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مسائل وحلول

TIMSS & IMO

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(TIMSS)

The Trends in International Mathematics and Science Study (TIMSS) provides reliable and timely data on the mathematics and science achievement of U.S. students compared to that of students in other countries. TIMSS data has been collected in 1995, 1999, and 2003. The United States will next collect TIMSS data in Spring 2007.

Test your mathematics and science knowledge by completing TIMSS items in the Dare to Compare

TIMSS is a worldwide research project, taking place every four years and providing data about trends in mathematics and science achievement over time. It assesses the knowledge and skills of students aged 9-10 and 13-14 in over 60 countries, and enables researchers to collect extensive background information about the quantity, quality, and content of teaching, which can be used to make comparisons between participating countries. Findings from the survey are used to inform education policy and to improve teaching and learning in maths and science for students around the world.

The International Mathematical Olympiad (IMO) is an annual mathematical olympiad for high school students. It is the oldest of the international science olympiads.

The first IMO was held in Romania in 1959. Since then it has been held every year except 1980. About 90 countries send teams of (at most) six students each (plus one team leader, one deputy leader and observers). Teams are not officially recognized - all scores are given only to individual contestants. Contestants must be under the age of 20 and must not have any post-secondary school education. Subject to these conditions, an individual may participate any number of times in the IMO.

The paper consists of six problems, with each problem being worth seven points. The total score is thus 42 points. The examination is held over two consecutive days; the contestants have four-and-a-half hours to solve three problems on each day. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. They require no knowledge of higher mathematics, and solutions are often short and elegant. Finding them, however, requires exceptional ingenuity and mathematical ability.

Each participating country, other than the host country, may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the six problems from the shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated from the contestants until the second examination has finished; the contestants are accompanied to the IMO by their deputy leaders (and maybe observers as well).

Each country's marks are agreed between that country's leader and deputy leader and Co-ordinators provided by the host country (the leader of the team whose country submitted the problem in the case of the marks of the host country), subject to the decisions of the Chief Coordinator and ultimately the Jury if any disputes cannot be resolved.

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أثبت أن الشرط اللازم والكافى لكى تتقاطع منصفات الزوايا الداخله لشبه منحرف فى نقطه واحده هو أن يكون :
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[أحمد سعد الدين]

[أحمد سعد الدين]

[أحمد سعد الدين]

[أحمد سعد الدين]

[أحمد سعد الدين]

[أحمد سعد الدين]