# Examples for secondary school students - page 4

- Ace

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

How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors? - Two cars

Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet? - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Circles

The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle. - Cylinders

Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much? - Vans

In how many ways can 9 shuttle vans line up at the airport? - Circle arc

Circle segment has a circumference of 135.26 dm and 2096.58 dm^{2}area. Calculate the radius of the circle and size of central angle. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Right

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

Crystal grows every month 1.2 promile of its mass. For how many months to grow a crystal from weight 177 g to 384 g? - Seating

How many ways can 5 people sit on 4 numbered chairs (e. G. , seat reservation on the train)? - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors? - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18 - Ravens

The tale of the Seven Ravens were seven brothers, each of whom was born exactly 2.5 years after the previous one. When the eldest of the brothers was 2-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur - Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Gutter

How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees. - Cone

Calculate volume and surface area of the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.

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