9000076008
Level:
B
Complete the statement. „The sum of any five consecutive integers ...”
is divisible by \(5\).
is divisible by \(3\).
is divisible by \(4\).
is divisible by \(6\).
is divisible by \(10\).
B
9000079208
Level:
B
Assuming \(x\neq 0\)
and \(y\neq 0\),
simplify the following expression.
\[
\left (\frac{x^{-2}y^{2}}
{x^{0}y^{-8}}\right )^{-2} : \frac{x^{2}}
{x^{-4}y^{7}}
\]
\(\frac{1}
{x^{2}y^{13}} \)
\(\frac{y^{13}}
{x^{2}} \)
\(\frac{y^{15}}
{x^{6}} \)
\(\frac{x^{4}}
{y^{27}} \)
9000076009
Level:
B
In the following list identify a set of the numbers where all the numbers are primes.
\(3,\ 7,\ 89\)
\(7,\ 15,\ 17\)
\(8,\ 11,\ 17\)
\(2,\ 7,\ 91\)
\(3,\ 27,\ 81\)
9000079204
Level:
B
Find the domain of the following expression.
\[
\frac{x^{2} - x}
{x + 1} : \frac{x^{2} - 1}
{x^{2} + 2x + 1}
\]
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\setminus \{ - 1;0;1\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1;0\}\)
9000076010
Level:
B
In the following list identify a set of the numbers where
any number has exactly three divisors (including the number
\(1\) and
itself).
\(4,\ 25,\ 289\)
\(1,\ 2,\ 3\)
\(25,\ 36,\ 49\)
\(1,\ 17,\ 289\)
\(25,\ 36,\ 121\)
9000079202
Level:
B
Find the set \(M\)
of all the real \(x\)
for which the following expression is not a well defined number.
\[
\frac{x - 4}
{x^{3} - 16x}
\]
\(M = \{ - 4;0;4\}\)
\(M = \{ - 4;4\}\)
\(M = \{0;4\}\)
\(M = \{0\}\)
9000078507
Level:
B
Assuming \(x\in \left (-\frac{1}
{2};6\right )\),
simplify the following expression.
\[
3 -|6 - x| + |2x + 1|
\]
\(3x - 2\)
\(x - 2\)
\(3x + 10\)
\(x + 8\)
9000078505
Level:
B
Assuming \(x\in (0;\infty )\),
simplify the following expression.
\[
3x -|2x|-|- x|
\]
\(0\)
\(2x\)
\(3x\)
\(4x\)
9000078902
Level:
B
If we decrease an unknown number \(x\)
by \(14\, \%\), we
get \(602\).
Find \(x\).
\(700\)
\(686.28\)
\(517.72\)
\(680\)
9000080902
Level:
B
Given the sets \(A = \{x\in \mathbb{Z}:x\geq - 2\}\)
and \(B = \{x\in \mathbb{N}: x\leq 5\}\) find the intersection \(A \cap B\).
\(\{1;2;3;4;5\}\)
\(\{0;1;2;3;4;5\}\)
\(\{0;1;2;3;4\}\)
\(\{ - 2;-1;0;1;2;3;4;5\}\)