# Examples for secondary school students

1. Gasoline
35 l of gasoline is to be divided into four canisters so that in the third canister was 5 l less than the first canister, the fourth canister 10 l more than in the third canister and the second canister half what in the first canister. How many liters of
2. Difference AP
Calculate the difference of arithmetic progression if the sum of its first 19 members Sn = 8075 and the first member is a1 = 20
3. Crates 2
In 6 crates is 45 kg of apples In  5 crates is equally In 1 in crate is 3 kg more How many kilograms in each crate?
4. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
5. Equation with abs value
How many solutions has the equation ? in the real numbers?
6. Office
Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400?
7. Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
8. Circular pool
The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
9. Pupils
Four pupils is going via dark hall. Start at one side and have to get to the other side for 17 minutes. They have only one lamp for the trip. The corridor is narrow, they can therefore go up two pupils at a time and go at the slower speed. Each pupil went
10. Vinegar
What percentage vinegar we get if we mix 1 if dm³ eight percent vinegar with 1.5 dm³ six percent vinegar?
11. Three numbers
Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67.
12. Friends
Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
13. Cuboid - complicatef
Three walls of the same cuboid has content 6 cm2, 10 cm2 and 15 cm2. Calculate the volume of the cuboid.
14. 4side pyramid
Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
Kamila wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes this two changes. How many opportunities have a choice?
16. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
17. Diamond
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
18. Triangle IRT
In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
19. Locomotive
Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done?
20. Rectangular triangles
The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8

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...