2001COMC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

2001 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 :

3)A regular hexagon is a six-sided figure which has all of its angles equal and all of its side lengths equal. If P and Q are points on a regular hexagon which has a side length of 1, what is the maximum possible length of the line segment PQ?

5)Triangle PQR is right-angled at Q and has side lengths PQ = 14 and QR = 48. If M is the midpoint of PR, determine the cosine of ∠MQP.

7)If a can be any positive integer and
2x + a = y
a + y = x
x + y = z
determine the maximum possible value for x + y + z.

Part B :

2)

1. Alphonse and Beryl are playing a game, starting with a pack of 7 cards. Alphonse begins by discarding at least one but not more than half of the cards in the pack. He then passes the remaining cards in the pack to Beryl. Beryl continues the game by discarding at least one but not more than half of the remaining cards in the pack. The game continues in this way with the pack being passed back and forth between the two players. The loser is the player who, at the beginning of his or her turn, receives only one card. Show, with justification, that there is always a winning strategy for Beryl.
2. Alphonse and Beryl now play a game with the same rules as in (a), except this time they start with a pack of 52 cards, and Alphonse goes first again. As in (a), a player on his or her turn must discard at least one and not more than half of the remaining cards from the pack. Is there a strategy that Alphonse can use to be guaranteed that he will win? (Provide justification for your answer.)

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|"]