Examples for secondary school students

  1. Bottles
    flasa_1 The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
  2. Bridge cards
    cards2 How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
  3. Area of garden
    garden_20 If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increa
  4. Cube, cuboid, and sphere
    cubes3_8 Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
  5. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  6. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  7. Cancel fractions
    zlomky_15 Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
  8. Speed of car
    autosalon_2 The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
  9. Candy and boxes
    cukriky_13 We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of
  10. Normal distribution GPA
    normal_d_3 The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
  11. Merchant
    sale_3 The merchant lower cost by 10% in December when it was not sold. Again in January lower cost by 20% and now costs 576 €. A. How much the goods stood originally? B, how much cost the goods after the first lowering? C, How many percents totally merchant l
  12. Young mathematician
    age_1 One young mathematician was bored again. He found that the average age of people in the room where the seminar is equal to its count. Then his 29-year-old brother entered this room. Even then, the average age of all present was the same as the count of pe
  13. Ratio of sides
    trojuholnik_5 The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
  14. Overload
    aircraft-02_10 What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
  15. A triangle
    triangle1_1 A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
  16. Employees
    penize_49 The company employs 1 440 employees (men and women). For over-average results, the premiums were 18.75% of all men and 22.5% of all women. 20% of employees were rewarded with premiums. How many men and how many women are employed in the company?
  17. Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  18. Geometric progression
    exp_1 In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
  19. Alice
    usd_10 Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack?
  20. Hexagon ABCDEF
    hexagon_2 In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.

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...