9000023904
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
4x - 3y & = -3, & &
\\x + 2y & = 13. & &
\end{aligned}\]
Find \(2x - 7y\).
\(- 29\)
\(- 41\)
\(- 11\)
\(31\)
A
9000023807
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{x + 3} = \frac{x}
{2}
\]
The solution is a multiple of \(2\).
The solution is a multiple of \(4\).
The solution is a multiple of \(8\).
The solution is a multiple of \(12\).
9000023905
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 5y & = 7, & &
\\ - 4x - 3y & = 7. & &
\end{aligned}\]
In the following list identify a true statement.
\(x^{2} + y^{2} = 25\)
\(x^{2} + y^{2} = 7\)
\(x^{2} - y^{2} = -7\)
\(y^{2} - x^{2} = 7\)
9000023808
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{x + 5} = x + 3
\]
The solution \(x\)
satisfies \(|x| = 1\).
The solution \(x\)
satisfies \(|x| = 2\).
The solution \(x\)
satisfies \(|x| = 3\).
The solution \(x\)
satisfies \(|x| = 4\).
9000023906
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = 4, & &
\\4x + 6y & = 9. & &
\end{aligned}\]
In the following list identify a true statement.
The system does not have any solution.
\(x < y\)
\(x > y\)
\(x = y\)
9000023809
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{16 - 5x} = 2 - x
\]
The solution \(x\)
satisfies \(|x| > 3\).
The solution \(x\)
satisfies \(|x| < 3\).
The solution \(x\)
satisfies \(|x + 1| < 3\).
The solution \(x\)
satisfies \(|x + 1| > 3\).
9000023907
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
- x + 2y & = 6, & &
\\2x + 3y & = 2. & &
\end{aligned}\]
In the following list identify a true statement.
\(|x| = |y|\)
\(|x| < |y|\)
\(|x| > |y|\)
The system does not have any solution.
9000022302
Level:
A
Complete the following statement, if possible: „The function \(f\colon y = -x^{2} - 2x + 15\) attains only
... values on the interval \([- 5;3] \).”
nonnegative
positive
negative
neither of the above is valid
9000023701
Level:
A
Identify a true statement which concerns the following equation.
\[
\sqrt{x - 3} = 1
\]
The solution is \(x = 4\).
The solution is \(x = 2\).
The solution is \(x = 5\).
The equation does not have any solution.
9000023709
Level:
A
Identify a true statement which concerns the following pair of equations.
\[
\begin{aligned}
\sqrt{
5 - x} & = 2 &\text{(1)}
\\
\sqrt{x + 5} & = 4 &\text{(2)}
\end{aligned}
\]
The solution of (1) is smaller than the solution of (2).
The solutions of both equations are prime numbers.
The solution of (1) is bigger than the solution of (2).
The solution of (1) equals to the solution of (2).