# Examples for secondary school students

1. Float boya A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/ A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
3. Area and two angles Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
4. Disinfecting solution How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
5. Arc-sector arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
6. Forth and back Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
7. Two pipes One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
8. Combinations of sweaters I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
9. Inscribed circle Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
10. Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
11. Banknotes \$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?
12. Cyclist Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?
13. Square If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
14. Three ints The sum of three consecutive integers is 2016. What numbers are they?
15. Bus stop Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to th On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
17. Dices throws What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
18. AS - sequence What are the first ten members of the sequence if a11=22, d=2.
19. Cube - wall V kocke ABCDEFGH je ?. Aký je povrch kocky?
20. Consecutive numbers Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).

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...