B

9000033703

Level: 
B
Find the domain of the following function. \[ f\colon y = \frac{x} {\sqrt{4x^{2 } - 9}} \]
\(\left (-\infty ;-\frac{3} {2}\right )\cup \left (\frac{3} {2};\infty \right )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \left \{-\frac{3} {2}; \frac{3} {2}\right \}\)
\(\left (-\frac{3} {2}; \frac{3} {2}\right )\)
\(\left [ -\frac{3} {2}; \frac{3} {2}\right ] \)
\(\left (-\infty ;-\frac{3} {2}\right ] \cup \left [ \frac{3} {2};\infty \right )\)

9000033803

Level: 
B
In the following list identify a true statement about the function \(f(x) =\sin x\), where \(x\in \left [ -\frac{\pi }{2}; \frac{\pi } {2}\right ] \).
The function \(f\) is increasing.
The function \(f\) is decreasing.
The function \(f\) is neither increasing nor decreasing.
The function \(f\) is non-increasing.

9000031102

Level: 
B
Solve the following system of equations and identify a correct statement. \[\begin{aligned} (x - 1)^{2} + y^{2} = 1 & & \\(x - 4)^{2} + y^{2} = 4 & & \end{aligned}\]
The system has a unique solution \(\left [x,y\right ]\), where \(y = 0\).
The system does not have any solution.
The system has a unique solution \(\left [x,y\right ]\), where \(y > 0\).
The system has two solutions \(\left [x_{1},y_{1}\right ]\), \(\left [x_{2},y_{2}\right ]\), where \(y_{1} = -y_{2}\).