B

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.

9000034302

Level: 
B
Find the solution set of the following equation in the set of complex numbers. \[ x^{3} + 8 = 0 \]
\(\{ - 2;\ 1 + \mathrm{i}\sqrt{3};\ 1 -\mathrm{i}\sqrt{3}\}\)
\(\{ - 2;\ -1 + \mathrm{i}\sqrt{3};\ -1 -\mathrm{i}\sqrt{3}\}\)
\(\{ - 2;\ \frac{1} {2} + \mathrm{i}\frac{\sqrt{3}} {2} ;\ \frac{1} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \}\)
\(\{ - 2;\ -\frac{1} {2} + \mathrm{i}\frac{\sqrt{3}} {2} ;\ -\frac{1} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \}\)

9000033806

Level: 
B
In the following list identify a true statement for the function \(i\colon y =\mathop{\mathrm{tg}}\nolimits x\), \(x\in \left ( \frac{\pi }{2}; \frac{3\pi } {2}\right )\).
The function \(i\) is increasing.
The function \(i\) is decreasing.
The function \(i\) is neither increasing nor decreasing.

9000034304

Level: 
B
Find the solution set of the following equation in the set of complex numbers. \[ x^{4} - 1 = 0 \]
\(\{1;\ -1;\ \mathrm{i};\ -\mathrm{i}\}\)
\(\{1 -\mathrm{i};\ -1 -\mathrm{i}\}\)
\(\{1 + \mathrm{i};\ -1 + \mathrm{i}\}\)
\(\{1 + \mathrm{i};\ 1 -\mathrm{i};\ -1 + \mathrm{i};\ -1 -\mathrm{i}\}\)