# Examples for secondary school students - page 51

1. Cycling trip At 8 am started a group of children from the camp to day cycling trip. After 9:00 weather deteriorated sharply and the leader decided to send for the children bus on the same route, which started at 10 hours. For how long and at what distance from the camp
2. Digits How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated.
3. Cards From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
4. Men, women and children On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
5. Cinema 4 In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?
6. Potatoes Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself.
7. Disco On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
8. Sequence Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
9. Hexagonal prism 2 The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
10. 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 contestan
11. Gas consumption The vessel consume 100 tons of gas in 250 miles. How many fuel will the vessel consume if it travels 400 miles?
12. Saving per cents The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
13. Variations 4/2 Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition.
14. 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.
15. Resistance Determine the resistance of the bulb with current 200 mA and is in regular lamp (230V).
16. Geometric sequence 4 It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).
17. Diameters of circles How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
18. Population What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
19. Geometric sequence 5 About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
20. Virus We have a virus that lives one hour. Every half hour produce two child viruses. What will be the living population of the virus after 3.5 hours?

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