# Examples for secondary school students

1. Traffic collision When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village
2. 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)
3. First class The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
4. Tree Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
5. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
6. Salt Sea water containing 5% salt. How many kg of fresh water necessary to pour into 40 kg of sea water so that the salinity fell to 2%?
7. Trapezoid How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
8. Trucks Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks b
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. Bags The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
11. Rope How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
12. V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
13. Cards From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
14. Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. If 5x + x² > 100, then x is not
16. Two aces From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
17. Cube in sphere The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
18. Circular segment Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
19. Sun rays If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current he
20. Electricity consumption cost Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago?

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