2015 AMC 8考题16-17

AMC 8数学竞赛专为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 16

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 1/3of all the ninth graders are paired with 2/5of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

Solution

We see that the minimum number of ninth graders is 6, because if there are 3then there is 1ninth grader with a buddy, which would mean 2.5sixth graders with a buddy, and that's impossible. With 6ninth graders, 2of them are in the buddy program, so there 2/(2/5)sixth graders total, two of whom have a buddy. Thus, the desired fraction is (2+2)/(5+6)=(B)4/11.

Problem 17

Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?

Solution 

We set up an equation in terms of  the distance and  the speed In miles per hour. We have

d=(1/3)x=(1/5)(x+18)

d=5x=3(x+18)

5x=3x+54

2x=54

x=27

so:

d=27/3=(D)9

以上就是小编对AMC 8数学竞赛官方真题以及解析的介绍，希望对你有所帮助，更多学习资料请持续关注AMC数学竞赛网！