Examples for secondary school students - page 192 of 230
Number of problems found: 4597
- 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 do we start? - Office
The 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 does CZK cost to plaster the building walls per 1 m square cost CZK 400? - Rectangle
The perimeter of the rectangle is 22 cm, and the area is 30 cm². Determine its dimensions if integers express the length of the sides of the rectangle in centimeters. - Equation with abs value
How many solutions has the equation (|x| +x) |x-3| = |x+1| in the real numbers? - Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Pupils
Four pupils are going via the 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 go up two pupils at a time and at a slower speed. Each pupil went different - Beta's number
Beta thought of a natural number with different digits and wrote it on the board. Below wrote the digits of the original number on the back and thus got a new number. By adding these two numbers, he got a number with the same number of digits as the inten - Vinegar
What percentage of vinegar do we get if we mix 1 dm³ of eight percent vinegar with 1.5 dm³ of six percent vinegar? - Three numbers
Find three numbers so that the second number is four times greater than the first and the third is lower by five than the second number. Their sum is 67. - Friends
Some friends had to collect the sum of 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Password dalibor
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 these two changes. How many opportunities do you have a choice? - Cuboid - complicated
Three walls of the same cuboid have an area of 6 cm², 10 cm², and 15 cm². Calculate the volume of the cuboid. - 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. - Triangle IRT
An isosceles right triangle ABC with a right angle at vertex C has vertex coordinates: A (-1, 2); C (-5, -2). Calculate the length of segment AB. - Diamond
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm - Boletus and cossacks
Paul has 8 dry boletus, 1/2 less oak boletus, 5x more cossacks than butter mushrooms. He has 3x more cossacks and butter mushrooms together than dry boletus. How many mushrooms does he have in total? And how many butter mushrooms and how many cossacks? - Railway
The railway line climbs 8 permille between points A and B, whose horizontal distance is 1.5 km. It climbs 14 permille between points B and C, which have a horizontal distance of 900 m. Calculate the differences in altitudes between points A and C. - Rectangular triangles
The lengths of the 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 areas of these triangles? A smaller rectangular triangle has legs 6 and - Locomotive
Locomotive pulled a permanent train load of 200 kN horizontally along the track of 5km. What work has it done?
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