9000121002
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(CD\)
and \(BH\).
\(54.74^{\circ }\)
\(60^{\circ }\)
\(35.26^{\circ }\)
\(39.23^{\circ }\)
A
9000120306
Level:
A
The lengths of a side, face diagonal and solid diagonal through the vertex
\(A\) in a rectangular
box \(ABCDEFGH\)
are \(|AB| = 6\, \mathrm{cm}\),
\(|AC| = 10\, \mathrm{cm}\),
\(|AG| = 15\, \mathrm{cm}\). Find
the surface area.
\(\left (96 + 140\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(600\, \mathrm{cm}^{2}\)
\(236\sqrt{5}\, \mathrm{cm}^{2}\)
\(\left (48 + 70\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(240\sqrt{5}\, \mathrm{cm}^{2}\)
9000121008
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(DB\)
and \(AG\).
\(90^{\circ }\)
\(45^{\circ }\)
\(35.26^{\circ }\)
\(53.13^{\circ }\)
9000120301
Level:
A
The length of a solid diagonal in a cube is
\(u = 2\sqrt{6}\, \mathrm{cm}\). Find
the surface area.
\(48\, \mathrm{cm}^{2}\)
\(24\, \mathrm{cm}^{2}\)
\(24\sqrt{2}\, \mathrm{cm}^{2}\)
\(16\sqrt{2}\, \mathrm{cm}^{2}\)
\(12\sqrt{6}\, \mathrm{cm}^{2}\)
9000121701
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(3\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
isosceles
equilateral
right
obtuse
9000117403
Level:
A
Determine whether the following planes
\(\rho \) and
\(\sigma \) are
parallel, identical or intersecting.
\[
\begin{aligned}[t] \rho \colon &x = -u + v, &
\\&y = u + 2v,
\\&z = -u - v;\ u,v\in \mathbb{R},
\\ \end{aligned}\qquad \sigma \colon x-2y-3z+1 = 0
\]
parallel, not identical
identical
intersecting
9000121702
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(3\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(5\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
right
isosceles
equilateral
obtuse
9000120302
Level:
A
A cuboid has sides \(a = 5\, \mathrm{cm}\),
\(b = 8\, \mathrm{cm}\), and
\(c = \sqrt{111}\, \mathrm{cm}\). Find the length of the cuboid’s space diagonal \(u\) (see the picture).
\(10\sqrt{2}\, \mathrm{cm}\)
\(\sqrt{222}\, \mathrm{cm}\)
\(20\, \mathrm{cm}\)
\(2\sqrt{10}\, \mathrm{cm}\)
\(5\sqrt{7}\, \mathrm{cm}\)
9000121703
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(4\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
equilateral
isosceles
right
obtuse
9000120309
Level:
A
The sides of a rectangular box shown in the picture are \(a = 3\, \mathrm{cm}\),
\(b = 4\, \mathrm{cm}\), and
\(c = 12\, \mathrm{cm}\). The space diagonal
is \(u_{t}\) and the longest
face diagonal is \(u_{s}\).
Find the ratio \(u_{t} : u_{s}\).
\(13\sqrt{10} : 40\)
\(13 : \sqrt{153}\)
\(13 : 12\)
\(4\sqrt{10} : 5\)
\(4\sqrt{10} : 13\)