# Examples for secondary school students - page 27

1. ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys
2. Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
3. Automaker
The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?
4. Resistors
Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of this resistors.
5. Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
6. Peak
Uphill leads 2 paths and 1 lift. a) How many options back and forth are there? b) How many options to get there and back by not same path are there? c) How many options back and forth are there that we go at least once a lift?
7. Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament.
8. Seating rules
In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.
9. 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.
10. Cinema
How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
11. Painters
The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge?
12. Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
13. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
14. Sum-log
The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
15. Medals
In how many ways can be divided gold, silver and bronze medal among 21 contestant?
16. Words
How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
17. Disinfecting solution
How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
18. Circles
In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
19. Against each other
From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them?
20. Interest
What is the annual interest rate on your account if we put 32790 and after 176 days received 33939.2?

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