9000101608
Level:
B
Expand \(\left (3x + y\right )\left (9x^{2} - 3xy + y^{2}\right )\).
\(27x^{3} + y^{3}\)
\(27x^{3} - y^{3}\)
\((3x + y)^{3}\)
\(27x^{3} + 3y^{3}\)
B
9000101102
Level:
B
Find the distance between the point \(A = [1,0,1]\)
and the line \(p\).
\[
\begin{aligned}p\colon x& = 2, &
\\y & = 3t,
\\z & = 1 - t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(1\)
\(0\)
\(2\)
\(3\)
9000101710
Level:
B
Factor the following polynomial.
\[
x^{2}y - x^{2}z - 4xyz + 4xy^{2} + 4y^{3} - 4y^{2}z
\]
\(\left (y - z\right )\left (x + 2y\right )^{2}\)
\(\left (y - z\right )\left (x - 2y\right )^{2}\)
\(\left (y - z\right )\left (x^{2} + 4y + 4y^{2}\right )\)
\(\left (y + z\right )\left (x - 2y\right )^{2}\)
9000101103
Level:
B
Find the distance between two parallel lines
\(p\) and
\(q\).
\[
\begin{aligned}p\colon x& = 2, &
\\y & = 3t,
\\z & = 1 - t,\ t\in \mathbb{R}
\\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = 3, &
\\y & = 6s,
\\z & = 1 - 2s,\ s\in \mathbb{R}
\\ \end{aligned}
\]
\(1\)
\(2\)
\(3\)
\(4\)
9000101704
Level:
B
Factor the following polynomial.
\[
16x^{2}y^{4} - 25x^{4}y^{2}
\]
\(\left (4xy^{2} - 5x^{2}y\right )\left (4xy^{2} + 5x^{2}y\right )\)
\(\left (4xy - 5x^{2}y\right )\left (4xy^{2} + 5xy\right )\)
\(\left (4x^{2}y^{2} - 5xy\right )\left (4x^{2}y^{2} + 5xy\right )\)
\(\left (4xy^{2} - 5x^{2}y\right )^{2}\)
9000101104
Level:
B
Find the distance between the point \(A = [-1,1,0]\)
and the plane \(\alpha \).
\[
\alpha \colon 12y + 5z - 2 = 0
\]
\(\frac{10}
{13}\)
\(\frac{15}
{13}\)
\(\frac{17}
{13}\)
\(\frac{14}
{13}\)
9000101706
Level:
B
Factor the following polynomial.
\[
8x^{4} - 48x^{3} + 72x^{2}
\]
\(8x^{2}\left (x - 3\right )^{2}\)
\(- 8x^{2}\left (3 - x\right )^{2}\)
\(8\left (x^{2} - 3\right )^{2}\)
\(8x\left (x^{2} - 3\right )^{2}\)
9000101106
Level:
B
In the following list identify a point which does not have zero distance from the line
\(m\).
\[
\begin{aligned}m\colon x& = s, &
\\y & = 8 - s,
\\z & = 1 + 3s,\ s\in \mathbb{R}
\\ \end{aligned}
\]
\([2,6,10]\)
\([0,8,1]\)
\([1,7,4]\)
\([8,0,25]\)
9000101702
Level:
B
Factor the following polynomial.
\[
3x^{3} + 3x^{2}y + 4xy + 4y^{2}
\]
\(\left (3x^{2} + 4y\right )\left (x + y\right )\)
\(\left (3x + y\right )\left (x^{2} + y^{2}\right )\)
\(\left (3x^{2} + 4\right )\left (x + y^{2}\right )\)
\(\left (3x + y^{2}\right )\left (x + y\right )\)
9000101107
Level:
B
Find the distance between the line \(p\)
and the plane \(\alpha \).
\[
\alpha \colon x-3y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] p\colon x& = 1 + t, &
\\y & = -3t,
\\z & = 2,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(0\)
\(\frac{5}
{\sqrt{17}}\)
\(2\)
\(1\)