1. The graph of the function $p(x)$ is sketched below.

Which equation could represent $p(x)$?

(1) $p(x) = (x^{2} - 9)(x - 2)$
(2) $p(x) = x^{3} - 2x^{2} + 9x + 18$
(3) $p(x) = (x^{2} + 9)(x - 2)$
(4) $p(x) = x^{3} + 2x^{2} - 9x - 18$

2. What is the solution to $8(2^{x + 3}) = 48$?

(1) $x = \dfrac{In6}{In2} - 3$
(2) $x = 0$
(3) $x = \dfrac{In48}{In16} - 3$
(4) $x = In4 - 3$

3. Cheap and Fast gas station is conduction a consumer satisfaction survey. Which method of collecting data would most likely lead to a biased sample?

(1) interviewing every $5th$ customer to come into the station
(2) interviewing customers chosen at random by a computer at the checkout
(3) interviewing customers who call an $800$ number posted on the customer’s receipts
(4) interviewing every customer who comes into the station on a day of the week chosen at random out of a hat

4. The expression $6xi^{3}(-4xi + 5)$ is equivalent to

(1) $2x - 5i$
(2) $-24x^{2} - 30xi$
(3) $-24x{2} + 30x - i$
(4) $26x - 24x^{2}i - 5i$

5. If $f(x) = 3|x| - 1$ and $g(x) = 0.03x^{3} - x + 1$, an approximate solution for the equation $f(x) = g(x)$ is

(1) $1.96$
(2) $11.29$
(3) $(-0.99, 1.96)$
(4) $(11.29, 32.87)$

6. Given the parent function $p(x) = \cos (x)$, which phrase best describes the transformation used to obtain the graph of $g(x) = \cos (x + a) - b$, if $a$ and $b$ are positive constants?

(1) right a units, up b units
(2) right a units, down b units
(3) left a units, up b units
(4) left a units, down b units

7. The solution to the equation $4x^{2} + 98 = 0$ is

(1) $\pm 7$
(2) $\pm 7i$
(3) $\pm \dfrac{7 \sqrt{2}}{2}$
(4) $\pm \dfrac{7i \sqrt{2}}{2}$

8. Which equation is represented by the graph shown below?

(1) $y = \dfrac{1}{2} \cos 2x$
(2) $y = \cos (x)$
(3) $y = \dfrac{1}{2} \cos (x)$
(4) $y = 2\cos \dfrac{1}{2}x$

9. A manufacturing company has developed a cost model, $C(x) = 0.15x^{3} + 0.01x^{2} + 2x + 120$, where $x$ is the number of items sold, in thousands. The sales price can be modeled by $S(x) = 30 - 0.01x$. Therefore, revenue is modeled by $R(x) = x \bullet S(x)$.

The company’s profit, $P(x) = R(x) - C(x)$, could be modeled by

(1) $0.15x^{3} + 0.02x^{2} - 28x + 120$
(2) $-0.15x^{3} - 0.02x^{2} + 28x - 120$
(3) $-0.15x^{3} + 0.01x^{2} - 2.01x - 120$
(4) $-0.15x^{3} + 32x + 120$

10. A game spinner is divided into $6$ equally sized regions, as shown in the diagram below.

For Miles to win, the spinner must land on the number $6$. After spinning the spinner $10$ times, and losing all $10$ times, Miles complained that the spinner is unfair. At home, his dad ran $100$ simulations of spinning the spinner $10$ times, assuming the probability of winning each spin is $\dfrac{1}{6}$. The output of the simulation is shown in the diagram below.

Which explanation is appropriate for Miles and his dad to make?

(1) The spinner was likely unfair, since the number $6$ failed to occur in about $20\%$ of the simulations.
(2) The spinner was likely unfair, since the spinner should have landed on the number $6$ by the sixth spin.
(3) The spinner was likely not unfair, since the number $6$ failed to occur in about $20\%$ of the simulations.
(4) The spinner was likely not unfair, since in the output the player wins once or twice in the majority of the simulations.

11. Which binomial is a factor of $x^{4} - 4x^{2} - 4x + 8$?

(1) $x - 2$
(2) $x + 2$
(3) $x - 4$
(4) $x + 4$

12. Given that $\sin^{2} + \cos^{2} 0 = 1$ and $\sin 0 = -\dfrac{\sqrt{2}}{5}$, what is possible value of $\cos 0$?

(1) $\dfrac{5 + \sqrt{2}}{5}$
(2) $\dfrac{\sqrt{23}}{5}$
(3) $\dfrac{3\sqrt{3}}{5}$
(4) $\dfrac{\sqrt{35}}{5}$

13. A student studying public policy created a model for the population of Detroit, where the population decreased $25\%$ over a decade. He used the model $P = 714(0.75)^{d}$, where $P$ is the population, in thousands, $d$ decades after 2010. Another student, Suzanne, wants to use a model that would predict the population after $y$ years. Suzanne’s model is best represented by

