1. The graphs of the equations $y = x^{2} + 4x - 1$ and $y + 3 = x$ are drawn on the same set of axes. One solution of this system is

(1) $(-5,-2)$
(2) $(-1,-4)$
(3) $(1,4)$
(4) $(-2,-1)$

2. Which statement is true about the graph of $f(x) = \dfrac{1}{8}^{x}$?

(1) The graph is always increasing.
(2) The graph is always decreasing.
(3) The graph passes through $(1, 0)$.
(4) The graph has an asymptote, $x = 0$.

3. For all values of $x$ for which the expression is defined, $\dfrac{x^{3} + 2x^{2} - 9x - 18}{x^{3} - x^{2} - 6x}$, in simplest form, is equivalent to

(1) $3$
(2) $-\dfrac{17}{2}$
(3) $\dfrac{x + 3}{x}$
(4) $\dfrac{x^{2} - 9}{x(x - 3)}$

4. A scatterplot showing the weight, $w$, in grams, of each crystal after growing $t$ hours is shown below.

The relationship between weight, $w$, and time, $t$, is best modeled by

(1) $w = 4^{t} + 5$
(2) $w = (1.4)^{t} + 2$
(3) $w = 5(2.1)^{t}$
(4) $w = 8(.75)^{t}$

5. Where $i$ is the imaginary unit, the expression $(x + 3i)^{2} - (2x - 3i)^{2}$ is equivalent to

(1) $-3x^{2}$
(2) $-3x^{2} - 18$
(3) $-3x^{2} + 18xi$
(4) $-3x^{2} - 6xi - 18$

6. Which function is even?

(1) $f(x) = \sin{x}$
(2) $f(x) = x^{2} - 4$
(3) $f(x) = |x - 2| + 5$
(4) $f(x) = x^{4} + 3x^{3} + 4$

7. The function $N(t) = 100e^{-0.023t}$ models the number of grams in a sample of cesium $-137$ that remain after $t$ years. On which interval is the sample’s average rate of decay the fastest?

(1) $[1, 10]$
(2) $[10, 20$
(3) $[15, 25]$
(4) $[1, 30]$

8. Which expression can be rewritten as $(x + 7)(x - 1)$?

(1) $(x + 3)^{2} - 16$
(2) $(x + 3)^{2} - 10(x + 3) - 2(x + 3) + 20$
(3) $\dfrac{(x - 1)(x^{2} - 6x - 7)}{(x + 1)}$
(4) $\dfrac{(x + 7)(x^{2} + 4x + 3)}{(x + 3)}$

9. What is the solution set of the equation $\dfrac{2}{x} - \dfrac{3x}{x + 3} = \dfrac{x}{x + 3}$?

(1) ${3}$
(2) ${\dfrac{3}{2}}$
(3) ${-2, 3}$
(4) ${-1, \dfrac{3}{2}}$

10. The depth of the water at a marker $20$ feet from the shore in a bay is depicted in the graph below.

If the depth, $d$, is measured in feet and time, $t$, is measured in hours since midnight, what is an equation for the depth of the water at the marker?

(1) $d = 5 \cos (\dfrac{\pi}{6}t) + 9$
(2) $d = 9 \cos (\dfrac{\pi}{6}t) + 5$
(3) $d = 9 \sin (\dfrac{\pi}{6}t) + 5$
(4) $d = 5 \sin (\dfrac{\pi}{6}t) + 9$

11. On a given school day, the probability that Nick oversleeps is $48\%$ and the probability he has a pop quiz is $25\%$. Assuming these two events are independent, what is the probability that Nick oversleeps and has a pop quiz on the same day?

(1) $73\%$
(2) $36\%$
(3) $23\%$
(4) $12\%$

12. If $x - 1$ is a factor of $x^{3} - kx^{2} + 2x$, what is the value of $k$?

(1) $0$
(2) $2$
(3) $3$
(4) $-3$

13. The profit function, $p(x)$, for a company is the cost function, $c(x)$, subtracted from the revenue function, $r(x)$. The profit function for the Acme Corporation is $p(x) = -0.5x^{2} + 250x - 300$ and the revenue function is $r(x) = -0.3x^{2} + 150x$. The cost function for the Acme Corporation is

(1) $c(x) = 0.2x^{2} - 100x + 300$
(2) $c(x) = 0.2x^{2}+ 100x + 300$
(3) $c(x) = -0.2x^{2}+ 100x - 300$
(4) $c(x) = -0.8x^{2} + 400x - 300$

14. The populations of two small towns at the beginning of 2018 and their annual population growth rate are shown in the table below.

