AMC数学竞赛真题2016年B 9-10

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：

Problem 9

All three vertices of lie on the parabola defined by , with at the origin and parallel to the -axis. The area of the triangle is . What is the length of ?

Solution

The area of the triangle is , so , giving a total distance across the top of , which is answer . 

Problem 10

A thin piece of wood of uniform density in the shape of an equilateral triangle with side length inches weighs ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side length of inches. Which of the following is closest to the weight, in ounces, of the second piece?

Solution 1

We can solve this problem by using similar triangles, since two equilateral triangles are always similar. We can then use

.

We can then solve the equation to get which is closest to

Solution 2

Also recall that the area of an equilateral triangle is so we can give a ratio as follows:

Cross multiplying and simplifying, we get

Which is

• Solution by

Solution 3

Note that the ratio of the two triangle's weights is equal to the ratio of their areas, as the height is negligible. The ratio of their areas is equal to the square of the ratio of their sides. So if denotes the  weight of the second triangle, we have

Solving gives us so the answer 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。