9000032102
Level:
A
Evaluate
\(\sin \left (0\right )\).
\(0\)
\(\frac{\sqrt{2}}
{2} \)
\(-\sqrt{3}\)
\(- 1\)
\(\sqrt{3}\)
\(-\frac{\sqrt{3}}
{3} \)
A
9000033301
Level:
A
Find the solution set of the following equation.
\[
\frac{3x + 6}
{2 - x} = 0
\]
\(\{ - 2\}\)
\(\emptyset \)
\(\{2\}\)
\(\mathbb{R}\setminus \{2\}\)
9000031105
Level:
A
Solve the following system of equations and identify a correct statement.
\[\begin{aligned}
\frac{1}
{x + 1} -\frac{1}
{y} = 0 & &
\\y^{2} = 1 & &
\end{aligned}\]
The system has two solutions.
The system does not have any solution.
The system has a unique solution.
The system has infinitely many solutions.
9000031201
Level:
A
Given complex numbers \(z_{1} = 1 - 2\mathrm{i}\)
and \(z_{2} = 3 + 5\mathrm{i}\),
find \(z_{1}z_{2}\).
\(13 -\mathrm{i}\)
\(13 + \mathrm{i}\)
\(- 7 -\mathrm{i}\)
\(13 + 11\mathrm{i}\)
9000031206
Level:
A
Find the opposite number to the complex number
\(z = \frac{1+\mathrm{i}}
{1-\mathrm{i}}\).
\(-\mathrm{i}\)
\(1\)
\(- 1\)
\(\mathrm{i}\)
9000031203
Level:
A
Find the real part of the complex number
\(z = \frac{2-\mathrm{i}}
{2+\mathrm{i}}\).
\(0.6\)
\(0.8\)
\(- 0.8\)
\(1\)
9000031202
Level:
A
Find the imaginary part of the complex number
\(z = \frac{2+\mathrm{i}}
{1-\mathrm{i}}\).
\(\frac{3}
{2}\)
\(-\frac{3}
{2}\)
\(\frac{1}
{2}\)
\(-\frac{1}
{2}\)
9000031204
Level:
A
Find the absolute value of the complex number
\(z = \frac{2-\mathrm{i}}
{2+\mathrm{i}}\).
\(1\)
\(5\)
\(\frac{\sqrt{7}}
{5} \)
\(\frac{\sqrt{5}}
{5} \)
9000031205
Level:
A
Find the complex conjugate of \(z = \mathrm{i}^{5} - 3\mathrm{i}^{10}\).
\(3 -\mathrm{i}\)
\(- 3 -\mathrm{i}\)
\(- 3 + \mathrm{i}\)
\(3 + \mathrm{i}\)
9000031104
Level:
A
Solve the following system of equations and identify a correct statement.
\[\begin{aligned}
\frac{x}
{y + 1} - \frac{2}
{x + 1} & = 0 & &
\\\frac{y}
{x} + \frac{2}
{x} & = -1 & &
\end{aligned}\]
The system has a unique solution.
The system does not have any solution.
The system has two solutions.
The system has infinitely many solutions.