# Examples for secondary school students - page 4

1. 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?
2. 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.
3. Forces
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
4. 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?
5. Cylinders
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
6. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
7. Vans
In how many ways can 9 shuttle vans line up at the airport?
8. Numbers
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
9. Triangle
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
10. Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
11. Crystal
Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g?
12. Seating
How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)?
13. 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?
14. Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
15. 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
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?
17. 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.
18. 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.
19. Cone
Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
20. Z9–I–1
In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir

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