The Learning Room Algebra II Assessment

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The short quiz is pulled from the 2022 released New York State Mathematics test. This quiz will cover Algebra II and what a student will be able to do by the end of the year. If you see that your student is struggling, we are here to help. Click here for a free assessment from one of our academic coaches.

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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?

1 point

most of its customers in New York State care most about being served quickly

coffee drinkers care less about taste and more about being served quickly

most of its customers at the Staten Island ferry terminal care most about being served quickly

most of its customers at transportation terminals and stations care most about being served quickly

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

1 point

x² + 4

x² - 4

x² - 2xi - 4

x² - 4xi - 4

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

Using this function below, the amplitude of the tide is?

1 point

π/6

4.8

5.1

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?

1 point

experimental

observational

a sample survey

a random assignment

In the diagram of a unit circle below, point A, (-⎷3/2, 1/2), represents the point where there terminal side of ø intersects the unit circle.

What is m∠ø?

1 point

30º

120º

135º

150º

Consider the function f(x) = 2x³ + x² - 18x - 9. Which statement is true?

1 point

2x - 1 is a factor of f(x)

x - 3 is a factor of f(x)

f(3) ≠ f(-1/2)

f(1/2) = 0

Which sketch could represent the function m(x) = -log₁₀₀(x - 2)?

1 point

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

1 point

x² - 6x + 10 = 0

x² + 6x - 10 = 0

x² - 10x + 6 = 0

x² + 10x - 6 = 0

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?

1 point

What is the total number of points of intersection of the graphs of the equations y = eˣ and xy = 20?

1 point

The amount of a substance, A(t), in grams, remaining after t days is modeled below.

What statement is false?

1 point

In 20 days, there is no substance remaining

After two half-lives, there is 25% of the substance remaining

The amount of the substance remaining can also be modeled by

After one week, there is less than 10g of the substance remaining

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

1 point

The expression below is equivalent to? *

1 point

Given: *

1 point

f(x) → -1

f(x) → 0

f(x) → 2

f(x) → -∞

For all values of x for which the expression is defined below, which is the equivalent? *

1 point

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

1 point

Which expression is equivalent? *

1 point

What is the solution set of the equation below?

1 point

{-1,6}

{1,-6}

{-1}

{1}

Given the polynomial identity below.

Which equation must also be true for all values of x and y?

1 point

Given the equation below on the interval -π <ø< π, the function p

1 point

decreases, then increases

increases, then decreases

decreases throughout the interval

increases throughout the interval

A company fired several employees in order to save money. The amount of money the company saved per year over five years following the loss of employees is shown in the table below.

Which expression determines the total amount of money saved by the company over 5 years?

1 point

A rush-hour commuter train has arrived on time 64 of its first 80 days. As arrivals continue, which equation can be used to find x, the number of consecutive days that the train must arrive on schedule to raise its on-time performance rate to 90%?

1 point

Given f(x) = -2/5x + 4, which statement is true of the inverse function f⁻¹(x)? *

1 point

f⁻¹(x) is a line with a slope 5/2

f⁻¹(x) is a line with a slope 2/5

f⁻¹(x) passes through the point (6,-5)

f⁻¹(x) has a y-intercept at (0,-4)

The amount of a substance, A(t), that reminds after t days can be given by the equation below, where A₀ represents the initial amount of the substance. An equation form of this equation is what? *

1 point

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