1998COMC加拿大數學公開賽真題答案免費下載

歷年 Canadian Open Mathematics Challenge加拿大數學公開賽

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1998 COMC真題答案免費下載

共計2.5小時考試時間

此套試卷由兩部分題目組成

Part A共8題，每題5分

Part B共4題，每題10分

共計12題，滿分80分

不可使用任何計算器

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部分真題預覽：

Part A Solutions:

A8) Using basic properties of symmetry we observe that the corner of the box, the centre of the small sphere and the centre of the large sphere all lie along the same straight line drawn from the origin. The distance from the corner of the box to the centre of the small sphere is r√3. If the distance from the corner of the box to the centre of the large sphere is 16√3 we can now write, r√3 + r + 15 = 16√3 or r = [16(√3)-15]/(√3+1).
The average was 0.6.

Part B Solutions:

B3)

1. In essence, Alphonse adopts a strategy that will make Beryl enter the last ring first. This guarantees a win because in the final ring the moves are necessarily successive and there are an even number of regions thus guaranteeing Alphonse the 2nd, 4th, 6th and 8th position, i.e. the winning position
2. Beryl adopts the strategy that will allow him to be the first to enter ring three and five. This guaranteese Beryl that he will always win because Alphonse will always be in an even position in these rings (if we label the regions 1,2,3,. . . ,9) when it is Beryl’s turn to move.
   The average was 2.7.

 

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