I have posted video explanations to all of the math questions in the 2017 December ACT Form A10 Test.

## Factorial mathematics: ACT Math Practice Question

##### Try this ACT math practice question on dealing with algebraic manipulation of factorial expressions..

Which of the following expressions is equivalent to

$$ \left[1 \quad – \quad\dfrac{(n!)^2}{(n+1)!(n-1)!}\right]$$ where $n>2$ and $n! = n(n-1)(n-2)\cdots 3 \cdot 2 \cdot 1$ ?

- $\quad \dfrac{n-2}{n+1}$
- $\quad \dfrac{1}{n+1}$
- $\quad \dfrac{2}{n^2-1}$
- $\quad \dfrac{1}{n-1}$
- $\quad \dfrac{n}{n+1}$

## ACT Math Practice Question: Coordinate plane, mid-point, and line intersections

##### Try this ACT math practice question that relies on finding the mid-point of the line segment connecting vertices of a triangle in the coordinate plane.

If $2x-3y=1$, $x+2y=4$, and $y=-2$ are equations that represent sides $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$ of triangle $ABC$ in the coordinate plane, what are the coordinates of the mid-point of side $\overline{BC}$?

- $\quad (4, 0)$
- $\quad (4, -1)$
- $\quad \left(\dfrac{9}{2}, -\dfrac{1}{4}\right)$
- $\quad \left(5, -\dfrac{1}{2}\right)$
- $\quad (5, -1)$

## ACT Math Practice Question: Rearranging algebraic fractions

##### Try this ACT math practice question on rearranging algebraic fractions:

For all values of $x$ where the expression is defined

$$ \dfrac{\dfrac{x-5}{x-2}}{\dfrac{1}{3}-\dfrac{1}{x-2}}=?$$

- $\quad -3$
- $\quad 3$
- $\quad 3(x-5)$
- $\quad \dfrac{x-2}{3(x-5)}$
- $\quad \dfrac{(x-5)^2}{3(x-2)^2}$

## 2017 June ACT Form 74C: Video Explanations

I have posted video explanations to all of the math questions in the 2017 June ACT Form 74C Test.

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