# Examples for secondary school students

- Goat

Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow? - Cylinder diameter

The surface of the cylinder is 149 cm^{2}. The cylinder height is 6 cm. What is the diameter of this cylinder? - Class - boys and girls

In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl? - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - Nuts

How many we must have at least nuts if we can equally divide it to 10 children, 12 children or 15 children and any nut left? - Triangle

Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17. - Computer

The computer was purchased 10000,-. Each year, the price of a computer depreciates always the same percentage of the previous year. After four years, the value of the computer is reduced to 1300,- How many percent was depreciated price of the computer eac - Interesting property

Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle? - Circles

In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both). - Mushrooms from the forest

Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda? - Friends in cinema

5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter? - The camp

At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged? - Three digits number

From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there? - Journey

The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pl - Trapezoid - diagonal

Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm^{2}. What is the area of the trapezoid? - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm. - Purchase

Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at th - Chess

How many different ways can initiate a game of chess (first pass)? - Three digits number

How many are three-digit integers such that in they no digit repeats? - Combinations

How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?

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