# Examples for secondary school students

1. 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?
2. Cylinder diameter The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?
3. 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?
4. 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.
5. 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?
6. Triangle Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
7. 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
8. 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?
9. 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).
10. 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?
11. 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?
12. 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?
13. 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?
14. 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
15. 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 cm2. What is the area of the trapezoid?
16. 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.
17. 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
18. Chess How many different ways can initiate a game of chess (first pass)?
19. Three digits number How many are three-digit integers such that in they no digit repeats?
20. Combinations How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?

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