Examples for secondary school students - page 92 of 232
Number of problems found: 4622
- Columns of two and three
When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are five more double columns than three columns. How many students are in the class? - Tank painting calculation
The septic tank is 6 m high and 2.4 m in diameter. If the painter consumes 1 kg per 5 m² and the paint is delivered in two kg cans, how many packages of insulating paint must he order? - Ticket code combinations
Tickets have 9 numbered windows. How many different codes can be set for each other if 3 or 4 windows are punched? - Central angle calculation
There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate the magnitude of the central angle that belongs to this chord. - Resistor circuit
Three resistors are connected according to the scheme (R1 in parallel with R2 and series with R3: R1||R2 + R3) so that R1=0.6 Ω, R2=2 Ω, R3=3 Ω, current I1 = 10 A. Calculate all the currents passing through the respective resistors R1, R2, R3 and all the - Two-digit number puzzle
In a two-digit number, the number of tens is three more than the number of ones. If we multiply the original number by a number written with the same digits but in the reverse order, we get the product 3 478. Determine the actual number. - In the dairy
The dairy had three times more milk packages than half a liter. Four times more liters remained when sold in 10 liters and 10 half-liter containers than in half-liter packages. How many packages were there originally? - Resistor parallel connection
Three resistors with resistances of 200 Ω, 400 Ω, and 600 Ω are connected next to each other (parallel). A current of 1.8 A flows through the first 200Ω resistor. a) What current passes through the second and what current through the third resistor? b) Wh - Lowest voltage
Three resistors with resistors R1 = 10 kΩ, R2 = 20 kΩ, R3 = 30 kΩ are connected in series and an external voltage U = 30 V is connected to them. On which resistor is the lowest voltage? - Hospital death probability
Statistically, in a city of 100,000 inhabitants, 600 people die in one year. During the year, 2,000 people received hospital treatment, and 120 of them died there. Calculate the probability that a citizen who comes to the hospital for treatment will die t - Marathon training distance
Peter trains for a half marathon every day. He ran 1,000m on the first day and increased the training length by 250m daily. On a certain day, Peter ran 21 km in training. That day, he calculated the total distance he had run since the start of training. H - Aircraft climbing
The average climb angle of the aircraft is 11° 20', and its average speed is 400 km/h. How long does it take to climb to a height of 3000m? - Quadratic function graph
The quadratic function has the formula y = x²-2x-3. Sketch a graph of this function. Find the intersections with the axes. Find the vertex coordinates. - Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Research in school For particular research in high school, four pupils are selected from a class of 30 pupils. Calculate the number of all possible results of the selection and further calculate the number of all possible results if it depends on the order in which the stud
- Scrap probability
Five hundred of the products in the series are to be inspected with a repeat check. The manufacturer guarantees 2% scrap for a given production. Determine the probability of scraps among the 500 products reviewed between 12 and 20. - Probability of failures
The probability of failure in specific productions is 0.01. Calculate the likelihood of more than one failure among the 100 selected products if we return them to the file after the check. - Started
A pedestrian leaves point A with a speed of v1 = 5 km/h. After 3 hours, a cyclist follows him from the same place at a speed of v2 = 20 km/h. But a car starts from point B, 50 km away at the same time as the cyclist. Calculate the distance and time at whi - Birthday paradox
How large is the group of people so that the probability that two people have a birthday on the same day of the year is greater than 90%? - The tent
The tent has the shape of a regular square pyramid. The edge of the base is 3 m long, and the tent's height is 2 m. Calculate how much cover (without a floor) is used to make a tent.
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