2000003601
Level:
B
Find the solution set of the inequality.
\[ x^2 >1 \]
\( (-\infty;-1) \cup (1;\infty) \)
\( (-\infty;-1 ] \cup [ 1;\infty) \)
\( (1;\infty) \)
\( (-1;\infty) \)
B
2000003306
Level:
B
A rectangle with the sides of \( 4\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \) is rotated around its longer side thus giving rise to a solid. Find the volume of such a solid?
\( 96\pi\,\mathrm{cm}^3 \)
\( 48\pi\,\mathrm{cm}^3 \)
\( 96\,\mathrm{cm}^3 \)
\( 144\pi\,\mathrm{cm}^3 \)
2000003305
Level:
B
The area of the axial section of a cylinder is \( 12\,\mathrm{cm}^2 \). The lateral surface area of the cylinder is:
\( 12\pi\,\mathrm{cm}^2 \)
\( 36\pi\,\mathrm{cm}^2 \)
\( 12\,\mathrm{cm}^2 \)
\( 36\,\mathrm{cm}^2 \)
2000003304
Level:
B
The radii of the bases of a cylinder and a cone are equal and the height of the cylinder is twice the height of the cone. The volume of the cylinder and the volume of the cone are in the ratio:
\( 6\ \colon 1\)
\( 3\ \colon 1\)
\( 2\ \colon 1\)
\( 12\ \colon 1\)
2000003303
Level:
B
The volume of a regular quadrilateral pyramid is \( 432\,\mathrm{cm} ^3\) and the base edge of the pyramid has the length equal to \( 12\,\mathrm{cm} \). The height of the pyramid is:
\( 9\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 36\,\mathrm{cm} \)
\( 27\,\mathrm{cm} \)
2000003302
Level:
B
Find the volume of a regular quadrilateral pyramid if the bottom edge is \(3\,\mathrm{cm}\) long and the pyramid height is \(5\,\mathrm{cm}\).
\( 15\,\mathrm{cm}^3 \)
\( 75\,\mathrm{cm}^3 \)
\( 25\,\mathrm{cm}^3 \)
\( 45\,\mathrm{cm}^3 \)
2000003301
Level:
B
The axial section of a cylinder is a square with the diagonal length of \( 5\sqrt{2}\,\mathrm{cm} \). The lateral surface area of the cylinder is equal to:
\( 25\pi\,\mathrm{cm}^2 \)
\( 25\,\mathrm{cm}^2 \)
\( 25\sqrt{2}\,\mathrm{cm}^2 \)
\( 25\sqrt{2}\pi\,\mathrm{cm}^2 \)
2010002009
Level:
B
Differentiate the following function.
\[
f(x) =\ln \left (\frac{2x}
{2 - x}\right )
\]
\(f^{\prime}(x) = \frac{2}
{(2-x)x} ;\ x\in \left (0;2\right )\)
\(f^{\prime}(x) = \frac{2}
{(2-x)x} ;\ x\in \mathbb{R}\setminus \left \{0;2\right \}\)
\(f^{\prime}(x) = \frac{2-x}
{2x};\ x\in \left (0;2\right )\)
\(f^{\prime}(x) = \frac{2-x}
{2x};\ x\in \mathbb{R}\setminus \left \{0;2\right \}\)
2010002008
Level:
B
Differentiate the following function.
\[
f(x) =\ln \left(3x^{2} - 5x \right)
\]
\(f^{\prime}(x) = \frac{6x-5}
{3x^{2}-5x};\ x\in \left (-\infty ;0\right )\cup \left (\frac{5}{3};\infty \right )\)
\(f^{\prime}(x) = \frac{6x-5}
{3x^{2}-5x};\ x\in \mathbb{R}\setminus \left \{0;\frac{5}
{3}\right \}\)
\(f^{\prime}(x) = \frac{1}
{3x^{2}-5x};\ x\in \left (-\infty ;0\right )\cup \left (\frac{5}{3};\infty \right )\)
\(f^{\prime}(x) = \frac{1}
{3x^{2}-5x};\ x\in \mathbb{R}\setminus \left \{0;\frac{5}
{3}\right \}\)
2010002007
Level:
B
Differentiate the following function.
\[
f(x) = \frac{\sqrt{x} +2}
{2-\sqrt{x} }
\]
\(f'(x) = \frac{2}
{\sqrt{x}}\frac{1}{(2-\sqrt{x})^{2}}, \ x \in (0 ;4)\cup
(4;\infty) \)
\(f'(x) = \frac{\sqrt{x}}
{2(2-\sqrt{x})^2}, \ x \in (0 ;4) \cup
(4;\infty) \)
\(f'(x) = \frac{1}
{(2-\sqrt{x})^2}, \ x \in (0 ;4) \cup
(4;\infty) \)
\(f'(x) = \frac{1}
{x(2-\sqrt{x})^2}, \ x \in (0 ;4) \cup
(4;\infty) \)