Question 1

If $k$ is a constant, what is the value of $k$ such that the polynomial $k^2x^3-6kx+9$  is divisible by $x - 1$?
Enter your answer in the box.

Accepted Answer

3

Question 2

Consider the equation $\frac {4^{x^2}}{2^x}=2$
Which equation is equivalent to the equation shown?

Accepted Answer

$2^{2x^2-x}=2$

Answer

$2^{x^2-x}=2$

Answer

$2^{2x}=2$

Answer

$2^{x^2}=2$

Question 3

What extraneous solution arises when the equation $\sqrt{x+3}=2x$ is solved for $x$ by first squaring both sides of the equation?
Enter your answer in the box.

Accepted Answer

-0.75

Question 4

Given that $x > 0$, which expression is equivalent to $5\sqrt{xy}+25 \sqrt x$?

Accepted Answer

$5x^{\frac1{2}}(y^{\frac1{2}}+5)$

Answer

$\sqrt x(25y^{\frac1{2}}+5)$

Answer

$25x^{\frac1{2}}(\sqrt y +5)$

Answer

$5(xy)^{-1}+25x^{-1}$

Question 5

Which equation has no real solutions?

Accepted Answer

$2x^2+4x+12=0$

Answer

$2x^2+3x=4x+12$

Answer

$2x^2+4x-12=0$

Answer

$2x^2+4x=0$

Question 6

Which expression is equivalent to $a^2x^2-2cx^2+a^2y-2cy$?

Accepted Answer

$(x^2+y)(a^2-2c)$

Answer

$(x^2+y)(a+c)$

Answer

$(x^2-y)(a+c)$

Answer

$(x^2-y)(a^2-2c)$

Question 7

Consider the expression $6x^3-5x^2y-24xy^2+20y^3$.

Accepted Answer

$x^2(6x-5y)-4y^2(6x-5y)$

Answer

$x^2(6x-5y)+4y^2(6x+5y)$

Answer

$x^2(6x-5y)-4y^2(6x+5y)$

Answer

$x^2(6x-5y)+4y^2(6x-5y)$

Question 8

Solve the equation $27^x=9^{x-3}$ for $x$.
Enter your answer in the box.

Accepted Answer

-6

Question 9

The functions f and g are defined by $f(x) = x^2$ and $g(x) = 2x$, respectively.
Which equation is equivalent to $h(x) =\frac {f(2x)g(-2x)}{2}$?

Accepted Answer

$h(x)=-8x^3$

Answer

$h(x)=x^2-2x$

Answer

$h(x)=-2x^3$

Answer

$h(x)=2x^2+2x$

Question 10

Deshawn is in his fifth year of employment as a patrol officer for the Metro Police. His salary for his first year of employment was $47,000. Each year after the first, his salary increased by 4% of his salary the previous year. 
What is the sum of DeShawn's salaries for his first five years of service?

Accepted Answer

$254,567

Answer

$188,000

Answer

$101,983

Answer

$219,932

Question 11

Deshawn is in his fifth year of employment as a patrol officer for the Metro Police. His salary for his first year of employment was $$\$47,000$$. Each year after the first, his salary increased by 4% of his salary the previous year.
If Deshawn continues his employment at the same rate of increase in yearly salary, for which year will the sum of his salaries first exceed $$\$1,000,000$$?
Give your answer to the nearest integer.
Enter your answer in the box.

Accepted Answer

16

Question 12

The London Eye, a Ferris wheel in England, has a diameter of 120 meters. The wheel completes a full rotation in 30 minutes to allow passengers to enter a capsule at the base of the Ferris wheel without stopping the wheel.  At the highest point, a capsule reaches a height of 135 meters above the ground. The height above the ground, in meters, of a capsule after $x$ minutes can be modeled by $f(x) =A \cdot cos(\frac {\pi}{15}x)+B$, where $A$ and $B$ are constants.

Given the situation, what is the value of $A$?
Enter your answer in the box.

Accepted Answer

-60

Question 13

Consider the polynomial function $f(x) = (2x - 1)(x + 4)(x - 2)$.
What is the $y$-intercept of the graph of the function in the xy-coordinate plane?
Enter your answer in the box.

