# Examples for secondary school students

1. Bearing A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
2. 925 USD Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them?
3. Square and rectangle Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square.
4. Angle Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
5. Angle in RT Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
6. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
7. Glass How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
8. Third member Determine the third member of the AP if a4=93, d=7.5.
9. Sum of members What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
10. Three friends Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.
11. Exponential equation Determine the value of having y in the expression (3^y): (4^-1)=36. Unknown y is a natural number greater than zero.
12. Kerosine and petrol if 4 litres of petrol containing 15% kerosine are added to another 7 litres of petrol containing 10% kerosine, what percentage of the petrol is kerosine?
13. Rectangle Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
14. Coefficient Determine the coefficient of this sequence: 7.2; 2.4; 0.8
15. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.
16. First man What is the likelihood of a random event where are five men and seven women first will leave the man?
17. Difference of two number The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers.
18. Three friends Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor.
19. Tetrahedral prism - rhomboid base Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
20. Lighthouse The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lighth

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