历年 Canadian Open Mathematics Challenge加拿大数学公开赛

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1997 COMC真题答案免费下载

共计2.5小时考试时间

此套试卷由两部分题目组成

Part A共8题，每题5分

Part B共4题，每题10分

共计12题，满分80分

不可使用任何计算器

完整版下载链接见文末

部分真题预览：

Part A Solutions:

A5)The colour on the top of the first cube is irrelevant. Once it is rolled, we must have three red faces and three blue faces on the second cube if the probability of like faces is 1/2.

The average score was 2.7.

A6) The solution to the problem is obtained from using the property that tangents to a circle from external point are equal. Using this fact and applying algebraic variables as needed, one obtains, from the resulting equation, CD=152.

The average score was 0.5.

A8) At the required time the depth f sand in the upper cone is two-thirds its original depth. Since volume varies as the cube of any dimension in regular figures, the time required is 1-(2/3)³ = 19/27 of an hour.

The average score was 0.7.

Part B Solutions:

B1) This is a straightforward problem. Solve for point B by substitution from the first equation to the second equation to obtain B as (6.8). The line through B perpendicular to l₁ meets the y-axis at (0,20).

The average score was 5.9.

 

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1997 COMC加拿大数学奥赛完整版真题免费下载

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1997 COMC真题题目

 

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