Examples for secondary school students - page 143 of 230
Number of problems found: 4582
- 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? - Four-sided 5917 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
- ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Triangle 5851
In a triangle, the first angle is half the second angle, and the third angle is the third of the first angle. How big are the angles in a triangle, and what is the type of triangle? - Tetrahedron - surface
Calculate the surface area of a regular tetrahedron whose height is 9 cm.
- Three workshops
2743 people are working in three workshops. In the second workshop, 140 people were more than in the first, and in the third work, 4.2 times more than in the second. How many people work in each workshop? - Percentage 5834
There are 1.5 times more women than men in the theater. What percentage of women are more than men in the theater? - Bamboo
At a certain height, the wind broke the bamboo high 32 feet, so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Possibilities 5822
Peter forgot the four-digit code to his school locker lock. Fortunately, his mother remembered some information about him. He knows that the first binary number is divisible by 15 and the second by 7. However, Peter is a big loser, so he has to try all th - Two forces
The two forces, F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
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