C

1003197403

Level: 
C
An express train of length \( 150\,\mathrm{m} \) travels at the constant speed of \( 144\,\mathrm{kph} \). On a parallel track in the opposite direction travels a freight train of length \( 240\,\mathrm{m} \) at the constant speed of \( 90\,\mathrm{kph} \). How long does it take for trains to pass each other?
\( 6\,\mathrm{s} \)
\( 1.\overline{6}\,\mathrm{s} \)
\( 7.\overline{2} \)
\( 26\,\mathrm{s} \)

1003197402

Level: 
C
Paul rides the bike at a constant speed of \( 18\,\mathrm{kph} \). Eighteen minutes after Paul starts his trip, Tom takes the same route on a motorbike at an average speed of \( 40\,\mathrm{kph} \). How far behind Paul will Tom be after \( 12 \) minutes of his ride?
\( 1\,\mathrm{km} \)
\( 60\,\mathrm{km} \)
\( 14\,\mathrm{km} \)
after \( 12 \) minutes of ride Tom will be in front of Paul

1003197401

Level: 
C
A man on a bike rides to a distant city at an average speed of \( 24\,\mathrm{kph} \). He will end the trip \( 12 \) minutes earlier, if he increases his average speed by \( 1\,\mathrm{kph} \). How distant is the city?
\( 120\,\mathrm{km} \)
\( 115.2\,\mathrm{km} \)
\( 300\,\mathrm{km} \)
\( 125\,\mathrm{km} \)

1003124806

Level: 
C
We should fence the land in a shape of an equilateral triangle. Choose the function that describes the dependence of the fenced land area \( S \) (in square meters) on the length \( d \) (in meters) of the fence used.
\( S=\frac{\sqrt3}{36} d^2 \)
\( S=\frac{\sqrt3}{18} d^2 \)
\( S=\frac{\sqrt3}4 d^2 \)
\( S=\frac1{36} d^2 \)

1003124805

Level: 
C
On a spool of mass \( 0.5\,\mathrm{kg} \) is winded an aluminium wire of length \( 100\,\mathrm{m} \). Choose the function that describes the dependence of a mass of the spool with the wire \( m \) (in kilograms) on a diameter of the wire \( d \) (in millimetres). Wire density is \( 2\,700\frac{kg}{m^3} \). \[ \] Hint: The density of an object is defined as the ratio of the mass and the volume of the object.
\( m=\frac{27\pi}{400} d^2+0.5 \)
\( m= 67 500\pi d^2+0.5 \)
\( m=\frac{27\pi}{400} d^2-0.5 \)
\( m=\frac{27\pi}{200} d^2+0.5 \)

1003124804

Level: 
C
In the centre of a square shaped square there is a water fountain. The fountain has a square ground plan with the side length \( 4.5\,\mathrm{m} \). The square should be paved with cobblestones of size \( 25\,\mathrm{cm} \times 25\,\mathrm{cm} \). Choose the function that describes the dependence of the number of cobblestones needed (\( n \)) on the length of the square (\( a \)) given in meters.
\( n=16a^2-324 \)
\( n=\frac{a^2}{625}-324 \)
\( n=16a^2-625 \)
\( n=\frac{a^2}{16}-324 \)

1003124803

Level: 
C
The annulus shaped component parts are punched from sheet metal. Diameter of the circular hole is \( 25\,\% \) of the diameter of the whole component part. Choose the function that describes the dependence of the area (\( S \)) of material used to produce one component part on its outside diameter (\( d \)).
\( S=\frac{15}{64}\,\pi d^2 \)
\( S=\frac38\,\pi d^2 \)
\( S=\frac{15}{32}\,\pi d^2 \)
\( S=\frac{31}{64}\,\pi d^2 \)

1003124802

Level: 
C
We want to plant flowers into rectangular flower bed with longer side by one meter longer than its shorter side. Each flower needs \( 1\,\mathrm{dm}^2 \) of free space. From the following functions, choose the one that describes the dependence of the number of planted flowers \( n \) on the length \( a \) of the shorter side of the flower bed. (Assume that the dimensions of the flower bed are given in whole meters.)
\( n=\left(a^2+a\right)\cdot100 \)
\( n=\left(a^2+a\right)\cdot\frac1{100} \)
\( n=(a+1)^2\cdot100 \)
\( n=\left(a^2+a\right) \)

1003124801

Level: 
C
Suppose we want to paint a cube so that there remains an unpainted stripe along all the edges on each face. The width of the stripe should be \( 1\,\mathrm{cm} \). The producer gives the paint consumption \( 100\,\mathrm{ml}/1\,\mathrm{m}^2 \). From the following functions choose the one that describes the dependence of the paint consumption \( V \) on the length of the cube edge \( a \). The paint consumption \( V \) is given in millilitres and the length of the cube edge \( a \) is given in meters.
\( V=\left(a-\frac1{50}\right)^2\cdot600 \)
\( V=\left(a-\frac1{50}\right)^2\cdot\frac3{50} \)
\( V=\left(a-\frac1{100}\right)^2\cdot600 \)
\( V=(a-2)^2\cdot100 \)

1103077011

Level: 
C
Consider a triangle \( ABC \) with \( a=1\,\mathrm{cm} \) and \( b = \sqrt3\,\mathrm{cm} \). The angle opposite the longer side is double the angle opposite the shorter side. Find the area of the triangle.
\( \frac{\sqrt3}2\,\mathrm{cm}^2 \)
\( 2\sqrt3\,\mathrm{cm}^2 \)
\( \sqrt3\,\mathrm{cm}^2 \)
\( \frac{\sqrt3}4\,\mathrm{cm}^2 \)