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.

9000031010

Level: 
B
Identify a true statement on the following equation. \[ x^{5} - x^{3} - 6x = 0 \]
The equation has three solutions in \(\mathbb{R}\).
The equation does not have solution in \(\mathbb{R}\).
The equation has five solutions in \(\mathbb{R}\).
The equation has one solution in \(\mathbb{R}\).

9000031208

Level: 
B
Find the polar form of the complex number \(z = -3 + 3\mathrm{i}\).
\(3\sqrt{2}\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right )\)
\(3\left (\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\)
\(3\left (\cos \frac{5\pi } {4} + \mathrm{i}\sin \frac{5\pi } {4}\right )\)
\(3\sqrt{2}\left (\cos \frac{7\pi } {4} + \mathrm{i}\sin \frac{7\pi } {4}\right )\)