9000033908
Level:
A
Convert \(\frac{8}
{3}\pi \)
radians to degrees.
\(480^{\circ }\)
\(240^{\circ }\)
\(300^{\circ }\)
\(330^{\circ }\)
A
9000034902
Level:
A
Find the domain of the following expression.
\[
\log _{2}\left [\left (\frac{2}
{3} - x\right )\left (x + \frac{1}
{4}\right )\right ]
\]
\(\left (-\frac{1}
{4}, \frac{2}
{3}\right )\)
\(\left (-\infty ,-\frac{1}
{4}\right ] \cup \left [ \frac{2}
{3},\infty \right )\)
\(\left (-\infty ,-\frac{1}
{4}\right )\cup \left (\frac{2}
{3},\infty \right )\)
\(\left [ \frac{1}
{4}, \frac{2}
{3}\right ] \)
9000033907
Level:
A
Convert \(\frac{6}
{5}\pi \)
radians to degrees.
\(216^{\circ }\)
\(432^{\circ }\)
\(116^{\circ }\)
\(378^{\circ }\)
9000034904
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\log _{\frac{1}
{4} }\left [\left (x + \frac{1}
{2}\right )\left (5 - 2x\right )\right ]
\]
\(\left (-\infty ,-\frac{1}
{2}\right ] \cup \left [ \frac{5}
{2},\infty \right )\)
\(\left [ -\frac{1}
{2}, \frac{5}
{2}\right ] \)
\(\left (-\frac{1}
{2}, \frac{5}
{2}\right )\)
\(\left (-\infty ,-\frac{1}
{2}\right )\cup \left (\frac{5}
{2},\infty \right )\)
9000033902
Level:
A
Associate the angle \(\frac{7}
{8}\pi \)
to the corresponding quadrant.
II.
I.
III.
IV.
9000033901
Level:
A
Associate the angle \(\frac{7}
{6}\pi \)
to the corresponding quadrant.
III.
I.
II.
IV.
9000034804
Level:
A
Find the absolute value of the complex number
\(z = 3 -\mathrm{i}\).
\(\sqrt{10}\)
\(2\)
\(2\sqrt{2}\)
\(\sqrt{2}\)
9000034709
Level:
A
Consider equation
\[
p(2 - p)x = 4p
\]
with a real parameter \(p\).
Solve the equation for \(p = 2\).
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{ \frac{4}
{2-p}\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)
9000034801
Level:
A
Given complex numbers \(z_{1} = 4 -\mathrm{i}\)
and \(z_{2} = 1 - 2\mathrm{i}\),
find \(z_{1} - z_{2}\).
\(3 + \mathrm{i}\)
\(3 - 3\mathrm{i}\)
\(5 - 3\mathrm{i}\)
\(3 -\mathrm{i}\)
9000033910
Level:
A
Convert the angle \(292.5^{\circ }\)
to radians.
\(\frac{13}
{8} \pi \)
\(\frac{11}
{4} \pi \)
\(\frac{15}
{8} \pi \)
\(\frac{13}
{4} \pi \)