# Examples for secondary school students

- Rings groups

27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups? - Candy - MO

Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles trian - Baskets of apples

Grandfather gathered apples into baskets. He filled one large and three small baskets. Small baskets are identical and each can hold 3 kg of apples less than in a large basket. In small baskets together 3 kg of apples over a large basket. How many kilogra - Potatoes

Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself. - The swing

To swing the two girls. Aneta weight 45 kg and Simon 35 kg weight. How far should sit Simon from the middle of swing so it is balanced, if we know that Aneta is sitting at distance 1,5m? How far are girls sitting apart? - Four integers

Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two. - Children

The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group? - Mrak - cloud

It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the - Octahedron - sum

On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also - Z9–I–1

In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the ci - Quadratic equation

Find the roots of the quadratic equation: 3x^{2}-4x + (-4) = 0. - Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth. - Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Three vectors

The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces. - Ravens

On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree? - Value

Find the value of the expression: 6!·10^-3 - Bearing

A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point. - 925 USD

Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them? - Square and rectangle

Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square. - Angle

Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.

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