2018AMC真题解析 突围AMC要备资料

2020的AMC比赛已经落下帷幕啦。在等新真题解答的时候，带大家回顾一下2018AMC真题解析。参加今年考试的同学可以对比一下自己的答题情况，备战明年考试的同学可以提前熟悉一下出题节奏。

AMC比赛简介

多年来，AMC扮演着为美国培育世界数学奥林匹克（IMO）选手的重责大任。因此AMC是世界上目前信度最高的数学测试：

每年全球有超60万人次参赛，其中中国区有近5万名学员参与。

在全球范围内与美国一起进行同步测试的有中国、加拿大、英国等几十个国家和地区的近3000所学校。

AMC不但是美国优质数学人才的人才库，也是学校看申请者数学能力与成就的重要参考依据。甚至被列为一些知名大学的申请必备项。

受疫情影响，许多考试都被迫取消，AMC可以说是在“夹缝中生存”下来的一个竞赛。这也让这门本就炙手可热的比赛又出圈不少。

Problem 1

Answer: A

Solution:

You can just do 289/20 and round your answer to get 14.

中文解析:

比例是1:20 ,真实建筑是289feet,所以因此复制品的高度是: 289/20约等于14feet. 答案是A.

Problem 2

Answer: D

Solution:

By adding up the numbers in each of the 6 parentheses, we have:(2/1)*(3/2)*(4/3)*(5/4)*(6/5)*(7/6) . Using telescoping, most of the terms cancel out diagonally. We are left with 7 .

中文解析:

=(2/1)*(3/2)*(4/3)*(5/4)*(6/5)*(7/6)=7/1=7. 答案是D.

Problem 3

Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in acircle. They start counting: Arn first, then Bob, and so forth. When thenumber containsa 7 as a digit (such as 47) or is a multiple of 7 that person

leaves the circle and the counting continues. Who is the last one present in

the circle?

(A) Arn  (B) Bob .  (C) Cyd  (D) Dan  (E) Eve 

Answer: D

Solution:

The five numbers which cause people to leave the circle are 7, 14, 17, 21,27. The most straightforward way to do this would be to draw out the circle with the people, and cross off people as you count. The last one standing is Dan.

中文解析:

依次离开圆圈的数字分别是7, 14, 17, 21, 27,... 直接把A, B, C, D, E 按圆形排列, 依次数, 去除出局的, 最后剩下的是D. 答案是D.

Problem 4

Answer: C

Solution:

We count 3*3=9 unit squares in the middle, and 4 small triangles each with an area of 1. Thus, the answer is 9+4=13.

中文解析:

这个12边形围起来的小正方形共有9个,其面积是9*1=9. 小三角形有8个,其面积是8*0.5=4. 因此面积=9+4=13. 答案是C.

Problem 5

Answer: E

Solution:

We can rewrite the given expression as1+(3-2)+(5-4)+…+(2017-2016)+(2019-2018)=1+1+1+…+1.The number of 1s is the same as the number of terms in 1,3,5,7, ……2017, 2019. Thus the answer is 1010.

中文解析:

把上式按下面的规则用小括号括起来:=1+(3-2)+(5-4)+(7-6)+...+(2017-2016)+(2019-2018)=1+1+1+1+...+1+1.除了第一个1外,还有: 2018/2=1009个1. 所以我们得到的和是1010. 答案是E.

Problem 6

Answer: C

Solution:

Since Anh spends half an hour to drive 10 miles on the coastal road, his speed is 10/0.5=20 mph. His speed on the highway then is 20*3=60 mph. He drives 50 miles, so he drives for 5/6 hours, which is equal to 50 minutes. The total amount of minutes spent on his trip is 30+50=80 minutes.

中文解析:

海滨道路上花费的时间是30分钟(0.5小时),路程是10英里，速度是: 10/0.5=20 . 则高速路的速度是3*20=60 mph. 高速路的距离是50mile, 则时间是50/60=5/6 小时=50分钟. 答案是A.

Problem 7

Answer: B

Solution:

We use the property that the digits of a number must sum to a multiple of 9 if it are divisible by 9. This means u=7. Since we are looking for the remainder when divided by 8, we can ignore the thousands. The remainder when 187 is divided by 8 is 3.

中文解析:

数能被9整除,因此 2+0+1+8+U 是9的倍数,因此u=7. 20187除以8的余数 只需要看后三位187除以3的余数. 余数是3. 答案是B.

Problem 8

Answer: C

Solution:

The mean, or average number of days is the total number of days divided by the number of students. The total number of days is (1*1+2*3+3*2+4*6+5*8+6*4+7*2)=109. The total number of students is 1+3+2+6+8+3+2=25. Hence, 109/25=4.36.

中文解析:

有1个小伙伴锻炼了1天, 3个小伙伴锻炼了2天, 2个小伙伴锻炼了3天, ....平均值是: (1+3*2+2*3+6*4+8*5+3*6+2*7)/(1+3+2+6+8+3+2)=109/25=4.36 答案是C.

Problem 9

Answer: B

Solution:

He will place （12*2）+（14*2）=52 tiles around the border. For the inner part of the room, we have 10*14=140 square feet. Each tile takes up 4 square feet, so he will use 140/4=35 tiles for the inner part of the room. Thus, the answer is 52+35=87.

中文解析:

1-foot 的正方形需要: 16*2+10*2=52块.中间剩下的面积是: 14*10=140. 2-foot的瓷砖的面积是2*2=4. 需要140/4=35块瓷砖.共需要: 52+35=87块瓷砖. 答案是B.

Problem 10

Answer: C

Solution:

The sum of the reciprocals is 1/1 + 1/2 +1/4=7/4. Their average is 7/12. Taking the reciprocal of this gives 12/7.

中文解析:

harmonic mean是先计算这组数的倒数的算数平均值,然后再求倒数. 1/1, 1/2, 1/4 的算数平均值是: 7/12. 其倒数是12/7. 因此harmonic mean是12/7. 答案是C.

Problem 11

Answer: C

Solution:

The total number of ways is C(6,2)=15, if we treat Abby and Bridget as a pair and distinguishable and forget the others. The total number of ways they are adjacent = 4 (for the rows) + 3 (for the columns) Therefore, P(Abby and Bridget sitting adjacent) is 7/15.

中文解析:

第一步安排A的座位, 第二步安排B的座位.A的座位可能位于4个角落之一,也可能位于两个中间位置之一. ,分两种情况.种, A的座位位于4个角落之一的可能性是4/6, 下一步安排B的座位, B和A相邻的可能性有: 2/5.

第二种, A的座位两个中间位置之一的可能性是2/6, 然后安排B的座位, B和A相邻的可能性有: 3/5.综合起来: 4/6*2/5 + 2/6 * 3/5 =7/15. 答案是C.

Problem 12

Answer: B

Solution:

We see that every 35 minutes the clock passes, the watch passes 30 minutes. That means that the clock is 7/6 as fast the watch, so when the car clock passes 7 hours, the watch has passed 6 hours, meaning that the time would be 6:00.

中文解析:

当实际时间过了30分钟时(从12:00 到12: 30), 题目里人的汽车表的时间过了35分钟. 其比值时30:35=6:7. 当汽车表显示7个小时时, 根据比例关系,实际时间应该是6点. 答案是B.

以上就是今天为大家整理的2018AMC真题解析（上）。不知道对比今年的考试，大家觉得难度是上升还是下降了呢？

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