# Examples for secondary school students - page 24

- Four-digit number

Find also a four-digit number, which quadrupled written backwards is the same number. - Number

Is number 5.146852 irrational? - Rhombus

The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides. - SAS triangle

The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle. - The body

The body on the figure consists of cubes with an edge length 6 cm. What surface has this body? - Workman - shift

The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components? - Mother and daughter

Three years ago mother was three times older than daughter. After nine years she will be only twice old. How old is mother (and daughter)? - Half life

Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes. - Warehouse cars

From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck? - Overload

Calculate how many g's (gravity accelerations) feel glider pilot when turning the horizontal circles of radius 148 m flying at 95 km/h. Centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius of rotation - Diagonals in diamond

In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals. - Cone container

Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package. - Spirit

From 55% and 80% spirit we would like to produce 0.2 kg of 60% spirit. How many of them we must use in a solution? - Chess

How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color? - Gasholder

The gasholder has spherical shape with a diameter 20 m. How many m^{3}can hold in? - Triangle

Calculate the area of the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius). - Bath

In the bath is 30 liters of hot water. Then added 36 liters of cold water at temperature of 19 °C decreased temperature of water to 41 °C. What was the initial temperature of the hot water? - Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal. - Elections

In elections candidate 10 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes. - Grandfather

The grandfather is three years older than an grandmother. The average age of the grandmother, the grandfather and their seven grandchildren is 28 years. The grandchildren have a total of 105 years. Calculate how old is grandfather.

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