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 \(x = 2\).
\(\left \{7\right \}\)
\(\left \{10\right \}\)
\(\left \{6\right \}\)
\(\left \{\frac{5} {2}\right \}\)

9000034809

Level: 
B
Given complex numbers \(z_{1} = 2\left (\cos \frac{\pi }{6} + \mathrm{i}\sin \frac{\pi }{6}\right )\) and \(z_{2} = \sqrt{3}\left (\cos \frac{4\pi } {3} + \mathrm{i}\sin \frac{4\pi } {3}\right )\), find the angle in the polar form of the product \(z_{1}z_{2}\).
\(\frac{3\pi } {2}\)
\(\frac{2} {9}\pi \)
\(\frac{5} {9}\pi \)
\(3\pi \)

9000034810

Level: 
B
Given complex numbers \(z_{1} = 2\left (\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\) and \(z_{2} = \sqrt{2}\left (\cos \frac{7\pi } {4} + \mathrm{i}\sin \frac{7\pi } {4}\right )\), find the angle in the polar form of the quotient \(\frac{z_{1}} {z_{2}} \).
\(\frac{\pi } {2}\)
\(- \frac{\pi } {2}\)
\(-\frac{3} {2}\pi \)
\(\frac{3} {2}\pi \)

9000033808

Level: 
B
In the following list identify a true statement for the function \(f\colon y =\sin x\) on the interval \(I = \left (-\frac{\pi }{2}; \frac{\pi } {2}\right )\).
The function \(f\) does not have a minimum or maximum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).

9000033807

Level: 
B
In the following list identify a true statement about the function \(f(x) =\cos x\) on the interval \(I = \left (-\frac{\pi }{2}; \frac{\pi } {2}\right )\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) does not have a minimum or maximum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).

9000034301

Level: 
B
Find the solution set of the following equation in the set of complex numbers. \[ x^{3} - 1 = 0 \]
\(\{1;\ -\frac{1} {2} + \mathrm{i}\frac{\sqrt{3}} {2} ;\ -\frac{1} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \}\)
\(\{1;\ -1 + \mathrm{i}\sqrt{3};\ -1 -\mathrm{i}\sqrt{3}\}\)
\(\{1;\ -\frac{1} {2} + \mathrm{i}\frac{\sqrt{3}} {2} \}\)
\(\{1;\ -\frac{1} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \}\)

9000033805

Level: 
B
In the following list identify a true statement for the function \(h\colon y =\mathop{\mathrm{cotg}}\nolimits x\), \(x\in \left (-\frac{\pi }{2};0\right )\cup \left (0; \frac{\pi } {2}\right )\).
The function \(h\) is neither increasing nor decreasing.
The function \(h\) is increasing.
The function \(h\) is decreasing.