# Examples for secondary school students - page 8

1. Recursion squares In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all
2. Shelf How many ways are there to arrange 6 books on a shelf?
3. Roller Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
4. Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
5. Profitable bank deposit 2012 Calculate the value of what money lose creditor with a deposit € 9500 for 4 years if the entire duration are interest 2.6% p.a. and tax on interest is 19% and annual inflation is 3.7% (Calculate what you will lose if you leave money lying idle at negative
6. Equilateral triangle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
7. Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
8. Leg and height Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
9. Ships At 8:40 the ship set sail at 12 km/h. At 19:10 followed by at 29 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took?
10. Similarity coefficient The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
11. Center Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
12. Balls Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
13. Chocolates In the market have 3 kinds of chocolates. How many ways can we buy 14 chocolates?
14. Gold wire From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3? How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
16. Axial section Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
17. Team The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player? Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B. Is equation ? solvable on the set of integers Z? Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.