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:
Which of the following numbers is not a perfect square?

We know that our answer must have an odd exponent in order for it to not be a square. Because  is a perfect square,
 is a perfect square,  is also a perfect square, so our answer must be
 is also a perfect square, so our answer must be  .
.
Find the value of the expression![\[100-98+96-94+92-90+\cdots+8-6+4-2.\]](/public/uploads/ueditor/20180827/1535350472171272.png)

We can group each subtracting pair together:![\[(100-98)+(96-94)+(92-90)+ \ldots +(8-6)+(4-2).\]](/public/uploads/ueditor/20180827/1535350474500358.png) After subtracting, we have:
After subtracting, we have:![\[2+2+2+\ldots+2+2=2(1+1+1+\ldots+1+1).\]](/public/uploads/ueditor/20180827/1535350476331666.png) There are
There are  even numbers, therefore there are
 even numbers, therefore there are  even pairs. Therefore the sum is
 even pairs. Therefore the sum is 
Since our list does not end with one, we divide every number by 2 and we end up with![\[50-49+48-47+ \ldots +4-3+2-1\]](/public/uploads/ueditor/20180827/1535350481647298.png) We can group each subtracting pair together:
We can group each subtracting pair together: There are now
There are now  pairs of numbers, and the value of each pair is
 pairs of numbers, and the value of each pair is  . This sum is
. This sum is  . However, we divided by
. However, we divided by  originally so we will multiply
 originally so we will multiply  to get the final answer of
 to get the final answer of 
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!
 
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