B

2010016506

Level: 
B
The volume of a right circular cone is \(96\pi\,\mathrm{cm}^3\) and its diameter and the perpendicular height are in the ratio \(3:2\). Find the surface \(S\) of the cone.
\( S=96\pi\,\mathrm{cm}^2 \)
\( S=60\pi\,\mathrm{cm}^2 \)
\( S=96\,\mathrm{cm}^2 \)
\( S=60\,\mathrm{cm}^2 \)

2010016504

Level: 
B
How much paper do we need to label the can of peaches with diameter of \( 12\,\mathrm{cm} \) and height of \( 18\,\mathrm{cm} \)? (Label covers the side of the can completely, the bottom and the top base are not labelled.) Round your result to \( 1 \) decimal place.
\( 678.6\,\mathrm{cm}^2 \)
\( 1357.1\,\mathrm{cm}^2 \)
\( 339.3\,\mathrm{cm}^2 \)
\( 904.8\,\mathrm{cm}^2 \)

2010016502

Level: 
B
The base of a triangular pyramid is an equilateral triangle with a side of \( 8\,\mathrm{cm} \) (see the picture). The volume of the pyramid is \( 16\sqrt3\,\mathrm{cm}^3 \). Find the perpendicular height of the pyramid.
\( 3\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( 3\sqrt3\,\mathrm{cm} \)

2010016408

Level: 
B
Consider the function \(f(x)=\mathop{\mathrm{cotg}}\nolimits x\) with domain restricted to the interval \( (0;\pi )\). In the following list identify the function with domain \(\left (0; \frac{\pi } {2}\right )\).
\(f(2\cdot x)\)
\(f(x+2)\)
\(f(x-2)\)
\(f(\frac{x}2)\)

2010016407

Level: 
B
Identify the transformation which transforms the graph of the function \(g(x) =\cos (2x)\) to the graph of the function \(f(x) =\cos (2x -1)\).
Shift of graph of \(g\) by \(\frac{1} {2}\) of a unit to the right.
Shift of graph of \(g\) by \(\frac{1} {2}\) of a unit to the left.
Shift of graph of \(g\) by \(1\) unit to the left.
Shift of graph of \(g\) by \(1\) unit to the right.

2010016406

Level: 
B
In the following list identify a true statement about the function \(f(x) =\sin x\) 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 minimum and no maximum on \(I\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).

2010016405

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