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
A
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.
\[
16x^{2} + 9y^{2} - 32x - 54y - 47 = 0
\]
\([1;3]\)
\([1;-3]\)
\([-1;3]\)
\([-1;-3]\)
9000146205
Level:
A
Factor the following expression.
\[
9a^{6} - 4b^{2}
\]
\(\left (3a^{3} - 2b\right )\left (3a^{3} + 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{3} - 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{2} + 2b\right )\)
\(\left (3a^{3} - 2b\right )\left (3a^{2} - 2b\right )\)
9000146704
Level:
A
Expand the following polynomial.
\[
(3 - x)(x - 2) - (x + 1)(x - 3)
\]
\(- 2x^{2} + 7x - 3\)
\(- 2x^{2} + 3x - 9\)
\(- 2x^{2} + 3x - 3\)
\(- 2x^{2} + 7x - 9\)
9000146703
Level:
A
Expand the following expression.
\[
(a - 2)(5a + 3) - (2a + 1)(3 - a)
\]
\(7a^{2} - 12a - 9\)
\(3a^{2} - 12a - 9\)
\(7a^{2} - 2a - 9\)
\(3a^{2} - 2a - 9\)
9000141905
Level:
A
Given the function \(g\) (see the picture),
find \(\lim _{x\to 1}g(x)\).
\[
g(x)=\begin{cases}
-\frac12(x-1)^2+2 & \text{if } x < 1,\\
\frac2{x^2}+1 & \text{if } x \geq 1
\end{cases}
\]
This limit does not exist.
\(3\)
\(2\)
\(1\)
9000141901
Level:
A
Given the function \(f\),
find \(\lim _{x\to 1}f(x)\).
\[
f(x)=\begin{cases}
x^3+1 & \text{if } x\neq 1,\\
3 & \text{if } x = 1
\end{cases}
\]
\(2\)
\(3\)
\(1\)
Does not exist