# Examples for secondary school students - page 67

1. AP RT triangle The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
2. Tropical, mild and arctic How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.
3. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
4. Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
5. Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
6. Two resistors Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
7. Lunch Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities?
8. Sum of inner angles Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
9. Borrowing I borrow 25,000 to 6.9% p.a.. I pay 500 per month. How much will I pay and for how long?
10. Water current speed. Two cities along the river are 100 km apart. The powerboat downstream runs for 4 hours, upstream for 10 hours. Determines the river's current speed.
11. Father 7 Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages?
12. Value Find the value of the expression: 6!·10^-3
13. Water reservoir One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously?
14. Clogging How much distilled water must the pharmacist add to 30g of a 30% hydrogen peroxide solution to obtain a 3% solution to clogging?
15. The big clock The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00.
16. Diagonals of the rhombus How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
17. Merchant The merchant lower cost by 10% in December when it was not sold. Again in January lower cost by 20% and now costs 576 €. A. How much the goods stood originally? B, how much cost the goods after the first lowering? C, How many percents totally merchant lo
18. Last digit What is the last number of 2016 power of 2017
19. Octane value I loaded 10L 95 octane gasoline and 5L 100 octane gasoline. What is the resulting octane value of the gasoline in the tank?
20. A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?

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