1997COMC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

真題與答案下載

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1997 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

完整版下載鏈接見文末

部分真題預覽：

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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