1103076901
Level:
B
Given a right-angled triangle \( ABC \) with the right angle at vertex \( C \), calculate \( \mathrm{tg}\,\beta \) if \( \cos\alpha=\frac5{13} \).
\( \frac5{12} \)
\( \frac5{13} \)
\( \frac{13}5 \)
\( \frac{12}{13} \)
B
1103129201
Level:
B
The thin lens equation \( \frac1a+\frac1{a'}=\frac1f \) describes the quantitative relationship between the object distance \( a \), the image distance \( a' \), and the focal length \( f \). Let the focal length of a thin lens be \( 0{.}5\,\mathrm{m} \). Choose the picture that shows the object distance vs. image distance graph, if \( a\in [0.1\,\mathrm{m};0.4\,\mathrm{m}]\cup [0.6\,\mathrm{m};3.0\,\mathrm{m}] \).
1103171104
Level:
B
From the given pictures choose the one that shows graphs of three functions corresponding to the formula \( f(x)=kx+2 \), where \( k\in\mathbb{R}^+ \).
1003138511
Level:
B
Solve
\[ \frac{\log(4x)}{\log(x-3)}=\frac{\log16}{\log4} \text{ .} \]
\( x = 9 \)
\( x_1=1,\ x_2=9 \)
\( x_1=-9,\ x_2=-1 \)
The equation has no solution.
1103162909
Level:
B
With aid of the graph of a function \( f \) find all \( x\), so that \( |f(x)|=3 \).
\( x\in\{-5,1\} \)
\(x\in \{1\} \)
\(x\in \{-2\} \)
\( x\in\{-5,5\} \)
1103162908
Level:
B
With aid of the given graph of a function \( f \), find all \( x \) so that \( |f(x)-2|=1 \).
\( x\in\{-4,-2\} \)
\( x\in\{-4,2\} \)
\( x\in\{-2,2\} \)
\( x\in\{-3\} \)
1003162907
Level:
B
Find the sum of all the roots of the equation \( |x+4|=|2x-7| \).
\( 12 \)
\( 11 \)
\( -11 \)
\( 23 \)
1003162906
Level:
B
Find the number of the roots of the equation \( |x+3|+|x+2|=6 \).
\( 2 \)
\( 1 \)
\( 4 \)
\( 3 \)
1003162902
Level:
B
Calculate for which value(s) of the parameter \( t \) the given equation has no solution.
\[ |x+4|-2=t \]
\( t\in(-\infty,-2) \)
\( t\in(-\infty,-4) \)
\( t\in(-4,\infty) \)
\( t\in(-\infty,2) \)
1003162901
Level:
B
Calculate for which value(s) of the parameter \( t \) the given equation has at least one solution.
\[ |x-5|=t \]
\( t\in[0,\infty) \)
\( t\in[5,\infty) \)
\( t\in\{0\} \)
\( t\in(-\infty,5] \)