Examples for secondary school students

  1. Seagull
    cajka Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (wi
  2. Rectangular trapezoid
    rt_licho The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
  3. Elements
    fact_1 If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
  4. Rectangle
    diagonal_rectangle_2 The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
  5. Sum of money
    penize_19 On a certain sum of money, invested at the rate of 10% compounded annually, the difference between the interests of the first year and the third year is 315 . Find the sum.
  6. Ratio iso triangle
    iso_triangle_2 The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
  7. Trapezium
    lichobeznik_mo_z8_2 The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
  8. Combinations
    trezor_1 How many elements can form six times more combinations fourth class than combination of the second class?
  9. Triangle ABC v2
    triangles_4 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
  10. Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  11. One half
    one_half One half of ? is: ?
  12. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  13. 7 heroes
    7statocnych 5 heroes galloping on 5 horses behind. How many ways can sort them behind?
  14. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  15. Vans
    shuttlevan In how many ways can 7 shuttle vans line up at the airport?
  16. Flags
    vlajka_cz How many different flags can be made from colors red, white, blue, black, yellow, green, purple, gray, orange so that each flag consisted of three different colors?
  17. Seating
    kupe_1 How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)?
  18. Football league
    football In the 2nd football league is 19 teams. How many ways can be filled first, second and third place?
  19. Guests
    hostia How many ways can 7 guests sit down on 9 seats standing in a row?
  20. Stock market
    money_1 Simon one day decided to invest € 48000 to the stock market. After six months he invested July 11 stock markets fell by 43%. Fortunately for Simon from July 11 5 to October 11 his shares have risen by 13%. Simon is then: ?

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