# Examples for secondary school students - page 6

1. Laws
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
2. Pedestrian up-down hill
Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
3. Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
4. Rotation
Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
5. Described
Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
6. Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
7. Infinity
In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
8. Trapezoid
Calculate area of trapezoid ABCD with sides |AD|= 57 cm, |DC|=30 cm, |CB|=7 cm, |AB|=40 cm..
9. VAT
John paid 100 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%.
10. Tower
The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of sheet is required to cover the top of the tower if we count 8% of the sheet waste?
11. TV fail
The TV has after 10,000 hours average 25 failures. Determine the probability of TV failure after 200 hours of operation.
12. R Trapezium
Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
13. One half
One half of ? is: ?
14. Word
What is the probability that a random word composed of chars T, H, A, M will be MATH?
15. The cyclist
The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town.
16. Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
17. 2nd class variations
From how many elements you can create 6972 variations of the second class?
18. Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
19. Inflation
Once upon a time, tsar owned a money printer and printed and printed. The result of printing money prices went up,in the first year 3.9 %, in the second 6%, in the third 4.7% and in the fourth 5.5%. Then tsar was failed in election. Calculate the aver
20. Pyramid roof
1/3 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 9 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?

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