Examples for secondary school students - page 20 of 237
Number of problems found: 4730
- Rows of chairs
There are 15 chairs in the first row. Each subsequent row has 3 more chairs than the previous row. How many chairs are there in the first 20 rows in total? - Penny and rolls
For one hundred crowns I need to buy exactly one hundred pieces of pastry at the following prices: rolls at 0.50 crowns each, bread at 10 crowns each, and buns at 3 crowns each. How many of each should I buy? (The Slovak koruna was the currency in Slovaki - 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 received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the end of the t - Traffic accidents
Of the total number of traffic accidents, 80% occur within built-up areas and 20% outside them. If the number of traffic accidents within built-up areas 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 instant water heater simultaneously. If water only flows in, the empty heater would be filled in 18 minutes. If water only flows out, the full heater would be emptied in 20 minutes. How many minutes will it take to fill the - Three numbers
The product of three natural numbers is 600. If one factor is reduced by 10, the product decreases by 400. If another factor is increased by 5 instead, the product doubles. Which three numbers have this property? - Train - start-up
A train weighing 1,200 tonnes 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 weight. - A car acceleration
A car increased its speed from 21.6 km/h to 108 km/h over a 54-metre-long track. Determine its acceleration, assuming that the motion is uniformly accelerated. - Preparing the mixture
The seller prepared 25 kg of a mixture priced at 264 CZK per kg. The first type cost 180 CZK per kg and the second 390 CZK per kg. How much of each did he need? - Green cards
We draw 4 cards from a deck of 32 cards. In how many ways can we draw: a) exactly 2 aces, b) exactly 3 green cards? - In the shipment
There are 40 products in a shipment, of which 4 are defective. In how many ways can 5 products be selected so that exactly 3 of them are non-defective? - Two workshops
Two workshops were supposed to produce 4,000 sets of kitchen utensils together. After completing the task, it was found that the first workshop produced 534 sets more than originally planned for it, while the second workshop fulfilled its plan at 80%. How - Shear friction
How much force must be applied to a box weighing 300 kg to move it at a constant speed along a horizontal floor, if the coefficient of sliding friction between the box 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 keeps a clean sheet in a match when facing 25 shots? What is the probability that he concedes at most 2 goals? - Four-digit number
George is thinking of a four-digit number and gives us the following clues: a) Its digit sum equals one hundredth of the number obtained by rounding the mystery number to the nearest hundred. b) Its last digit is 1 more than the second-to-last digit. c) T - Maturitný - RR - base
In an isosceles triangle ABC with base AB, ∠BAC = 20° and AB = 4. The angle bisector from vertex B intersects side AC at point P. Calculate the length of segment AP. Give the result to two decimal places. - Segments on the hypotenuse
A right triangle ABC has a hypotenuse c = 26 cm. The altitude from C to the hypotenuse is h_c = 12 cm. What are the lengths of the two segments of the hypotenuse? What are the lengths of sides a and b? What are the angles at vertices A and B? - In trapezoid 3
In trapezoid ABCD, the following elements are given: lengths of the parallel sides a = 20 cm and c = 11 cm, angle α = 63°36', and angle β = 79°36'. Calculate the lengths of the other two sides and the sizes of the remaining angles. - Given is
The circle is given by the equation x² + y² − 4x + 2y − 11 = 0. Calculate the area of the regular hexagon inscribed in this circle. - Missile 3
A missile penetrated an embankment to a depth of 1.2 m. What was its speed when it hit the surface of the embankment, if the missile's movement through the ground lasted 0.021 seconds and the motion was uniformly decelerated?
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