Assuming the trend continues, approximately how many years after the beginning of 2018 will it take for the populations to be equal?

(1) $7$
(2) $20$
(3) $68$
(4) $125$

15. What is the inverse of $f(x) = x^{3} - 2$?

(1) $f^{-1}(x) = \sqrt[3]{x} + 2$
(2) $f^{-1}(x) = \pm \sqrt[3]{x} + 2$
(3) $f^{-1}(x) = \sqrt[3]{x + 2}$
(4) $f^{-1}(x) = \pm \sqrt[3]{x + 2}$

16. A 4th degree polynomial has zeros $-5, 3, i$, and $-i$. Which graph could represent the function defined by this polynomial?

(1)
(2)
(3)
(4)

17. The weights of bags of Graseck’s Chocolate Candies are normally distributed with a mean of $4.3$ ounces and a standard deviation of $0.05$ ounces. What is the probability that a bag of these chocolate candies weighs less than $4.27$ ounces?

(1) $0.2257$
(2) $0.2743$
(3) $0.7257$
(4) $0.7757$

18. The half-life of iodine $-131$ is $8$ days. The percent of the isotope left in the body $d$ days after being introduced is $I=100(\dfrac{1}{2})^\frac{d}{8}$. When this equation is written in terms of the number $e$, the base of the natural logarithm, it is equivalent to $I = 100e^{kd}$. What is the approximate value of the constant, $k$?

(1) $-0.087$
(2) $0.087$
(3) $-11.542$
(4) $11.542$

19. The graph of $y = log_{2}x$ is translated to the right $1$ unit and down $1$ unit. The coordinated of the $x$-intercept of the translated graph are

(1) $(0, 0)$
(2) $(1, 0)$
(3) $(2, 0)$
(4) $(3, 0)$

20. For positive values of $x$, which expression is equivalent to $\sqrt{16x^{2}} \bullet x^\frac{2}{3} + \sqrt[3]{8x^{5}}$?

(1) $6 \sqrt[5]{x^{3}}$
(2) $6 \sqrt[3]{x^{5}}$
(3) $4 \sqrt[3]{x^{2}} + 2\sqrt[3]{x^{5}}$
(4) $4 \sqrt{x^{3}} + 2\sqrt[5]{x^{3}}$

21. Which equation represents a parabola with a focus of $(-2,5)$ and a directrix of $y = 9$?

(1) $(y - 7)^{2} = 8(x + 2)$
(2) $(y - 7)^{2} = -8(x + 2)$
(3) $(x + 2)^{2} = 8(y - 7)$
(4) $(x + 2)^{2} = -8(y - 7)$

22. Given the following polynomials

$x=(a + b + c)^{2}$,
$y=a^{2} + b^{2} + c^{2}$
$z=ab + bc + ac$

Which identity is true?

(1) $x= y - z$
(2) $x= y + z$
(3) $x= y - 2z$
(4) $x= y + 2z$

23. On average, college seniors graduation in 2012 could compute their growing student loan debt using the function $D(t) = 29,400(1.068)^{t}$, where $t$ is time in years. Which expression is equivalent to $29,400(1.068)^{t}$ and could be used by students to identify an approximate daily interest rate on their loans?

(1) $29,400(1.068^\frac{1}{365})^{t}$
(2) $29,400(\dfrac{1.068}{365})^{365t}$
(3) $29,400(1 + \dfrac{0.068}{365})^{t}$
(4) $29,400(1.068^\frac{1}{365})^{365t}$

24. A manufacturing plant produces two different-sized containers of peanuts. One container weighs $x$ ounces and the other weighs $y$ pounds. If a gift set can hold one of each size container, which expression represents the number of gift sets needed to hold $124$ ounces?

(1) $\dfrac{124}{16x + y}$
(2) $\dfrac{x + 16y}{124}$
(3) $\dfrac{124}{x + 16y}$
(4) $\dfrac{16x + y}{124}$