Examples for secondary school students - page 192 of 231
Number of problems found: 4614
- To the cinema
Jane at 8 AM got a message that all 1093 school pupils would go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way, the message spread further. At what time do all the scho - Triangle ABC
There is the triangle ABC with the side BC of length 2 cm. Point K is the middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at point K. Determine the lengths of the sides AB, AC tr - Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when the angle between the vectors u, v is: a) 60° b) 45° c) 120° - construction triangle problem
Construct the vertices C of all triangles ABC, if given side AB, height vb on side b, and length of line tc on side c. Build all the solutions. Mark the vertices C1, C2,. .. - Car value
The car loses value by 15% every year. Determine a time (in years) when its price will halve. - Square grid
A square grid consists of a square with sides of a length of 1 cm. Draw at least three patterns, each with an area of 6 cm² and a circumference of 12 cm, and their sides in a square grid. - Alcohol mixing
How much 55% alcohol must we pour into 1500 g 80% alcohol to form a 60% alcohol? How much is 60% alcohol created? - Spirit From 55% and 80% spirit, we would like to produce 0.2 kg of 60% spirit. How many of them must we use in a solution?
- Lord Ram
When lord Ram was founded, the breed of white sheep was eight more than black. White sheep are four times higher than at the beginning, and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black s - Ballistic curve
The soldier fired the ballistic grenade at a 45° angle. The first half ascended, and the second fell. How far and height did it reach if his average speed was 1200 km/h, and what 12 seconds were taken from the shot to impact? - Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille. - Sheep
Shepherd is tending the sheep. Tourists asked him how much they had. The shepherd said, "there are fewer than 500. If I lined up in 4-row, three remain. If in 5-row, four remain. If in 6-row, five remain. But I can form 7-row." How many sheep have a sheph - Gasoline
35 l of gasoline is to be divided into four canisters so that in the third canister is 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 - Phone number
A phone number with nine digits, none of which are repeated. The middle number in the second three-digit number is 3 times greater than the 6th and twice greater than the 7th. The three-digit number in the middle 3 numbers is 2 times greater than the last - Variations 3rd class
From how many elements can we create 13,800 variations of the 3rd class without repeating? - Crates 2
In six crates is 45 kg of apples Five crates are equally apples. In the first crate is 3 kg more apples. How many kilograms are in each crate? - Difference AP
Calculate the difference of arithmetic progression if the sum of its first 10 members Sn = 1325 and the first member is a1 = 20 - 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.
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