Mathematical Olympiad + quadratic equation - practice problems
Number of problems found: 7
- Subtract 10001
For five whole numbers, if we add one to the first, multiply the second by the second, subtract three from the third, multiply the fourth by four, and divide the fifth by five, we get the same result each time. Find all five of the numbers that add up to - MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning, they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David. - Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, the average age was again equal to the number present. How many people were original to celebrate? - Expression 4451
Find the largest natural number d that has that property for any natural number the number n is the value of the expression V (n) = n ^ 4 + 11n²−12 is divisible by d.
- Coefficients 4445
Find all triplets P (x) = a * x² + b * x + c with the integer coefficients a, b, and c to which it applies P (1) - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball. - Square grid
A square grid consists of a square with sides of a length of 1 cm. Draw at least three patterns, each with an area of 6 cm² and a circumference of 12 cm, and their sides in a square grid.
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