# Examples for secondary school students - page 27

- 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. - Tournament

Determine how many ways can be chosen two representatives from 34 students to school tournament. - 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. - 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? - 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? - Angle

A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis. - Sum-log

The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers. - Words

How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition - Medals

In how many ways can be divided gold, silver and bronze medal among 21 contestant? - Trigonometry

Is true equality? ? - 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). - Cinema

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

Car A1 goes at average speed of 106 km/h and the second car A2 goes at 103 km/h. How many second will it take car A1 to circulate car A2? Assume that both cars are 5 meters long and the safety gap between cars is 1.5 meters. - 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? - 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? - Interest

What is the annual interest rate on your account if we put 32790 and after 176 days received 33939.2? - Permill

How many permill is 978 from 84370? - Disinfecting solution

How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution? - Pipeline

How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter? - Ray

Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 7 identical plates?

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