9000013506
Level:
A
Write the number \(\root{3}\of{16000}\)
in an equivalent form with smallest possible number under the radical.
\(20\root{3}\of{2}\)
\(10\root{3}\of{4}\)
\(100\root{3}\of{2}\)
\(4\root{3}\of{10}\)
A
9000013509
Level:
A
Simplify the expression \((1 + \sqrt{2})^{2}\).
\(3 + 2\sqrt{2}\)
\(3\)
\(3 - 2\sqrt{2}\)
\(3 + \sqrt{2}\)
9000013508
Level:
A
Write the fraction \(\frac{\sqrt{7}}
{\sqrt{3}}\)
in an equivalent form which does not contain radical in the denominator.
\(\frac{\sqrt{21}}
{3} \)
\(\frac{\sqrt{10}}
{3} \)
\(\frac{\sqrt{7}+\sqrt{3}}
{3} \)
\(\frac{7}
{3}\)
9000013510
Level:
A
Write the fraction \(\frac{1}
{1+\sqrt{2}}\)
in an equivalent form which does not contain radical in the denominator.
\(\sqrt{2} - 1\)
\(\sqrt{2}\)
\(\frac{1}
{\sqrt{2}}\)
\(1 -\sqrt{2}\)
9000009910
Level:
A
A body is deformed continuously in a machine press. The density
\(\rho \) is inversely proportional
to the volume \(V \) of the body,
i.e. there exists a constant \(k\)
such that
\[
\rho = \frac{k}
{V }.
\]
Find the constant \(k\)
(including the correct unit) if it is known that the density was
\(\rho = 25\: \frac{\mathrm{kg}}
{\mathrm{m}^{3}} \) when the body
had volume \(V = 2\, \mathrm{dm}^{3}\).
\(50\, \mathrm{g}\)
\(12.5\, \mathrm{g}\)
\(12.5\, \mathrm{m}\)
\(50\, \mathrm{m}\)
9000010509
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{3}\of{x^{11}}
\]
\(x^{4}\root{3}\of{x^{2}}\)
\(x^{11}\root{3}\of{x}\)
\(x^{12}\root{3}\of{x}\)
\(x\root{3}\of{x}\)
9000010605
Level:
A
Identify a function which is decreasing on
\((-\infty ;1)\).
\(f(x) = -x^{3}\)
\(f(x) = -x^{2}\)
\(f(x) = x^{3}\)
\(f(x) = -x^{4}\)
\(f(x)= x^{-2}\)
\(f(x) = x^{2}\)
9000010606
Level:
A
Identify a function which is increasing on
\((-1;3)\).
\(f(x) = (x + 2)^{2}\)
\(f(x) = x^{2} + x\)
\(f(x) = x^{2} - x\)
\(f(x) = (x - 2)^{2}\)
\(f(x) = -x^{3}\)
\(f(x) = x^{2} + 1\)
9000011103
Level:
A
In the following list identify an increasing function.
\(f(x) = x^{5}\)
\(f(x) = x^{2}\)
\(f(x) = x^{-3}\)
\(f(x) = x^{-4}\)
\(f(x) = 2x^{0}\)
9000010607
Level:
A
Identify a function which is one-to-one on the interval
\([ - 2;2] \).
\(f(x) = x^{3} - 2\)
\(f(x) = x^{2} - 2\)
\(f(x) = -x^{2} + 2\)
\(f(x) = x^{-2} + 2\)
\(f(x) = \frac{1}
{x} - 2\)
\(f(x) = x^{4}\)