Mathematical Olympiad - practice for 13 year olds - last page
Number of problems found: 68
- MO - triangles
On the AB and AC sides of the ABC triangle lies successive points E and F, and on segment EF lie point D. The EF and BC lines are parallel. It is true this ratio FD:DE = AE:EB = 2:1. The area of the ABC triangle is 27 hectares, and line segments EF, AD, a - Keyboards keys
Michael had small keys on the shelf, which you can see in the picture. Their tones were marked on the white keys. Little Clara found the keys. As she took them off the shelf, they fell out of her hand, and all the white keys spilled out. So that the broth - Katy MO
Kate drew a triangle ABC. The middle of the line segment AB has marked as X and the center of the side AC as Y. On the side BC, she wants to find point Z so that the area of a 4gon AXZY is the greatest. What part of the ABC triangle can maximally occupy 4 - Pentagon
Within a regular pentagon ABCDE point, P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
- 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. - Christmas Day
In leap years was 53 Sundays. On what day of the week fell Christmas Day? - Characteristics 2104
Betka thought of a natural number with different digits and wrote it on the board. Podeň wrote the digits of the original number on the back and thus got a new number. By adding these two numbers, he got a number with the same number of digits as the inte - Pytagoriade
Two fifth-graders teams compete in math competitions - Mathematical Olympiad and Pytagoriade. Of the 33 students who competed in at least one of the contests, 22 students. Students who competed only in Pytagoriade were twice as many who just competed in t
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