The most difficult problems

  1. The quadrilateral pyramid
    jehlan_4b_obdelnik The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
  2. The bridge
    bridge2 A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
  3. Angled cyclist turn
    cyclistTurn The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
  4. Rotaty motion
    rotaryMotion What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
  5. Two divided
    fractions14 Two divided by nine tenths.
  6. Tenths digit
    numbers2 For 10.932, which digit is in the tenths place?
  7. Two dogs
    calendar Izzy's dog is 10 1/2 years old. Paige's dog is 18 months old. How many years older is Izzy's dog?
  8. Two accounts
    bank A banker divided $5000 between 2 accounts, one paying 10% annual interest and the second paying 8% annual interest. Express the amount invested in the 10% account in the terms of the amount invested in the 8% account.
  9. The percent 2
    penize The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i
  10. One third power
    cube-root Which equation justifies why ten to the one-third power equals the cube root of ten?
  11. College 2
    fuel College student is moving into a dormitory. The student rent a truck for $19.95 plus $0.99 per mile. Before returning the truck the student fills the tank with gasoline, which cost $65.32. Total cost $144.67. Using a linear equation, explain the process t
  12. Parallel and orthogonal
    vectors2 I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w
  13. Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  14. Regular hexagonal pyramid
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
  15. Octagonal pyramid
    octagonl_pyramid2 Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
  16. Possible lengths
    triangles Find the most possible lengths for the third side of a triangle with sides 20 and 18.
  17. Find the 12
    circle_eq Find the equation of the circle with center (3,7) and circumference 8π units.
  18. Hexagonal pyramid
    hex_pyramid Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
  19. Doug biked
    cyclist Doug biked 5 1/4 miles in 3/4 of an hour. What is his average speed?
  20. Earnings per share
    usd The table below shows the stock price, earnings per share, and dividends per share for three companies for a recent year: Deere &Co. Price $65.70 earnings per share $4.40 Dividends per share $1.16 Google price $528.33 earnings per share $27.72 Dividends

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...