2010015905
Level:
B
Find the solution set of the following inequality.
\[
\frac{-1}
{x^2+x-20} \geq 0
\]
\( (-5;4)\)
\(\emptyset\)
\((-\infty;-5) \cup (4;\infty) \)
\((-4;5) \)
B
2010015904
Level:
B
An inequality is solved graphically as shown in the picture. The solution is marked in red. Choose the corresponding inequality.
\(3\leq \frac{x-2}
{x} \)
\(3\geq -\frac{2}
{x} \)
\(3\geq \frac{x-2}
{x} \)
\(3\leq -\frac{2}
{x} \)
2010015903
Level:
B
Find the solution set of the following inequality.
\[
\frac{x -2}
{x +3} > 1
\]
\(( -\infty; -3) \)
\((-3;\infty) \)
\(( -\infty; 2) \)
\((2;\infty) \)
2010015902
Level:
B
Find the solution set of the following inequality.
\[
\frac{x+3}
{1-2x} \geq 0
\]
\(\left[ -3; \frac12 \right) \)
\( [ -3;\infty )\)
\( \left(-\infty;\frac12\right)\)
\( (-\infty;-3 ] \cup \left(\frac12;\infty\right)\)
2010015901
Level:
B
Find all real values of \(x\) for which the fraction \(\frac{2}{x+3}\) is negative.
\( x < -3\)
\( x>-3\)
\( x< 3\)
\(x>3\)
2010015810
Level:
B
The picture shows a square pyramid. The side of a base square is
\(a = 10\; \mathrm{cm}\) and the height of
the pyramid is \(v = 10\; \mathrm{cm}\).
Find the angle \(\varphi \) between the lateral edge and the edge of the base of the pyramid.
\(\mathop{\mathrm{tg}}\nolimits {\varphi} = \sqrt5
\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 65^{\circ }54^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{\sqrt5}
{5}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 24^{\circ }6^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}{2} = \frac{\sqrt5}
{5}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 48^{\circ }11^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits {\varphi} = \frac{\sqrt{10}}
{2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 57^{\circ }41^{\prime}\)
2010015809
Level:
B
The picture shows a square pyramid \(ABCDV\). The side of a base square is
\(a = 6\; \mathrm{cm}\) and the height of
the pyramid is \(v = 8\; \mathrm{cm}\).
Find the angle \(\varphi \) between the opposite lateral edges (the angle \(AVC\)).
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}2 = \frac{3\sqrt2}
{8}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 55^{\circ }53'\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{3\sqrt2}
{8}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 27^{\circ }56^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}{2} = \frac{3}
{8}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 41^{\circ }7^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}2 = \frac{8}
{3\sqrt2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 124^{\circ }7^{\prime}\)
2010015808
Level:
B
The picture shows a square pyramid. The side of a base square is
\(a = 6\; \mathrm{cm}\) and the height of
the pyramid is \(v = 10\; \mathrm{cm}\).
Find the angle \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{10}
{3\sqrt2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 67^{\circ }\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{10}
{3}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 73^{\circ }18^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}{2} = \frac{3\sqrt2}
{10}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 45^{\circ }59^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}2 = \frac{3}
{10}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 33^{\circ }24^{\prime}\)
2010015804
Level:
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 6\,\mathrm{cm} \). The height of the pyramid is \( 3\sqrt2\,\mathrm{cm} \). Find the distance between the point \( A \) and the line \( CV \) (see the picture).
\( 6\,\mathrm{cm} \)
\( 3\sqrt{3}\,\mathrm{cm} \)
\( 9\,\mathrm{cm} \)
\( 3\sqrt{2}\,\mathrm{cm} \)
2010015604
Level:
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 4\,\mathrm{cm} \). The height of the pyramid is \( 6\,\mathrm{cm} \). Find the distance between the point \( A \) and the point \( S_{VB} \), where \( S_{VB} \) is the midpoint of the edge \( VB \).
\( \sqrt{19}\,\mathrm{cm} \)
\( \sqrt{35}\,\mathrm{cm} \)
\( 3\sqrt{3}\,\mathrm{cm} \)
\( \sqrt{5}\,\mathrm{cm} \)