9000121801
Level:
B
Find the number of diagonals in the regular decagon (a regular polygon with
\(10\)
vertices).
\(35\)
\(7\)
\(10\)
\(70\)
B
9000136908
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x + 1\above 0.0pt
x} \right) -\left ({x + 1\above 0.0pt
1} \right) = 1
\]
The equation has no solution.
\(- 1\)
\(1\)
\(2\)
\(0\)
9000121805
Level:
B
For a regular pentagon find the interior angle. In the figure a regular pentagon with an interior angle marked in red is shown.
\(108\)
\(144\)
\(112\)
\(72\)
9000136909
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x + 1\above 0.0pt
x} \right) +\left ({x + 2\above 0.0pt
x + 1}\right) = 19
\]
\(8\)
\(10\)
\(12\)
\(19\)
The equation has no solution.
9000121806
Level:
B
The measure of the interior angle in a regular polygon is \(160^{\circ}\). Find the number of vertices of this polygon. In the figure the interior angle (marked in red) of a regular hexagon is shown.
\(18\)
\(16\)
\(32\)
\(9\)
9000136910
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x\above 0.0pt
0}\right) +\left ({x\above 0.0pt
1}\right) +\left ({x + 1\above 0.0pt
x} \right) = 25
\]
The equation has no solution.
\(9\)
\(1\)
\(5\)
\(7\)
9000121808
Level:
B
The number of diagonals in a polygon is three times bigger than the number of sides
of this polygon. Find the number of vertices of this polygon.
\(9\)
\(12\)
\(6\)
\(15\)
9000128807
Level:
B
The base \(ABCD\) of a square
pyramid \(ABCDV \) has side
\(6\, \mathrm{cm}\). The height of the
pyramid is \(4\, \mathrm{cm}\). Find the
angle between the planes \(DCV \)
and \(ABC\).
Round to two decimal places.
\(53.13^{\circ }\)
\(59.04^{\circ }\)
\(43.31^{\circ }\)
9000138301
Level:
B
Two dices are rolled. Find the probability that the sum of the numbers on both dices does not
exceed the number \(6\).
\(\frac{15}
{36}\doteq 0{.}4167\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{18}
{36}=0{.}5\)
\(\frac{12}
{36}\doteq 0{.}3333\)
9000128808
Level:
B
The base \(ABCD\) of a square
pyramid \(ABCDV \) has side
\(6\, \mathrm{cm}\). The height of the
pyramid is \(4\, \mathrm{cm}\). Find the
angle between the planes \(ADV \)
and \(BCV \).
Round to two decimal places.
\(73.74^{\circ }\)
\(36.87^{\circ }\)
\(61.93^{\circ }\)