# Examples for secondary school students - page 15

1. N-gon How many diagonals has convex 11-gon?
2. Cinema Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
3. Circular sector I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
4. Euclid2 In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
5. Sea How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
6. Purchase Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the
7. Cyclist A cyclist is moving at 35 km/h and follow pedestrian who is walking at speed 4 km/h. Walker has an advantage 19 km. How long take cyclist to catch up with him?
8. Triangular prism The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
9. Electronics: Resistors in parallel From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω
10. Car factory Carmaker now produce 2 cars a day more than last year, so the production of 70312 cars will save just one full working day. How many working days needed to manufacture 70312 cars last year?
11. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
12. Trapezoid trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
13. Event probability The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (probability is same)?
14. Lord Ram When lord Ram founded the breed white sheep was 8 more than black. Currently white sheep are four times higher than at the beginning and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black sh
15. MO circles Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a ci
16. Triangle KLB It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
17. Cathethus and the inscribed circle In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
18. Subsets How many are all subsets of set ??
19. Machine Price of the new machine is € 62000. Every year is depreciated 15% of residual value. What will be the value of the machine after 3 years?
20. Distance Calculate distance between two points X[18; 19] and W[20; 3].

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