# Examples for secondary school students - page 55

- Rectangle

The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm. - Money

Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael. - Inscribed sphere

How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube? - Baskets of apples

Grandfather gathered apples into baskets. He filled one large and three small baskets. Small baskets are identical and each can hold 3 kg of apples less than in a large basket. In small baskets together 3 kg of apples over a large basket. How many kilogram - Air pressure

The meteorological station measured the air pressure of 1060 hPa (hectopascals). In addition to measuring instruments, there is a residential house that has a flat roof with dimensions of 10 m and 28 m. What pressure force in MN (meganewtons) force the ai - Pyramid

The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid. - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Variance and average

Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx). - Two trains

There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway - Unknown amount of money

Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis. - Permutations without repetition

From how many elements we can create 720 permutations without repetition? - The pool

The pool has a volume of 40 m^{3}and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C? - Probably member

Look at the series 2,6,25,96,285, ? What number should come next? - Desribed circle to rectangle

Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%). - First class

The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective? - GP - 8 items

Determine the first eight members of a geometric progression if a_{9}=512, q=2 - Blueberries

Miko and Anton have a total of 1,580 blueberries. Miko and Anton have them in the ratio 2: 3. Determine how much each of them has. - 3 masons

3 masons received 7,700 CZK. The second half received 1/2 more than the first and third twice more than the second mason. How much they each got crowns? - Combinations

From how many elements we can create 990 combinations 2nd class without repeating? - Exponential equation

Solve for x: (4^x):0,5=2/64.

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