9000149710
Level:
B
Find the vertex of the following parabola.
\[
x^{2} - 6x - 12y - 3 = 0
\]
\([3;-1]\)
\([3;1]\)
\([-3;1]\)
\([-3;-1]\)
B
9000149709
Level:
B
Find the vertex of the following parabola.
\[
y^{2} - 12x + 4y + 64 = 0
\]
\([5;-2]\)
\([5;2]\)
\([-5;2]\)
\([-5;-2]\)
9000149305
Level:
B
Given a translation \(T\)
of a plane, find the lines which are mapped to the same line by
\(T\).
All lines parallel to the translation vector are mapped into itself.
All lines perpendicular to the translation vector are mapped into itself.
There are no lines which are mapped into itself by the translation.
Every line is mapped into itself by the translation.
9000149409
Level:
B
Find all lines which are parallel to \(p\colon x - 3y + 2 = 0\)
and the distance from every of these lines to
\(p\) is
\(\sqrt{10}\).
\(p_{1}\colon x - 3y + 12 = 0\),
\(p_{2}\colon x - 3y - 8 = 0\)
\(p\colon x - 3y = 0\)
\(p\colon x - 3y + \sqrt{10} = 0\)
\(p_{1}\colon x - 3y + \sqrt{10} = 0\),
\(p_{2}\colon x - 3y -\sqrt{10} = 0\)
9000149408
Level:
B
On the \(x\)-axis
find the points such that the distance from these points to the line
\(p\colon x - 2y + 2 = 0\) is
\(\sqrt{5}\).
\([3;0]\),
\([-7;0]\)
\([5;0]\)
\(\left [\sqrt{5};0\right ]\),
\(\left [-\sqrt{5};0\right ]\)
\([3;7]\)
9000149708
Level:
B
Find the vertex of the following parabola.
\[
x^{2} + 8x - 4y + 24 = 0
\]
\([-4;2]\)
\([-4;-2]\)
\([4;2]\)
\([4;-2]\)
9000149401
Level:
B
Find the distance from the point \(P = [-4;2]\)
to the line \(3x - 4y - 5 = 0\).
\(5\)
\(1\)
The line contains \(P\).
\(\sqrt{5}\)
9000141508
Level:
B
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
\left({x\above 0.0pt
x}\right) +\left ({x + 1\above 0.0pt
x} \right) +\left ({x + 2\above 0.0pt
x} \right) +\left ({x + 3\above 0.0pt
x} \right) = \frac{x^{3} + 59}
{6}
\]
\(\{1\}\)
\(\{4\}\)
\(\{10\}\)
9000142006
Level:
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ;0)\)
and \((1;\infty )\), concave
down on \((0;1)\), a unique
inflection at \(x = 0\)
concave up on \((-\infty ;0)\)
and \((1;\infty )\), concave
down on \((0;1)\),
inflection at \(x_{1} = 0\)
and \(x_{2} = 1\)
concave up on \((-\infty ;0)\cup (1;\infty )\),
concave down on \((0;1)\), a
unique inflection at \(x = 0\)
concave up on \((0;1)\),
concave down on \((-\infty ;0)\)
and \((1;\infty )\),
inflection at \(x_{1} = 0\)
and \(x_{2} = 1\)
9000141509
Level:
B
Assuming \(x\in \mathbb{N}\),
find the solution set of the following inequality.
\[
2\cdot \left({x - 1\above 0.0pt
x - 3}\right) + x\cdot (x - 9)\leq - 8
\]
\(\{3;4;5\}\)
\(\{1;2;3;4;5\}\)
\([ 1;5] \)