9000091207
Level:
A
Consider the circle \(k\colon x^{2} - 6x + y^{2} + 2y + 6 = 0\).
Find the center of the circle.
\(S = [3;-1]\)
\(S = [-3;-1]\)
\(S = [3;1]\)
\(S = [-3;1]\)
A
9000091208
Level:
A
Consider the circle \(k\colon x^{2} + 2x + y^{2} - 4y + 2 = 0\).
Find the center of the circle.
\(S = [-1;2]\)
\(S = [-1;-2]\)
\(S = [1;-2]\)
\(S = [1;2]\)
9000091209
Level:
A
Consider the circle \(k\colon x^{2} - 6x + y^{2} + 4y + 9 = 0\).
Find the center of the circle.
\(S = [3;-2]\)
\(S = [-3;-2]\)
\(S = [3;2]\)
\(S = [-3;2]\)
9000091210
Level:
A
Consider the circle \(k\colon x^{2} + 8x + y^{2} - 2y + 12 = 0\).
Find the center of the circle.
\(S = [-4;1]\)
\(S = [-4;-1]\)
\(S = [4;1]\)
\(S = [4;-1]\)
9000091203
Level:
A
Consider the circle \(x^{2} - 2x + y^{2} - 6y + 8 = 0\).
Find the radius of the circle.
\(\sqrt{2}\)
\(2\)
\(3\)
\(4\)
9000100703
Level:
A
Given the vectors \(\vec{a}\),
\(\vec{b}\), and
\(\vec{c}\), find
\(2\vec{a} + 3\vec{b} -\vec{ c}\).
\((13;-5)\)
\((7;-5)\)
\((7;7)\)
\((7;0)\)
9000100701
Level:
A
Given vectors \(\vec{a}\),
\(\vec{b}\),
\(\vec{c}\),
\(\vec{d}\), find
\(\vec{a} +\vec{ b} +\vec{ c} +\vec{ d}\).
\((-1;-2)\)
\((17;7)\)
\((6;10)\)
\((2;-3)\)
9000100702
Level:
A
Given vectors \(\vec{a} = (x;-1)\),
\(\vec{b} = (3;y)\), find
\(x\) and
\(y\) such
that \(2\vec{a} - 3\vec{b} = (-5;4)\).
\(x = 2\),
\(y = -2\)
\(x = -2\),
\(y = 2\)
\(x = 2\),
\(y = 5\)
\(x = 2\),
\(y = 2\)
9000088810
Level:
A
Simplify the following expression.
\[
\left (x -\frac{1}
{x}\right )\cdot \left (1 - \frac{x}
{x + 1}\right )
\]
\(\frac{x - 1}
{x} \)
\(\frac{x - 1}
{x + 1}\)
\(\frac{1 - x}
{x + 1}\)
\(\frac{1 - x}
{x} \)
9000091201
Level:
A
Consider the circle \(k\colon x^{2} - 4x + y^{2} + 6y + 12 = 0\).
Find the radius of the circle.
\(1\)
\(2\)
\(3\)
\(4\)