B

9000034905

Level: 
B
The solution set of one of the following quadratic inequalities is the interval \(\left [ -\frac{7} {6}, \frac{3} {4}\right ] \). Determine this inequality.
\(\left (x + \frac{7} {6}\right )\left (x -\frac{3} {4}\right )\leq 0\)
\(\left (x + \frac{7} {6}\right )\left (x -\frac{3} {4}\right )\geq 0\)
\(\left (x -\frac{7} {6}\right )\left (x + \frac{3} {4}\right )\geq 0\)
\(\left (x -\frac{7} {6}\right )\left (x + \frac{3} {4}\right )\leq 0\)

9000034704

Level: 
B
Solve the inequality \[ ax - 2 > 0 \] with a real unknown \(x\) and a nonpositive real parameter \(a < 0\).
\(\left (-\infty , \frac{2} {a}\right )\)
\(\left (-\infty ,-\frac{2} {a}\right )\)
\(\left (\frac{2} {a},\infty \right )\)
\(\left (-\frac{2} {a},\infty \right )\)

9000034705

Level: 
B
Solve the inequality \[ 2x + b > 0 \] with a real unknown \(x\) and a real parameter \(b\in \mathbb{R}\).
\(\left (-\frac{b} {2},\infty \right )\)
\(\left (\frac{b} {2},\infty \right )\)
\(\left (-\infty , \frac{b} {2}\right )\)
\(\left (-\infty ,-\frac{b} {2}\right )\)

9000033805

Level: 
B
In the following list identify a true statement for the function \(h\colon y =\mathop{\mathrm{cotg}}\nolimits x\), \(x\in \left (-\frac{\pi }{2},0\right )\cup \left (0, \frac{\pi } {2}\right )\).
The function \(h\) is neither increasing nor decreasing.
The function \(h\) is increasing.
The function \(h\) is decreasing.

9000033806

Level: 
B
In the following list identify a true statement for the function \(i\colon y =\mathop{\mathrm{tg}}\nolimits x\), \(x\in \left ( \frac{\pi }{2}, \frac{3\pi } {2}\right )\).
The function \(i\) is increasing.
The function \(i\) is decreasing.
The function \(i\) is neither increasing nor decreasing.

9000033807

Level: 
B
In the following list identify a true statement about the function \(f(x) =\cos x\) on the interval \(I = \left (-\frac{\pi }{2}, \frac{\pi } {2}\right )\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) does not have a minimum or maximum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).

9000033808

Level: 
B
In the following list identify a true statement for the function \(f\colon y =\sin x\) on the interval \(I = \left (-\frac{\pi }{2}, \frac{\pi } {2}\right )\).
The function \(f\) does not have a minimum or maximum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).