B

2010006506

Level: 
B
Solve the following system of equations in \( \mathbb{R} \times \mathbb{R}\) and identify the correct statement. \[\begin{aligned} x^2 - y^2 = 5 & & \\2x + y = 1 & & \end{aligned}\]
The system does not have any solution.
The system has a unique solution.
The system has more than two solutions.
The system has two solutions.

2010006306

Level: 
B
The equation of a hyperbola with the center \( S=[1,-3] \), the focus \( F=[1,2] \), and the vertex \( A=[1,0] \) is given by:
\( \frac{(y+3)^2}{9}-\frac{(x-1)^2}{16} =1 \)
\( \frac{(x-1)^2}{16}-\frac{(y+3)^2}{9} =1 \)
\( \frac{(x-1)^2}{9}-\frac{(y+3)^2}{16} =1 \)
\( \frac{(y+3)^2}{16}-\frac{(x-1)^2}{9} =1 \)
\( \frac{(x+1)^2}{16}-\frac{(y-3)^2}{9} =1 \)

2010006209

Level: 
B
The angle \( \beta \) is by \( 20\% \) smaller than the angle \( \gamma \) and by \( 100\% \) greater than the angle \( \alpha \). The angle \( \alpha \) is
by \( 60\% \) smaller than \( \gamma \).
by \( 40\% \) smaller than \( \gamma \).
by \( 20\% \) smaller than \( \gamma \).
by \( 80\% \) smaller than \( \gamma \).

2010006208

Level: 
B
There are \(14\) right-handed and \(18\) left-handed children among the children attending the ceramic group. Find the difference between percentages of right-handers and left-handers in the group. (Round the result to one decimal place.)
differ by \(27.3\, \%\)
differ by \(63.6\, \%\)
differ by \(36.4\, \%\)
differ by \(57.1\, \%\)