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
\(P\colon x^{2} - 4x - 6y - 17 = 0\).
\(y + 5 = 0\)
\(y - 3 = 0\)
\(x + 4 = 0\)
\(x - 2 = 0\)
9000101904
Level:
B
Find the angle between the \(x\)-axis
and the line \(p\).
\[
\begin{aligned}p\colon x& = 2 - t, &
\\y & = 3t,
\\z & = 1;\ t\in \mathbb{R}
\\ \end{aligned}
\]
Round your answer to the nearest minute.
\(71^{\circ }34'\)
\(0^{\circ }\)
\(69^{\circ }17'\)
\(90^{\circ }\)
9000105406
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
\(P\colon y^{2} + 4y + 4x - 4 = 0\).
\(x - 3 = 0\)
\(x + 4 = 0\)
\(y + 1 = 0\)
\(y - 2 = 0\)
9000101905
Level:
B
The points \(A = [0;5;0]\),
\(B = [5;5;0]\),
\(C = [5;0;0]\),
\(D = [0;0;0]\) define the cube
\(ABCDEFGH\). Find the angle
between the lines \(BF\)
and \(AC\).
Round your answer to the nearest minute.
\(90^{\circ }\)
\(0^{\circ }\)
\(45^{\circ }\)
\(73^{\circ }47'\)
9000105408
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
\(P\colon x^{2} - 8x + 6y + 19 = 0\).
\(y - 1 = 0\)
\(y + 2 = 0\)
\(x + 4 = 0\)
\(x - 3 = 0\)
9000101906
Level:
B
Find the angle between the planes \(\alpha \)
and \(\beta \).
\[
\alpha \colon 2x - 5y + 3z - 4 = 0,\qquad \beta \colon x - 3 = 0
\]
Round your answer to the nearest minute.
\(71^{\circ }4'\)
\(21^{\circ }42'\)
\(82^{\circ }19'\)
\(85^{\circ }2'\)
9000101907
Level:
B
The general plane \(\alpha \)
has the equation
\[
\alpha \colon 3z - 4 = 0
\]
and the plane \(\beta \) has a
normal vector \(\vec{n} = (0;0;1)\). Find
the angle between \(\alpha \)
and \(\beta \)
and round your answer to the nearest degree.
\(0^{\circ }\)
\(30^{\circ }\)
\(45^{\circ }\)
\(90^{\circ }\)
9000101909
Level:
B
Given points \(A = [1;0;2]\),
\(B = [1;0;0]\) and the
plane \(\alpha \),
\[
\alpha \colon 2x - 4y = 0,
\]
find the angle between the line \(AB\)
and the plane \(\alpha \).
Round your answer to the nearest minute.
\(0^{\circ }\)
\(22^{\circ }48'\)
\(45^{\circ }19'\)
\(90^{\circ }\)