C

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?
\(49\, \mathrm{km}\)
\(39\, \mathrm{km}\)
\(35\, \mathrm{km}\)
\(45\, \mathrm{km}\)

9000007203

Level: 
C
Consider the function \[ f(x) =\mathop{ \mathrm{sgn}}\nolimits (x - 2) \] defined on \(\mathop{\mathrm{Dom}}(f) =\mathbb{R} ^{-}\). Find the parameters \(a\) a \(b\) and domain of the linear function \[ g(x) = ax + b \] which ensure that \(f\) and \(g\) are identical functions. \[ \] Hint: The function \(y =\mathop{ \mathrm{sgn}}\nolimits (x)\) is the sign function. The values of sign function is \(1\) for each positive \(x\), \(- 1\) for each negative \(x\) and \(0\) if \(x = 0\).
\(a = 0\), \(b = -1\); \(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{-}\)
\(a = 0\), \(b = 1\); \(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{+}\)
\(a = 1\), \(b = 0\); \(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{-}\)
\(a = -1\), \(b = 0\); \(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{+}\)

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 \(U\).
\(I = \frac{2} {3}U -\frac{4}{3};U\in [2;\infty) \)
\(I = \frac{3} {2}U - 2;U\in [2;\infty) \)
\(I = \frac{3} {2}U + 2;U\in [2;\infty) \)
\(I = \frac{2} {3}U + 2;U\in [2;\infty) \)

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?
\(63\)
\(9\)
\(62\)
\(125\)
\(126\)