A

1103020801

Level: 
A
Find the coordinates of the midpoints of the line segments \( AB \), \( BC \), \( AC \). For coordinates of the points \( A \), \( B \) and \( C \), see the picture.
\( S_{AB}=\left[-\frac12,1 \right]\text{, }\ S_{BC}=[4,2 ]\text{, }\ S_{AC}=\left[\frac12, 4\right] \)
\( S_{AB}=\left[-\frac32,2 \right]\text{, }\ S_{BC}=[1,3 ]\text{, }\ S_{AC}=\left[\frac52, 4\right] \)
\( S_{AB}=\left[\frac12,1 \right]\text{, }\ S_{BC}=[4,2 ]\text{, }\ S_{AC}=\left[-\frac12, 4\right] \)
\( S_{AB}=\left[1,-\frac12 \right]\text{, }\ S_{BC}=[2,4 ]\text{, }\ S_{AC}=\left[4,\frac12\right] \)

1103020808

Level: 
A
Let \( ABC \) be a triangle. In the picture, the midpoint of the side \( BC \) and the centroid of the triangle are indicated. Out of the following vector relations select the one that is not true.
\( \overrightarrow{ST}= \frac12 \overrightarrow{AT} \)
\( \overrightarrow{AT}= \frac23\overrightarrow{AS} \)
\( \overrightarrow{ST} = -\frac13\overrightarrow{AS} \)
\( \overrightarrow{SA}= -3\overrightarrow{TS} \)

1003055508

Level: 
A
In a chess tournament \( 70\% \) of all participants were boys. Girls were \( 20\% \) of the number of boys. Other participants of the event were coaches and judges. Find the percentage of girls with the reference to all the participants of the tournament.
\( 14\% \) of all participants
\( 30\% \) of all participants
\( 50\% \) of all participants
Not enough information to find a solution.

1003055506

Level: 
A
A notebook and a pen cost the same amount of money. The price of the notebook was increased by \( 3\% \), and the price of the pen was increased by \( 5\% \). For the set consisting of \( 5 \) notebooks and \( 5 \) pens you need to pay more than before the rise
by \( 4\% \).
by \( 8\% \).
by \( 5\% \).
by \( 15\% \).

1103055505

Level: 
A
In the warehouse there were \( 400 \) kilograms of fruit. The diagram shows the percentage composition of fruit in the warehouse according to their weight. How many kilograms of pears were there?
\( 140\,\mathrm{kg} \)
\( 150\,\mathrm{kg} \)
\( 145\,\mathrm{kg} \)
\( 155\,\mathrm{kg} \)