C

9000010609

Level: 
C
Identify a function which is a possible inverse to the function graphed in the picture.
\(y = x^{-1}\), \(x\in (0,\infty )\)
\(y = x\), \(x\in (0,\infty )\)
\(y = -x\), \(x\in (0,\infty )\)
\(y = -x^{-1}\), \(x\in (0,\infty )\)
\(y = x^{2}\), \(x\in (0,\infty )\)
\(y = -x^{2}\), \(x\in (0,\infty )\)

9000010610

Level: 
C
Identify a function which is a possible inverse to the function graphed in the picture.
\(y = x^{2}\), \(x\in (-\infty ,0] \)
\(y = x^{-2}\), \(x\in (-\infty ,0] \)
\(y = -x^{2}\), \(x\in [ 0,\infty )\)
\(y = x^{\frac{1} {2} }\), \(x\in [ 0,\infty )\)
\(y = -x^{\frac{1} {2} }\), \(x\in [ 0,\infty )\)
\(y = -2x\), \(x\in (-\infty ,0] \)

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?
\(40\, \mathrm{min}\)
\(10\, \mathrm{min}\)
\(20\, \mathrm{min}\)
\(30\, \mathrm{min}\)

9000009311

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

9000007809

Level: 
C
The price of a goods in a shop is \(\$15\) per item. The Internet price in an e-shop is cheaper by \(\$2\) per item. The shipping cost of the e-shop is \(\$125\). What is the minimal number of items, which makes the total cost for a transaction smaller in the e-shop?
\(63\)
\(9\)
\(62\)
\(125\)
\(126\)

9000009301

Level: 
C
An automatic machine produces \(12\) components per minute and stores them in a box with capacity \(1\: 500\) components. The machine starts with an initial amount of \(240\) components in the box. In what time will be the box full?
\(1\, \mathrm{h}\) \(45\, \mathrm{min}\)
\(1\, \mathrm{h}\) \(55\, \mathrm{min}\)
\(2\, \mathrm{h}\) \(5\, \mathrm{min}\)
\(2\, \mathrm{h}\) \(15\, \mathrm{min}\)

9000009302

Level: 
C
An automatic machine produces \(12\) components per minute and stores them in a box with capacity \(1\: 500\) components. The machine starts with an initial amount of \(240\) components in the box. In what time will the box contain \(1\: 020\) components?
\(1\, \mathrm{h}\) \(5\, \mathrm{min}\)
\(55\, \mathrm{min}\)
\(1\, \mathrm{h}\)
\(1\, \mathrm{h}\) \(10\, \mathrm{min}\)

9000007210

Level: 
C
Jane has to reach the opposite shore of a lake. She has three possibilities how to cross. She can use her own boat, start immediately and sail at the velocity \(4\, \mathrm{km}/\mathrm{h}\). Another option is to wait for her friend, Peter, with a faster boat. Peter's boat is capable to sail at the velocity \(10\, \mathrm{km}/\mathrm{h}\). However, his boat will be available in \(1.5\) hours from now. The last option is to use the regular passenger transportation line which will departure in \(2.25\) hours from now and sails at the speed \(20\, \mathrm{km}/\mathrm{h}\). Find the interval of distances to the opposite shore for which the fastest option is to use Peter's boat.
between \(10\) and \(15\) kilometers
up to \(10\) kilometers
between \(15\) and \(20\) kilometers
larger that \(20\) kilometers