9000033901
Level:
A
Associate the angle \(\frac{7}
{6}\pi \)
to the corresponding quadrant.
III.
I.
II.
IV.
A
9000033903
Level:
A
In the interval \([0;2\pi )\) find the angle
equivalent to the angle \(\frac{21}
{6} \pi \).
\(\frac{3}
{2}\pi \)
\(\frac{\pi }{2}\)
\(\frac{\pi }
{3}\)
\(\frac{2}
{3}\pi \)
9000034706
Level:
A
Consider the inequality
\[
px^{2} - 2x + 2 > 0
\]
with the real parameter \(p\).
Solve this inequality for \(p = 0\).
\((-\infty ;1)\)
\((-\infty ;-1)\)
\((-1;\infty )\)
\((1;\infty )\)
9000034804
Level:
A
Find the absolute value of the complex number
\(z = 3 -\mathrm{i}\).
\(\sqrt{10}\)
\(2\)
\(2\sqrt{2}\)
\(\sqrt{2}\)
9000034708
Level:
A
Consider the equation
\[
2x^{2} + 5px + 2 = 0
\]
with the real parameter \(p\).
Solve the equation for \(p = -\frac{4}
{5}\).
\(\left \{1\right \}\)
\(\left \{-1\right \}\)
\(\left \{0\right \}\)
\(\emptyset \)
9000034901
Level:
A
Find the domain of the following expression.
\[
\sqrt{\left (2x - 3 \right ) \left (3x + 1 \right )}
\]
\(\left (-\infty ;-\frac{1}
{3}\right ] \cup \left [ \frac{3}
{2};\infty \right )\)
\(\left [ -\frac{1}
{3}; \frac{3}
{2}\right ] \)
\(\left (-\frac{1}
{3}; \frac{3}
{2}\right )\)
\(\left (-\infty ;-\frac{1}
{3}\right )\cup \left (\frac{3}
{2};\infty \right )\)
9000034710
Level:
A
Solve the following equation with a real parameter
\(t\), assuming
\(t\neq - 1\) and
\(t\neq 1\).
\[
x(t^{2} - 1) = t - 1
\]
\(\left \{ \frac{1}
{t+1}\right \}\)
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{0\right \}\)
9000034707
Level:
A
Consider the equation
\[
x^{2}(1 - q) + 2x + 1 + q = 0
\]
with the real parameter \(q\).
Solve the equation for \(q = 3\).
\(\left \{-1;2\right \}\)
\(\left \{1\right \}\)
\(\left \{-2\right \}\)
\(\emptyset \)
9000032004
Level:
A
Evaluate
\(\mathop{\mathrm{tg}}\nolimits \left (-\frac{3\pi }
{2}\right )\).
undefined
\(0\)
\(1\)
\(-\frac{\sqrt{3}}
{3} \)
\(- 1\)
\(\frac{\sqrt{3}}
{3} \)
9000032107
Level:
A
Evaluate
\(\cos \left (\pi \right )\).
\(- 1\)
\(\sqrt{3}\)
\(\frac{\sqrt{3}}
{3} \)
\(-\sqrt{3}\)
\(-\frac{\sqrt{3}}
{3} \)
\(0\)