# Examples for 9th grade - page 5

- Numbers

Determine the number of all positive integers less than 2937474 if each is divisible by 11, 23, 17. What is its sum? - IS triangle

Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long. - Steps

How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 298 steps. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Square diagonal

Calculate length of the square diagonal if the perimeter is 200 cm. - Gutter

How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material. - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 5 hours, the second tractor plow whole field 5 hours longer. How long take plow whole field with two tractors? - Vans

In how many ways can 7 shuttle vans line up at the airport? - Ace

From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace? - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long. - Cyclist

Cyclist goes uphill 1 km for 6.3 minutes and downhill minutes for 2.1 minutes, both applied to the pedals same force. How long he pass 1 km by plane? - Spherical cap

From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere? - Seating

How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)? - Pentagon

Calculate the area of regular pentagon, which diagonal is u=14. - Engineer Kažimír

The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri - Motion

Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D - Road repair

Road repair took 16 days for 34 workers if they worked 6 hours a day. How many days take repair same road 33 workers if they work 6 per day? - Circles

The areas of the two circles are in the ratio 1:15. The larger circle has diameter 25. Calculate the radius of the smaller circle. - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.

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