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 m³ 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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