1999COMC加拿大数学公开赛真题免费下载

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

真题与答案下载

COMC加拿大数学公开赛

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1999 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 :

6)trapezoid, DEFG, is circumscribed about a circle that has centre C and radius 2, as is shown. The shorter of the two parallel sides, DE, has length 3 and angles DEF and EFG are right angles. Determine the area of the trapezoid.1999COMC加拿大数学奥赛真题与答案免费下载

7)The sector OAB of a circle, with centre O, has a perimeter of 12. Determine the radius of the circle which maximizes the area of the sector.1999COMC加拿大数学奥赛真题与答案免费下载

8)Find the smallest positive integer k so that the expression (14k+17)/(k-9) becomes a fraction in the form pd/qd where p, q and d are positive integers, p and q have no common divisors, and neither q nor d equals 1.

Part B :

1)

  1. Two identical triangles each have an area of 24. Their vertices are determined by the intersection of the lines with equations y = -4,x = 0 and y = (-3/4) x + b. Determine the two possible values for b.
  2. For either of the two given triangles, a circle can be drawn to pass through its three vertices. What is the radius of this circle?

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