1. Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
2. Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
3. The cylindrical container
The container has a cylindrical shape the base diameter 0.8 meters has a content area of the base is equal to the content area of the shell. How many full liters of water can be poured maximally into the container?
4. Tractor wheels
Smaller tractor wheel has a circumference of 3 meters, bigger 4 meters. On what path executes smaller wheel 6 turns over more bigger?
5. Profits
Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?
6. 9.A
9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
7. Bank deposit
Ms Jana after the withdraw amount of 2,500 euros after year saving in bank. What was her deposit if the interest rate was 2.5% p.a..
8. Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
9. Two workers
Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker?
10. Stock
Enterprise sold 7/12 of their products to foreign markets and 2/5 of the remainder sold at home. How many % of the products is still in stock?
11. A family
A family of four pays for garbage collection per year 1800 Kč. How many crowns a year the waste company get from the house where lives 93 people?
12. Four-digit number
Find also a four-digit number, which quadrupled written backwards is the same number.
13. Three digits number 2
Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one positions is one of the numbers 1,3,4, on the place of hundreds 4 or 2.
14. 10 pieces
How to divide the circle into 10 parts (geometrically)?
What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?
16. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
17. Two months
Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
18. Trapezium
The area of trapezium is 35cm2 find its altitude if the bases are 6cm and 8cm.
19. The city
In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
20. Holidays
Of the 35 students of class were 7 on holiday in Germany and just as much in Italy. 5 students visited Austria. In none of these countries was 21 students, all three visited by one student . In Italy and Austria were 2 students and in Austria and Germany

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