Examples for secondary school students - page 52

  1. Tree
    stromcek_1 Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
  2. Cards
    cards_8 From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
  3. Three numbers
    trojuhelnikova_cisla What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
  4. Roof 8
    veza_1 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
  5. VCP equation
    combinatorics3 Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
  6. Cards
    cards_2 Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
  7. Bags
    kufor The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
  8. Angles in ratio
    angles_1 The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
  9. Water reservoir
    vodojem The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
  10. AP 6
    progression_ao Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
  11. De Moivre's formula
    sqrt3_complex There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
  12. Calculation
    pocty How much is sum of square root of six and the square root of 225?
  13. Balls
    spheres_1 The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
  14. Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  15. Stadium
    sphere_segment A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
  16. The city 3
    city_2 The city has 22,000 residents. How long it is expected to have 25,000 residents if the average annual population growth is 1.4%?
  17. Remuneration
    cnb Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received?
  18. Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  19. Krkonose CZ
    krkonose Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t
  20. Cube in sphere
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.

Do you have interesting mathematical example that you can't solve it? Enter it and we can try to solve it.



To this e-mail address we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.