2000003801
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^2(x-1)=0
\]
\( \{0;1\}\)
\( \{-1;0\}\)
\( \{-1;1\}\)
\( \{-1;0;1\}\)
A
2000003706
Level:
A
The length of a rectangle is extended twice its original length. How must its width be changed so that the area of the rectangle remains the same?
the width is reduced to half (of its original width)
the width is increased by half (of its original width)
the width is reduced by a quarter (of its original width)
the width is increased to double (of its original width)
2000003705
Level:
A
A car going at a speed \(60\,\mathrm{km/h}\) covers the distance from city \(A\) to city \(B\) in \(30\) minutes. If the distance has to be covered in \(20\) minutes, how many times does the driver have to increase the speed when leaving \(A\).
\(1.5\) times
\(1.\overline{3}\) times
\(1.\overline{6}\) times
\(1.2\) times
2000003704
Level:
A
A car going at a speed \(60\,\mathrm{km/h}\) covers the distance from city \(A\) to city B in \(30\) minutes. If the distance has to be covered in \(20\) minutes, by how many \(\mathrm{km/h}\) must the driver increase the speed when leaving \(A\).
by \(30\,\mathrm{km/h}\)
by \(20\,\mathrm{km/h}\)
by \(40\,\mathrm{km/h}\)
by \(45\,\mathrm{km/h}\)
2000003703
Level:
A
The pool is filled with eight equally powerful pumps in \(6\) hours. During the maintenance of some of the pumps, it took \(24\) hours to fill the pool. How many pumps were running?
\(2\) pumps
\(3\) pumps
\(4\) pumps
\(6\) pumps
2000003702
Level:
A
Four workers assembled a garden pool in \(5\) hours. How long would it take eight workers to do the same job?
\(2\,\mathrm{h}\,30\,\mathrm{min}\)
\(2\,\mathrm{h}\,40\,\mathrm{min}\)
\(2\,\mathrm{h}\,20\,\mathrm{min}\)
\(2\,\mathrm{h}\,45\,\mathrm{min}\)
2000003701
Level:
A
Group of mountaineers would climb the top of the mountain at an ascent speed of \(400\,\mathrm{m}\) per day in \(10\) days. However, due to the weather, they have to conquer the peak in \(8\) days. How many more meters per day do they have to cover?
\(100\) meters more
\(80\) meters more
\(120\) meters more
\(90\) meters more
2010002112
Level:
A
There is a part of the function \(f\) and the point \(x_0\) in the picture. Choose the true statement about the derivative at the point \(x_0=4\).
\( 0 < f'(x_0)< 1\)
\( -1 < f'(x_0)< 0\)
\( f'(x_0)>1\)
\( f'(x_0)< -1\)
2010002111
Level:
A
There is a part of the function \(f\) and the point \(x_0\) in the picture. Choose the true statement about the derivative at the point \(x_0=4\).
\(-1 < f'(x_0)< 0\)
\(0 < f'(x_0)< 1\)
\(f'(x_0)>1\)
\(f'(x_0)< - 1\)
2010002110
Level:
A
There is a part of the function
\[
f(x)=\left\{\begin{matrix}
&(x+6)^{-2}+2& x \in (-\infty;-5)\setminus\{-6\} \\
&3, & x \in [ -5;-3 ] \\
&1, & x \in (-3;-1) \\
&|x-1|-1& x \in [ -1,\infty)\setminus \{6\}\\
\end{matrix}\right.
\]
in the picture. Use the graph to determine at how many points of the given interval \([ -8; 7 ]\) is the function \(f\) defined and is not differentiable.
\( 4\)
\(3\)
\(5\)
\(6\)