# Examples for 9th grade

- Garden pond

Concrete garden pond has bottom shape of a semicircle with a diameter 1.7 m and is 79 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 28 cm? - 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? - 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 - 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. - Tank and water

Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in? - Chess

How many different ways can initiate a game of chess (first pass)? - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3}. Calculate the volume, surface and diameter of the sphere. - Shoes

Peter decided to measure shoes size of his three friends. Measured accurately and wrote as follows: Venda and Jenda together 52 cm Jenda and Zdenda together 58 cm Zdenda and Venda together 54 cm a) How long measures Vendy, Jenda and Zdenda shoes togethe - Three digits number

How many are three-digit integers such that in they no digit repeats? - Freight and passenger car

The truck starts at 8 pm at 30 km/h. Passenger car starts at 8 pm at 40 km/h. Passenger arrives in the destination city 1 hour and 45 min earlier. What is the distance between the city of departure and destination city? - Combinations

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

The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it? - Otto and Joachim

Otto and Joachim go through the woods. After some time Otto tire and make 15 minutes stop. Joachim meanwhile continues at 5 km/h. Otto when he set off again, first running speed of 7 km/h, but it keep only 30 sec and 1 minute must continue at 3 km/h. This - Parallelogram ABCD

The area of parallelogram ABCD is 440 cm^{2}. Points M and N are the midpoints of the sides AB and BC. What is the area of a quadrilateral MBND? - Parcel

Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage? - Obtuse angle

The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Three workers

Three workers were rewarded CZK 9200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received? - Circles

Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?

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