Examples for secondary school students - page 19 of 231
Number of problems found: 4605
- Unit circle
In the Cartesian coordinate system, a unit circle is given on which points A and B lie. Point O is the origin and has coordinates (0,0) and point B has coordinates (1,0). The size of angle BOA is 151°. Determine the x-coordinate of point A. - X-ray intensity
The intensity of X-ray radiation is reduced by half when passing through a 13.5 mm thick lead layer. Determine the thickness of the lead plate that will reduce the radiation intensity to one tenth of the original value. If we know that the intensity decre - Equation - integers
Solve the equation with the unknown x from the field of natural numbers 1+6+11+16+. ... +x=970 - Rows of chairs
There are 15 chairs in the first row. There are 3 more chairs in each row. How many chairs are there in the first 20 rows? - Penny and rolls
For a hundred crowns I have to buy a hundred pieces of pastry at the prices of rolls of 0.50 crowns, bread 10 crowns, and a roll of 3 crowns. How much of what should I buy? (The Slovak koruna was the currency in Slovakia before the euro or the Czech korun - In a football
In a football tournament of eight teams, where each team played each other exactly once, points were awarded as follows: the winner of the match received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the - Traffic accidents
Of the total number of traffic accidents, 80% occur in the village and 20% outside the village. If the number of traffic accidents in the village were reduced by 40%, by what percentage would the total number of traffic accidents decrease? - Instantaneous water heater
Water flows into and out of an instantaneous water heater at the same time. If water only flows in, the empty water heater would be filled in 18 minutes. If water only flows out, the full water heater would be emptied in 20 minutes. How many hours will it - Three numbers
The product of three natural numbers is 600. If we reduced one factor by 10, the product would decrease by 400. If we increased one factor by 5 instead, the product would increase to twice the original value. Which three numbers have this property? - Train - start-up
A train weighing 1200 tons is supposed to reach a speed of 15 m/s in 45 s when starting up. Determine its acceleration and the magnitude of the force it must exert if the friction force is 0.005 of the train's gravity. - A car acceleration
A car increased its speed from 21.6 km/h to 108 km/h on a 54 meter long track. Determine its acceleration, assuming that the motion is uniformly accelerated. - Preparing the mixture
The seller prepared 25 kg of the mixture for 264 CZK per 1 kg. The first type was 180 CZK per 1 kg and the second was 390 CZK per kg. How much of each did he need? - Green cards
We draw 4 cards from 32 cards. In how many ways can we draw a) exactly 2 aces, b) 3 green ones - In the shipment
There are 40 products in the shipment. Of these, 4 are defective. In how many ways can we select 5 products so that exactly 3 of them are good? - Two workshops
Two workshops were supposed to produce 4000 sets of kitchen utensils together. After completing this task, it was found that the first workshop produced 534 sets more than was originally set for it, while the second workshop fulfilled its task by 80%. How - Shear friction
How much force must we apply to a box weighing 300 kg to move it uniformly along a horizontal floor if the coefficient of shear friction between the box's edge and the floor is 0.5? - Hockey - game
A hockey goalkeeper has a save success rate of 93.5%. What is the probability that he will keep a clean sheet in a match when facing 25 shots? What is the probability that he will concede a maximum of 2 goals? - Four-digit number
Juraj is thinking of a four-digit number that he told us about: (a) Its digit sum is one hundredth of the number that I get by rounding the imaginary number to hundreds. (b) Its last digit is 1 more than the second-to-last. (c) The sum of its last two dig - Maturitný - RR - base
In an isosceles triangle ABC with base AB, ∠BAC = 20°, AB = 4. The axis of the interior angle at vertex B intersects side AC at point P. Calculate the length of the segment AP. Give the result to two decimal places. - Segments on the hypotenuse
A right triangle ABC has a hypotenuse of c=26cm. How many segments does the height vc=12 cm cut out on the hypotenuse c? What are the lengths of the sides a and b? What are the angles at the vertices A and B?
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