9000034808
Level:
B
Find the algebraic form of the complex number
\(z = 2\left (\cos \pi + \mathrm{i}\sin \pi \right )\).
\(- 2\)
\(2\)
\(- 2\mathrm{i}\)
\(2\mathrm{i}\)
B
9000034905
Level:
B
The solution set of one of the following quadratic inequalities is the interval
\(\left [ -\frac{7}
{6}; \frac{3}
{4}\right ] \).
Determine this inequality.
\(\left (x + \frac{7}
{6}\right )\left (x -\frac{3}
{4}\right )\leq 0\)
\(\left (x + \frac{7}
{6}\right )\left (x -\frac{3}
{4}\right )\geq 0\)
\(\left (x -\frac{7}
{6}\right )\left (x + \frac{3}
{4}\right )\geq 0\)
\(\left (x -\frac{7}
{6}\right )\left (x + \frac{3}
{4}\right )\leq 0\)
9000034701
Level:
B
Identify a set of the values of the real parameter
\(m\) which
ensure that the equation
\[
\frac{m}
{x} - 8 = \frac{1}
{x} -\frac{m + 3}
{2}
\]
has solution \(x = 2\).
\(\left \{7\right \}\)
\(\left \{10\right \}\)
\(\left \{6\right \}\)
\(\left \{\frac{5}
{2}\right \}\)
9000033306
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{3} < \frac{2 + x}
{3 + x}
\]
\((-\infty ;-3)\cup (0;\infty )\)
\(\mathbb{R}\)
\((-3;\infty )\)
\((-3;0)\)
9000033304
Level:
B
Find the solution set of the following inequality.
\[
\frac{x + 4}
{x + 2}\leq 0
\]
\([ - 4;-2)\)
\((-\infty ;-4] \cup [ 2;\infty )\)
\((-\infty ;-4)\cup (-2;\infty )\)
\((-4;-2] \)
9000033305
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{x + 1}\geq 1
\]
\((-1;1] \)
\([ - 1;1)\)
\((-\infty ;-1)\cup [ 1;\infty )\)
\((-\infty ;1] \)
9000033307
Level:
B
Find the solution set of the following inequality.
\[
\frac{4}
{x^{2} - x - 6}\leq 0
\]
\((-2;3)\)
\(\mathbb{R}\)
\((-\infty ;-2)\cup (3;\infty )\)
\((-3;2)\)
9000033703
Level:
B
Find the domain of the following function.
\[
f\colon y = \frac{x}
{\sqrt{4x^{2 } - 9}}
\]
\(\left (-\infty ;-\frac{3}
{2}\right )\cup \left (\frac{3}
{2};\infty \right )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \left \{-\frac{3}
{2}; \frac{3}
{2}\right \}\)
\(\left (-\frac{3}
{2}; \frac{3}
{2}\right )\)
\(\left [ -\frac{3}
{2}; \frac{3}
{2}\right ] \)
\(\left (-\infty ;-\frac{3}
{2}\right ] \cup \left [ \frac{3}
{2};\infty \right )\)
9000033701
Level:
B
Find out, how many integer solutions the following inequality has.
\[
m^{2} + 2m - 4 < 0
\]
Five integer solutions.
Less than five integer solutions.
More than five integer solutions.
9000033803
Level:
B
In the following list identify a true statement about the function
\(f(x) =\sin x\), where
\(x\in \left [ -\frac{\pi }{2}; \frac{\pi } {2}\right ] \).
The function \(f\)
is increasing.
The function \(f\)
is decreasing.
The function \(f\)
is neither increasing nor decreasing.
The function \(f\) is non-increasing.