Examples for secondary school students - page 64 of 232
Number of problems found: 4622
- Above water surface
If we remove the stone from the water, we apply a force of 120N. How much force will we exert if we move the stone above the water? The stone's density is 5000 kg/m³. - Two workers
One worker makes a part 4 hours and the second 9 hours later than they would make the same part together. How long does it take for each worker to make the part himself? - Hockey Championships
At the 2021 World Hockey Championships, there are eight teams in Group A, each playing seven matches. There are 4 points for each team to gain points (3-2-1-0), but it is always paired with the opponent's points ( 0-1-2-3). How many points are there possi - Tower board placement
How many ways can we build eight indistinguishable towers on an 8 × 8 board so they don't endanger each other? - Two cars
Two cars (trucks and passengers) drove simultaneously from two places 50 km away. If they go against each other, they will meet in 30 minutes. If they follow each other in the same direction, the car will catch up with the truck in 2.5 hours. What is the - Harmonic oscillation equation
Write the harmonic oscillation equation if the oscillation's amplitude is 5 cm and its period is 0.5 s. - Bottle, cup and jug
The bottle and the cup have the same weight as the jug. The bottle has the same weight as the cup and plate. Two jugs have the same weight as three plates. What is the weight of the bottle if the weight of the cup is 100g? - Siblings savings distribution
Three siblings saved CZK 1,445. Adela saved 10% less than Martin and David 10% more than Adela. How many crowns did each of them save? - Three surveyors
Three surveyors are tasked with measuring the height of a mast standing on a flat plain. The first surveyor, standing 100 m from the mast, measured the elevation angle (a), the second, 200 m from the mast, measured the elevation angle (b), and the third, - Radio signal oscillations
The time signal in the radio consists of four sound marks with a frequency of 1,000 Hz, of which the first three have a duration of 100 ms and the fourth 500 ms. How many oscillations will occur at each mark? - Two pendulums
In 24 s, the first pendulum performed 12 oscillations and the second 16 oscillations. Determine the periods and frequencies of both pendulums. - Beam force distribution
A body weighing 400 kg is suspended at a distance of 1 m from one end of the beam on a beam weighing 100 kg and 5 m. How large do forces act at the ends of the beam? - Isosceles trapezoid
Find the height in an isosceles trapezoid if the area is 520 cm² and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid. - 3 positive charges
Three equal positive charges Q are located at the vertices of an isosceles right triangle ABC. The right angle is at vertex A. The length of side AB is 1m. What is the electric field strength at the center S of side BC, i.e., what force would act on a pos - School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm³ - A machine
A machine produces steel rods of normally distributed length, the mean length and the standard deviation being 50.0 cm and 0.5 cm, respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in - Arithmetic mean median
Calculate the arithmetic mean, median, and mode of numbers x1, x2. .., x15, if the number 2 occurs between them five times, the number 7 eight times, and the numbers 10 and 12 once. - Thermometer
Immerse a thermometer with a heat capacity of 2.0 J/K in water weighing 67.0 grams. Before water immersion, the thermometer showed a temperature of 17.8 degrees Celsius. After reaching equilibrium, the temperature is 32.4 degrees. What was the water tempe - A married
A married couple planned to have three children. i. List the possible combinations of the sexes of 3 children. Use B for a boy and G for a girl. ii. Calculate the probability that all three children would be of the same gender - Diver hydrostatic pressure
The Czech Martin Štěpánek became the world record holder in May 2003, diving in the open sea in Cyprus with only fins to a depth of 93 m for 3 min and 34 s. Calculate the hydrostatic pressure acting on it at this depth.
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