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 \(A \cap B\).
\(\{1;2;3;4;5\}\)
\(\{0;1;2;3;4;5\}\)
\(\{0;1;2;3;4\}\)
\(\{ - 2;-1;0;1;2;3;4;5\}\)
B
9000078903
Level:
B
The number \(234\)
is by \(20\, \%\) bigger
than \(x\).
Find \(x\).
\(195\)
\(187.2\)
\(280.8\)
\(205\)
9000080904
Level:
B
Given the sets \(A =\mathbb{N}\)
and \(B = \{x\in \mathbb{Z}\colon x > 8\}\),
find the union \(A\cup B\).
\(\mathbb{N}\)
\(\emptyset \)
\(\{x\in \mathbb{Z};x > 8\}\)
\(\mathbb{Z}\)
9000072705
Level:
B
We are given four consecutive terms of an arithmetic sequence. Find
\(x\).
\[
3\, ,\ a\, ,\ 0\, ,\ x
\]
\(x = -1.5\)
\(x = -3\)
\(x = 6\)
\(x = -6\)
9000073002
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 \(a_{6} = 5\)
and \(q = 1\),
find the sum of the first five terms of the sequence.
\(s_{5} = 25\)
\(s_{5} = 31\)
\(s_{5} = 6\)
\(s_{5} = 30\)
9000072708
Level:
B
We are given six consecutive terms of an arithmetic sequence. Find
\(x\).
\[
\frac52,\ a,\ x,\ b,\ c,\ 5
\]
\(x = 3.5\)
\(x = 3\)
\(x = 4\)
\(x = 3.75\)
9000072806
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
2\, ,\ 1\, ,\ a\, ,\ x
\]
\(\frac{1}
{4}\)
\(\frac{1}
{2}\)
\(-\frac{1}
{2}\)
\(- 1\)
9000073408
Level:
B
Find the values of \(x\)
which ensure that the following infinite series is convergent.
\[
\sum _{n=1}^{\infty }\log ^{n-1}x
\]
\(x\in \left ( \frac{1}
{10};10\right )\)
\(x\in (1;+\infty )\)
\(x\in (1;10)\)
\(x\in \mathbb{R}^{+}\)
9000073407
Level:
B
Find all the values of \(x\)
such that the following infinite series is convergent.
\[
1 + 3 - 2x + (3 - 2x)^{2} + (3 - 2x)^{3}+\cdots
\]
\(x\in (1;2)\)
\(x\in (-\infty ;-1)\)
\(x\in (1;+\infty )\)
\(x\in \mathbb{R}\)
9000072701
Level:
B
The following numbers form an arithmetic sequence. Find
\(x\).
\[
1\, ,\ x\, ,\ 3
\]
\(x = 2\)
\(x = -2\)
\(x = 2.5\)
\(x = 1.5\)