Examples for secondary school students - page 187 of 237
Number of problems found: 4731
- Beam on platform
A homogeneous wooden beam of length 6.00 m and mass 72.0 kg lies on a horizontal platform high above the ground and overhangs by 1.80 m over the edge of the platform a) Decide whether a person with a mass of 60.0 kg can stand on the overhanging end of the - Contestants
In the competition, it was possible to get 0-5 points. Five of the 15 best contestants have earned 5 points or 4 points (which have won 10 contestants). The number of contestants who scored 3 points was the same as those who did not get any points. Calcul - Sum probability
Natural numbers 4,5,7,11,12 are given. Calculate the probability of the event that the sum of three randomly selected numbers is less than 22. - AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38 - Salary in enterprise
The average salary in the company is 27,000 CZK. 30% of workers have the lowest average income of 19,000 CZK. The wages in this group increased by 2%. How much did this increase the average wage across the company? - Row pupils
There are 48 pupils in the third row and 17 more in each subsequent row than in the previous one. Find how many pupils there are in the first and tenth rows. - Centre of mass
The vertices of triangle ABC are from the line p distances 3 cm, 4 cm, and 8 cm. Calculate the distance from the center of gravity of the triangle to line p. - Cards
The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace - Segment in a triangle
In a triangle ABC with the side/AB/ = 24 cm constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance of 1 cm from AB. Calculate the height of the triangle ABC to side AB. - Metals
Eight teams play in the Hockey World Cup. Determine how many ways gold, silver, and bronze medals can be awarded. - Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm. - Raspberry baskets
Find how many raspberries are in the third and tenth baskets, if there are three raspberries in the first and eight raspberries more in each. - Weight ratio
Andrew, Michael, Patrick, and George together weigh 128 kg. Their weights are in the ratio 1:6:7:2. Determine what weight each of them has. - Three numbers
Find three numbers so that the second number is three times larger than the first and the third is six larger than the second number. Their sum is 62 - Inscribed circle
XYZ is a right triangle with a right angle at the vertex X and an inscribed circle with a radius of 5 cm. Find the area of the triangle XYZ if XZ = 14 cm. - Prize How many ways can 9 participants be rewarded with the first, second, and third prizes in a sports competition?
- Octahedron
All walls of the regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - Calculate a cone
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - Permutations without repetition
From how many elements can we create 720 permutations without repetition? - Cone container
The Rotary cone-shaped container has a volume of 1000 cubic cm and a height of 12 cm. Calculate how much metal we need to make this package.
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