Rational functions

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 \(45\,\mathrm{km/h}\)

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

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)

2000018801

Level: 
A
Consider a triangle with area of \(5\, \mathrm{cm}^{2}\). Find the formula which relates the length of its side \(a\) to the length of the height \(v_a\) , where \(v_a\) is the height to the side \(a\).
\(v_a = \frac{10} {a}\)
\(v_a = \frac{5} {a}\)
\(v_a =5 {a}\)
\(v_a = \frac{5} {2a}\)

2000018805

Level: 
A
The test driver drove from Ostrava to Warsaw at an average speed of \(66\, \mathrm{km}/\mathrm{h}\) and the journey took him \(6\) hours. After him, the same route took several other drivers. (Each driver took a different driving time.) Choose the function giving the average speed \(v\) of each of these drivers as a function of the total driving time \(t\) from Ostrava to Warsaw.
\( v=\frac{396}t,\ \ t\in(0;\infty) \)
\( v=\frac{66}t,\ \ t\in(0;\infty) \)
\( v=66 t,\ \ t\in(0;\infty) \)
\( v=\frac{t}{396},\ \ t\in(0;\infty) \)

2010009905

Level: 
A
Let \( f(x)=\frac{-3}{x} \). Find the false statement.
The function \(f\) is bounded above.
The range of \( f \) is \( \left(-\infty;0\right)\cup\left(0;\infty\right) \).
The function \( f \) is increasing on \( \left(-\infty;0\right) \).
The function \( h \) defined by \(h(x)=-f(x)\) is an odd function.