Linear functions

9000009311

Level: 
C
The graph shows the speed of a train as a function of time. Find an analytic expression for this function.
\(v = 30 - \frac{3}{4}t,\ t\in [ 0;20] \)
\(v = 30 + \frac{3}{4}t,\ t\in [ 0;20] \)
\(v = 15 +\frac{3}{4}t,\ t\in [ 0;20] \)
\(v = 30 - \frac{4}{3}t,\ t\in [ 0;20] \)

9000009304

Level: 
C
A tank contains \(1\: 000\) litres of petrol. The petrol escapes at a constant speed \(20\) litres per minute. In what time will there be just \(200\) litres of the petrol in the tank?
\(40\, \mathrm{min}\)
\(10\, \mathrm{min}\)
\(20\, \mathrm{min}\)
\(30\, \mathrm{min}\)

9000009305

Level: 
C
Anne decided to make a bicycle trip with his friend which lives \(10\, \mathrm{km}\) from Anne house. Anne went from her house to the house of her friend first. Then they started to measure the time and went on a constant velocity \(18\, \mathrm{km}/\mathrm{h}\). In what time will be the total distance traveled by Anne equal to \(34\, \mathrm{km}\)?
\(1\, \mathrm{h}\) \(20\, \mathrm{min}\)
\(1\, \mathrm{h}\) \(58\, \mathrm{min}\)
\(2\, \mathrm{h}\) \(26\, \mathrm{min}\)
\(2\, \mathrm{h}\) \(30\, \mathrm{min}\)

9000009306

Level: 
C
Anne decided to make a bicycle trip with his friend which lives \(10\, \mathrm{km}\) from Anne house. Anne went from her house to the house of her friend first. Then they started to measure the time and went on a constant velocity \(18\, \mathrm{km}/\mathrm{h}\) for \(2\, \mathrm{h}\) \(10\, \mathrm{min}\). What is the total distance traveled by Anne?
\(49\, \mathrm{km}\)
\(39\, \mathrm{km}\)
\(35\, \mathrm{km}\)
\(45\, \mathrm{km}\)

9000009307

Level: 
C
The sound velocity at the temperature \(0\, ^{\circ } \mathrm{C}\) is \(331\, \mathrm{m}/\mathrm{s}\). An increase of the temperature by \(1\, ^{\circ } \mathrm{C}\) increases the speed of velocity by \(0.6\, \mathrm{m}/\mathrm{s}\). Estimate the sound speed at the temperature \(18\, ^{\circ } \mathrm{C}\).
\(341.8\, \mathrm{m}/\mathrm{s}\)
\(341.2\, \mathrm{m}/\mathrm{s}\)
\(348\, \mathrm{m}/\mathrm{s}\)
\(349\, \mathrm{m}/\mathrm{s}\)

9000007207

Level: 
C
Identify a function which has the following three properties: it has at least one minimum or maximum, it is an increasing function and the range of this function is the set of all nonnegative numbers.
\(f(x) = 2x - 2\), \(x\in [ 1;+\infty )\)
\(f(x) = 2x + 2\), \(x\in (-1;+\infty )\)
\(f(x) = -2x + 2\), \(x\in (-\infty ;1] \)
\(f(x) = -2x - 2\), \(x\in \mathbb{R}\)

9000007208

Level: 
C
Paul's home is \(6\, \mathrm{km}\) from the school. At the time \(t = 0\) Paul starts to walk from his home to the school along a straight street at a constant velocity \(5\, \mathrm{km}/\mathrm{h}\). Find the function which describes Paul's remaining distance to the school as a function of time.
\(s = 6 - 5t\)
\(s = 5t - 6\)
\(s = 5t\)
\(s = 5t + 6\)

9000007209

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