B

9000101705

Level: 
B
Factor the following polynomial expression. \[ 16a^{2}b^{2} - 4a^{2}c^{2} - 16b^{2}d^{2} + 4c^{2}d^{2} \]
\(4\left (a - d\right )\left (a + d\right )\left (2b + c\right )\left (2b - c\right )\)
\(4\left (a + b\right )^{2}\left (2b + c\right )^{2}\)
\(4\left (a - b\right )\left (a + b\right )\left (2b + c\right )\left (2b - c\right )\)
\(4\left (a - c\right )\left (a + c\right )\left (2b + d\right )\left (2b - d\right )\)

9000101108

Level: 
B
Find the distance between the line \(q\) and the plane \(\beta \). \[ \beta \colon x+4y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] q\colon x& = 4, & \\y & = -2t, \\z & = 1 + 4t;\ t\in \mathbb{R} \\ \end{aligned} \]
\(\frac{2} {\sqrt{21}}\)
\(\frac{4} {\sqrt{21}}\)
\(0\)
\(1\)

9000101802

Level: 
B
Among vectors \(\vec{u} = \left (- \frac{2} {\sqrt{2}};2\sqrt{2}\right )\), \(\vec{v} = (-5;10)\), \(\vec{w} = (2.5;-5)\), \(\vec{r} = (-3.5;6)\) find the vector which is not parallel to the vector \(\vec{a} = (1;-2)\).
\(\vec{r}\)
\(\vec{w}\)
\(\vec{v}\)
\(\vec{u}\)

9000100004

Level: 
B
The function \(f(x)= x^{2} + 2\) is graphed in the picture. Consider the region bounded by the graph of the function, both axes and the line \(x = -1\). Determine the solid of revolution obtained by revolving this region about \(x\)-axis.
A general solid which is neither cone nor cylinder.
Cone with base of radius \(1\).
Cylinder with base of radius \(2\).
Cone with base of radius \(2\).