# Examples for secondary school students

#### Number of problems found: 2029

- Car factory

Carmaker now produce 2 cars a day more than last year, so the production of 70312 cars will save just one full working day. How many working days needed to manufacture 70312 cars last year? - Square pyramid

Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees. - 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 - Wood in the forest

The amount of wood in the forest was estimated at 6000 m^{3}. How much wood will be in forest after 2 years if the annual growth of wood is 2.5% each year and logging 30 m^{3}each year? - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - Mushrooms from the forest

Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda? - Dimensions of the trapezoid

One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm^{2} - Candies

There are two types of candies in the store at 20 CZK/kg and 80 CZK/kg. How much will be cost a mix if we mix 22kg cheaper and 4kg more expensive candies? - Arc-sector

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

The tent has the shape of a triangular prism. The front and rear walls are isosceles triangles with a height of 18 dm and arms 19.5 dm long. The tent is 1.5 m wide and 2 m long. How many square meters of fabric is needed to make a tent? How much air is in - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - The farm

The farm harvested 390 tons of grain. Wheat was 15% more than barley, and rye was 126 tons less than wheat and barley combined. How many tons of wheat, how many tons of barley, and how much rye did the team get? - Potatoes

Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself. - Square

Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm^{2}. Determine the side length of the original square. - Cylinders

The area of the side of two cylinders is the same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much? - 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. - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm^{3}. Calculate the radius of the base circle and height of the cone. - Uboid volume

Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm² - Cuboid diagonals

The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.

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