9000104303
Level:
B
Assuming \(a < 3\),
solve the following inequality.
\[
ax - 3\geq 3x - a
\]
\(\left (-\infty ,-1\right ] \)
\(\left (-\infty ,-1\right )\)
\(\left (-1,\infty \right )\)
\(\mathbb{R}\)
B
9000101909
Level:
B
Given points \(A = [1,0,2]\),
\(B = [1,0,0]\) and the
plane \(\alpha \),
\[
\alpha \colon 2x - 4y = 0,
\]
find the angle between the line \(AB\)
and the plane \(\alpha \).
Round your answer to the nearest minute.
\(0^{\circ }\)
\(22^{\circ }48'\)
\(45^{\circ }19'\)
\(90^{\circ }\)
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 \(\alpha \).
\[
\alpha \colon x-3y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] p\colon x& = 1 + t, &
\\y & = -3t,
\\z & = 2,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(0\)
\(\frac{5}
{\sqrt{17}}\)
\(2\)
\(1\)
9000101703
Level:
B
Factor the following polynomial.
\[
\left (5x - y\right )^{2} -\left (x - y\right )^{2}
\]
\(4x\left (6x - 2y\right )\)
\(x\left (5x - y\right )\)
\(6x\left (6x - 2y\right )\)
\(- 32x^{2}\)
9000101108
Level:
B
Find the distance between the line \(q\)
and the plane \(\beta \).
\[
\beta \colon x+4y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] q\colon x& = 4, &
\\y & = -2t,
\\z & = 1 + 4t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(\frac{2}
{\sqrt{21}}\)
\(\frac{4}
{\sqrt{21}}\)
\(0\)
\(1\)
9000101606
Level:
B
Expand \(\left (x - y\right )^{3} - x\left (x + y\right )^{2}\).
\(- y^{3} - 5x^{2}y + 2xy^{2}\)
\(y^{3} - 5x^{2}y + 2xy^{2}\)
\(- y^{3} - 5x^{2}y - 4xy^{2}\)
\(- y^{3} - 5x^{2}y + 4xy^{2}\)
9000101109
Level:
B
The points \(A = [0,5,0]\),
\(B = [5,5,0]\),
\(C = [5,0,0]\),
\(D = [0,0,0]\) define a cube
\(ABCDEFGH\). Find the distance
between the line \(AB\)
and the plane \(EFG\).
\(5\)
\(3\)
\(4\)
\(6\)