NY Regents Algebra II Practice Questions

The Hot and Tasty Coffee chain conducts a survey of its customers at its location at the Staten Island ferry terminal. After the survey is completed, the statistical consultant states that 70% of customers who took the survey said the most important factor in choosing where to get their coffee is how fast they are served. Based on this result, Hot and Tasty Coffee can infer that

Given that $i$ is the imaginary unit, the expression $(x - 2i)^2$ is equivalent to

The equation below can be used to model the height of a tide in feet, $H(t)$, on a beach at $t$ hours.

$H(t) = 4.8 \sin \left(\frac {\pi}{6} (t + 3)\right) + 5.1$

Using this function, the amplitude of the tide is

In watching auditions for lead singer in a band, Liem became curious as to whether there is an association between how animated the lead singer is and the amount of applause from the audience. He decided to watch each singer and rate the singer on a scale of 1 to 5, where 1 is the least animated and 5 is the most animated. He did this for all 5 nights of auditions and found that the more animated singers did receive louder applause.

The study Liem conducted would be best described as

In the diagram of a unit circle below, point $A$, $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$, represents the point where the terminal side of $\theta$ intersects the unit circle.

What is $\mathrm{m}\angle \theta$?

Consider the function $f(x) = 2x^{3} + x^{2} - 18x - 9$. Which statement is true?

Which sketch could represent the function $m(x) = -\log_{100}(x - 2)$?

Which equation has roots of $3 + i$ and $3 - i$?

A local university has a current enrollment of 12,000 students. The enrollment is increasing continuously at a rate of $2.5\%$ each year.

Which logarithm is equal to the number of years it will take for the population to increase to 15,000 students?

What is the total number of points of intersection of the graphs of the equations $y = e^x$ and $xy = 20$?

The amount of a substance, $A(t)$, in grams, remaining after $t$ days is modeled by $A(t) = 50(0.5)^{\frac{t}{3}}$. Which statement is false?

A parabola that has a vertex at (2,1) and a focus of $(2, -3)$ has an equation of

The expression $\left(a\sqrt[3]{2b^2}\right)\left(\sqrt[3]{4a^2b}\right)$ is equivalent to

Given $f(x) = 3^{x - 1} + 2$, as $x \to -\infty$

For all values of $x$ for which the expression is defined, $\frac{x^2 + 3x}{x^2 + 5x + 6}$ is equivalent to

A recursive formula for the sequence 64, 48, 36, ... is

Which expression is equivalent to $\frac{x^3 - 2}{x - 2}$?

What is the solution set of the equation $\frac{4}{k^2 - 8k + 12} = \frac{k}{k - 2} + \frac{1}{k - 6}$?

Given the polynomial identity $x^6 + y^6 = (x^2 + y^2)(x^4 - x^2y^2 + y^4)$, which equation must also be true for all values of $x$ and $y$?

Given $p(\theta) = 3\sin \left(\frac{1}{2}\theta\right)$ on the interval $-\pi < \theta < \pi$, the function $p$