Examples for secondary school students - page 27

  1. Maple
    tree_javor 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.
  2. Tournament
    turnaj Determine how many ways can be chosen two representatives from 34 students to school tournament.
  3. Seating rules
    school_class 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.
  4. Painters
    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?
  5. Reflector
    lamp 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?
  6. Angle
    atan A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
  7. Sum-log
    complex_log The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
  8. Words
    words How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
  9. Medals
    medails In how many ways can be divided gold, silver and bronze medal among 21 contestant?
  10. Trigonometry
    sinus Is true equality? ?
  11. Circles
    pyt_theorem 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).
  12. Cinema
    stale_kvoka How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
  13. Two cars
    car_racing 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.
  14. Against each other
    Lotus_Esprit 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?
  15. The camp
    diary At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
  16. Interest
    MoneyHouse What is the annual interest rate on your account if we put 32790 and after 176 days received 33939.2?
  17. Permill
    permille How many permill is 978 from 84370?
  18. Disinfecting solution
    desinfect How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
  19. Pipeline
    pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
  20. Ray
    luc-slnka 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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