Accepted Answer

8

Question 14

Consider the polynomial function $f(x) = (2x - 1)(x + 4)(x - 2)$.
What is the end behavior of the graph of the function?

Accepted Answer

As $x \rightarrow - \infty, f(x) \rightarrow - \infty$, and as $x\rightarrow \infty, f(x)\rightarrow \infty$.

Answer

As $x \rightarrow - \infty, f(x) \rightarrow  \infty$, and as $x\rightarrow \infty, f(x)\rightarrow \infty$.

Answer

As $x \rightarrow - \infty, f(x) \rightarrow  \infty$, and as $x\rightarrow \infty, f(x)\rightarrow -\infty$.

Answer

As $x \rightarrow - \infty, f(x) \rightarrow - \infty$, and as $x\rightarrow \infty, f(x)\rightarrow -\infty$.

Question 15

Consider the polynomial function $f(x) = (2x - 1)(x + 4)(x - 2)$.
How many relative maximums does the function have?

Accepted Answer

one

Answer

three

Answer

none

Answer

two

Question 16

Functions $f$ and $g$ are defined below. 
$\begin{cases} f(x)= \frac{1}{2x} \ g(x) = x^2 \end {cases}$

The graphs of $y = f(x)$ and $y = g(x)$ intersect at point $P$.
Determine the $x$-coordinate of $P$. Round your answer to the nearest tenth.
Enter your answer in the box.

Accepted Answer

freetextm://0.7:0.8

Question 17

What are the solutions to the equation $2x^2 - x + 1 = 0$?

Accepted Answer

$\frac{1}{4}-(\frac {\sqrt7}{4})i$ and $\frac{1}{4} +(\frac {\sqrt7}{4})i$

Answer

$\frac{1}{4}-\frac {\sqrt5}{4}$ and $\frac{1}{4} +\frac {\sqrt5}{4}$

Answer

$\frac{1}{4}-(\frac {\sqrt5}{4})i$ and $\frac{1}{4} +(\frac {\sqrt5}{4})i$

Answer

$\frac{1}{4}-\frac {\sqrt7}{4}$ and $\frac{1}{4} +\frac {\sqrt7}{4}$

Question 18

The apothem of a regular polygon is the distance from the center to any side.  
If the length of the apothem remains constant at 10 inches, the formula for the perimeter of a regular polygon as a function of the number of sides $n$ is $P(n) = 10(tan \frac{360 \degree}{2n})(2n)$.
As the regular polygon changes from a pentagon (5 sides) to an octagon (8 sides), what is the approximate average rate of change in the perimeter?

Accepted Answer

decrease of 2.13 inches for each additional side

Answer

decrease of 6.38 inches for each additional side

Answer

decrease of 4.56 inches for each additional side

Answer

decrease of 0.80 inches for each additional side

Question 19

The two-way table shows the classification of students in a mathematics class by gender and dominant hand. A student who is ambidextrous uses both hands equally well. 
What is the probability that a randomly selected student in the class is female given that the student is right-handed?

Accepted Answer

$\frac{12}{23}$

Answer

$\frac{1}{12}$

Answer

$\frac{12}{30}$

Answer

$\frac{23}{30}$

Question 20

The two-way table shows the classification of students in a mathematics class by gender and dominant hand. A student who is ambidextrous uses both hands equally well. 
One student will be selected at random from the class.
Consider the events:
$X$: the selected student is female
$Y$: the selected student is right-handed
Which statement about events $X$ and $Y$ is true?

Accepted Answer

The events are not independent because the probability of $X$ is not equal to the probability of $X$ given $Y$.

Answer

The events are not independent because for one of the dominant hand categories the number of female students is 0.

Answer

The events are independent because the number of right-handed students in the class is larger than the number of female students.

Answer

The events are independent because the number of categories for dominant hand is different from the number of categories for gender.

Question 21

If $\sqrt{3 \sqrt{(x+1)^5}}=(x+1)^a$, for $x \ge-1$, and $a$ is a constant, what is the value of $a$?

