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.
B
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.
\[
\frac{2}
{x + 1}\geq 1
\]
\((-1,1] \)
\([ - 1,1)\)
\((-\infty ,-1)\cup [ 1,\infty )\)
\((-\infty ,1] \)
9000033306
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{3} < \frac{2 + x}
{3 + x}
\]
\((-\infty ,-3)\cup (0,\infty )\)
\(\mathbb{R}\)
\((-3,\infty )\)
\((-3,0)\)
9000033307
Level:
B
Find the solution set of the following inequality.
\[
\frac{4}
{x^{2} - x - 6}\leq 0
\]
\((-2,3)\)
\(\mathbb{R}\)
\((-\infty ,-2)\cup (3,\infty )\)
\((-3,2)\)
9000033704
Level:
B
Find the values of real parameter \(p\)
which ensure that the following quadratic equation has solutions with nonzero
imaginary part.
\[
px^{2} + 4x - p + 5 = 0
\]
\(p\in \left (1,4\right )\)
\(p\in [ 1,4] \)
\(p\in \left (-\infty ,1\right )\cup \left (4,\infty \right )\)
\(p\in \left (-\infty ,1\right ] \cup \left [ 4,\infty \right )\)
9000033703
Level:
B
Find the domain of the following function.
\[
f\colon y = \frac{x}
{\sqrt{4x^{2 } - 9}}
\]
\(\left (-\infty ,-\frac{3}
{2}\right )\cup \left (\frac{3}
{2},\infty \right )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \left \{-\frac{3}
{2}, \frac{3}
{2}\right \}\)
\(\left (-\frac{3}
{2}, \frac{3}
{2}\right )\)
\(\left [ -\frac{3}
{2}, \frac{3}
{2}\right ] \)
\(\left (-\infty ,-\frac{3}
{2}\right ] \cup \left [ \frac{3}
{2},\infty \right )\)
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.
9000033804
Level:
B
In the following list identify a true statement for the function
\(g\colon y =\sin x\),
\(x\in [ - 2\pi ,-\pi ] \).
The function \(g\)
is neither increasing nor decreasing.
The function \(g\)
is increasing.
The function \(g\)
is decreasing.
9000033801
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(m\colon y =\cos x\)?
\(4\pi \)
\(\pi \)
\(5\pi \)
\(3\pi \)