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. $\quad (x-2)^2 + (y+3)^2 = 64$

 
Here is a practice question on subtracting exponent expressions, remember that there are no general rules for adding and subtracting exponent terms.

$\dfrac{1}{3^{30}} – \dfrac{2}{3^{31}}$ is equal to

1. $\quad \dfrac{2}{3^{61}}$
2. $\quad \dfrac{1}{3^{31}}$
3. $\quad \dfrac{1}{3^{30}}$
4. $\quad \dfrac{2}{3^{30}}$
5. $\quad \dfrac{1}{3}$

 
Here is a practice question on sequences where you need to identify a repeating pattern.

When the fraction $\dfrac{4}{7}$ is written in the decimal form, what is the $277$th digit to the right of the decimal point?

1. $\quad 1$
2. $\quad 2$
3. $\quad 5$
4. $\quad 7$
5. $\quad 8$

 
Here is an ACT math practice question on rearrangement of algebraic expressions and isolating the relevant variable.

In the equation $s = \dfrac{1}{2}(u+v)t$, $s$ is the distance traveled by an object in time $t$ with an initial velocity of $u$ and a final velocity equal to $v$. Which of the following solves this formula for $v$ ?

1. $\quad \dfrac{2su}{t}$
2. $\quad \dfrac{2s-u}{t}$
3. $\quad \dfrac{2s-ut}{t}$
4. $\quad \dfrac{2s-t}{u}$
5. $\quad 2s – ut$

 
I just posted the video explanations to all of the math questions in the April 2014 ACT 71H test.The question number 56 and 59 were the most challenging ones in this test.