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2020: NY Regents - Algebra 1

By Sara Cowley
Last updated 2 days ago
37 Questions
From the New York State Education Department. The University of the State of New York Regents High School Examination Algebra 1 January 2020. Internet. Available from https://www.nysedregents.org/algebraone/120/algone12020-exam.pdf; accessed 3, May, 2023.

If f(x) = 2(3^x\ ) +1, what is the value of f(2)?

A high school sponsored a badminton tournament. After each round, one-half of the players were eliminated. If there were 64 players at the start of the tournament, which equation models the number of players left after 3 rounds?

Given 7x + 2 ≥ 58, which number is not in the solution set?

Which table could represent a function?

Which value of x makes \frac{^{x-3}}{4}+\frac{2}{3}=\frac{17}{12} true?

Which expression is equivalent to 18x^2\ - 50?

The functions f(x) = x^2\ -6x+9 and g(x) = f(x)+k are graphed below.


Which value of k would result in the graph of g(x)?

The shaded boxes in the figures below represent a sequence.


If figure 1 represents the first term and this pattern continues, how many shaded blocks will be in figure 35?

The zeros of the function f(x) = x^3\ -9x^2 are

A middle school conducted a survey of students to determine if they spent more of their time playing games or watching videos on their tablets. The results are shown in the table below.


Of the students who spent more time playing games on their tablets, approximately what percent were boys?

Which statement best describes the solutions of a two-variable equation?

The expression x^2\ -10x+24 is equivalent to

Which statement is true about the functions f(x) and g(x), given below?

f(x) = -x^2\ -4x- 4

The equation V(t) = 12,000(0.75)^t represents the value of a motorcycle t years after it was purchased. Which statement is true?

The solutions to (x+4)^2\ - 2 = 7 are

Which expression is not equivalent to -4x^3\ + x^2-6x+8?

Which situation could be modeled as a linear equation?

The range of the function f(x) =|x + 3|- 5 is

A laboratory technician used the function t(m) = 2(3)^2m+1
I. 6(3)^2m II. 6(6)^2m III. 6(9)^m

The function t(m) is equivalent to

Which system of equations has the same solutions as the system below?
3x - y = 7
2x + 3y = 12

A population of paramecia, P, can be modeled using the exponential function P(t) = 3(2)^t , where t is the number of days since the population was first observed. Which domain is most appropriate to use to determine the population over the course of the first two weeks?

Given the following data set:
65, 70, 70, 70, 70, 80, 80, 80, 85, 90, 90, 95, 95, 95, 100
Which representations are correct for this data set?

A recursively defined sequence is shown below.
a_1=5
a_n+ 1 = 2a_n - 7

The value of a_4 is

Which polynomial has a leading coefficient of 4 and a degree of 3?

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.

Graph f(x) = \sqrt[]{x}\ +\ 1 on the set of axes below.


Maria orders T-shirts for her volleyball camp. Adult-sized T-shirts cost $6.25 each and youth-sized T-shirts cost $4.50 each. Maria has $550 to purchase both adult-sized and youth-sized T-shirts. If she purchases 45 youth-sized T-shirts, determine algebraically the maximum number of adult-sized T-shirts she can purchase.


A news report suggested that an adult should drink a minimum of 4 pints of water per day. Based on this report, determine the minimum amount of water an adult should drink, in fluid ounces, per week.


Express (3x-4)(x+7)\ -\frac{1}{4}x^2 as a trinomial in standard form.


John was given the equation 4(2a +3) = -3(a - 1) + 31 - 11a to solve. Some of the steps and
their reasons have already been completed. State a property of numbers for each missing reason.

4(2a + 3) = -3(a - 1) + 31 - 11a
8a + 12 = -3a + 3 + 31 -11a
8a + 12 = 34 - 14a
22a + 12 = 34

State whether the product of \sqrt[]{3}\ & \sqrt[]{9} is rational or irrational. Explain your answer.


Use the method of completing the square to determine the exact values of x for the equation
x^2\ - 8x + 6 = 0

A formula for determining the finite sum, S, of an arithmetic sequence of numbers is S= \frac{n}{2}\left(a+b\right), where n is the number of terms, a is the first term, and b is the last term.
Express b in terms of a, S, and n.


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.

Michael threw a ball into the air from the top of a building. The height of the ball, in feet,
is modeled by the equation h = 16t^2\ + 64t + 60, where t is the elapsed time, in seconds.
Graph this equation on the set of axes below.


Determine the average rate of change, in feet per second, from when Michael released the ball to when the ball reached its maximum height.


Graph the system of inequalities:
-x + 2y - 4 < 0
3x + 4y + 4 ≥ 0


Stephen says the point (0,0) is a solution to this system. Determine if he is correct, and explain your reasoning.


The following table represents a sample of sale prices, in thousands of dollars, and number of new homes available at that price in 2017.


State the linear regression function, f(p), that estimates the number of new homes available at a specific sale price, p. Round all values to the nearest hundredth.

State the correlation coefficient of the data to the nearest hundredth. Explain what this means in the context of the problem.


The length of a rectangular sign is 6 inches more than half its width. The area of this sign is 432 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this sign.

Solve this equation algebraically to determine the dimensions of this sign, in inches.


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.

Two families went to Rollercoaster World. The Brown family paid $170 for 3 children and 2 adults. The Peckham family paid $360 for 4 children and 6 adults.

If x is the price of a child’s ticket in dollars and y is the price of an adult’s ticket in dollars, write a system of equations that models this situation.

Graph your system of equations on the set of axes below.


State the coordinates of the point of intersection.
Explain what each coordinate of the point of intersection means in the context of the problem.