# Examples for secondary school students - page 53

1. 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
2. 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?
3. 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?
4. 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)
5. 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?
6. Equation Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
7. 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
8. 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.
9. Wall height Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
10. Metals In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
11. 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?
12. 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.
13. Apples in baskets 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.
14. 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?
15. 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.
16. Hockey match The hockey match ended with result 3:1. How many different storylines may have the match?
17. 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?
18. Five members Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
19. Average If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ?
20. Banknotes \$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?

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