2002COMC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

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2002 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 :

6)Two mirrors meet at an angle of 30o at the point V. A beam of light, from a source S, travels parallel to one mirror and strikes the other mirror at point A, as shown. After a number of reflections, the beam comes back to S. If SA and AV are both 1 metre in length, determine the total distance travelled by the beam.

7)N is a five-digit positive integer. A six-digit integer P is constructed by placing a 1 at the right-hand end of N. A second six-digit integer Q is constructed by placing a 1 at the left-hand end of N. If P is three times Q, determine the value of N.

8)Suppose that M is an integer with the property that if x is randomly chosen from the set { 1,2,3,...,999,1000}, the probability that x is a divisor of M is 1/100 . If M ≤ 1000, determine the maximum possible value of M.

Part B :

1)Square ABCD has vertices A(0,0), B(0,8), C(8,8), and D(8,0). The points P(0,5) and Q(0,3) are on side AB , and the point F(8,1) is on side CD.

1. What is the equation of the line through Q parallel to the line through P and F?
2. If the line from part (a) intersects AD at the point G, what is the equation of the line through F and G?
3. The centre of the square is the point H(4,4). Determine the equation of the line through H perpendicular to FG.
4. A circle is drawn with centre H that is tangent to the four sides of the square. Does this circle intersect the line through F and G? Justify your answer. (A sketch is not sufficient justification.)

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