Examples for secondary school students - page 132 of 237
Number of problems found: 4730
- Hexagon in circle
Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle. - Children weight puzzle
Max and Katy weigh 75 kg together, Katy and Tina weigh 71 kilograms, and Max and Tina weigh 80 kilograms. Thus, each of the children weighs 75 kilograms. - Symmetry by plane
Determine the coordinates of an image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0 - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7 - Water reservoir
One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously? - Darts Score Combinations
Adam was practicing for a darts competition in class. Every day at home, he threw darts at a target in which the individual fields were worth 1,3 and 5 points. He threw 9 darts every day and always scored 27 points. He is in good form and never missed a t - Three-digit numbers
Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there? - Inequality proof
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - Confectionery
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Hiker Path Lengths
The hiker went from A to B and back in 3 hours and 41 minutes. The road from A to B is first uphill, then flat, and finally downhill. A hiker walked up a hill at a speed of 4 km/h, on a flat surface at a speed of 5 km/h, and down a hill at a speed of 6 km - Tea Left in Kindergarten
The children in the kindergarten drank 20% of the prepared tea in the morning. They drank another 10% of the left tea afternoon. After the whole day, there were still 9 liters of tea left. How many liters of tea was prepared in the kindergarten in the mor - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62 cm. Calculate the trapezium area in cm square and calculate how many different perimeters - Grandparents
Grandfather set aside €1,200 for savings. At the beginning of each month, he deposited €100 into the bank at an annual interest rate of 3%. At the end of the year, he had €1,219.68 in the bank. Grandma immediately deposited the entire amount of €1,200 int - Clothing company
A clothing company manufactures three kinds of coats. The weekly production is 400 of the first type, 370 of the second, and 230 of the third type. By long-term observation it was found that among the quality coats there are 2/3 of the first type, 7/9 of - Sowing equipment
Farmer Jadrný sowed wheat in autumn with a large sowing equipment and rye with a small sowing equipment. The area of all fields sown with wheat in 7.5 h was twice as large as the area of all fields sown with rye in 6 h. The sum of the areas of all fields - Std-deviation
Calculate the standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90 - Cars Meeting Time
The distance from Žilina to Košice is 260 km. From both places, 2 cars started opposite each other simultaneously. A car from Žilina travels at a speed of 58 km/h. The speed of a car from Košice is 72 km/h. In how many hours will these two cars meet? - Opening of a safe
How great a force would need to be exerted to open the rectangular door of a water-tight safe with dimensions 30 cm x 20 cm, built into the wall of a cabin of the sunken Titanic, which has been lying for more than 105 years on the bottom of the Atlantic O - A car
A car weighing 1.05 tonnes, travelling at the maximum speed limit in a village (50 km/h), crashes into a solid concrete barrier. Calculate the height from which the car would have to fall onto a concrete surface to produce the same impact force as in the
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