9000021704
Level:
B
Solve the following inequality.
\[
\frac{x + 1}
{4} -\frac{x + 2}
{3} > \frac{x + 3}
{6} -\frac{3x - 4}
{12}
\]
\(x\in \emptyset \)
\(x\in \mathbb{R}\)
\(x\in (-\infty ;29)\)
\(x\in \{0\}\)
B
9000020406
Level:
B
The ratio of the sides of a rectangle is
\(3 : 4\). The length of
the diagonal is \(100\, \mathrm{cm}\).
Find the perimeter of the rectangle.
\(280\, \mathrm{cm}\)
\(150\, \mathrm{cm}\)
\(480\, \mathrm{cm}\)
\(300\, \mathrm{cm}\)
9000018104
Level:
B
Find the maximal integer which solves the following inequality.
\[
1 - 3x > 3\left (4 - x\right ) + 2x
\]
\(- 6\)
\(- 5\)
\(- 3\)
\(- 2\)
9000014803
Level:
B
The graph of the function \(f(x) = 6x^{2} + 3\) is a parabola. Which of the following points is the vertex of this parabola?
\([0;3]\)
\([3;0]\)
\([1;9]\)
\([1;2]\)
9000018106
Level:
B
Find the set of all the positive integers
\(x\) for which the
expression \(\frac{3x-7}
{14} \) is
smaller than \(\frac{7-2x}
{7} \).
\(\left \{1;2\right \}\)
\(\left \{1;2;3;4\right \}\)
\(\left \{1;2;3\right \}\)
\(\left \{1\right \}\)
9000014804
Level:
B
The graph of the function \(f(x) = x^{2} - 4x + 13\) is a parabola. Which of the following points is the vertex of this parabola?
\([2;9]\)
\([-2;13]\)
\([-4;13]\)
\([0;13]\)
9000018107
Level:
B
Solve the following inequality in the set of negative integers.
\[
\frac{x}
{6} + \frac{3x - 2}
{2} > -5
\]
\(x\in \left \{-2;-1\right \}\)
\(x\in \left \{-3;-2;-1\right \}\)
\(x\in \left \{-3;-2\right \}\)
\(x\in \left \{-1\right \}\)
9000014805
Level:
B
Find the minimum value of the quadratic function
\(f(x)= 4x^{2} - 4x + 7\).
\(6\)
\(7\)
does not exist
\(- 4\)
9000019805
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^{4} + 2x^{2} + 1 = 0
\]
\(\emptyset \)
\(\left \{-1;1\right \}\)
\(\left \{-2;2\right \}\)
\(\left \{0\right \}\)
9000018004
Level:
B
Find the maximal integer which satisfies the following inequality:
\[
2x - 5 < 4 - x
\]
\(2\)
\(- 3\)
\(- 2\)
\(3\)