2014COMC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

 

翰林國際教育全網首發

力爭超快速發布最全資料

助你在升學路上一帆風順

為你

千千萬萬遍

2014 COMC真題免費下載

共計2.5小時考試時間

此套試卷由三部分題目組成

4題簡答題，每題4分

4題挑戰題，每題6分

4題解答題，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 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.

完整版真題資料可以底部二維碼免費領取↓↓↓

[vc_btn title="查看更多COMC加拿大數學奧賽相關詳情" color="primary" align="center" i_icon_fontawesome="fa fa-globe" css_animation="zoomIn" button_block="true" add_icon="true" link="url:http%3A%2F%2Fwww.linstitute.net%2Farchives%2F99767||target:%20_blank|"]