B

9000038902

Level: 
B
Consider the function \(f\colon y = A\cdot \sin (B\cdot x + C)\), with real nonzero parameters \(A\), \(B\) and \(C\). Which of the following operations makes the amplitude of the function five times bigger?
Decrease \(A\) by a factor \(5\).
Increase \(A\) by a factor \(5\).
Increase \(B\) by a factor \(5\).
Decrease \(B\) by a factor \(5\).
Increase \(C\) by a factor \(5\).
Decrease \(C\) by a factor \(5\).

9000038609

Level: 
B
Find the algebraic form of the following complex number. \[ 5\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right ) \]
\(-\frac{5\sqrt{2}} {2} + \mathrm{i}\frac{5\sqrt{2}} {2} \)
\(\frac{5\sqrt{2}} {2} -\mathrm{i}\frac{5\sqrt{2}} {2} \)
\(\frac{5} {2} + \mathrm{i}\frac{5} {2}\)
\(\frac{5} {2} -\mathrm{i}\frac{5} {2}\)

9000034906

Level: 
B
The solution set of one of the following quadratic inequalities is \(\left (-\infty ;-\frac{3} {5}\right )\cup \left (\frac{1} {6};\infty \right )\). Determine this inequality.
\(\left (5x + 3\right )\left (1 - 6x\right ) < 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) < 0\)
\(\left (5x + 3\right )\left (1 - 6x\right ) > 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) > 0\)

9000034907

Level: 
B
Find all \(x\in \mathbb{R}\) for which the following expression takes nonnegative values. \[ -2\left (x - 3\right )\left (2 - x\right ) \]
\(\left (-\infty ;2\right ] \cup \left [ 3;\infty \right )\)
\(\left [ 2;3\right ] \)
\(\left (2;3\right )\)
\(\left (-\infty ;2\right )\cup \left (3;\infty \right )\)

9000034908

Level: 
B
Find all \(x\in \mathbb{R}\) for which the following expression is nonpositive. \[ \left (x + 1\right )\left (4 + x\right ) \]
\(\left [ -4;-1\right ] \)
\(\left (-\infty ;-4\right ] \cup \left [ -1;\infty \right )\)
\(\left (-4;-1\right )\)
\(\left (-\infty ;-4\right )\cup \left (-1;\infty \right )\)

9000035003

Level: 
B
The tree of the height \(12\, \mathrm{m}\) is observed from the place horizontal with the base of the tree. The angle of elevation is \(10^{\circ }\). Find the distance of the observer from the base and round to the nearest meters.
\(68\, \mathrm{m}\)
\(2\, \mathrm{m}\)
\(12\, \mathrm{m}\)
\(48\, \mathrm{m}\)

9000035008

Level: 
B
Sun shines to the road at the angle \(53^{\circ }22'\). An electric column near the road casts the shadow of the length \(4.5\, \mathrm{m}\). Find the height of the column and round your answer to the nearest meters.
\(6\, \mathrm{m}\)
\(3\, \mathrm{m}\)
\(4\, \mathrm{m}\)
\(5\, \mathrm{m}\)