C

9000009309

Level: 
C
The speed of a swimmer in a \(50\, \mathrm{m}\)-pool is \(0.8\, \mathrm{m}/\mathrm{s}\). How fast will he swim two pool lengths (one pool length is \(50\) meters), if he/she needs \(2\, \mathrm{s}\) to turn at the end of the pool?
\(127\, \mathrm{s}\)
\(82\, \mathrm{s}\)
\(84\, \mathrm{s}\)
\(129\, \mathrm{s}\)

9000009906

Level: 
C
Consider a function \[ f(x) = \frac{k} {x} \] with a nonzero real parameter \(k\). Describe what happens with the function \(f\) if the coefficient \(k\) changes the sign.
The function changes the type of monotonicity on the sets \(\mathbb{R}^{+}\) and \(\mathbb{R}^{-}\) (either from an increasing function into a decreasing function or vice versa).
The function changes its parity (from an odd function into an even function or from an even function into an odd function).
The domain of the function changes.
None of the above, both functions have the same parity, monotonicity and domain.

9000009907

Level: 
C
Consider a function \[ f(x) = \frac{k} {x} \] with a nonzero real parameter \(k\). Suppose that the value of the coefficient \(k\) changes, but the sign of \(k\) remains the same. Describe which of the properties of \(f\) is changed.
None of the above, both functions have the same parity, monotonicity and range.
The function changes its parity (from an odd function into an even function or from en even function into an odd function).
The range of the function changes.
The function changes the type of monotonicity on the sets \(\mathbb{R}^{+}\) and \(\mathbb{R}^{-}\) (either from an increasing function into a decreasing function or vice versa).

9000007209

Level: 
C
A current-voltage characteristics is shown in the graph. Find the current \(I\) as a function of the voltage \(U\).
\(I = \frac{2} {3}U -\frac{4}{3},U\in [2,\infty) \)
\(I = \frac{3} {2}U - 2,U\in [2,\infty) \)
\(I = \frac{3} {2}U + 2,U\in [2,\infty) \)
\(I = \frac{2} {3}U + 2,U\in [2,\infty) \)

9000007810

Level: 
C
A fuel tank in a car has the capacity \(40\) litres. The current volume of the fuel in the fuel tank is \(6\) litres. The speed of fuelling is \(1\) litre of gasoline each \(3\) seconds. Find the function which describes the volume of the gasoline in the fuel tank (in litres) as a function of time (in seconds).
\(V = \frac{1} {3}t + 6,\ t\in [ 0,102] \)
\(V = 3t + 6,\ t\in [ 0,102] \)
\(V = 3t + 6,\ t\in [ 0,40] \)
\(V = 3t + 6,\ t\in \mathbb{R}_{0}^{+}\)
\(V = \frac{1} {3}t + 6,\ t\in [ 0,40] \)