2010007904
Level:
B
Find out, how many integer solutions the following inequality has.
\[
x^{2} + 3x - 1 \leq 0
\]
More than three integer solutions.
Three integer solutions.
Less than three integer solutions.
B
2010007902
Level:
B
For an integer variable \(x\),
find the solution set of the following quadratic inequality.
\[
2x^{2} +5x - 12 < 0
\]
\(\{ -3,-2,-1,0,1\}\)
\(\{-4, -3,-2,-1,0,1\}\)
\(\{-4, -3,-2,-1,0,1,2\}\)
\(\{-1,0,1,2,3\}\)
2010007901
Level:
B
The solution set of one of the following inequalities is
\( \left( -\infty, -2\right) \cup \left( 5, \infty \right) \).
Identify this inequality.
\(x^{2} - 3x -10 > 0\)
\(x^{2} + 3x -10 > 0\)
\(x^{2} - 3x -10 < 0\)
\(x^{2} + 3x -10 < 0\)
2010007705
Level:
B
Find the solution of the inequality.
\[
\sqrt{-x^2+x+2}\geq 4
\]
\(x\in\emptyset\)
\(x\in [ -3,4]\)
\(x\in\mathbb{R}\)
\(x\in [ -1,2]\)
2010007605
Level:
B
For \(n\in \mathbb{N}\), the difference \(\left({n+1\above 0.0pt
n} \right) -\left ({ n+1\above 0.0pt
n+1}\right)\)
equals to:
\(n\)
\(0\)
\(n+1\)
\(2(n+1)\)
2010007604
Level:
B
The sum \(\left({19\above 0.0pt
6} \right) +\left ({19\above 0.0pt
7} \right)\) equals to:
\(\left({20\above 0.0pt
7} \right)\)
\(\left({20\above 0.0pt
6} \right)\)
\(\left({19\above 0.0pt
8} \right)\)
\(\left({38\above 0.0pt
13} \right)\)
2010007503
Level:
B
The number \( 2\cdot6\cdot11 \) has exactly:
twelve positive integer divisors
six positive integer divisors
four positive integer divisors
ten positive integer divisors
2010007502
Level:
B
The number \( 3\cdot4\cdot11 \) has exactly:
twelve positive integer divisors
six positive integer divisors
four positive integer divisors
ten positive integer divisors
2010007501
Level:
B
The number \( 3\cdot7\cdot13 \) has exactly:
eight positive integer divisors
six positive integer divisors
three positive integer divisors
five positive integer divisors
2010007305
Level:
B
One side of a rectangle is \(40\, \%\) longer than the other. The length of the diagonal is \(\sqrt{666}\,\mathrm{cm}\). Find the area of the rectangle.
\(315\, \mathrm{cm}^2\)
\(777\, \mathrm{cm}^2\)
\(140\, \mathrm{cm}^2\)
\(135\, \mathrm{cm}^2\)