Accepted Answer

$\frac{5}{6}$

Answer

$\frac{10}{3}$

Answer

$\frac{5}{3}$

Answer

$\frac{3}{10}$

Question 22

Angle $	heta$ is in Quadrant II, and $sin 	heta=\frac{4}{5}$. What is the value of $cos	heta$?

Accepted Answer

$-\frac{3}{5}$

Answer

$\frac{3}{5}$

Answer

$-\frac{4}{5}$

Answer

$\frac{4}{5}$

Question 23

The graph represents the temperature, in degrees Fahrenheit $(\degree F)$, of tea for the first 120 minutes after it was poured into a cup. 
Based on the graph, what was the temperature of the tea when it was first poured into the cup?

Accepted Answer

$204 \degree$

Answer

$114 \degree$

Answer

$68 \degree$

Answer

$136 \degree$

Question 24

The graph represents the temperature, in degrees Fahrenheit $(\degree F)$, of tea for the first 120 minutes after it was poured into a cup. 
Based on the graph, as the number of minutes increased, what temperature did the tea approach?

Accepted Answer

$68 \degree$

Answer

$204 \degree$

Answer

$114 \degree$

Answer

$136 \degree$

Question 25

A circular spinner is divided into five sectors of different colors. A student spun the arrow on the spinner 200 times and recorded that the arrow stopped on the orange sector 38 times out of the 200 spins. To test whether the spinner was fair, the student used a computer to simulate the number of times the arrow stops on orange in 200 spins of a fair spinner equally divided into five sectors of different colors. The results of 1,000 trials of the simulation are shown.
Based on the results of the simulation, is there statistical evidence that the spinner is not fair?

Accepted Answer

No, because an outcome of 38 or less is not unusual.

Answer

No, because the distribution is approximately normal.

Answer

Yes, because about 8% of the outcomes were 38.

Answer

Yes, because 38 was the most frequent outcome.

Question 26

The manager of food services at a local high school is interested in assessing student opinion about a new lunch menu in the school cafeteria. The manager is planning to conduct a sample survey of the student population.
Which of the listed methods of sample selection would be the 'most' effective at reducing bias?

Accepted Answer

Randomly select 30 students from a list of all the students in the school.

Answer

Randomly select one day of the week and then select the first 30 students who enter the cafeteria on that day.

Answer

Randomly select one classroom in the school and then select the first 30 students who enter that classroom.

Answer

Post the survey on the school Web site and use the first 30 surveys that are submitted.

Question 27

The manager of food services at a local high school is interested in assessing student opinion about a new lunch menu in the school cafeteria. The manager is planning to conduct a sample survey of the student population.
The manager wants to know if a student's gender is related to the student's opinion about the menu. Which statement 'best' describes the study?

Accepted Answer

This is an observational study, and therefore, the manager will not be able to establish a cause-and-effect relationship between gender and opinion.

Answer

This is an experimental study, and therefore, the manager will be able to establish a cause-and-effect relationship between gender and opinion.

Answer

This is an observational study, and therefore, the manager will be able to establish a cause-and-effect relationship between gender and opinion.

Answer

This is an experimental study, and therefore, the manager will not be able to establish a cause-and-effect relationship between gender and opinion.

Question 28

The distribution of weights (rounded to the nearest whole number) of all boxes of a certain cereal is approximately normal with mean 20 ounces and standard deviation 2 ounces.
A sample of the cereal boxes was selected, and the weights of the selected boxesare summarized in the histogram shown. 
If $w$ is the weight of a box of cereal, which range of weights includes all of the weights of cereal boxes that are within 1.5 standard deviations of the mean?

Accepted Answer

$17 \le w \le 23$

Answer

$19 \le w \le 21$

Answer

$20 \le w \le 23$

Answer

$18.5 \le w \le 21.5$

Question 29

The distribution of weights (rounded to the nearest whole number) of all boxes of a certain cereal is approximately normal with mean 20 ounces and standard deviation 2 ounces.
A sample of the cereal boxes was selected, and the weights of the selected boxesare summarized in the histogram shown.
Which of these values is the 'best' estimate of the number of boxes in the sample with weights that are more than 1.5 standard deviations above the mean?

