2000000203
Level:
B
Solve the following inequality.
\[
(x+1)^{2}>0
\]
\(x \in \mathbb{R}\setminus \{-1\}\)
\(x \in \mathbb{R}\setminus \{1\}\)
\(x \in (-1 ;1)\)
\(x \in (-\infty ;-1)\cup (1;\infty )\)
B
2000000202
Level:
B
Solve the following inequality.
\[
x^{2} + 9\leq 0
\]
\(x \in \emptyset \)
\(x \in \mathbb{R}\)
\(x \in (-3 ;3)\)
\(x \in (-\infty ;-3)\cup (3;\infty )\)
2000000201
Level:
B
Solve the following inequality.
\[
x^2+1>0
\]
\(x \in \mathbb{R}\)
\(x \in \emptyset \)
\(x \in (-1;1)\)
\(x \in (-\infty ;-1)\cup (1;\infty )\)
1003085210
Level:
B
The common difference of an arithmetic sequence $\{a_n\}_{n=1}^{\infty}$ is $-\mathrm{e}$. Find the second term, if the sum of the $4$th term up to $9$th term is $6\pi-27\mathrm{e}$.
$\pi$
$\pi+\mathrm{e}$
$\pi-\mathrm{e}$
$\pi-2\mathrm{e}$
$\mathrm{e}-\pi$
1003085209
Level:
B
The sum of the $2$nd and the $4$th term of an arithmetic sequence is $1.2$, the sum of the first $10$ terms is $3.5$. Find the first term.
$0.8$
$0.3$
$0.35$
$-0.1$
$-0.5$
1003085207
Level:
B
Given an arithmetic sequence $\{a_n\}_{n=1}^{\infty}$, where $a_5=\frac{11}2$, $a_{10}=-2$ and $s_k=a_1+\dots+a_k=15$, find $k$.
$15$
$11$
$10$
$9$
$13$
1003085206
Level:
B
Find the sum of the first $15$ positive terms of the arithmetic sequence: $\left(3n-7\right)_{n=1}^{\infty}$.
$345$
$255$
$238$
$260$
$322$
1003085205
Level:
B
Find the sum of the $10$th up to $20$th term of an arithmetic sequence given by: $a_{n+1}=a_n+2$ for all $n\in\mathbb{N}$ and $a_1=-4$.
$264$
$240$
$480$
$-320$
$-352$
1003085204
Level:
B
Evaluate the sum: $\sum\limits_{n=3}^{15}(-2n+5)$.
$-169$
$299$
$-156$
$-338$
$-312$
1003085203
Level:
B
What is the sum of all positive multiples of $7$ smaller than $100$?
$735$
$637$
$728$
$105$
$686$