# Examples for secondary school students

1. Closed circuit In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage.
2. Students Students Aleš, Bohouš, Cyril, and Dušan were on a brigade. They divided the total revenue as follows: Aleš received two-fifths of the revenue, Bohouš received one-sixth of the revenue, Cyril received three-tenths of the revenue, and Dušan received the res
3. Energy consumption The device is connected to 230V and draws 3.5A current. Power consumption is 1932kJ. How many minutes has this device been in operation?
4. The test The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer
5. Birthdays In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
6. Cone roof How many m2 of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
7. Double probability The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
8. Spherical cap The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
9. The rescue helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
10. Embankment The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?
11. RT triangle and height Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
12. Working together Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone?
13. Black diamond run Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet.
14. An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
15. Compound interest 4 3600 dollars is placed in an account with an annual interest rate of 9%. How much will be in the account after 25 years, to the nearest cent?
16. The angle of view Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
17. Two groves Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
18. Contestants The three best contestants are to divide the total prize of CZK 4,200. The second gets 20% more than the third. And the first one gets 200 CZK less than the second and the third together. How much will everyone get?
19. Triangular prism - regular The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
20. Permille of alcohol I have 2 per mille of alcohol in my blood. How many milliliters is it when I have 5 liters of blood?

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...