# Examples for secondary school students - page 17

1. Rectangle Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
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. 2nd class combinations From how many elements you can create 4560 combinations of the second class?
4. Cuboid Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
5. Bits, bytes Calculate how many different numbers can be encoded in 16-bit binary word?
6. 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.
7. Party At the party everyone clink with everyone. Together, they clink 406 times. How many people were at the party?
8. Horizon The top of a lighthouse is 19 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.]
9. Kids How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
10. 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?
11. Perpendicular What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
12. 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.
13. 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.
14. 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.
15. 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
16. Tiles From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
17. 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.
18. 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.
19. 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.
20. 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.

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