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AMC数学竞赛8真题2016年 7-8

2018-08-27 重点归纳

AMC数学竞赛8专为8年级及以下的初中学生设计,但近年来的数据显示,越来越多小学4-6年级的考生加入到AMC 8级别的考试行列中,而当这些学生能在成绩中取得“A”类标签,则是对孩子数学天赋的优势证明,不管是对美高申请还是今后在数学领域的发展都极其有利!那么接下来跟随小编来看一下AMC 8的官方真题以及官方解答吧:

Problem 7

Which of the following numbers is not a perfect square?

amc竞赛

Solution

We know that our answer must have an odd exponent in order for it to not be a square. Because $4$ is a perfect square, $4^{2019}$ is also a perfect square, so our answer must be amc数学竞赛.

Problem 8

Find the value of the expression\[100-98+96-94+92-90+\cdots+8-6+4-2.\]amc真题

Solution

We can group each subtracting pair together:\[(100-98)+(96-94)+(92-90)+ \ldots +(8-6)+(4-2).\]After subtracting, we have:\[2+2+2+\ldots+2+2=2(1+1+1+\ldots+1+1).\]There are $50$ even numbers, therefore there are $\dfrac{50}{2}=25$ even pairs. Therefore the sum is amc竞赛

Solution 2

Since our list does not end with one, we divide every number by 2 and we end up with\[50-49+48-47+ \ldots +4-3+2-1\]We can group each subtracting pair together:amc真题There are now $25$ pairs of numbers, and the value of each pair is $1$. This sum is $25$. However, we divided by $2$ originally so we will multiply $2*25$ to get the final answer of $\boxed{\textbf{(C) }50}$

以上就是小编对AMC竞赛官方真题以及解析的介绍,希望对你有所帮助,更多AMC真题下载请持续关注AMC数学竞赛网