9000080907
Level:
B
Find \(B'_{A}\) (the
complement to \(B\)
in \(A\))
for \(A =\mathbb{Z}\)
and \(B = \{x\in \mathbb{Z};\left |x\right | > 3\}\).
\(\{ - 3;-2;-1;0;1;2;3\}\)
\(\{ - 2;-1;0;1;2\}\)
\(\{0;1;2;3\}\)
\(\{1;2;3\}\)
B
9000085306
Level:
B
The ski has been sold for a reduced price in a sale after the season. The discount
\(18\, \%\)
of the original price resumed in a price which was cheaper by
\(\$36\). Find
the original price of the ski.
\(\$200\)
\(\$250\)
\(\$450\)
\(\$500\)
9000080908
Level:
B
Find the set difference \(A\setminus B\)
for \(A = \{ - 2;-1;0;1;2\}\)
and \(B = \{x\in \mathbb{Z};x < 2\}\).
\(\{2\}\)
\(\{ - 2;-1;0;1;2\}\)
\(\{0;1\}\)
\(\emptyset \)
9000083601
Level:
B
Find the conditions on \(x\)
under which the expression
\[
\frac{\frac{x-y}
{x+y} -\frac{x+y}
{x-y}}
{ \frac{xy}
{x^{2}-y^{2}} }
\]
is well-defined.
\(x\neq 0,\; y\neq 0,\; x\neq \pm y\)
\(x\neq - y\)
\(x\neq \pm y\)
\(x\neq 0,\; y\neq 0\)
9000080909
Level:
B
Find the set difference \(B\setminus A\)
for \(A = \{x\in \mathbb{Z};x < 2\}\)
and \(B = \{x\in \mathbb{Z};x < 5\}\).
\(\{2;3;4\}\)
\(\{x\in \mathbb{Z};x < 2\}\)
\(\{3;4\}\)
\(\emptyset \)
9000083609
Level:
B
Assuming \(x\neq 0\),
\(x\neq \pm y\),
\(y\neq 0\),
simplify the expression.
\[
\frac{\frac{x^{2}+y^{2}}
{x} - 2y}
{\left ( \frac{1}
{y^{2}} - \frac{1}
{x^{2}} \right )\cdot \frac{xy}
{x+y}}
\]
\(y(x - y)\)
\(\frac{x-y}
{y} \)
\(x(x - y)\)
\(\frac{x-y}
{x} \)
9000081408
Level:
B
For \(x\in \mathbb{R}^{-}\) consider
expressions \(|x|\),
\(|- x|\),
\(-|x|\) and
\(- x\).
Which of these attains only negative values?
\(-|x|\)
\(|x|\)
\(|- x|\)
\(- x\)
9000084909
Level:
B
Among the following numbers, find the number so that in its factorization into primes each prime is squared.
\(36\)
\(24\)
\(120\)
\(360\)
\(512\)
9000084901
Level:
B
Which of the following numbers is a prime?
\(17\)
\(1\)
\(27\)
\(91\)
\(289\)
9000084908
Level:
B
From the following list of numbers choose the one that has in its prime factorization the highest power of a prime.
\(1\: 024\)
\(21\)
\(100\)
\(330\)
\(486\)