2100002001
Level:
C
Identify a possible graph of the function \(f(x) = \frac{1}{|x|}-1\).
C
2000001508
Level:
C
Which of the given numbers is not the solution of the equation \((x-i)(2x+i)=0\)?
\(x=1\)
\(x=i\)
\(x=-\frac{1}{2}i\)
\(x=\cos{\frac{\pi}{2} }+ i\sin{\frac{\pi}{2}}\)
2000000507
Level:
C
Find the solution set of the following inequality.
\[
16^x -4^x\leq 0
\]
\( (-\infty; 0] \)
\( [ 0; \infty) \)
\( [ 1; \infty) \)
\( (-\infty; 1] \)
2000000503
Level:
C
The set of all solutions of the inequality \(4^{\frac{2}{x+3}}>1\) is the interval:
\( (-3;\infty)\)
\( (-\infty;3)\)
\( (3;\infty)\)
\( (-\infty;-3)\)
2000000501
Level:
C
The set of all solutions of the inequality \(0.7^{-x} > 0.7^{4+x}\) is the interval:
\( (-2 ;\infty)\)
\( (-\infty;2)\)
\( (2 ;\infty)\)
\( (-\infty ;-2)\)
2000000407
Level:
C
Which number belongs to the set of all solutions of the inequality \(\log_{x}4< 2\)?
\(x=\sqrt{8}\)
\(x=-2\)
\(x=2\)
\(x=\sqrt{2}\)
2000000406
Level:
C
Which number does not belong to the set of all solutions of the inequality \(\log_{2x}(x+2)< 1\)?
\(x=2\)
\(x=3\)
\(x=4\)
\(x=5\)
2000000405
Level:
C
Which number belongs to the set of all solutions of the inequality \(\log_{2x-2}x< 1\)?
\(x=3\)
\(x=1\)
\(x=0\)
\(x=0.5\)
2000000301
Level:
C
Find the value of the parameter \( m \) so that the solution set of the inequality
\[
\left(\frac{1}{7}\right)^x \leq m
\]
is the interval \([ 2;\infty)\).
\( m = \frac{1}{49} \)
\( m = 49\)
\(m = 2\)
\( m=14\)
1103266407
Level:
C
Our task is to support a square tarp sized $4\,\mathrm{m}\times 4\,\mathrm{m}$ in the centers of its opposite sides to create a hay roof, as shown in the picture. What should be the height $v$ of the pillars to make the shelter space (volume) as large as possible?
$\sqrt2\,\mathrm{m}$
$\frac{\sqrt2}2\,\mathrm{m}$
$2\,\mathrm{m}$
$\sqrt3\,\mathrm{m}$
$\frac{\sqrt3}2\,\mathrm{m}$