# Examples for secondary school students

1. Repairman
Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
2. Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
3. Hiker and cyclist
At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?
4. MO - triangles
On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB s
5. Cube 9
What was the original edge length of the cube if after cutting 39 small cubes with an edge length 2 dm left 200 dm3?
6. Cards
Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probab
7. Triangle ABC
Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
8. Average mark
Calculate average mark in English, if a student got a couple of 3's, 20% less 2 than 3, and 50% more 1's than the 2's.
9. Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
10. Disco
On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
11. Air pressure
The meteorological station measured the air pressure of 1060 hPa (hectopascals). In addition to measuring instruments, there is a residential house that has a flat roof with dimensions of 10 m and 28 m. What pressure force in MN (meganewtons) force the a
12. Family
Family has 4 children. Ondra is 3 years older than Matthew and Karlos 5 years older than the youngest Jane. We know that they are together 30 years and 3 years ago they were together 19 years. Determine how old the children are.
13. Flywheel
Flywheel turns 450 rev/min (RPM). Determine the magnitude of the normal acceleration of the flywheel point which are at a distance of 10 cm from the rotation axis.
14. Division
Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
15. Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
16. Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
17. Train 2
The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
18. Property
The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cos
19. Traffic laws
Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the w