2018-11-27 重点归纳
AMC10数学竞赛是美国高中数学竞赛中的一项,是针对高中一年级及初中三年级学生的数学测试,该竞赛开始于2000年,分A赛和B赛,于每年的2月初和2月中举行,学生可任选参加一项即可。不管是对高校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AMC10数学竞赛真题以及官方解答吧:
Carl decided to fence in his rectangular garden. He bought
fence posts, placed one on each of the four corners, and spaced out the
rest evenly along the edges of the garden, leaving exactly
yards between neighboring posts. The longer side of his garden,
including the corners, has twice as many posts as the shorter side,
including the corners. What is the area, in square yards, of Carl’s
garden?
If the dimensions are , then one side will have
posts (including corners) and the other
.
The total number of posts is .
Solve the system to get
. Then the area is
which is
.
To do this problem, we have to draw a rectangle. We also have to keep
track of the fence posts. Putting a post on each corner leaves us with
only posts. Now there are twice as many posts on the longer side then the shorter side. From this we can see that we can put
posts on the longer side and
posts on the shorter side. On the shorter side, we have
spaces between the
posts. On the longer side, we have 7 spaces between the 8 fence posts. There are
yards between each post. Therefore, the answer is
.
Two different numbers are selected at random from and multiplied together. What is the probability that the product is even?
The product will be even if at least one selected number is even, and
odd if none are. Using complementary counting, the chance that both
numbers are odd is , so the answer is
which is
.
以上就是小编对AMC10数学竞赛真题以及解析的介绍,希望对你有所帮助,如果想了解更多关于AMC数学竞赛报考点、AMC美国大学生数学竞赛、美国数学竞赛AMC有用吗以及AMC学习资料等信息请持续关注AMC数学竞赛网。
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