2012 AMC amc8 真题 答案 详解

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中英双语真题

2012 AMC8
Problem 1
Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?
Rachelle 用 3 磅肉为她的家人做了 8 个汉堡包。那么为邻里野餐做 24 个汉堡包需要多少磅肉？
(A) 6 (B) (6\frac{2}{3}) (C) (7\frac{1}{2}) (D) 8 (E) 9

Problem 2
In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
在 East Westmore 这个国家，统计学家们估计，每 8 小时就会有一个婴儿出生，并且每天都会有一人去世。那么每年 East Westmore 国家的人口数会增加多少？结果精确到百位。
(A) 600 (B) 700 (C) 800 (D) 900 (E) 1000

Problem 3
On February 13 The Oshkosh Northwestern listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57AM, and the sunset as 8:15PM. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
在 2 月 13 号这天，The Oshkosh Northwestern 给出的白天时长是 10 小时 24 分钟，日出是早上 6:57，日落是晚上 8:15。白天时长和日出时间是对的，但日落时间不对。那么正确日落时间是多少？
(A) 5:10PM (B) 5:21PM (C) 5:41PM (D) 5:57PM (E) 6:03PM

英文真题

Compiled on: January 1, 2021 AMC8 2012 Problems Page 39 of 109 Q1. Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic? A) 6 B) (6\frac{2}{3}) C) (7\frac{1}{2}) D) 8 E) 9 Q2. In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year? A) 600 B) 700 C) 800 D) 900 E) 1000 Q3. On February 13 "The Oshkosh Northwestern" listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57AM, and the sunset as 8:15PM. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set? A) 5:10PM B) 5:21PM C) 5:41PM D) 5:57PM E) 6:03PM Q4. Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat? A) (\frac{1}{24}) B) (\frac{1}{12}) C) (\frac{1}{8}) D) (\frac{1}{6}) E) (\frac{1}{4}) Q5. In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , X in centimeters? A) 1 B) 2 C) 3 D) 4 E) 5 Q6. A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches? A) 36 B) 40 C) 64 D) 72 E) 88 Q7. Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test? A) 90 B) 92 C) 95 D) 96 E) 97 Q8. A shop advertises everything is “half price in today’s sale”. In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?

真题文字详解(英文)

Problem 1 Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?
(A) 6 (B) (6\frac{2}{3}) (C) (7\frac{1}{2}) (D) 8 (E) 9

Solution 1 Since Rachelle uses 3 pounds of meat to make 8 hamburgers, she uses (\frac{3}{8}) pounds of meat to make one hamburger. She'll need 24 times that amount of meat for 24 hamburgers, or (\frac{3}{8} \cdot 24 = (E) 9).

Solution 2 We have the proportion (\frac{3}{8}=\frac{x}{24}). To solve for x, multiply the left side of the equation by (\frac{3}{8}). This gives us (\frac{9}{24}=\frac{x}{24}). For (\frac{9}{24}) to equal (\frac{x}{24}), we find that (x=9). The answer is then (E).

Problem 2 In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
(A) 600 (B) 700 (C) 800 (D) 900 (E) 1000

Solution There are (24 \div 8 = 3) births and one death every day in East Westmore. Therefore, the population increases by (3 - 1 = 2) people everyday. Thus, there are (2 \times 365 = 730) people added to the population every year. Rounding, we find the answer is (B) 700.

Problem 3 On February 13 The Oshkosh Northwestern listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57AM, and the sunset as 8:15PM. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
(A) 5:10PM (B) 5:21PM (C) 5:41PM (D) 5:57PM (E) 6:03PM

Solution 1 The problem wants to find the time of sunset and gives us the length of daylight and time of sunrise. So all we have to do is add the length of daylight to the time of sunrise to obtain the answer. Convert 10 hours and 24 minutes into 10:24 in order to add easier. Adding, we find that the time of sunset is (6:57AM + 10:24 \Rightarrow 17:21 \Rightarrow (B) 5:21PM).

Solution 2 (Answer choices) The length of daylight is 10 hours and 24 minutes, but for now, we can just look at the 24 minutes. Add 24 minutes to 57 part of sunrise, and you see that the sunset time must end in a 21. We see that the only option that ends with 21 is (\Rightarrow (B) 5:21PM).

真题文字详解(中英双语)

Problem 1 Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic? 拉切尔用3磅肉为家人做了8个汉堡。她为社区野餐需要多少磅肉来做24个汉堡？
(A) 6 (B) (6\frac{2}{3}) (C) (7\frac{1}{2}) (D) 8 (E) 9

Solution 1 Since Rachelle uses 3 pounds of meat to make 8 hamburgers, she uses (\frac{3}{8}) pounds of meat to make one hamburger. She'll need 24 times that amount of meat for 24 hamburgers, or (\frac{3}{8} \cdot 24 = \boxed{(E) 9}). 由于拉切尔用3磅肉做8个汉堡，他用(\frac{3}{8})磅肉做一个汉堡。他将需要24倍的这个数量的肉，即(\frac{3}{8} \cdot 24 = \boxed{(E) 9})。

Solution 2 We have the proportion (\frac{3}{8} = \frac{x}{24}). To solve for (x), multiply the left side of the equation by (\frac{3}{8}). This gives us (\frac{9}{24} = \frac{x}{24}). For (\frac{9}{24}) to equal (\frac{x}{24}), we find that (x = 9). The answer is then (\boxed{(E)}). ~Andrew_Lu with some small edits from: TabHawaii 我们有比例(\frac{3}{8} = \frac{x}{24})。为了求解(x)，将方程的左边乘以(\frac{3}{8})。这给我们(\frac{9}{24} = \frac{x}{24})。为了使(\frac{9}{24})等于(\frac{x}{24})，我们找到(x = 9)。答案是(\boxed{(E)})。~Andrew_Lu，有一些小修改来自：TabHawaii

Problem 2 In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year? 在东西摩尔国家，统计学家估计每8小时就有一个婴儿出生，每天都有一个死亡。到最近的百人，东西摩尔国家每年有多少人被加入到人口中？
(A) 600 (B) 700 (C) 800 (D) 900 (E) 1000

Solution There are 24 hours ÷ 8 hours = 3 births and one death every day in East Westmore. Therefore, the population increases by 3 - 1 = 2 people everyday. Thus, there are 2 × 365 = 730 people added to the population every year. Rounding, we find the answer is (\boxed{(B) 700}). 东西摩尔每天有24小时÷8小时=3个出生和一个人死亡。因此，人口每天增加3-1=2人。所以每年有2×365=730人被加入到人口中。四舍五入后，我们得到答案是(\boxed{(B) 700})。