1997COMC加拿大數學公開賽真題免費下載

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 :

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 five 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 filled 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 first quadrant. A line through B, perpendicular to l1 cuts the y-axis at P(0, t). Determine the value of t.