# Examples for secondary school students

1. Circle inscribed Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
2. Inscribed triangle To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
3. Two cars From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what
4. Half life Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes.
5. Hockey game In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?
6. Saving per cents The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
7. Warehouse cars From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck?
8. Hollow sphere Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
9. Blackjack TU160 Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. A
10. Candies If Alena give Lenka 3 candy will still have 1 more candy. If Lenka give Alena 1 candy Alena will hame twice more than Lenka. How many candies have each of them?
11. Pot Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
12. Three-digit numbers How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
13. Surface area The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
14. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
15. Paper box Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m2 of the paper consumed 100 such boxes?
16. 3 days Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day.
17. The fence I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord
18. The hall The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
19. Hockey match The hockey match ended with result 3:1. How many different storylines may have the match?
20. Field with vegetables Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?

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