C

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.
\( V=\left(a-\frac1{50}\right)^2\cdot600 \)
\( V=\left(a-\frac1{50}\right)^2\cdot\frac3{50} \)
\( V=\left(a-\frac1{100}\right)^2\cdot600 \)
\( V=(a-2)^2\cdot100 \)

1103171504

Level: 
C
The picture shows velocity-time graphs of movements of cars \( A \), \( B \), \( C \) and \( D \). Which of the cars speeds up with constant acceleration of \( 0.8\,\frac{\mathrm{m}}{\mathrm{s}^2} \)? \[ \] Hint: An acceleration \( a \) is the rate of change of velocity \( \Delta v \) of an object with respect to time \( \Delta t \), i.e. \( a=\frac{\Delta v}{\Delta t} \).
\( A \)
\( B \)
\( C \)
\( D \)

1103171503

Level: 
C
Trains run between the towns \( M \) and \( N \) in both directions. The lines in the distance-time diagram correspond to the uniform movements of trains \( A \), \( B \), \( C \) and \( D \) between the towns. Find out which of the trains is the fastest. \[ \] Note: The distance-time diagram as seen in the picture is a graphical representation of trains operating schedule for a certain rout (or routs). Connections are displayed as broken-lines or line segments in rectangular coordinate system, where horizontal is the time axis with the time during an operating day and vertical is the distance axis with distances of the traffic nodes (e.g. railroad stations, cities) from one chosen reference node (in our case the town \( N \)). Connections in one direction (from \( N \) to \( M \)) are displayed by the lines skewed to the right (trains \( B \) and \( C \)) and back-connections in other direction (from \( M \) to \( N \)) are displayed by the lines skewed to the left (trains \( A \) and \( D \)).
\( A \)
\( B \)
\( C \)
\( D \)

1103171501

Level: 
C
Ohm's law states that the current \( I \) through a conductor is directly proportional to the voltage \( U \) between the endpoints of the conductor. This relationship is described by the equation \( I=\frac UR \), where \( R \) is the resistance of the conductor. Current-voltage characteristics of the conductors \( A \) and \( B \) are in the picture. Which of the conductors has greater resistance?
\( A \)
\( B \)
Both conductors have the same resistance.
It is not possible to answer the question based on the graph.

1103206102

Level: 
C
There are graphs of three quadratic functions in the picture. Choose the formula which corresponds to all three functions graphed in the picture.
\( y=-(x+a)^2+3 \), \( a\in(-\infty; 0] \)
\( y=-(x+a)^2+3 \), \( a\in\mathbb{R}^+ \)
\( y=-(x+3)^2+a \), \( a\in\mathbb{R}^+ \)
\( y=-(x-3)^2+a \), \( a\in\mathbb{R}^+ \)

1003171301

Level: 
C
The freezing point and the boiling point of water (both under the normal atmospheric pressure) are the base of the most commonly used temperature scale around Europe. It is Celsius temperature scale in Celsius degrees (\( ^{\circ}\mathrm{C} \)). Fahrenheit temperature scale in Fahrenheit degrees (\( ^{\circ}\mathrm{F} \)) is of general common use in English speaking countries especially in the USA. The basic temperature points in mentioned scales have the values: \[ \begin{array}{l} \text{Water freezing point } \dots\ 0\,^{\circ}\mathrm{C} / 32\,^{\circ}\mathrm{F} \\ \text{Water boiling point } \dots\ 100\,^{\circ}\mathrm{C} / 212\,^{\circ}\mathrm{F} \end{array} \] From the following equations choose the one that can be used to convert a temperature from its Celsius representation to the Fahrenheit value, provided you know that the relationship between the scales is linear. (In equations, \( F \) is a numerical value of a temperature in Fahrenheits and \( C \) is a numerical value of a temperature in Celsius.)
\( F=\frac95 C+32 \)
\( F=\frac59C+32 \)
\( F=\frac59 C-\frac{160}9 \)
\( F=32C+100 \)
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