2016 AMC amc8 真题 答案 详解

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中英双语真题

2016 AMC8
Problem 1
The longest professional tennis match lasted a total of 11 hours and 5 minutes. How many minutes is that?
时间最长的职业网球赛总共持续了11小时5分钟。问一共多少分钟？
(A) 605 (B) 655 (C) 665 (D) 1005 (E) 1105

Problem 2
In rectangle ABCD, AB = 6 and AD = 8. Point M is the midpoint of (\overline{AD}). What is the area of △AMC?
在矩形ABCD中，AB=6，AD=8，点M是(\overline{AD})的中点。那么△AMC 的面积是多少？
(A) 12 (B) 15 (C) 18 (D) 20 (E) 24

Problem 3
Four students take an exam. Three of their scores are 70, 80, and 90. If the average of their four scores is 70, then what is the remaining score?
4个学生参加一个考试。其中3个的分数是70、80、90。若他们的平均分是70分，那么剩下那个学生的分数是多少？
(A) 40 (B) 50 (C) 55 (D) 60 (E) 70

英文真题

Compiled on: January 1, 2021 AMC8 2016 Problems Page 23 of 109 Q1. The longest professional tennis match lasted a total of 11 hours and 5 minutes. How many minutes is that? A) 605 B) 655 C) 665 D) 1005 E) 1105 Q2. In rectangle ABCD, AB = 6 and AD = 8. Point M is the midpoint of \overline{AD}. What is the area of △AMC? A) 12 B) 15 C) 18 D) 20 E) 24 Q3. Four students take an exam. Three of their scores are 70, 80, and 90. If the average of their four scores is 70, then what is the remaining score? A) 40 B) 50 C) 55 D) 60 E) 70 Q4. When Cheenu was a boy he could run 15 miles in 3 hours and 30 minutes. As an old man he can now walk 10 miles in 4 hours. How many minutes longer does it take for him to travel a mile now compared to when he was a boy? A) 6 B) 10 C) 15 D) 18 E) 30 Q5. When N is divided by 9, the remainder is 1. When N is divided by 10, the remainder is 3. What is the remainder when N is divided by 11? A) 0 B) 2 C) 4 D) 5 E) 7 Q6. The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names?

真题文字详解(英文)

Problem 1 The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes. How many minutes was this?
(A) 605 (B) 655 (C) 665 (D) 1005 (E) 1105

Solutions
Solution 1
It is best to split 11 hours and 5 minutes into two parts, one of 11 hours and another of 5 minutes. We know that there are 60 minutes in an hour. Therefore, there are $11 \cdot 60 = 660$ minutes in 11 hours. Adding the second part (the 5 minutes) we get $660 + 5 = \textbf{(C)}\ 665$.
Solution 2
The best method comes when you remember your multiplication tables. Thus trivial, we get our answer of $\textbf{(C)}\ 665$.
Solution 3
$11$ hours $5$ min $= (11 \cdot 60) + 5$ min $= 665$ min, therefore $\textbf{(C)}$.
Carmen

Problem 2 In rectangle ABCD, AB = 6 and AD = 8. Point M is the midpoint of ( \overline{AD} ). What is the area of ( \triangle AMC )?
(A) 12 (B) 15 (C) 18 (D) 20 (E) 24

Solutions
Solution 1
Using the triangle area formula for triangles: ( A = \frac{bh}{2} ), where ( A ) is the area, ( b ) is the base, and ( h ) is the height. This equation gives us
( A = \frac{4 \cdot 6}{2} = \frac{24}{2} = \textbf{(A)}\ 12 ).
Solution 2

真题文字详解(中英双语)

Problem 1 The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes. How many minutes was this?
有史以来最长的职业网球比赛持续了总共11小时和5分钟。这是多少分钟？
(A) 605 (B) 655 (C) 665 (D) 1005 (E) 1105

Solutions Solution 1 It is best to split 11 hours and 5 minutes into 2 parts, one of 11 hours and another of 5 minutes. We know that there is 60 minutes in a hour. Therefore, there are 11 · 60 = 660 minutes in 11 hours. Adding the second part(the 5 minutes) we get 660 + 5 = (C) 665.
最好将11小时5分钟分成两部分，一部分是11小时，另一部分是5分钟。我们知道一个小时有60分钟。因此，11小时里有11·60=660分钟。加上第二部分（5分钟），我们得到660+5=(C) 665.

Solution 2 The best method comes when you remember your multiplication tables. Thus trivial, we get our answer of (C)665.
当你记得你的乘法表时，最好的方法就来了。因此很简单，我们得到了答案(C)665.

Solution 3 11 hours 5 min = (11 · 60) + 5min = 665min, therefore (C).
11小时5分钟=(11·60)+5min=665min，因此(C)。

Carmen Problem 2 In rectangle ABCD, AB = 6 and AD = 8. Point M is the midpoint of (\overline{AD}). What is the area of △AMC?
在矩形ABCD中，AB=6和AD=8。点M是(\overline{AD})的中点。(\triangle AMC)的面积是多少？