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.

9000031208

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

9000031101

Level: 
B
Solve the following system of equations and identify a correct statement. \[\begin{aligned} (x - 3)^{2} + (y - 1)^{2} = 1 & & \\2x^{2} + 2y^{2} - 12x - 4y + 18 = 0 & & \end{aligned}\]
The system has more than two solutions.
The system does not have any solution.
The system has a unique solution.
The system has two solutions.

9000031103

Level: 
B
Solve the following system of equations in \( \mathbb{R} \times \mathbb{R}\) and identify the correct statement.\[\begin{aligned} x - 2y + 5 = 0 & & \\x^{2} + y^{2} = 9 & & \end{aligned}\]
The system has two solutions.
The system does not have any solution.
The system has a unique solution.
The system has more than two solutions.

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 \(y_{1} = -y_{2}\).

9000029301

Level: 
B
Find the solution set of the following inequality. \[ \left (x - 1\right )\left (x - 2\right )\left (x - 3\right )\geq 0 \]
\(\left [ 1,2\right ] \cup \left [ 3,\infty \right )\)
\(\left (-\infty ,\infty \right )\)
\(\left (-\infty ,1\right )\cup \left (2,3\right )\)
\(\emptyset \)
\(\{0\}\)