Examples for secondary school students

  1. Concentration
    hcl_1 How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%?
  2. Hydrochloric acid
    hcl Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?
  3. Costume
    zlatovlaska Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand D
  4. Solution
    chemia What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
  5. Gp - 80
    gp_1 Sum of the first four members of a geometric progression is 80. Determine they if we know that the fourth member is nine times greater than the second.
  6. AP 6
    progression_ao Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
  7. Contestants
    avg_1 In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contesta
  8. Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
  9. Cards
    cards_4 The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
  10. Salary in enterprise
    1000czk The average salary in the company is 27 000 CZK, 30% of workers have the lowest average income of 19 thousand CZK. There were an increase in the salary in this group by 2%. How much % increased the average salary across the company?
  11. Metals
    metals_2 In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
  12. Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
  13. Segment in a triangle
    priecka In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
  14. Inscribed circle
    inscribed_circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
  15. Prize
    metals_1 How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?
  16. Octahedron
    octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
  17. Permutations without repetition
    permutations_3 From how many elements we can create 720 permutations without repetition?
  18. Combinations
    math_2 From how many elements we can create 990 combinations 2nd class without repeating?
  19. Average height
    vyska In a class are 34 students. The average height of students is 165 cm. What will be the average height of students in the classroom when two pupils tall 176 cm and 170 cm moved from this school/class?
  20. Olympics metals
    olympics In how many ways can be win six athletes medal positions in the Olympics? Metal color matters.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...