# Examples for secondary school students

1. Concentration How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%?
2. Hydrochloric acid Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?
3. Costume Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand D
4. Solution What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
5. Gp - 80 Sum of the first four members of a geometric progression is 80. Determine they if we know that the fourth member is nine times greater than the second.
6. AP 6 Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
7. Contestants In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contesta
8. Centre of mass The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
9. Cards The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
10. Salary in enterprise The average salary in the company is 27 000 CZK, 30% of workers have the lowest average income of 19 thousand CZK. There were an increase in the salary in this group by 2%. How much % increased the average salary across the company?
11. Metals In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
12. Hexagonal pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
13. Segment in a triangle In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
14. Inscribed circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
15. Prize How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?
16. Octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
17. Permutations without repetition From how many elements we can create 720 permutations without repetition?
18. Combinations From how many elements we can create 990 combinations 2nd class without repeating?
19. Average height In a class are 34 students. The average height of students is 165 cm. What will be the average height of students in the classroom when two pupils tall 176 cm and 170 cm moved from this school/class?
20. Olympics metals In how many ways can be win six athletes medal positions in the Olympics? Metal color matters.

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