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

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1997 COMC真题免费下载

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 :

4)Given three distinct digits a; b and c, it is possible, by choosing two digits at a time, to form six two-digit numbers. Determine all possible sets fa; b; cg for which the sum of the six two-digits numbers is 484.

5)Two cubes have their faces painted either red or blue. The first cube has five red faces and one blue face. When the two cubes are rolled simultaneously, the probability that the two top faces show the same colour is 1/2 . How many red faces are there on the second cube?

8)An hourglass is formed from two identical cones. Initially, the upper cone is filled with sand and the lower one is empty. The sand flows at a constant rate from the upper to the lower cone. It takes exactly one hour to empty the upper cone. How long does it take for the depth of sand in the lower cone to be half the depth of sand in the upper cone? (Assume that the sand stays level in both cones at all times.)

Part B :

1)The straight line l1 with equation x-2y+10 = 0 meets the circle with equation x² +y² = 100 at B in the first quadrant. A line through B, perpendicular to l1 cuts the y-axis at P(0, t). Determine the value of t.

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