9000149701
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} - 4x + 6y - 12 = 0
\]
\([2;-3]\)
\([-2;3]\)
\([2;3]\)
\([-2;-3]\)
A
9000149301
Level:
A
Which of the following is true for a reflection through a line?
It is a congruent mapping (preserves shapes and dimensions).
It is a similar mapping (preserves shapes, may change dimensions and position).
It is an identity mapping (objects are mapped to itself).
9000149702
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} + 2x - 8y + 13 = 0
\]
\([-1;4]\)
\([-1;-4]\)
\([1;4]\)
\([1;-4]\)
9000149302
Level:
A
Given a line in a plane, find how many points are mapped onto itself with reflection
through this line.
infinitely many
none
one
two
9000149703
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} - 10x - 2y + 10 = 0
\]
\([5;1]\)
\([5;-1]\)
\([-5;1]\)
\([-5;-1]\)
9000149303
Level:
A
Which of the following answers contains three letters with point symmetry? (A letter
has a point of symmetry if there exists a point, such that the reflection through this
point maps the letter into itself.)
O, N, Z
A, M, O
A, O, B
H, O, U
9000149704
Level:
A
Find the center of the following ellipse.
\[
9x^{2} + 4y^{2} + 54x - 32y + 109 = 0
\]
\([-3;4]\)
\([-3;-4]\)
\([3;4]\)
\([3;-4]\)
9000149705
Level:
A
Find the center of the following ellipse.
\[
16x^{2} + 9y^{2} - 32x - 54y - 47 = 0
\]
\([1;3]\)
\([1;-3]\)
\([-1;3]\)
\([-1;-3]\)
9000148910
Level:
A
The player throws a dice in a desktop game. If he gets the number
\(6\), he
throws again and his score is the sum of both numbers. Find how many possibilities
are there for the player's score.
\(5 + 6=11\)
\(2\cdot 6=12\)
\(1 + 6=7\)
\(6\cdot 6=36\)
9000148901
Level:
A
The current Czech vehicle registration plate number has the form NLN-NNNN, where N stands
for a digit from \(0\)
to \(9\)
and L stands for a letter from an alphabet containing
\(26\)
letters. How many different registration plates are possible?
\(26\cdot 10^{6}\)
\(10^{6}\)
\(15\cdot 10^{6} + 6\cdot 10^{5}= 156\cdot 10^{5}\)
\(16\cdot 10^{6}\)