2010 AMC amc8 真题 答案 详解

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中英双语真题

2010 AMC8

Problem 1
At Euclid Middle School, the mathematics teachers are Miss Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest?
In Euclid Middle School, the math teachers are Miss Germain, Mr. Newton, and Mrs. Young. There are 11 students in Miss Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class participating in the AMC 8 this year. How many math students at Euclid Middle School will participate in this competition?
(A) 26 (B) 27 (C) 28 (D) 29 (E) 30

Problem 2
If ( a @ b = \frac{a \times b}{a + b} ) for ( a, b ) positive integers, then what is ( 5 @ 10 )?
For ( a, b ) as positive integers, if ( a @ b = \frac{a \times b}{a + b} ), what is ( 5 @ 10 )?
(A) ( \frac{3}{10} ) (B) 1 (C) 2 (D) ( \frac{10}{3} ) (E) 50

英文真题

Compiled on: January 1, 2021 AMC8 2010 Problems Page 48 of 109 Q1. At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest? A) 26 B) 27 C) 28 D) 29 E) 30 Q2. If a@b = \frac{a \times b}{a + b} for a,b positive integers, then what is 5@10? A) \frac{3}{10} B) 1 C) 2 D) \frac{10}{3} E) 50 Q3. The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price? A) 50 B) 62 C) 70 D) 89 E) 100 Q4. What is the sum of the mean, median, and mode of the numbers 2, 3, 0, 3, 1, 4, 0, 3? A) 6.5 B) 7 C) 7.5 D) 8.5 E) 9 Q5. Alice needs to replace a light bulb located 10 centimeters below the ceiling in her kitchen. The ceiling is 2.4 meters above the floor. Alice is 1.5 meters tall and can reach 46 centimeters above the top of her head. Standing on a stool, she can just reach the light bulb. What is the height of the stool, in centimeters? A) 32 B) 34 C) 36 D) 38 E) 40 Q6. Which of the following figures has the greatest number of lines of symmetry? A) equilateral triangle B) non-square rhombus C) non-square rectangle D) isosceles trapezoid E) square Q7. Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?

真题文字详解(英文)

Problem 1
At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest?
(A) 26 (B) 27 (C) 28 (D) 29 (E) 30

Solution
Given that these are the only math teachers at Euclid Middle School and we are told how many from each class are taking the AMC 8, we simply add the three numbers to find the total. $11 + 8 + 9 = \boxed{\textbf{(C)}\ 28}$

Problem 2
If $a @ b = \frac{a \times b}{a + b}$ for a, b positive integers, then what is $5 @ 10$?
(A) $\frac{3}{10}$ (B) 1 (C) 2 (D) $\frac{10}{3}$ (E) 50

Solution
Substitute $a = 5$ and $b = 10$ into the expression for $a @ b$ to get:
$5 @ 10 = \frac{5 \times 10}{5 + 10} = \frac{50}{15} = \frac{10}{3}$
Thus, answer choice $\boxed{\textbf{(D)}\ \frac{10}{3}}$ is correct.

Problem 3
The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?

真题文字详解(中英双语)

Problem 1

At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest?

在欧几里得中学，数学老师有格梅因夫人、牛顿先生和杨夫人。格梅因夫人的班级有11名学生，牛顿先生的班级有8名学生，杨夫人的班级有9名学生今年参加AMC 8。欧几里得中学有多少名数学学生参加了这次竞赛？

(A) 26 (B) 27 (C) 28 (D) 29 (E) 30

Solution

Given that these are the only math teachers at Euclid Middle School and we are told how many from each class are taking the AMC 8, we simply add the three numbers to find the total. 11 + 8 + 9 = (C) 28.

既然这些是欧几里得中学唯一的数学老师，而且我们知道每个班级有多少人参加AMC 8，我们只需将这些数字相加即可得出总数。11 + 8 + 9 = (C) 28.

Problem 2

If a@b = \frac{a \times b}{a + b} for a, b positive integers, then what is 5@10?

如果a@b = \frac{a \times b}{a + b} 是a,b个正整数，那么5@10是什么？

(A) \frac{3}{10} (B) 1 (C) 2 (D) \frac{10}{3} (E) 50

Solution

Substitute a = 5 and b = 10 into the expression for a@b to get:

将a=5和b=10代入a@b的表达式，得到：

5@10 = \frac{5 \times 10}{5 + 10} = \frac{50}{15} = \frac{10}{3}

Thus, answer choice (D) \frac{10}{3} is correct.

因此，答案选项(D) \frac{10}{3} 是正确的。

Problem 3

The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?

该图显示了年内前十个月五加仑汽油的价格。最高价比最低价高百分之多少？