# Examples for secondary school students - page 17

1. 2nd class combinations From how many elements you can create 4560 combinations of the second class?
2. Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
3. Party At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
4. Horizon The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
5. 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.
6. Boat A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
7. Kids How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
8. Similarity n-gon 9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm2 and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.
9. Perpendicular What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
10. Geometric mean Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
11. Rectangle The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
12. Two runners Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
13. Tiles From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
14. Icerink Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water.
15. Aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
16. Rhombus base Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 10 cm. Prism height is twice base edge length.
17. ISO trapezium Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
18. Fall The body was thrown vertically upward at speed v0 = 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach?
19. Triangle TBC TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
20. Lines In how many points will intersect 14 different lines, where no two are parallel?

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