Examples for secondary school students - page 106 of 214
Number of problems found: 4271
- Different 7860
How many different triplets can be created from 4 pupils if it does not matter the order of the pupils in the triplets? - Mast shadow
The mast has a 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at an angle of 15°. Determine the height of the mast if the sun above the horizon is at an angle of 33°. Use the law of sines. - Lampshade 7846
Lampshade for the face of a truncated cone with a height of 20 cm. The upper diameter of the shade is 13 cm, the lower 36 cm, and the side forms an angle of 60 degrees with the lower diameter. At least how much fabric is needed to make this shade? - Pyramid-shaped 7820
The pyramid-shaped tent has a square base with a side size of 2.2m and a height of 1.8m. How many square meters of tent canvas are needed to make it if we count an extra five percent for the foundation?
- The observatory
The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal need to be covered to cover it, and must we add 15 percent to the minimum amount due to joints and waste? - Quadrilateral 7815
The area of the mantle of a regular quadrilateral pyramid is equal to twice the area of its base. Calculate the pyramid's volume if the base edge's length is 20 dm. - Three workers
The three workers received € 2,850 together for the work done. They divided them according to the time worked so that the first received 20% less than the second and the third € 50 more than the second. How much EUR did each worker receive? - Securities 7805
Mr. Vlaško bought securities for 30,000 euros. The year he sold them, they were 15% more expensive. Mr. Vlaško paid a 15% tax on this profit. How much tax did he pay? - Rectangular 7801
The length of the sides of the rectangular garden is 4:3. The junction of the centers of adjacent sides is 20 m long. Calculate the area of the garden.
- Two gears
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM - Calculate 3
Calculate the cube volume whose edge is 3x-1,3x-1,3x-1 - Car and motorcyclist
A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds. - Lee is
Lee is eight years more than twice Parker's age. Four years ago, Lee was three times as old. How old was Lee 4 years ago? - Rectangular plot
The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the plot's perimeter is 36m. Find the area of the diagonal of the plot.
- Divisors 7779
Two numbers are guessing. The second number is five times greater than the first number, and the square of the first number is equal to 3/5 of the second number. Find the sum of the two numbers and all its divisors. - Vítovcová 7776
Ms. Vítovcová and Ms. Kupcová went to Paris for a few days. Mrs. Vítovcová exchanged 30 marks and 100 francs at the exchange office and paid a total of 1,200 CZK. Ms. Kupcová paid a total of CZK 1,400 for 10 marks and 200 francs. How many crowns was the m - Following 7774
The store sells 3 types of cakes: poppy, cottage cheese, and jam. They all cost the same. As of yesterday, the following offer applies: If you buy any 8 of these cakes, you will pay for only 5. How much percent less will I pay now for 8 of these cakes? - Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle? - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an
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