Examples for secondary school students - page 4

  1. Observer
    ohrada The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
  2. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  3. 7 heroes
    7statocnych 9 heroes galloping on 9 horses behind. How many ways can sort them behind?
  4. Eiffel Tower
    eiffel_tower Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?
  5. Pipes
    water_pipe Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
  6. Area of RT
    right_triangle_sepia Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
  7. Circles
    two_circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
  8. Two cars
    cars_racing Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?
  9. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  10. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
  11. Ace
    ace From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace?
  12. Flags
    vlajka_cz How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors?
  13. Circle arc
    pizza Circle segment has a circumference of 72.95 cm and 1386.14 cm2 area. Calculate the radius of the circle and size of central angle.
  14. Numbers
    ten Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
  15. Vans
    shuttlevan In how many ways can 6 shuttle vans line up at the airport?
  16. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  17. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
  18. Crystal
    crystal Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g?
  19. Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  20. Tractors
    tractors Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors?

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