# Examples for secondary school students

1. 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.
2. 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
3. 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.
4. Goniometric form
Determine goniometric form of a complex number ?.
5. 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+....
6. 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.
7. Rotary cone
The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
8. Cards
How many ways can give away 32 playing cards to 5 player?
9. Ace
From complete sets of playing cards (32 cards), we pulled out one card. What is the probability of pulling the ace?
10. 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
11. Dices
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
12. 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?
13. MATES
In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
14. 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.
15. n-gon II
What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
16. n-gon
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
17. Cinema
How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
18. 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/m3.
19. 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
20. 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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