Try this ACT math practice question on ellipses and intercepts.
The graph of the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ has a y-intercept at which of the following points?
- $\quad (0,1)$
- $\quad (0,2)$
- $\quad (0,3)$
- $\quad (0,4)$
- $\quad (0,9)$
Sheet of paper and a cylindrical tube: ACT Math Practice Question
Try this ACT math practice question on cylinders and rectangles.
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?
- $\quad \dfrac{16}{\pi}$
- $\quad \dfrac{48}{\pi}$
- $\quad 16$
- $\quad \dfrac{96}{\pi}$
- $\quad 96$
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
$$ \dfrac{\dfrac{x-5}{x-2}}{\dfrac{1}{3}-\dfrac{1}{x-2}}=?$$
- $\quad -3$
- $\quad 3$
- $\quad 3(x-5)$
- $\quad \dfrac{x-2}{3(x-5)}$
- $\quad \dfrac{(x-5)^2}{3(x-2)^2}$
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