9000149308
Level:
B
Consider a rotation through an angle either
\(\alpha = 180^{\circ }\) or
\(\alpha = 360^{\circ }\). How
many lines which are mapped into itself exists for this rotation?
infinitely many
none
one
two
B
9000149401
Level:
B
Find the distance from the point \(P = [-4,2]\)
to the line \(3x - 4y - 5 = 0\).
\(5\)
\(1\)
The line contains \(P\).
\(\sqrt{5}\)
9000149403
Level:
B
Find the distance from the point \(M = [1,1]\)
to the line \(p\).
\[
\begin{aligned}p\colon x& = 3 + t, &
\\y & = 1 + t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(\sqrt{2}\)
\(2\)
\(1\)
\(0\) (the point is
on the line \(p\) )
9000149404
Level:
B
Given points \(A = [-3,13]\),
\(K = [0,4]\),
\(L = [-5,-6]\), find the distance
from the point \(A\)
to the line \(KL\).
\(3\sqrt{5}\)
\(3\)
\(5\)
\(\sqrt{5}\)
9000149405
Level:
B
Find all the values of the parameter
\(c\) so that the distance from the point \(M = [2,-1]\)
to the line \(3x + 4y + c = 0\) is \(5\).
\(c\in \{ - 27,23\}\)
\(c\in \{25\}\)
\(c\in \{5,25\}\)
\(c\in \{ - 25,25\}\)
9000149406
Level:
B
Given points \(A = [2,-5]\),
\(B = [2,3]\) and
\(C = [-4,-1]\), find the length of the altitude of the triangle \(ABC\) through the point \(C\). Hint: The altitude through the point
\(C\) of a triangle
\(ABC\) is the perpendicular line segment drawn from the vertex \(C\) to the line containing the side \(AB\).
\(6\)
\(\sqrt{2}\)
\(\frac{3}
{2}\)
The points \(A\),
\(B\),
\(C\) do
not define a triangle.
9000141502
Level:
B
Let \(A\) be set with
\(n\) mutually different elements.
The number of \(5\)-permutations
with repetition is \(1024\).
Find \(n\). (The term
„\(k\)-permutation
with repetition” stands for an ordered arrangement of
\(k\) objects from
a set of \(n\)
objects, when each object can be chosen more than once.)
\(4\)
\(5\)
\(2\)
9000142004
Level:
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ,1)\),
concave down on \((1,\infty )\),
no inflection
concave up on \((-\infty ,1)\),
concave down on \((1,\infty )\),
inflection at \(x = 1\)
concave up on \((1,\infty )\),
concave down on \((-\infty ,1)\),
inflection at \(x = 1\)
concave up on \((1,\infty )\),
concave down on \((-\infty ,1)\),
no inflection
9000141503
Level:
B
Let \(A\) be a
set with \(n\)
mutually different elements. If two elements are removed from
\(A\), the number of all
permutations of set \(A\)
decreases \(20\)-times.
Find \(n\).
\(5\)
\(4\)
\(5\) or
\(- 4\)
9000142005
Level:
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-1,0)\)
and \((1,\infty )\), concave
down on \((-\infty ,-1)\)
and \((0,1)\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
concave up on \((-1,0)\cup (1,\infty )\),
concave down on \((-\infty ,-1)\cup (0,1)\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
concave up on \((-\infty ,-1)\)
and \((0,1)\), concave
down on \((-1,0)\)
and \((1,\infty )\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
concave up on \((-\infty ,-1)\cup (0,1)\),
concave down on \((-1,0)\cup (1,\infty )\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)