# Examples for secondary school students

1. Win in raffle The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
2. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
3. Railway Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
4. Chimney Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney.
5. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
6. Coffee shop To the coffee shop brought 2 types of coffee totally 50 kg. The first type was CZK 220 per kilogram, coffee second type 300 CZK per 1 kg. For all the coffee trader earned CZK 12,000. How many kilograms of coffee of first type and how many kilograms of co
7. Water reservoir The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?
8. Equilateral triangle v2 Equilateral triangle has a perimeter 36 dm. What is its area?
9. Jar From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
10. Cube from sphere What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
11. SD - mean Mean is 10 and standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range 6.5 to 13.5?
12. The cone The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base c
13. Water In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water?
14. Hexagonal pyramid Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
15. Height of the arc - formula Calculate the height of the arc if the length of the arc is 77 and chord length 40. Does exist a formula to solve this?
16. Tetrahedral prism Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
17. Prism The volume of tetrahedral prism is 2.43 m3. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.
18. Three friends Divide 570 euros to three friends so that first will get 50 euros less than the second and third twice more than the first. How many euros will get everyone?
19. Dollars Mama split 760 dollars Jane, Dane and Eva as follows: Jane got three times more than Dane and Dane and got 40 more than Eva. How much does get each of them?
20. Moivre 2 Find the cube roots of 125(cos 288° + i sin 288°).

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