9000033801
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(m\colon y =\cos x\)?
\(4\pi \)
\(\pi \)
\(5\pi \)
\(3\pi \)
B
9000033802
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(n\colon y =\mathop{\mathrm{tg}}\nolimits x\)?
\(3\pi \)
\(\frac{\pi }{2}\)
\(- \frac{\pi } {2}\)
\(\frac{3\pi }
{2}\)
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.
9000031210
Level:
B
Given complex numbers \(z_{1} = 2\sqrt{3}\left (\cos \frac{\pi }{6} + \mathrm{i}\sin \frac{\pi }{6}\right )\)
and \(z_{2} = \sqrt{3}\left (\cos \frac{4\pi }
{3} + \mathrm{i}\sin \frac{4\pi }
{3}\right )\), find the
quotient \(\frac{z_{1}}
{z_{2}} \).
\(-\sqrt{3} + \mathrm{i}\)
\(\sqrt{3} -\mathrm{i}\)
\(\sqrt{3} + \mathrm{i}\)
\(-\sqrt{3} -\mathrm{i}\)
9000031209
Level:
B
Given complex numbers \(z_{1} = 2\sqrt{2}\left (\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\)
and \(z_{2} = \sqrt{2}\left (\cos \frac{7\pi }
{4} + \mathrm{i}\sin \frac{7\pi }
{4}\right )\), find
the product \(z_{1}z_{2}\).
\(4\)
\(4\mathrm{i}\)
\(- 4\mathrm{i}\)
\(- 4\)
9000033306
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{3} < \frac{2 + x}
{3 + x}
\]
\((-\infty ;-3)\cup (0;\infty )\)
\(\mathbb{R}\)
\((-3;\infty )\)
\((-3;0)\)
9000028307
Level:
B
Solve the following equation.
\[
x^{3} + 6x^{2} - 8x = 0
\]
\(0\),
\(- 3 -\sqrt{17}\),
\(- 3 + \sqrt{17}\)
\(0\),
\(3 -\sqrt{17}\),
\(3 + \sqrt{17}\)
\(0\),
\(- 3\),
\(\sqrt{
17}\)
\(0\),
\(3\),
\(-\sqrt{17}\)
9000029301
Level:
B
Find the solution set of the following inequality.
\[
\left (x - 1\right )\left (x - 2\right )\left (x - 3\right )\geq 0
\]
\(\left [ 1;2\right ] \cup \left [ 3;\infty \right )\)
\(\left (-\infty ;\infty \right )\)
\(\left (-\infty ;1\right )\cup \left (2;3\right )\)
\(\emptyset \)
\(\{0\}\)
9000028308
Level:
B
Solve the following equation.
\[
x^{4} - 20x^{2} + 99 = 0
\]
\(-\sqrt{11}\),
\(- 3\),
\(3\),
\(\sqrt{
11}\)
\(0\),
\(- 3 -\sqrt{17}\),
\(- 3 + \sqrt{17}\)
\(0\),
\(3 -\sqrt{17}\),
\(3 + \sqrt{17}\)
\(-\sqrt{17}\),
\(- 3\),
\(3\),
\(\sqrt{
17}\)
9000029302
Level:
B
Find the solution set of the following inequality.
\[
x^{4} - 16 > 0
\]
\(\mathbb{R}\setminus \left [ -2;2\right ] \)
\(\mathbb{R}\)
\(\left (-\infty ;-4\right )\cup \left (4;\infty \right )\)
\(\left (-2;2\right )\)
\(\left (-4;4\right )\)