C

9000009909

Level: 
C
Consider the system \[\begin{aligned} y & = \frac{k} {x}, & & \\y & = a, & & \end{aligned}\] where \(a\), \(k\) are real parameters and \(x\), \(y\) are real variables. Determine the conditions for \(a\) and \(k\) so that the system has a unique solution in \(\mathbb{R}^{-}\times \mathbb{R}^{-}\).
\(a < 0\) and \(k > 0\)
\(a < 0\) and \(k < 0\)
\(a > 0\) and \(k < 0\)
\(a > 0\) and \(k > 0\)

9000010610

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

9000010608

Level: 
C
Identify a function which is a possible inverse to the function graphed in the picture.
\(y = x^{3}\), \(x\in (-\infty ;\infty )\)
\(y = x^{-3}\), \(x\in (-2;2)\)
\(y = x^{\frac{1} {3} }\), \(x\in (0;\infty )\)
\(y = -x^{\frac{1} {3} }\), \(x\in (-\infty ;\infty )\)
\(y = 8x\), \(x\in (-\infty ;\infty )\)
\(y = -4x\), \(x\in (-\infty ;\infty )\)

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 \(18\, ^{\circ } \mathrm{C}\).
\(341.8\, \mathrm{m}/\mathrm{s}\)
\(341.2\, \mathrm{m}/\mathrm{s}\)
\(348\, \mathrm{m}/\mathrm{s}\)
\(349\, \mathrm{m}/\mathrm{s}\)

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?
\(127\, \mathrm{s}\)
\(82\, \mathrm{s}\)
\(84\, \mathrm{s}\)
\(129\, \mathrm{s}\)