9000062410
Level:
B
Find the line perpendicular to the graph of the function
\(f(x) = x^{3}\) at the
point \(T = [-1,y_{0}]\).
\(x + 3y + 4 = 0\)
\(3x - y + 2 = 0\)
\(3x + y - 4 = 0\)
\(x - 3y - 2 = 0\)
B
9000060603
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = -x\),
\(a_{2} = -5\) and
\(a_{3} = 0\) are
three consecutive terms of an arithmetic sequence.
\(x = 10\)
\(x = 0\)
\(x = -5\)
\(x = 5\)
\(x = -10\)
9000046608
Level:
B
Identify an inequality which is true for both
\(x = \frac{\pi } {6}\) and
\(x = -\frac{\pi }{6}\).
\(\cos x > 0\)
\(\sin x > \frac{1}
{2}\)
\(|\mathop{\mathrm{tg}}\nolimits x| < \frac{1}
{2}\)
\(\mathop{\mathrm{cotg}}\nolimits x\leq - 1\)
9000060606
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = 5x + 1\),
\(a_{2} = x\) and
\(a_{3} = 7x + 3\) are
three consecutive terms of an arithmetic sequence.
\(x = -0.4\)
\(x = 0.4\)
\(x = 2.5\)
\(x = -2.5\)
\(x = 5\)
9000060602
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = -12\),
\(a_{2} = x\) and
\(a_{3} = 24\) are
three consecutive terms of an arithmetic sequence.
\(x = 6\)
\(x = 0\)
\(x = 12\)
\(x = -24\)
\(x = -2\)
9000039302
Level:
B
Find \(N\),
the number of the turns, as a function of the other variables in the formula for the
magnetic induction of a solenoid.
\[
B =\mu \frac{NI}
{l}
\]
\(N = \frac{Bl}
{\mu I} \)
\(N = \frac{Bl\mu }
{I} \)
\(N = B -\mu \frac{I}
{l} \)
\(N = \frac{Bl}
{\mu } - I\)
9000045708
Level:
B
Given a regular hexagon with the side
\(a\), find the
radius \(\rho \) of
the circle inscribed to this hexagon.
\(\rho = \frac{a}
{2\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }\)
\(\rho = \frac{2a}
{\mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 60^{\circ }\)
9000039303
Level:
B
Find the time \(t\)
as a function of the other variables in the formula for the distance of a motion in the
form \(s = v_{0}t + s_{0}\).
\(t = \frac{s-s_{0}}
{v_{0}} \)
\(t = \frac{s}
{t+s_{0}} \)
\(t = \frac{s+s_{0}}
{v_{0}} \)
\(t = \frac{v_{0}}
{s-s_{0}} \)
9000046405
Level:
B
A circle is circumscribed to the regular octagon. The perimeter of the octagon is
\(16\, \mathrm{cm}\). Find
the radius of the circle and round the result to two decimal places. (The regular
octagon is a polygon which has eight sides of equal length. The perimeter of the
octagon is the sum of the length of all eight sides.) Circle circumscribed to the regular octagon.
\(2.61\, \mathrm{cm}\)
\(1.08\, \mathrm{cm}\)
\(1.41\, \mathrm{cm}\)
9000039304
Level:
B
Find the focus length \(f\)
as a function of the other variables from the following equation relating this distance with object
and image distances \(a\)
and \(a'\).
\[
\frac{1}
{f} = \frac{1}
{a} + \frac{1}
{a'}
\]
\(f = \frac{aa'}
{a+a'}\)
\(f = \frac{a-a'}
{a+a'}\)
\(f = a + a'\)
\(f = \frac{a}
{a'}\)