# Examples for secondary school students - page 27

1. 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?
2. 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.
3. 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.
4. Disinfecting solution
How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
5. 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?
6. 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?
7. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
8. Medals
In how many ways can be divided gold, silver and bronze medal among 21 contestant?
9. 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?
10. Sum-log
The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
11. Words
How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
12. 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).
13. Permill
How many permill is 978 from 84370?
14. Train 2
The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
15. Interest
What is the annual interest rate on your account if we put 32790 and after 176 days received 33939.2?
16. Trigonometry
Is true equality? ?
17. The camp
At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
18. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
19. Pipeline
How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
20. Inclined plane
On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.

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