2010007905
Level:
B
Find all \(x\) such that the expression \( 2x^2+8\) is negative.
No such \(x\)
exists.
\(x\in \mathbb{R}\)
\(x\in (-2;2)\)
\(x\in (-\infty ;-2)\cup (2;+\infty )\)
Quadratic equations and inequalities
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.
2010007903
Level:
A
Choose the interval which contains all the solutions of the following quadratic
equation.
\[
6x^{2} + 13x +5 = 0
\]
\(\left(-2;-\frac12 \right]\)
\(\left[ \frac12;2 \right)\)
\(\left(-\frac32; \frac12 \right]\)
\(\left(-1;\frac53 \right]\)
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.
\(x^{2} - 3x -10 > 0\)
\(x^{2} + 3x -10 > 0\)
\(x^{2} - 3x -10 < 0\)
\(x^{2} + 3x -10 < 0\)
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.
\(315\, \mathrm{cm}^2\)
\(777\, \mathrm{cm}^2\)
\(140\, \mathrm{cm}^2\)
\(135\, \mathrm{cm}^2\)
2010007304
Level:
C
Which of the given sets contains exactly all non-negative integers that satisfy the inequality \( \sqrt{(3x+6)^2} \leq 12 \)?
\( \{0;1;2\} \)
\( \{0;1;2;3;4;5;6\} \)
\( \{2;3;4;5\} \)
\( \{1;2\} \)
2010007303
Level:
B
The area of the rectangle is \( 735\,\mathrm{cm}^2 \). Its length is by \( 14\,\mathrm{cm} \) longer than its width. Find the perimeter of the rectangle.
\( 112\,\mathrm{cm} \)
\( 56\,\mathrm{cm} \)
\( 252\,\mathrm{cm} \)
\( 92\,\mathrm{cm} \)
2010007302
Level:
C
The surface area of a cuboid is \( 19\,942\,\mathrm{cm}^2 \). Its dimensions are in the ratio \( 2:5:7 \). Find the volume of the cuboid.
\( 153\,790\,\mathrm{cm}^3 \)
\( 615\,160\,\mathrm{cm}^3 \)
\( 76\,895\,\mathrm{cm}^3 \)
\( 175\,760\,\mathrm{cm}^3 \)
2010004505
Level:
B
Find all the values of \(x\)
at which the following expression attains negative value.
\[
2 x^{2} - 7x - 4
\]
\(x\in \left (-\frac{1}{2};4 \right )\)
\(x\in \left (-\infty ;-\frac{1}{2} \right )\cup \left (4;\infty \right )\)
\(x\in \left( -4;\frac{1}{2}\right) \)
\(x\in \left (-\infty ;-4\right )\cup \left (\frac{1}{2};\infty \right )\)
\(x\in \left( -4;-\frac{1}{2}\right) \)