Examples for secondary school students - page 234 of 237

Number of problems found: 4733

Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 810 cm.
Bulbs
The probability that the bulb can operate 4000 hours is 0.3. What is the probability that exactly one of the eight bulbs can operate 4000 hours?
Geometric mean
Calculate the geometric mean of 15.2 and 25.6. Also determine the mean by geometric construction, treating 15.2 and 25.6 as lengths of line segments.
Golden ratio
Divide the line of length 871 cm into two sections so that the ratio of shorter to greater is the same as the ratio of the greater section to the whole length of the line.
Wind drift
A plane flies at 780 km/h airspeed. It covers a distance of 1200 km with the wind and then the same distance against the wind in a total of 3 h 5 min. What is the wind speed?
The cyclist
A cyclist travelled from a village to a town. The first half of the journey was at 24 km/h. The second half, which was mostly downhill, was at 38 km/h. The entire journey took 94 minutes. Calculate the distance from the village to the town.
Circle and angle
What is the arc length of a circle with radius r = 432 dm corresponding to a central angle of 0.53 rad?
Roller
The lateral surface area of a cylinder equals the area of one of its bases. The cylinder height is 23 dm. What is the radius of the base of the cylinder?
Geometric progression 2
There is a geometric sequence with a₁=3.6 and quotient q=-2.1. Calculate a₁₇.
Cylinder - A&V
A cylinder has a volume of 463. Its base has a radius of 4. What is the total surface area of the cylinder?
Similarity n-gon
6-gones ABCDEF and A'B'C'D'E'F' are similar. The area of 6-gon ABCDEF is S₁=248 m², and the diagonal length FA is 28 m. Calculate the area of the 6-gon A'B'C'D'E'F' if F'A' = 36 m.
Rectangle - sides ratio
Calculate the area of a rectangle whose sides are in the ratio 2:16 and whose perimeter is 1289.
Electronics: Resistors in parallel
Concerning calculating the resistance of the parallel combination of resistors: (1)/(R) = (1)/(R₁) + (1)/(R₂) Calculate the R, if R₁ = 17Ω a R₂ = 20Ω
Tractors
Two tractors with different capacities are to plough a field. The first tractor can plough the entire field in 14 hours. The second tractor can plough the entire field 8 hours déle. How long does it take both tractors to plough the entire field working to
Bits, bytes
Calculate how many different numbers can be encoded in a 64-bit binary word.
Rectangle Anton
The difference between the length and width of a rectangle is 3. The length is 2 times greater than the width. Calculate the dimensions of the rectangle.
Radioactivity
After 113 hours decreases, the activity of a radioactive substance to 1/6 of the initial value. What is the half-life of the substance?
Exponential equation
Solve exponential equation (in real numbers): 2^3x-6=9
Morse alphabet
Calculate how many words of Morse code to create compiling dashes and dots in the words of one to piatich characters.
Examination
The class is 25 students. How many ways can we choose 5 students for examination?

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