(1) $P = 714(0.6500)^{y}$
(2) $P = 714(0.8500)^{y}$
(3) $P = 714(0.9716)^{y}$
(4) $P = 714(0.9750)^{y}$

14. The probability that Gary and Jane have a child with blue eyes is $0.25$, and the probability that they have a child with blond hair is $0.5$. The probability that they have a child with both blue eyes and blond hair is $0.125$. Given this information, the events blue eyes and blond hair are

I: dependent
II: independent
III: mutually exclusive

(1) I, only
(2) II, only
(3) I and III
(4) II and III

15. Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees $F$, can be modeled by the equation $B(x) = 23.914 \sin (0.508x - 2.116) + 55.300$. The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation $P(x) = 20.238 \sin (0.525x - 2.148) + 86.729$.

Which statement can not be concluded based on the average monthly temperature models $x$ months after starting data collection?

(1) The average monthly temperature variation is more in Bar Harbor than in Phoenix.
(2) The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix.
(3) The maximum average monthly temperature for Bar Harbor is $79^{\circ}$F, to the nearest degree.
(4) The minimum average monthly temperature for Phoenix is $20^{\circ}$F, to the nearest degree.

16. For $x \neq 0$, which expressions are equivalent to one divided by the sixth root of $x$?

I. $\dfrac{\sqrt[6]{x}}{\sqrt[3]{x}}$
II. $\dfrac{x^\frac{1}{6}}{x^\frac{1}{3}}$
III. $x^\frac{-1}{6}$

(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III

17. A parabola has its focus at $(1,2)$ and its directrix is $y = -2$. The equation of this parabola could be

(1) $y = 8(x + 1)^{2}$
(2) $y = \dfrac{1}{8} (x + 1)^{2}$
(3) $y = 8(x - 1)^{2}$
(4) $y = \dfrac{1}{8} (x - 1)^{2}$

18. The function $p(t) = 110e^{0.03922t}$ models the population of a city, in millions, $t$ years after 2010. As of today, consider the following two statements:

I. The current population is $110$ million.
II. The population increases continuously by approximately $3.9\%$ per year.

This model supports

(1) I, only
(2) II, only
(3) both I and II
(4) neither I nor II

19. To solve $\dfrac{2x}{x - 2} - \dfrac{11}{x} = \dfrac{8}{x^{2} - 2x}$, Ren multiplied both sides by the least common denominator. Which statement is true?

(1) $2$ is an extraneous solution.
(2) $\dfrac{7}{2}$ is an extraneous solution.
(3) $0$ and $2$ are extraneous solutions.
(4) This equation does not contain any extraneous solutions.

20. Given $f(9) = -2$, which function can be used to generate the sequence $-8, -7, -6.5, -5.75,$…?

(1) $f(n) = -8 + 0.75n$
(2) $f(n) = -8 - 0.75(n - 1)$
(3) $f(n) = -8.75 + 0.75n$
(4) $f(n) = -0.75 + 8(n - 1)$

21. The function $f(x) = 2^{-0.25x} \bullet \sin(\dfrac{\pi}{2}x)$ represents a damped sound wave function. What is the average rate of change for this function on the interval $[-7, 7]$, to the nearest hundredth?

(1) $-3.66$
(2) $-0.30$
(3) $-0.26$
(4) $3.36$

22. Mallory wants to buy a new window air conditioning unit. The cost for the unit is $\329.99$. If she plans to run the unit three months out of the year for an annual operating cost of $\108.78$, which function models the cost per year over the lifetime of the unit, $C(n)$, in terms of the number of years, $n$, that she owns the air conditioner?

(1) $C(n) = 329.99 + 108.78n$
(2) $C(n) = 329.99 + 326.34n$
(3) $C(n) = \dfrac{329.99 + 108.78n}{n}$
(4) $C(n) = \dfrac{329.99 + 326.34n}{n}$

23. The expression $\dfrac{-3x^{2} - 5x + 2}{x^{3} + 2x^{2}}$ can be rewritten as

(1) $\dfrac{-3x - 3}{x^{2} + 2x}$
(2) $\dfrac{-3x - 1}{x^{2}}$
(3) $-3x^{-1} + 1$
(4) $-3x^{-1} + (x)^{-2}$

24. Jasmine decides to put $\100$ in a savings account each month. The account pays $3\%$ annual interest, compounded monthly. How much money, $S$, will Jasmine have after one year?

(1) $S = 100(1.03)^{12}$
(2) $S = \dfrac{100 - 100(1.0025)^{12}}{1 - 1.0025}$
(3) $S = 100(1.0025)^{12}$
(4) $S = \dfrac{100 - 100(1.03)^{12}}{1 - 1.03}$