9000146701
Level:
A
Expand the following polynomial.
\[
2 - (2x + 1) + x(5 - 2x) - 3(x - 2)
\]
\(- 2x^{2} + 7\)
\(- 2x^{2} + 9\)
\(- 2x^{2} - 3\)
\(- 2x^{2} - 5\)
A
9000146702
Level:
A
Expand the following expression.
\[
a - 4(2 - a) - a(5a + 1) + 2a(3 - 2a)
\]
\(- 9a^{2} + 10a - 8\)
\(- 9a^{2} + 12a - 8\)
\(- 9a^{2} + 2a - 8\)
\(- 9a^{2} + 4a - 8\)
9000146203
Level:
A
Expand the following expression.
\[
\left (x^{5} -\sqrt{2}y\right )^{2}
\]
\(x^{10} - 2\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} - 2\sqrt{2}x^{5}y - 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y - 2y^{2}\)
9000146204
Level:
A
Expand the following expression.
\[
\left (\frac{a}
{2} + 4b^{3}\right )^{2}
\]
\(\frac{a^{2}}
{4} + 4ab^{3} + 16b^{6}\)
\(\frac{a^{2}}
{4} + 2ab^{3} + 16b^{6}\)
\(\frac{a^{2}}
{4} + 4ab^{3} + 16b^{5}\)
\(\frac{a^{2}}
{4} + 2ab^{3} + 16b^{5}\)
9000139309
Level:
A
There are \(20\) tablets in an
e-shop. From this amount \(18\)
tablets are new and \(2\)
tablets have been returned by customers. The e-shop manager gets an order
containing three tablets and he wants to get rid of the returned tablets first. How
many possibilities exist to complete the order?
\(18\)
\(\frac{18!}
{3!\; 15!}=816\)
\(18\cdot 16\cdot 3=864\)
\(20\cdot 19\cdot 18=6\:840\)
9000139509
Level:
A
The average year income in a company was
\(200\: 000\, \mathrm{Euro}\) two years ago. This
income increased by \(10\%\)
a year ago and by \(80\: 000\, \mathrm{Euro}\)
this year. Find the average percentage increase in the average income per one year
and round to the nearest percent.
\(22\%\)
\(23\%\)
\(25\%\)
\(50\%\)
9000139310
Level:
A
There are \(20\) tablets in an
e-shop. From this amount \(18\)
tablets are new and \(2\)
tablets have been returned by customers. The e-shop manager gets an order
containing three tablets and he wants to use only the new tablets for this order. How
many possibilities exist to complete the order?
\(\frac{18!}
{3!\; 15!}\)
\(18\)
\(18\cdot 16\cdot 3\)
\(20\cdot 19\cdot 18\)
9000139510
Level:
A
The price of a butter increased by \(8\%\)
in the year \(2013\)
and by \(34\%\) in
the year \(2014\).
Find the average percentage growth of the price of the butter per one year in the period
\(2012\)-\(2014\).
Round your answer to the nearest percent.
\(20\%\)
\(21\%\)
\(14\%\)
\(26\%\)
9000139701
Level:
A
There are \(15\)
athletes in an athletic meeting. Determine in how many ways it is possible to
obtain the results on the first six places of the scoreboard if the place on
scoreboard cannot be shared (one athlete per one place on scoreboard).
\(\frac{15!}
{9!} =3\:603\:600\)
\(6^{15}=470\:184\:984\:576\)
\(15!\, 6!=941\:525\:544\:960\:000\)
\(\frac{15!}
{9!\, 6!}=5\:005\)
9000139502
Level:
A
The average mass of \(30\)
eggs on a plate is \(60\, \mathrm{g}\).
From this amount we remove five eggs. The total mass of these five eggs is
\(280\, \mathrm{g}\).
Find the change in the average mass of the remaining eggs on the plate.
The average mass of eggs increases by \(0.8\, \mathrm{g}\).
The average mass of eggs decreases by
\(4\, \mathrm{g}\).
The average mass of eggs increases by
\(4\, \mathrm{g}\).
The average mass of eggs increases by
\(12\, \mathrm{g}\).