2019 (Jan.): NY Regents - Algebra 1

The scatter plot below shows the relationship between the number of members in a family and the amount of the family’s weekly grocery bill.

The most appropriate prediction of the grocery bill for a family that consists of six members is

The function g(x) is defined as g(x) = -2x^{2}+3x. The value of g(-3) is

Which expression results in a rational number?

The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6500 to spend and purchases 30 textbooks, how many laptops can they buy?

What is the solution to the equation \frac{3}{5}\left(x+\frac{4}{3}\right)=1.04?

The area of a rectangle is represented by 3x^2\ -10x-8. Which expression can also be used to represent the area of the same rectangle?

Which relation does not represent a function?

Britney is solving a quadratic equation. Her first step is shown below.

Problem: 3x^{2}-8-10x = 3(2x + 3)

Step 1: 3x^{2}-10x-8 = 6x + 9

Which two properties did Britney use to get to step 1?

I. addition property of equality

II. commutative property of addition

III. multiplication property of equality

IV. distributive property of multiplication over addition

The graph of y = \frac{1}{2}x^2-x-4is shown below. The points A(-2,0), B(0, -4), and C(4,0) lie on this graph.

Which of these points can determine the zeros of the equation y = \frac{1}{2}x^2-x-4?

Given the parent function f(x) = x^3, the function g(x) = (x - 1)^3\ - 2 is the result of a shift of f(x)

If C = 2a^2\ - 5 and D=3-a, then C-2D equals

Marc bought a new laptop for $1250. He kept track of the value of the laptop over the next three years, as shown in the table below.

Which function can be used to determine the value of the laptop for x years after the purchase?

The height of a ball Doreen tossed into the air can be modeled by the function h(x) = -4.9x^2\ + 6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents

The function f(x) = 2x^2\ + 6x - 12 has a domain consisting of the integers from -2 to 1, inclusive. Which set represents the corresponding range values for f(x)?

Which equation has the same solution as x^2\ + 8x - 33 = 0?

The table below shows the weights of Liam’s pumpkin, l(w), and Patricia’s pumpkin, p(w), over a four-week period where w represents the number of weeks. Liam’s pumpkin grows at a constant rate. Patricia’s pumpkin grows at a weekly rate of approximately 52%.

Assume the pumpkins continue to grow at these rates through week 13. When comparing the weights of both Liam’s and Patricia’s pumpkins in week 10 and week 13, which statement is true?

The function f(x) is graphed below.

The domain of this function is

Which pair of equations would have (–1,2) as a solution?

Which function could be used to represent the sequence 8, 20, 50, 125, 312.5,..., given that a_1 = 8?

The formula for electrical power, P, is P = I^{2}R, where I is current and R is resistance. The formula for I in terms of P and R is

The functions f(x), q(x), and p(x) are shown below.

When the input is 4, which functions have the same output value?

Using the substitution method, Vito is solving the following system of equations algebraically:

y + 3x = -4

2x-3y=-21

Which equivalent equation could Vito use?

Materials A and B decay over time. The function for the amount of material A is A(t) = 1000(0.5)^2t and for the amount of material B is B(t) = 1000(0.25)^t , where t represents time in days. On which day will the amounts of material be equal?

The following conversion was done correctly:

\frac{3\space\mathrm{miles}}{1\space\mathrm{hour}}\cdot\frac{1\space\mathrm{hour}}{60\space\mathrm{minutes}}\cdot\frac{5280\space\mathrm{feet}}{1\space\mathrm{mile}}\cdot\frac{12\space\mathrm{inches}}{1\space\mathrm{foot}}

What were the final units for this conversion?

Solve algebraically for x: 3600+1.02x<2000+1.04x

Graph the function f(x)=2^{x}-7 on the set of axes in the Show Your Work space.

If g(x)=1.5x-3, determine if f(x) > g(x), when x = 4. Justify your answer.

Determine algebraically the zeros of f(x) = 3x^3\ + 21x^2 + 36x.

Santina is considering a vacation and has obtained high-temperature data from the last two weeks for Miami and Los Angeles.

Which location has the least variability in temperatures? Explain how you arrived at your answer.

Solve the quadratic equation below for the exact values of x.

4x^2\ - 5 = 75