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2021: NY Regents - Algebra 1

By Sara Cowley
Last updated about 2 months ago
46 Questions
From the New York State Education Department. Algebra I June 2021 (v202) Exam. Internet. Available from https://www.nysedregents.org/algebraone/621/algone-v202-exam.pdf; accessed 28, March, 2022.
1.

A high school club is researching a tour package offered by the Island Kayak Company. The company charges $35 per person and $245 for the tour guide. Which function represents the total cost, C(x), of this kayak tour package for x club members?

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2.

The expression 3(x +4) - (2x + 7) is equivalent to

3.

A function is defined as
The value of K(-3) is

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Which relation is not a function?
4.
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5.

The value of Tony’s investment was $1140 on January 1st. On this date three years later, his investment was worth $1824. The average rate of change for this investment was $19 per

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6.

The solution to 3(x -8) + 4x = 8x + 4 is

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7.

An ice cream shop sells ice cream cones, c, and milkshakes, m. Each ice cream cone costs $1.50 and each milkshake costs $2.00. Donna has $19.00 to spend on ice cream cones and milkshakes. If she must buy 5 ice cream cones, which inequality could be used to determine the maximum number of milkshakes she can buy?

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8.

When written in standard form, the product of (3 + x) and (2x - 5) is

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9.

If
which expression results in a rational number?

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10.

Which product is equivalent to

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11.

Given:
Four statements about this system are written below.

I. f(4) = g(4)
II. When x=12, (f)x = g(x)
III. The graphs of f(x) and g(x) intersect at (12,4).
IV. The graphs of f(x) and g(x) intersect at (4,12).
Which of these statements are true?

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Which sketch represents the polynomial function
12.
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13.

If the parent function of f(x) is p(x) = x2, then the graph of the function f(x) = (x - k)2 +5, where k > 0, would be a shift of

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14.

Which expression is equivalent to

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Which function has the smallest y-intercept?
15.
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16.

Which domain would be the most appropriate to use for a function that compares the number of emails sent (x) to the amount of data used for a cell phone plan (y)?

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17.

Eric deposits $500 in a bank account that pays 3.5% interest, compounded yearly. Which type of function should he use to determine how much money he will have in the account at the end of 10 years?

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18.

Given: the sequence 4, 7, 10, 13,...
When using the arithmetic sequence formula
to determine the 10th term, which variable would be replaced with the number 3?

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19.

Below are two representations of data.

A: 2, 5, 5, 6, 6, 6, 7, 8, 9

Which statement about A and B is true?

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20.

Which system has the same solution as the system below?
x+3y=10
-2x-2y=4

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21.

Given the pattern below, which recursive formula represents the number of triangles in this sequence?

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22.

Students were asked to write an expression which had a leading coefficient of 3 and a constant term of -4. Which response is correct?

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23.

Sarah travels on her bicycle at a speed of 22.7 miles per hour. What is Sarah’s approximate speed, in kilometers per minute?

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24.

Which ordered pair does not fall on the line formed by the other three?

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25.

Solve algebraically for y:

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26.

Graph the function
over the interval -8 ≤ x ≤ 0.

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The table below shows the height in feet, h(t), of a hot-air balloon and the number of minutes, t, the balloon is in the air.
The function h(t) = 30.5t + 8.7 can be used to model this data table
27.

Explain the meaning of the slope in the context of the problem.

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28.

Explain the meaning of the y-intercept in the context of the problem.

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29.

Factor x4 -16 completely

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30.

Mike knows that (3,6.5) and (4,17.55) are points on the graph of an exponential function, g(x), and he wants to find another point on the graph of this function.

First, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5,28.6) is a point on g(x).

Is he correct? Explain your reasoning.

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31.

Use the method of completing the square to determine the vertex of
State the coordinates of the vertex.

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32.

The temperature inside a cooling unit is measured in degrees Celsius, C. Josh wants to find out how cold it is in degrees Fahrenheit, F. Solve the formula
for F so that Josh can convert Celsius to Fahrenheit

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33.

Solve
algebraically for w, to the nearest hundredth.

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Joey recorded his heart rate, in beats per minute (bpm), after doing different numbers of jumping jacks. His results are shown in the table below.

34.

State the linear regression equation that estimates the heart rate per number of jumping jacks.

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35.

State the correlation coefficient of the linear regression equation, rounded to the nearest hundredth.

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36.

Explain what the correlation coefficient suggests in the context of this problem.

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Hannah went to the school store to buy supplies and spent $16. She bought four more pencils than pens and two fewer erasers than pens. Pens cost $1.25 each, pencils cost $0.55 each, and erasers cost $0.75 each.
37.

If x represents the number of pens Hannah bought, write an equation in terms of x that can be used to find how many of each item she bought.

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38.

Use your equation to determine algebraically how many pens Hannah bought.

Graph the system of inequalities on the set of axes below


39.

Graph the system of inequalities

40.

Is (6,3) a solution to the system of inequalities? Explain your answer.

A ball is projected up into the air from the surface of a platform to the ground below. The height of the ball above the ground, in feet, is modeled by the function
where t is the time, in seconds, after the ball is projected.
41.

State the height of the platform, in feet.

42.

State the coordinates of the vertex. Explain what it means in the context of the problem.

43.

State the entire interval over which the ball’s height is decreasing.

At a local garden shop, the price of plants includes sales tax. The cost of 4 large plants and 8 medium plants is $40. The cost of 5 large plants and 2 medium plants is $28.
44.

If l is the cost of a large plant and m is the cost of a medium plant, write a system of equations that models this situation.

45.

Could the cost of one large plant be $5.50 and the cost of one medium plant be $2.25? Justify your answer.

46.

Determine algebraically both the cost of a large plant and the cost of a medium plant.