# Examples for 8th grade

- 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. - 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 cm^{2}. Calculate how many liters of oil is in the tin. - 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? - 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? - 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? - 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? - 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.. - 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. - 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? - 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? - 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? - Four-digit number

Find also a four-digit number, which quadrupled written backwards is the same number. - 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. - 10 pieces

How to divide the circle into 10 parts (geometrically)? - angles in quadrilateral

What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13? - 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. - 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? - Trapezium

The area of trapezium is 35cm^{2}find its altitude if the bases are 6cm and 8cm. - The city

In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)? - 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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