# Examples for secondary school students

1. Fall sum or same
Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.
2. Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
3. Coordinates of a centroind
Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
4. Corona virus
Calculate an estimate of the percentage of GDP (Gross Domestic Product) declined due to the quarantine related to the corona COVID-19 virus that lasts for 2 months, during which time the economic activity is down by 80%.
5. Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
6. What percentage
What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
7. Self-oscillation period
The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s.
8. Tropics and polar zones
What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'
9. Researchers
Researchers ask 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the families
10. Tetrahedral pyramid 8
Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p
11. Birth
Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?
Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.
13. Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
14. Power line pole
From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
15. Growth of wood
The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
16. Percents from percent
How much is 13% of 20% of 500 greater than 8% of 14% of 200?
17. The university
At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in t