IOAA 2014, Теория, окончателен вариант — Задача 1. Lagrange Points

1. In your folder you will find the following items:

   a. Answer sheets

   b. Rough work sheets

   c. The envelope with the problems The solutions of the problems should be written only on the answer sheets you receive. PLEASE WRITE ONLY ON THE PRINTED SIDE OF THE PAPER SHEET. DON’T USE THE REVERSE SIDE. The evaluator will not take into account what is written on the reverse side of the answer sheet.

2. The rough worksheets are for your own use for doing calculations, write some numbers etc. BEWARE: These sheets are not taken into account for the evaluation. At the end of the test they will be collected separately. Everything you consider as part of the solutions should be written on the answer sheets.

3. Each problem should be started on a separate answer sheet.

4. On each answer sheet please fill in the designated boxes as follows:

   a. In the „PROBLEM NO.” box write down only the number of the problem: i.e. 1 – 12 for each short problems, 13 – 15 for each long problems. Each sheet containing the solutions of a certain problem, should have in the box the number of the problem;

   b. In „Student ID” – fill in your ID that you will find on your envelope, consisting of 3 letters and 2 digits.

   c. In the „page no.” box you will fill in the number of page, starting from 1. We advise you to fill this boxes after you finish the test

5. We don’t understand your language, but the language of Mathematics is universal, so, please, use as many mathematical expressions as you think that may help the evaluator to better understand your solutions. If you want to explain something in words we kindly ask you to use short phrases(if possible in English).

6. Use the pen you find out on the desk. It is advisable to use a pencil for the sketches.

7. At the end of the test:

   d. Don’t forget to put your papers in order.

   e. Put the answer sheets in folder 1. Please verify that all the pages contain your ID, correct numbering of the problems and all pages are in the right order and numbered. This will help us to understanding your solutions.

   f. Verify with the assistant the correct number of answer sheets used and fill in this number on the cover of the folder and sign it.

   g. Put the draft papers in the designated folder. Put the test papers back in the envelope.

   h. Go to swim

GOOD LUCK !

ALL THE CORRECT SOLUTIONS WHICH ARE DIFFERENT FROM THE AUTHOR’S SOLUTION WILL BE EVALUATED AND MARKED ACORDINGLY TO THE MARKING SCHEME.