Here is a practice question on logarithms to get you ready for the April 2015 ACT. Best wishes.

What value of $x$ satisfies the equation below
$$ \log_{27} x + \log_{9} x = -\dfrac{5}{3} $$

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

 
Here is a practice question on parabolas in the coordinate plane.

In the $(x, y)$ coordinate plane, a parabola with an equation of $y=a(x-h)^2 + k$ has a vertex at $(-2, 2)$. If $(2, -1)$ is a point that falls on the parabola, then which one of the following points also falls on the parabola?

1. $\quad (-10, -8)$
2. $\quad (-6, -1)$
3. $\quad (-3, -2)$
4. $\quad (0, -2)$
5. $\quad (0, -1)$

 
Here is a practice question on parabolas in the coordinate plane.

What does $i – i^2 + i^3 – i^4 + \cdots + i^{97} – i^{98}$ equal, where the imaginary number $i$ is defined as $i^2=-1$ ?

1. $\quad -i-1$
2. $\quad -i+1$
3. $\quad 0$
4. $\quad i-1$
5. $\quad i+1$

 
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. $\quad \dfrac{10}{3}$