9000105404
Level:
B
The parabola \(P\colon y^{2} + 4y + 6x - 5 = 0\) has
two \(y\)-intercepts.
Find their distance.
\(6\)
\(8\)
\(10\)
\(4\)
B
9000101902
Level:
B
Given points \(A = [0;1;2]\),
\(B = [1;2;0]\),
\(C = [1;2;3]\), find the angle
between the lines \(AB\)
and \(AC\).
Round your answer to the nearest degree.
\(90^{\circ }\)
\(0^{\circ }\)
\(30^{\circ }\)
\(60^{\circ }\)
9000105405
Level:
B
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon x^{2} - 4x - 6y - 17 = 0\).
\(y + 5 = 0\)
\(y - 3 = 0\)
\(x + 4 = 0\)
\(x - 2 = 0\)
9000100707
Level:
B
Consider points \(A = [-2;-1]\),
\(B = [1;y]\),
\(C = [3;-4]\). Find the coordinate
\(y\) which ensures
that the vectors \(\overrightarrow{AB } \)
and \(\overrightarrow{AC } \)
are perpendicular.
\(y = 4\)
\(y = -4\)
\(y = 0.8\)
\(y = -0.8\)
9000101706
Level:
B
Factor the following polynomial.
\[
8x^{4} - 48x^{3} + 72x^{2}
\]
\(8x^{2}\left (x - 3\right )^{2}\)
\(- 8x^{2}\left (3 - x\right )^{2}\)
\(8\left (x^{2} - 3\right )^{2}\)
\(8x\left (x^{2} - 3\right )^{2}\)
9000100708
Level:
B
Given points \(A = [-2;-1]\),
\(B = [x;-3]\),
\(C = [4;-4]\), find the coordinate
\(x\) which ensures
that the vectors \(\overrightarrow{AB } \)
and \(\overrightarrow{AC } \)
are parallel.
\(x = 2\)
\(x = 7\)
\(x = -3\)
\(x = 3\)
9000101702
Level:
B
Factor the following polynomial.
\[
3x^{3} + 3x^{2}y + 4xy + 4y^{2}
\]
\(\left (3x^{2} + 4y\right )\left (x + y\right )\)
\(\left (3x + y\right )\left (x^{2} + y^{2}\right )\)
\(\left (3x^{2} + 4\right )\left (x + y^{2}\right )\)
\(\left (3x + y^{2}\right )\left (x + y\right )\)
9000101101
Level:
B
Find the distance from the point \(A = [0;1;-3]\)
to the point \(B = [-1;3;0]\).
\(\sqrt{14}\)
\(3\)
\(4\)
\(\sqrt{26}\)
9000101703
Level:
B
Factor the following polynomial.
\[
\left (5x - y\right )^{2} -\left (x - y\right )^{2}
\]
\(4x\left (6x - 2y\right )\)
\(x\left (5x - y\right )\)
\(6x\left (6x - 2y\right )\)
\(- 32x^{2}\)
9000101102
Level:
B
Find the distance between the point \(A = [1;0;1]\)
and the line \(p\).
\[
\begin{aligned}p\colon x& = 2, &
\\y & = 3t,
\\z & = 1 - t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(1\)
\(0\)
\(2\)
\(3\)