# Examples for secondary school students - page 14

- Divisibility

Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16. - Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm^{2}and 198 cm^{2}. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - 3y inflation

Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll. - Nine-gon

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm. - Sphere and cone

Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone? - Side c

In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c. - Road

Average climb of the road is given by ratio 1:15. By what angle road average climb? - Black building

Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m^{2}for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin - Pit

Pit has shape of a truncated pyramid with rectangular bases and is 3.5 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.8 l of green colour. How many liters of paint is needed when w - Lock

Combination lock will open when the right choice of 3 numbers (from 1 to 25 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately? - Circle

From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x_{0}, y_{0}] and radius of the circle r. - AVG of INT

What is the average of the integers from 9 throuht 52 inclusive? - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=5 cm, v_{b}=7 cm and side b is 5 cm shorter than side a. - Sea

How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Circular sector

I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector? - Purchase

Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the - Cuboid

Find the cuboid that has the same surface area as the volume. - Euclid2

In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.

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