2018COMC加拿大数学公开赛真题答案免费下载

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

真题与答案下载

2018 COMC真题答案免费下载

共计2.5小时考试时间

此套试卷由三部分题目组成

4题简答题，每题4分

4题挑战题，每题6分

4题解答题，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

部分真题答案预览：

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.