# Examples for secondary school students

- Pyramid

Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges. - Balls

Ping pong balls have a diameter of approximately 5.1 cm. They are sold in boxes of 10 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled - JUDr. Usury

Judge JUDr. Usury approved the agreement on guilt and punishment where confessed to pay daily interest 0.18%. How big is a yearly interest? Year has 360 days. - Goniometric form

Determine goniometric form of a complex number ?. - Sum of series

Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+.... - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - Cards

How many ways can give away 32 playing cards to 5 player? - Ace

From complete sets of playing cards (32 cards), we pulled out one card. What is the probability of pulling the ace? - Future of libraries

You know that thanks to the Internet, electronic communications and developing online resources on the Internet annually declining number of traditional readership by 17%. These deal is irreversible evolutionary shift from old books from libraries to imme - Dices

We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2? - Boat

A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight? - MATES

In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is? - Maple

Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple. - n-gon II

What is the side length of the regular 5-gon circumscribed circle of radius 11 cm? - n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm? - Cinema

How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners? - Plastic pipe

Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m^{3}. - Price of state

Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 868 (super-gross wage).Then tax him 35.2% employer contribution - Block

Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°

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