# Examples for secondary school students - page 53

1. Potatoes 6 The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes d
2. Equation with abs value How many solutions has the equation ? in the real numbers?
3. Remuneration Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received?
4. Forces Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
5. Krkonose CZ Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t
6. Ice cream Annie likes much ice cream. In the shop are six kinds of ice cream. In how many ways she can buy ice cream to three scoop if each have a different flavor mound and the order of scoops doesn't matter?
7. Hydrostatic force What hydrostatic force is applied to an area of 30 cm2 in water at a depth of 20 m? (Water density is 1000 kg/m3)
8. Equation Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
9. Savings Paul has a by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have 3 boys together?
10. Wall height Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
11. Difference AP Calculate the difference of arithmetic progression if the sum of its first 19 members Sn = 8075 and the first member is a1 = 20
12. Chairs Determine the number of seats in the seventh row and ninth row, if 3rd row has 14 seats and in every next row of seats has five more than the previous row.
13. Metals In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
14. Paper box Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?
15. Truncated cone 3 The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. Determine how many apples are in baskets when in the first basket are 4 apples, and in any other is 29 apples more than the previous, and we have eight baskets.
17. Cone The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
18. Hockey match The hockey match ended with result 3:1. How many different storylines may have the match?
19. Circle's chords In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
20. Alcohol mixture From 55% and 80% alcohol we have to produce 0.2 kg of 60% alcohol. How many of them do we use in solution?

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