9000033304
Level:
B
Find the solution set of the following inequality.
\[
\frac{x + 4}
{x + 2}\leq 0
\]
\([ - 4;-2)\)
\((-\infty ;-4] \cup [ 2;\infty )\)
\((-\infty ;-4)\cup (-2;\infty )\)
\((-4;-2] \)
B
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.
9000029309
Level:
B
Find the solution set of the following inequality.
\[
(x - 1)(x - 2)(x - 3) < (x - 1)(x - 2)
\]
\((-\infty ;1)\cup (2;4)\)
\(\emptyset \)
\((0;3)\)
\((-\infty ;-3)\cup (3;\infty )\)
\((-3;3)\)
9000031101
Level:
B
Solve the following system of equations and identify a correct statement.
\[\begin{aligned}
(x - 3)^{2} + (y - 1)^{2} = 1 & &
\\2x^{2} + 2y^{2} - 12x - 4y + 18 = 0 & &
\end{aligned}\]
The system has more than two solutions.
The system does not have any solution.
The system has a unique solution.
The system has two solutions.
9000029310
Level:
B
Find the solution set of the following inequality.
\[
(x + 2)(x^{2} + 4x + 3) > x^{2} + 5x + 6
\]
\((-3;-2)\cup (0;\infty )\)
\((-\infty ;-3)\cup (3;\infty )\)
\((-\infty ;-1)\cup (1;\infty )\)
\((-1;1)\)
\(\mathbb{R}\)
9000031103
Level:
B
Solve the following system of equations in \( \mathbb{R} \times \mathbb{R}\) and identify the correct statement.\[\begin{aligned}
x - 2y + 5 = 0 & &
\\x^{2} + y^{2} = 9 & &
\end{aligned}\]
The system has two solutions.
The system does not have any solution.
The system has a unique solution.
The system has more than two solutions.