The most difficult problems

  1. Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  2. A library
    bookshelf A library has 12,500 fiction books and 19,000 non fiction books. Currently 2/5 of the fiction books are checked out. Currently 2/5 of the non fiction books are checked out. Of the books checked out, only 1/10 are due back this week. How many books are due
  3. Tropics and polar zones
    circles_on_Earth What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'
  4. Tetrahedral pyramid 8
    pyramid_4s Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p
  5. Runners
    runners If John has a running speed of 3.5miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 am and Lucy starts running at 10:30 am, at what time will they meet? (as soon as possible)
  6. The university
    family_1 At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in t
  7. Triangular prism,
    prism3s The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l).
  8. Mortage hypo loan
    hypo The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?
  9. Profitable company
    penize Three businessman decide to open up their own company. They agree to distribute the yearly profits made in the same ratio as their initial investments. They invest R 50 000, R 75 000 and R25 000, respectively. The profit made by the company in the first y
  10. Marlon
    meter Marlon drew a scale drawing of a summer camp. In real life, the sand volleyball court is 8 meters wide. It is 4 centimeters wide in the drawing. What is the drawing's scale factor? Simplify your answer and write it as a ratio, using a colon.
  11. Perimeters
    triangles A rectangle has a perimeter of 16p centimeters, it had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8.
  12. The spacecraft
    Sputnik_670 The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered
  13. Suppose
    linear_eq Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
  14. Empty and full
    vaha2 An empty can has a mass of 1/6 lb. When it is filled with sand, it has a mass of 7/12 lb. Find the mass of the sand in the can?
  15. Hexagonal pyramid
    hexa_pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
  16. Quadrilateral pyramid
    ihlan_rez In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area.
  17. Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  18. 3/8 off
    sale_2 A shirt cost 38.95 How much will you pay for the shirt if it has a discount tag for 3/8 off? Round to the nearest cent
  19. Sick days
    flu In Canada, there are typically 261 working days per year. If there is a 4.9% chance that an employee takes a sick day. .. what is the probability an employee will use 17 OR MORE sick days in a year?
  20. Skid friction
    trenie Find the smallest coefficient of skid friction between the car tires and the road so that the car can drive at a 200 m radius at 108 km/h and does not skid.

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...