# Examples for secondary school students

1. Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
3. A fisherman
A fisherman buys carnivores to fish. He could buy either 6 larvae and 4 worms for \$ 132 or 4 larvae and 7 worms per \$ 127. What is the price of larvae and worms? Argue the answer.
4. A photograph
A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
5. Here is
Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.
6. Rectangular garden 2
A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
7. RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
8. One three
We throw two dice. What is the probability that max one three falls?
9. Find the 10
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
10. Carla
Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter’s age was twice the sum of Carla’s and Jim’s age. Find the present age of each one of them.
11. Height of the room
Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
12. Perimeter of RT
Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
13. Sphere floating
Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
14. Bonuses
Five employees of the company were paid bonuses so that each successor received a 550 USD less than the previous employee. How much did everyone get, if a total of USD 11,000 has paid?
15. Lathe
95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
16. Former price
The price of an article is cut by 10%, to restore it to the former value, by what percent the new price must be increased?
17. Percent change
If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
18. Curiosity factor
A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?.