2018COMC加拿大數學公開賽真題答案免費下載

歷年 Canadian Open Mathematics Challenge加拿大數學公開賽

真題與答案下載

2018 COMC真題答案免費下載

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

部分真題答案預覽：

p A – 4 marks each

A1. Suppose x is a real number such that x(x + 3) = 154. Determine the value of (x + 1)(x + 2).Solution 1: The answer is 156 .

Solution 1: The answer is 156 .

Expanding x(x + 3) = 154 yields x
2 + 3x = 154.
Hence, (x + 1)(x + 2) = x
2 + 3x + 2 = 154 + 2 = 156.

Solution 2: The answer is 156 .

154 = 11 × 14 = (?11) × (?14). In the former case x = 11 and 12 × 13 = 156. In the latter case x = ?14
and (?13) × (?12) = 156.

A2. Let v, w, x, y, and z be five distinct integers such that 45 = v × w × x × y × z. What is the sum of the integers?

Solution: The answer is 5 .

Notice that 45 = 3 × 3 × 5. It stands to reason that, to write 45 as a product of five integer factors, each of its prime factors must appear, along with ±1 (we can’t use fractions). Further, to have exactly 5 distinct integers ?3 and ?1 must each appear once. We have 45 = (?1) × 1 × (?3) × 3 × 5. The sum of these five factors is 5.

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