# Examples for secondary school students

- 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 - Hydrostatic force

What hydrostatic force is applied to an area of 30 cm^{2}in water at a depth of 20 m? (Water density is 1000 kg/m3) - 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? - 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? - 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. - 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%? - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - 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 - 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? - 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. - 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)? - 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 - 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? - 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. - Quadratic inequation

If 5x + x² > 100, then x is not - 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? - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - 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) - 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 - 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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