is positive or negative.

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

Pitanje 33
33.
Pitanje 34
34.
Pitanje 35
35.

Graph c(x)=-9(3)^{x-4}+2 on the axes in the Show Your Work space.

Describe the end behavior of c(x) as x approaches positive infinity.

Describe the end behavior of c(x) as x approaches negative infinity.

Pitanje 36
36.

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided to determine your answer. Note that diagrams are not necessarily drawn to scale. A correct numerical answer with no work shown will receive only 1 credit.

Pitanje 37
37.