9000007608
Level:
C
Find the range of the function \(f(x) = 1 + \left | \frac{1}
{2(x-2)}\right |\).
\((1,\infty )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \{1\}\)
\((0,\infty )\)
\(\mathbb{R}\setminus \{2\}\)
C
9000007603
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{2(x-2)}\right |\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{4\}\)
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\)
9000007609
Level:
C
Find the range of the function \(f(x) = 1 + \left | \frac{1}
{|x|+1}\right |\).
\((1,2] \)
\(\mathbb{R}\setminus \{ - 1,1\}\)
\((0,\infty )\)
\((1,\infty )\)
\(\mathbb{R}\)
9000008008
Level:
C
Given the functions
\[
\text{$f(x) = -\frac{2}
{x}$ and $g(x)= \frac{k}
{x}$}
\]
find the value of the parameter \(k\in \mathbb{R}\setminus \{0\}\)
which ensures
\[
g(2) = 2f(-2).
\]
\(4\)
\(2\)
\(- 1\)
\(- 2\)
9000007610
Level:
C
Find the range of the function \(f(x) = 1 + \left | \frac{1}
{-|x|+1}\right |\).
\((1,\infty )\)
\(\mathbb{R}\setminus \{ - 1\}\)
\((0,\infty )\)
\(\mathbb{R}\setminus \{ - 1,1\}\)
\(\mathbb{R}\)
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.
\(s = 6 - 5t\)
\(s = 5t - 6\)
\(s = 5t\)
\(s = 5t + 6\)
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?
\(1\, \mathrm{h}\)
\(5\, \mathrm{min}\)
\(55\, \mathrm{min}\)
\(1\, \mathrm{h}\)
\(1\, \mathrm{h}\)
\(10\, \mathrm{min}\)
9000009303
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 be the tank empty?
\(50\, \mathrm{min}\)
\(60\, \mathrm{min}\)
\(40\, \mathrm{min}\)
\(30\, \mathrm{min}\)