From the New York State Education Department. The University of the State of New York Regents High School Examination Algebra 1 August 2019. Internet. Available from https://www.nysedregents.org/algebraone/819/algone82019-exam.pdf; accessed 3, May, 2023.
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1.
Bryan’s hockey team is purchasing jerseys. The company charges $250 for a onetime set-up fee and $23 for each printed jersey. Which expression represents the total cost of x number of jerseys for the team?
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2.
Which table represents a function?
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3.
Which expression is equivalent to 2(x^2-1)+3x(x-4) ?
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4.
The value of x that satisfies the equation \frac{4}{3}=\frac{x+10}{15} is
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5.
Josh graphed the function f(x) =3(x - 1)^2\ + 2. He then graphed the function
g(x) = 3(x - 1)^2\ - 5 on the same coordinate plane.
The vertex of g(x) is
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6.
A survey was given to 12th-grade students of West High School to determine the location for the senior class trip. The results are shown in the table below.
To the nearest percent, what percent of the boys chose Niagara Falls?
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7.
Which type of function is shown in the graph below?
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8.
The expression 16x^2\ - 81 is equivalent to
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9.
The owner of a landscaping business wants to know how much time, on average, his workers spend mowing one lawn. Which is the most appropriate rate with which to calculate an answer to his question?
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10.
A ball is thrown into the air from the top of a building. The height, h(t), of the ball above the ground t seconds after it is thrown can be modeled by h(t) =-16t^2\ + 64t + 80. How many seconds after being thrown will the ball hit the ground?
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11.
Which equation is equivalent to y = x^2\ + 24x - 18?
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12.
When (x) (x -5) (2x+3) is expressed as a polynomial in standard form, which statement about the resulting polynomial is true?
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13.
The population of a city can be modeled by P(t) = 3810(1.0005)^7t, where P(t) is the population after t years. Which function is approximately equivalent to P(t)?
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14.
The functions f(x) and g(x) are graphed on the set of axes below.
For which value of x is f(x) \ne g(x)?
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15.
What is the range of the box plot shown below?
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16.
Which expression is not equivalent to 2x^2\ + 10x +12?
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17.
The quadratic functions r(x) and q(x) are given below.
q(x) = x^2\ + 2x - 8
The function with the smallest minimum value is
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18.
A child is playing outside. The graph below shows the child’s distance, d(t), in yards from home over a period of time, t, in seconds.
Which interval represents the child constantly moving closer to home?
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19.
If a_1 = 6 and a_n=3+2\left(a_{n-1}\right)^2, then a_2 equals
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20.
The length of a rectangular patio is 7 feet more than its width, w. The area of a patio, A(w), can be represented by the function
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21.
A dolphin jumps out of the water and then back into the water. His jump could be graphed on a set of axes where x represents time and y represents distance above or below sea level. The domain for this graph is best represented using a set of
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22.
Which system of linear equations has the same solution as the one shown below?
x - 4y = -10
x + y = 5
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23.
Which interval represents the range of the function h(x) = 2x^2\ -2x - 4?
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24.
What is a common ratio of the geometric sequence whose first term is 5 and third term is 245?
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25.
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. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
If g(x) = -4x^2\ - 3x + 2, determine g(-2).
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26.
A student is in the process of solving an equation. The original equation and the first step are shown below.
Original: 3a + 6 = 2 - 5a + 7
Step one: 3a + 6 = 2 + 7 - 5a
Which property did the student use for the first step? Explain why this property is correct.
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27.
On the set of axes below, graph the line whose equation is 2y = -3x - 2.
This linear equation contains the point (2,k). State the value of k.
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28.
The formula a=\frac{v_f-v_i}{t} is used to calculate acceleration as the change in velocity over the period of time.
Solve the formula for the final velocity, v_f , in terms of initial velocity, v_i , acceleration, a, and
Is the product of two irrational numbers always irrational? Justify your answer.
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31.
Solve 6x^2\ - 42 = 0 for the exact values of x.
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32.
Graph the function: h(x) = { 2x-3, x < 0
x^2\ -4x-5, 0 ≤ x ≤ 5
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33.
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. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
On the set of axes below, graph the following system of inequalities:
2x + y ≥ 8
y - 5 < 3x
Determine if the point (1,8) is in the solution set. Explain your answer.
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34.
On the day Alexander was born, his father invested $5000 in an account with a 1.2% annual growth rate. Write a function, A(t), that represents the value of this investment t years after Alexander’s birth.
Determine, to the nearest dollar, how much more the investment will be worth when Alexander turns 32 than when he turns 17.
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35.
Stephen collected data from a travel website. The data included a hotel’s distance from Times Square in Manhattan and the cost of a room for one weekend night in August. A table containing these data appears below.
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for this data set, to the nearest hundredth.
Explain what the sign of the correlation coefficient suggests in the context of the problem.
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36.
A snowstorm started at midnight. For the first 4 hours, it snowed at an average rate of one-half inch per hour.
The snow then started to fall at an average rate of one inch per hour for the next 6 hours.
Then it stopped snowing for 3 hours.
Then it started snowing again at an average rate of one-half inch per hour for the next 4 hours until the storm was over.
On the set of axes below, graph the amount of snow accumulated over the time interval of the storm.
Determine the average rate of snowfall over the length of the storm. State the rate, to the nearest hundredth of an inch per hour.
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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. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
Allysa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each.
Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased.
Determine algebraically how many of each type of chicken Allysa purchased.
Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.
