2014COMC加拿大數(shù)學(xué)公開賽真題免費(fèi)下載

歷年 Canadian Open Mathematics Challenge加拿大數(shù)學(xué)公開賽

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2014 COMC真題免費(fèi)下載

共計(jì)2.5小時(shí)考試時(shí)間

此套試卷由三部分題目組成

4題簡答題，每題4分

4題挑戰(zhàn)題，每題6分

4題解答題，每題10分

共計(jì)12題，滿分80分

不可使用任何計(jì)算器

完整版下載鏈接見文末

部分真題預(yù)覽：

Part A Introductory Questions:

Question A3)A positive integer m has the property that when multiplied by 12, the result is a four-digit number n of the form 20A2 for some digit A. What is the 4 digit number, n?

Question A3)Alana, Beatrix, Celine, and Deanna played 6 games of tennis together. In each game, the four of them split into two teams of two and one of the teams won the game. If Alana was on the winning team for 5 games, Beatrix for 2 games, and Celine for 1 game, for how many games was Deanna on the winning team?

Part B Challenging Questions:

Question B3)5 Xs and 4 Os are arranged in the below grid such that each number is covered by either an X or an O. There are a total of 126 different ways that the Xs and Os can be placed. Of these 126 ways, how many of them contain a line of 3 Os and no line of 3 Xs?
A line of 3 in a row can be a horizontal line, a vertical line, or one of the diagonal lines 1?5?9 or 7 ? 5 ? 3.

Part C Long-form Proof Problems:

Question C2)The line L given by 5y + (2m ? 4)x ? 10m = 0 in the xy-plane intersects the rectangle with vertices O(0, 0), A(0, 6), B(10, 6), C(10, 0) at D on the line segment OA and E on the line segment BC.

1. Show that 1 ≤ m ≤ 3.
2. Show that the area of quadrilateral ADEB is 1/3 the area of rectangle OABC.
3. Determine, in terms of m, the equation of the line parallel to L that intersects OA at F and BC at G so that the quadrilaterals ADEB, DEGF , FGCO all have the same area.

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