9000078901
Level:
B
If we increase an unknown number \(x\)
by \(5\, \%\), we
get \(378\).
Find \(x\).
\(360\)
\(359.1\)
\(396.9\)
\(350\)
B
9000078910
Level:
B
There is \(19\)
girls and \(12\)
boys in the class. Find the difference between the percentage of the girls and boys in
this class.
\(22.6\, \%\)
\(15.1\, \%\)
\(18.5\, \%\)
\(23.5\, \%\)
9000073401
Level:
B
In the following list identify the expression which equals
\(3.3\overline{12}\).
\(3.3 +\sum _{ n=1}^{\infty }12\cdot 10^{-2n-1}\)
\(3 +\sum _{ n=1}^{\infty }312\cdot 10^{-2n-1}\)
\(3 +\sum _{ n=1}^{\infty }312\cdot 10^{-3n}\)
\(3.3 +\sum _{ n=1}^{\infty }12\cdot 10^{-3n}\)
9000073006
Level:
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\).
Let \(q\) be the quotient
and \(s_{n}\) be the sum
of the first \(n\)
terms. Given \(a_{1} = 1\)
and \(a_{4} = -8\),
find the sum of the first five terms of the sequence.
\(s_{5} = 11\)
\(s_{5} = 31\)
\(s_{5} = 16\)
\(s_{5} = -16\)
9000073408
Level:
B
Find the values of \(x\)
which ensure that the following infinite series is convergent.
\[
\sum _{n=1}^{\infty }\log ^{n-1}x
\]
\(x\in \left ( \frac{1}
{10},10\right )\)
\(x\in (1,+\infty )\)
\(x\in (1,10)\)
\(x\in \mathbb{R}^{+}\)
9000073402
Level:
B
In the following list identify the expression which equals
\(- 1.0\overline{345}\).
\(- 1 -\sum _{n=1}^{\infty }345\cdot 10^{-3n-1}\)
\(- 1 -\sum _{n=1}^{\infty }345\cdot 10^{-3n}\)
\(-\sum _{n=1}^{\infty }(10 + 345\cdot 10^{-3n-1})\)
\(1 -\sum _{n=1}^{\infty }345\cdot 10^{-3n}\)
9000072801
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
2\, ,\ 4\, ,\ x
\]
\(8\)
\(5\)
\(6\)
\(16\)
9000073403
Level:
B
Find the sum of the following infinite series.
\[
-5\cdot 10^{-1} - 5\cdot 10^{-2} - 5\cdot 10^{-3} - 5\cdot 10^{-4}-\cdots
\]
\(- 0.\overline{5}\)
\(- 0.0\overline{5}\)
\(0\)
\(0.\overline{5}\)
9000072804
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
x\, ,\ a\, ,\ 3\, ,\ b\, ,\ 9
\]
\(1\)
\(- 1\)
\(- 3\)
\(\sqrt{3}\)
9000076001
Level:
B
In the following list identify a set of a numbers which give remainder
\(2\) after division by
\(3\), i.e. the numbers can
be written in the form \(3k + 2\),
\(k\in \mathbb{N}_{0}\).
\(5,\ 8,\ 11\)
\(5,\ 10,\ 15\)
\(3,\ 6,\ 9\)
\(15,\ 25,\ 30\)
\(4,\ 5,\ 6\)