# Examples for secondary school students

1. Polygon 42
Which polygon has 42 more diagonals than sides?
2. PIN - codes
How many five-digit PIN - code can we create using the even numbers?
3. 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).
4. 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
5. 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?
6. 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? ?
7. 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.
8. 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.
9. 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?
10. Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
11. Tenth member
Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
12. 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.
13. The city 2
Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%?
14. Rhombus base
Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 10 cm. Prism height is twice base edge length.
15. 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?
16. Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
17. 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.
18. 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
19. 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.
20. 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?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...