9000033305
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{x + 1}\geq 1
\]
\((-1;1] \)
\([ - 1;1)\)
\((-\infty ;-1)\cup [ 1;\infty )\)
\((-\infty ;1] \)
B
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.
9000033704
Level:
B
Find the values of real parameter \(p\)
which ensure that the following quadratic equation has solutions with nonzero
imaginary part.
\[
px^{2} + 4x - p + 5 = 0
\]
\(p\in \left (1;4\right )\)
\(p\in [ 1;4] \)
\(p\in \left (-\infty ;1\right )\cup \left (4;\infty \right )\)
\(p\in \left (-\infty ;1\right ] \cup \left [ 4;\infty \right )\)
9000031005
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following algebraic equation.
\[
(x + 1)^{4} - 5(x + 1)^{2} + 4 = 0
\]
\( \{ - 3;-2;0;1\}\)
\( \{1;4\}\)
\( \{ - 2;-1;1;2\}\)
\( \{ - 1;3\}\)
9000031008
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following equation.
\[
4x^{3} - 3x^{2} - x = 0
\]
\( \left \{-\frac{1}
{4};0;1\right \}\)
\(\{0;1;4\}\)
\( \{1;4\}\)
\( \{0\}\)
9000031010
Level:
B
Identify a true statement on the following equation.
\[
x^{5} - x^{3} - 6x = 0
\]
The equation has three solutions in \(\mathbb{R}\).
The equation does not have solution in
\(\mathbb{R}\).
The equation has five solutions in \(\mathbb{R}\).
The equation has one solution in \(\mathbb{R}\).
9000031002
Level:
B
One of the solutions of the following equation is
\(x = 2\). Find
the set of all solutions.
\[
x^{3} + 2x^{2} - 5x - 6 = 0
\]
\(\{ - 3;-1;2\}\)
\( \{ - 3;-1\}\)
\( \{ - 3;0;2\}\)
\(\{ - 1;2;3\}\)