Examples for secondary school students - page 143 of 230

Number of problems found: 4597

Dimensions 5996
How many cubes with an edge of 10 cm will fit into a block with dimensions of 2 dm, 3 dm, and 5 dm?
Coordinate axes
Find the triangle area given by line -7x+7y+63=0 and coordinate axes x and y.
Deformed 5992
Fifty small metal cubes with an edge length of 2 cm were deformed, and we made one large cube from this material. What is its surface?
Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
Depreciation 5990
The price of the car was € 15,000. What will be the price of a car with an annual depreciation of 1% in 8 years?
Everyone 5965
We bought towels for CZK 432. If there were six more towels for the same money, everyone would be 66 CZK cheaper. How many towels were there?
Disembarked 5962
Twenty-two passengers boarded in Žilina. Everyone gradually disembarked on the Teplička, Strečno, Vrútky, and Martin lines (the wagon was already empty in Martin). How many ways could they come out?
Subsets
How many 19 element subsets can be made from the 26 element set?
Four-sided 5957
How much m² of the galvanized sheet is used to cover the roof of the tower, which has the shape of a four-sided pyramid, whose base edge is 6 m long? The height of the tower is 9m. When covering, is 5% metal waste expected?
Raffle
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least four winnings for a group of people who have bought five tickets together?
Kilometers 5928
The tourist traveled 78 km in three hours. For part of the journey, he traveled by bus at an average speed of 30 km/h, and for the rest, he walked at an average speed of 6 km/h. How long did he walk, and how many kilometers did he walk?
Resistance - ohms
If the resistance of the first resistor is 300 ohms and the resistance of the second resistor is 100 ohms. What is the resulting resistance?
Last storm - tree
Mr. Radomír had a misfortune during the last storm; a tree fell on his roof in the shape of a regular four-sided pyramid and destroyed it all. The roof has a base edge length of 8m and a side edge length of 15m. How many m² of roofing will he have to buy?
Proportion 5904
A kilogram of one kind of nut is sold for 130 CZK. A kilogram of another type of nuts for 250 CZK. In what proportion are the two kinds of nuts mixed in a mixture whose price is CZK 220 per kilogram?
Inscribed circle
Calculate the magnitude of the BAC angle in triangle ABC if it is three times less than the angle BOC, where O is the center of the circle inscribed in triangle ABC.
Geometric 5895
A2 + a3 = -6 a1 + a2 + a3 + a4 = 20 Geometric sequence q, a1?
The coil
How many ropes (a diameter of 8 mm) fit on the coil (threads are wrapped close together)? The coil has the following dimensions: The inner diameter is 400mm. The outside diameter is 800mm. The length of the coil is 470mm.
Determine 5893
Determine the largest integer n for which the square table n×n can be filled with natural numbers from 1 to n² (n squared) so that at least one square power of the integer is written in each of its 3×3 square parts.
Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm³. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
Difference 5867
Calculate the value of the first term and the difference in the arithmetic sequence a1 + a7 = 42 a10-a3 = 21

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