Here is a practice question on simplifying trigonometric expressions.

For all $\theta$, $\quad \sin \theta + {(\cot \theta})(\cos{\theta})$ is equivalent to

1. $\quad \csc \theta$
2. $\quad \sec \theta$
3. $\quad \cot \theta$
4. $\quad \tan \theta$
5. $\quad \cos \theta$

 
Here is a practice question on straight lines in the coordinate plane.

If the point $(a, -2)$ falls on the straight line $2y-3x=-6$ in the standard $(x, y)$ coordinate plane, then $a=$ ?

1. $\quad -\dfrac{3}{2}$
2. $\quad -\dfrac{2}{3}$
3. $\quad \dfrac{2}{3}$
4. $\quad \dfrac{3}{2}$
5. $\quad \dfrac{10}{3}$

 
Here is a practice question on how the volume of a cylinder varies with its height and radius.

The radius of a right circular cylinder is doubled and the height of the cylinder is halved to form a new right circular cylinder. The volume of the new
cylinder is how many times the volume of the original cylinder?

1. $\quad \dfrac{1}{4}$
2. $\quad \dfrac{1}{2}$
3. $\quad 1$
4. $\quad 2$
5. $\quad 4$

 
Here is a practice question on how the equation of a circle in the coordinate plane is related to the coordinates of its center and radius.

In the standard $(x, y)$ plane, a circle has a center at $(2, -3)$ and a circumference of $8\pi$. Which of the following is an equation for this circle?

1. $\quad (x-2)^2 + (y-3)^2 = 16$
2. $\quad (x+2)^2 + (y-3)^2 = 16$
3. $\quad (x-2)^2 + (y+3)^2 = 16$
4. $\quad (x+2)^2 + (y-3)^2 = 64$
5. $\quad (x-2)^2 + (y+3)^2 = 64$