C

9000153303

Level: 
C
A student performed repeated measurements of a length (in meters) and evaluated the main statistical characteristics: mean, standard deviation, variance and the coefficient of variation. Unit of which of these characteristics is meter?
the mean and the standard deviation
only the variance
only the standard deviation
only the mean
the standard deviation and the variance
the standard deviation, the variance and the coefficient of variation

9000150505

Level: 
C
The iron support has the shape of the right triangle \(ABC\) with the side \(AB\) of the length \(30\, \mathrm{cm}\) and the hypotenuse \(AC\) of the length \(50\, \mathrm{cm}\) (see the picture). The maximal allowed force \(F_{1}\) on \(AB\) is \(270\, \mathrm{N}\). Find the maximal force \(G\) allowed at the point \(A\). Hint: The load \(G\) at the point \(A\) can be decomposed to the direction of the hypotenuse and the other side of the triangle as shown in the picture.
\(360\, \mathrm{N}\)
\(450\, \mathrm{N}\)
\(540\, \mathrm{N}\)
\(162\, \mathrm{N}\)

9000150503

Level: 
C
A pendulum constituted of a rope of the length \(l\) and a body is displaced from it's equilibrium. The force due to gravity on the body \(F_{g} = 20\, \mathrm{N}\). The body is higher by \(h = 10\, \mathrm{cm}\) in the displaced position (comparing to the equilibrium position). The tension in the rope in the displaced position is \(F_{1} = 12\, \mathrm{N}\). Find the length of the rope \(l\). Hint: Using a parallelogram, the force of gravity on the body can be decomposed into a force \(F_{1}\) in the direction of the rope and \(F_{2}\) in the perpendicular direction.
\(25\, \mathrm{cm}\)
\(25\, \mathrm{m}\)
\(6\, \mathrm{cm}\)
\(16\frac{2} {3}\, \mathrm{cm}\)

9000146710

Level: 
C
Divide the following two polynomials using long division. \[ \left (x^{3} + 3x^{2} - x + 4\right ) : \left (x^{2} - x + 1\right ) \]
\(x + 4 + \frac{2x} {x^{2}-x+1}\)
\(x + 4 + \frac{2x+8} {x^{2}-x+1}\)
\(x + 2 + \frac{6-2x} {x^{2}-x+1}\)
\(x + 2 + \frac{2x+2} {x^{2}-x+1}\)

9000149309

Level: 
C
Consider a dilatation which maps \(A\) onto \(B\). The center is the dilatation is \(S\). Find a correct statement.
The point \(S\) is on the line through the points \(A\) and \(B\).
The points \(S\), \(A\) and \(B\) form a right triangle \(ABS\).
The distance from \(S\) to \(A\) is smaller than the distance from \(A\) to \(B\).
The points \(S\), \(A\) and \(B\) form a triangle \(ABS\) with at least two sides of equal length.

9000150104

Level: 
C
Evaluate the following integral on \(\mathbb{R}\). \[ \int \cos x\cdot \left (-3 +\sin x\right )^{5}\, \mathrm{d}x \]
\(\frac{\left (-3+\sin x\right )^{6}} {6} + c\text{, }c\in \mathbb{R}\)
\(6\left (-3 +\sin x\right )^{6} + c,\ c\in \mathbb{R}\)
\(\frac{\left (-3+\cos x\right )^{6}} {6} + c,\ c\in \mathbb{R}\)
\(6\left (-3 +\cos x\right )^{6} + c,\ c\in \mathbb{R}\)