# Examples for secondary school students

- 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/ - Stadium

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. - 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°. - Disinfecting solution

How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution? - Arc-sector

arc length = 17 cm area of sector = 55 cm^{2}arc angle = ? the radius of the sector = ? - 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? - 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? - Combinations of sweaters

I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done? - Inscribed circle

Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1]. - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Banknotes

$ 1390 was collected. How much was in $20 notes and how many in $50 notes in that order? How many solutions exists? - 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? - Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2}. Determine the side length of the original square. - Three ints

The sum of three consecutive integers is 2016. What numbers are they? - 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 - Road drop

On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane? - 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 - AS - sequence

What are the first ten members of the sequence if a11=22, d=2. - Cube - wall

V kocke ABCDEFGH je ?. Aký je povrch kocky? - Consecutive numbers

Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).

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