# Examples for secondary school students - page 6

- Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? - 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? - Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°. - Rotation

Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone. - Described

Calculate perimeter of the circle described by a triangle with sides 478, 255, 352. - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 21 cm and t_{b}=12 cm. - 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. - Trapezoid

Calculate area of trapezoid ABCD with sides |AD|= 57 cm, |DC|=30 cm, |CB|=7 cm, |AB|=40 cm.. - VAT

John paid 100 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%. - Tower

The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m^{2}of sheet is required to cover the top of the tower if we count 8% of the sheet waste? - TV fail

The TV has after 10,000 hours average 25 failures. Determine the probability of TV failure after 200 hours of operation. - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - One half

One half of ? is: ? - Word

What is the probability that a random word composed of chars T, H, A, M will be MATH? - 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. - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 33 and corresponding angle is ?. - 2nd class variations

From how many elements you can create 6972 variations of the second class? - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - 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 - 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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