9000034710
Level:
A
Solve the following equation with a real parameter
\(t\), assuming
\(t\neq - 1\) and
\(t\neq 1\).
\[
x(t^{2} - 1) = t - 1
\]
\(\left \{ \frac{1}
{t+1}\right \}\)
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{0\right \}\)
A
9000034707
Level:
A
Consider the equation
\[
x^{2}(1 - q) + 2x + 1 + q = 0
\]
with the real parameter \(q\).
Solve the equation for \(q = 3\).
\(\left \{-1;2\right \}\)
\(\left \{1\right \}\)
\(\left \{-2\right \}\)
\(\emptyset \)
9000034903
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\sqrt{\left (3x + 4 \right ) \left (\frac{1}
{5} - x\right )}
\]
\(\left (-\infty ;-\frac{4}
{3}\right )\cup \left (\frac{1}
{5};\infty \right )\)
\(\left [ -\frac{4}
{3}; \frac{1}
{5}\right ] \)
\(\left (-\infty ;-\frac{4}
{3}\right ] \cup \left [ \frac{1}
{5};\infty \right )\)
\(\left (-\frac{4}
{3}; \frac{1}
{5}\right )\)
9000034709
Level:
A
Consider equation
\[
p(2 - p)x = 4p
\]
with a real parameter \(p\).
Solve the equation for \(p = 2\).
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{ \frac{4}
{2-p}\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)
9000034803
Level:
A
Find the complex conjugate of \(z = 1 - 3\mathrm{i}\).
\(1 + 3\mathrm{i}\)
\(- 1 - 3\mathrm{i}\)
\(- 1 + 3\mathrm{i}\)
\(1 - 3\mathrm{i}\)
9000034801
Level:
A
Given complex numbers \(z_{1} = 4 -\mathrm{i}\)
and \(z_{2} = 1 - 2\mathrm{i}\),
find \(z_{1} - z_{2}\).
\(3 + \mathrm{i}\)
\(3 - 3\mathrm{i}\)
\(5 - 3\mathrm{i}\)
\(3 -\mathrm{i}\)
9000034802
Level:
A
Find the opposite number to the complex number
\(z = 3 -\mathrm{i}\).
\(- 3 + \mathrm{i}\)
\(- 3 -\mathrm{i}\)
\(3 + \mathrm{i}\)
\(3 -\mathrm{i}\)
9000033906
Level:
A
In the interval \([0^{\circ };360^{\circ })\) find the angle
coterminal with the angle \(1\: 000^{\circ }\).
\(280^{\circ }\)
\(180^{\circ }\)
\(240^{\circ }\)
\(300^{\circ }\)
9000034806
Level:
A
Simplify \(\mathrm{i}^{15}\).
\(-\mathrm{i}\)
\(- 1\)
\(1\)
\(\mathrm{i}\)
9000034902
Level:
A
Find the domain of the following expression.
\[
\log _{2}\left [\left (\frac{2}
{3} - x\right )\left (x + \frac{1}
{4}\right )\right ]
\]
\(\left (-\frac{1}
{4}; \frac{2}
{3}\right )\)
\(\left (-\infty ;-\frac{1}
{4}\right ] \cup \left [ \frac{2}
{3};\infty \right )\)
\(\left (-\infty ;-\frac{1}
{4}\right )\cup \left (\frac{2}
{3};\infty \right )\)
\(\left [ \frac{1}
{4}; \frac{2}
{3}\right ] \)