In the figure above, the length of side $AB$ of triangle $ABC$ is $3$, and $\angle A = \angle C= 30^{\circ}$. What is the area of the triangle $ABC$?

1. $\quad \dfrac{9\sqrt{3}}{8}$
2. $\quad \dfrac{9}{4}$
3. $\quad \dfrac{9\sqrt{3}}{4}$
4. $\quad \dfrac{9}{2}$
5. $\quad \dfrac{27\sqrt{3}}{8}$

An object thrown directly upward is at a height of $h$ feet after $t$ seconds, where $h = -16t^2 + 12t + 24$. The number $24$ in this equation represents which of the following?

1. $\quad$ The highest distance the ball is from the ground.
2. $\quad$ The distance the ball is from the ground when it is thrown upward.
3. $\quad$ The number of seconds the ball will take to reach the highest point.
4. $\quad$ The number of seconds the ball will take to reach the ground.
5. $\quad$ The velocity of the ball when it is thrown.

The graph of the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ has a y-intercept at which of the following points?

1. $\quad (0,1)$
2. $\quad (0,2)$
3. $\quad (0,3)$
4. $\quad (0,4)$
5. $\quad (0,9)$

A rectangular sheet with a length of 8 inches and a width of 6 inches is rolled up so that the two shorter edges just meet, creating a circular tube(right circular cylinder) of height 6 inches. What is the volume, in cubic inches, of the space inside this cylindrical tube?

1. $\quad \dfrac{16}{\pi}$
2. $\quad \dfrac{48}{\pi}$
3. $\quad 16$
4. $\quad \dfrac{96}{\pi}$
5. $\quad 96$

Which of the following expressions is equivalent to
$$ \left[1 \quad – \quad\dfrac{(n!)^2}{(n+1)!(n-1)!}\right]$$ where $n>2$ and $n! = n(n-1)(n-2)\cdots 3 \cdot 2 \cdot 1$ ?

1. $\quad \dfrac{n-2}{n+1}$
2. $\quad \dfrac{1}{n+1}$
3. $\quad \dfrac{2}{n^2-1}$
4. $\quad \dfrac{1}{n-1}$
5. $\quad \dfrac{n}{n+1}$