# Examples for secondary school students

- Polygon 42

Which polygon has 42 more diagonals than sides? - PIN - codes

How many five-digit PIN - code can we create using the even numbers? - Digits A, B, C

For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product). - Tea blend

Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive - Ten dices

When you hit ten dices at the same time you get average 35. How much do you hit if every time you get six, you're throwing the dice again? - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ? - RTriangle 17

The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs. - Clock face

clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles. - Miraculous tree

Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days? - Volume from surface area

What is the volume of the cube whose surface area is 96 cm^{2}? - Tenth member

Calculate the tenth member of geometric sequence when given: a_{1}=1/2 and q=2 - Tray

Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm. - The city 2

Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%? - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 12 cm and u_{2}= 10 cm. Prism height is twice base edge length. - Insert into GP

Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert? - Circle inscribed

Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm. - Inscribed triangle

To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle. - Two cars

From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what - Half life

Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes. - Hockey game

In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?

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