澳大利亚中级数学奥林匹克竞赛 (AIMO) -历年真题

AIMO学术活动全称Australian Intermediate Mathematics Olympiad，即“澳大利亚中级数学奥林匹克学术活动”。由澳大利亚数学权威机构AMT（澳大利亚数学联合会）主办，并由澳大利亚奥数委员会评卷，成绩含金量极高，被澳大利亚奥数国家队作为选拔集训队的最重要依据。

正是因为上述原因，每年都会吸引大量澳洲数学爱好者参赛。

历年真题:

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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