Accepted Answer

6

Answer

2

Answer

17

Answer

36

Question 30

$\begin {cases} y=1-x^2 \ y=2-x \end {cases}$
How many points of intersection does the given system of equations have?

Accepted Answer

none

Answer

infinitely many

Answer

one

Answer

two

Question 31

The population of country $A$ was 40 million in the year 2000 and has grown continually in the years following. The population $P$, in millions, of the country $t$ years after 2000 can be modeled by the function $P(t) = 40e^{0.027t}$, where $t \ge0$.

Based on the model, what was the average rate of change, in millions of people per year, of the population of country $A$ from 2000 to 2005? Give your answer to the nearest hundredth.
Enter your answer in the box.

Accepted Answer

1.16

Question 32

The population of country $A$ was 40 million in the year 2000 and has grown continually in the years following. The population $P$, in millions, of the country $t$ years after 2000 can be modeled by the function $P(t) = 40e^{0.027t}$, where $t \ge0$.

Based on the model, the solution to the equation $50 =40e^{0.027t}$ gives the number of years it will take for the population of country $A$ to reach 50 million. What is the solution to the equation expressed as a logarithm?

Accepted Answer

$\frac{ln(1.25)}{0.027}$

Answer

$ln(\frac{0.027}{1.25})$

Answer

$0.027ln(1.25)$

Answer

$ln(\frac{1.25}{0.027})$

Question 33

The population of country $A$ was 40 million in the year 2000 and has grown continually in the years following. The population $P$, in millions, of the country $t$ years after 2000 can be modeled by the function $P(t) = 40e^{0.027t}$, where $t \ge0$.

For another country, country $B$, the population $M$, in millions, $t$ years after 2000 can be modeled by the function $M(t) = 35e^{-0.042t}$ t, where $t\ge0$. Based on the models, what year will be the first year in which the population of country $B$ will be greater than the population of country $A$?

Accepted Answer

The population of country $B$ will not exceed the population of country $A$.

Answer

2021

Answer

2009

Answer

2012

Question 34

To investigate housing needs in the future, a town planning committee created a model to help predict the growth of the population of the town. The committee created a model based on data about the population of the town for five years. The data are shown in the table.
Which model for $P(t)$, the population of the town $t$ years after 1985, 'best' fits the data?

Accepted Answer

$P(t) = 5.24(1.030)^t$

Answer

$P(t) = 5.35(1.029)^t$

Answer

$P(t) = 5.35 + 0.228t$

Answer

$P(t) = 4.95 + 0.229t $

Question 35

To investigate housing needs in the future, a town planning committee created a model to help predict the growth of the population of the town. The committee created a model based on data about the population of the town for five years. The data are shown in the table.
Consider the value predicted by the model for the year 2010. Which statement is true?

Accepted Answer

The model underpredicts the actual population of the town by fewer than 1,000 people.

Answer

The model underpredicts the actual population of the town by more than 1,000 people.

Answer

The model overpredicts the actual population of the town by fewer than 1,000 people.

Answer

The model overpredicts the actual population of the town by more than 1,000 people.

Question 36

Select 'each' statement that is true about the graph of $f(x) = sin(x + 3) - 2$.

Accepted Answer

amplitude: 1

Answer

midline: y = 2

Answer

$y$-intercept: (0, -2)

Answer

amplitude: 2

Question 37

Consider the expression $3^x-3^{x-2}$
Which is an equivalent form of the given expression?

Accepted Answer

$3^x-\frac{3^x}{9}$

Answer

$3^x-9(3^x)$

Answer

$3^x-\frac{3^x}{2}$

Answer

$3^x-2(3^x)$

Question 38

Consider the expression $3^x-3^{x-2}$.
This expression can also be rewritten in the form  $a(3^x)$ where $a$ is a constant. What is the value of $a$?

Accepted Answer

$\frac{8}{9}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{9}$

Answer

$\frac{3}{2}$

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