澳大利亞中級數學奧林匹克競賽 (AIMO)?-歷年真題

AIMO學術活動全稱Australian Intermediate Mathematics Olympiad，即“澳大利亞中級數學奧林匹克學術活動”。由澳大利亞數學權威機構AMT（澳大利亞數學聯合會）主辦，并由澳大利亞奧數委員會評卷，成績含金量極高，被澳大利亞奧數國家隊作為選拔集訓隊的最重要依據。

正是因為上述原因，每年都會吸引大量澳洲數學愛好者參賽。

歷年真題:

1. Gaston and Jordon are two budding chefs who unfortunately always misread the cooking time required for a recipe. For example, if the required cooking time is written as 1:32, meaning 1 hour and32 minutes, Jordon reads it as 132 minutes while Gaston reads it as1.32 hours. For one particular recipe, the difference between Jordon's and Gaston's misread times is exactly 90 minutes. What is the actual cooking time in minutes?

2. An integer has 3 digits in base 10. When it is interpreted in base 6 and multiplied by 4, the result is 2 more than 3 times the same number when it is interpreted in base 7. What is the largest integer, in base 10, that has this property?

3.Let x denote a single digit.The tens digit in the product of 2r7 and 39 is 9.Find r.

4.The circumcircle of a square ABCD has radius 10.A semicircle is drawn on AB outside the square.Find the area of the region inside the semicircle but outside the circumcircle.

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