2010 AMC amc12b 真题 答案 详解

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中英双语真题

2010 AMC12B

Problem 1
Makarla attended two meetings during her 9-hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
Markala 在她工作的9小时里参加了2次会议。第一场会议耗时45分钟，第二场会议时长是第一场的2倍。问她工作总时间的百分之多少是花在了会议上？
(A) 15 (B) 20 (C) 25 (D) 30 (E) 35

Problem 2
A big L is formed as shown. What is its area?
一个大的L字形如下图所示。问它的面积是多少？
(A) 22 (B) 24 (C) 26 (D) 28 (E) 30

Problem 3
A ticket to a school play cost x dollars, where x is a whole number. A group of 9th graders buys tickets costing a total of $48, and a group of 10th graders buys tickets costing a total of $64. How many values for x are possible?
一张学校戏剧票要花x美元，其中x是整数。一组九年级学生买的票总共花了48美元，一组十年级学生买的票总共花了64美元。问x有多少个可能的值？
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

英文真题

2010 AMC 12B Problems Problem 1 Makarla attended two meetings during her 9-hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
(A) 15 (B) 20 (C) 25 (D) 30 (E) 35

Problem 2 A big L is formed as shown. What is its area?
(A) 22 (B) 24 (C) 26 (D) 28 (E) 30

Problem 3 A ticket to a school play cost $x$ dollars, where $x$ is a whole number. A group of 9th graders buys tickets costing a total of $48$, and a group of 10th graders buys tickets costing a total of $64$. How many values for $x$ are possible?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Problem 4 A month with 31 days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

Problem 5 Lucky Larry's teacher asked him to substitute numbers for $a, b, c, d,$ and $e$ in the expression $a - \left( b - \left( c - \left( d + e \right) \right) \right)$ and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for $a, b, c,$ and $d$ were $1, 2, 3,$ and $4,$ respectively. What number did Larry substitute for $e$?
(A) -5 (B) -3 (C) 0 (D) 3 (E) 5

Problem 6 At the beginning of the school year, 50% of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and 50% answered "No". At the end of the school year, 70% answered "Yes" and 30% answered "No". Altogether, $x\%$ of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of $x$?
(A) 0 (B) 20 (C) 40 (D) 60 (E) 80

Problem 7 Shelby drives her scooter at a speed of 30 miles per hour if it is not raining, and 20 miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of 16 miles in 40 minutes. How many minutes did she drive in the rain?
(A) 18 (B) 21 (C) 24 (D) 27 (E) 30

真题文字详解(英文)

Problem 1 The following problem is from both the 2010 AMC 12B #1 and 2010 AMC 10B #2, so both problems redirect to this page. Makarla attended two meetings during her 9-hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
(A) 15 (B) 20 (C) 25 (D) 30 (E) 35

Solution The total number of minutes in her 9-hour work day is $9 \times 60 = 540$. The total amount of time spend in meetings in minutes is $45 + 45 \times 2 = 135$. The answer is then $\frac{135}{540} = 25\%$ or (C).

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Problem 2

A big L is formed as shown. What is its area?

(A) 22 (B) 24 (C) 26 (D) 28 (E) 30

Solution We find the area of the big rectangle to be $8 \times 5 = 40$, and the area of the smaller rectangle to be $(8 - 2) \times (5 - 2) = 18$. The answer is then $40 - 18 = 22$ (A).

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See also Problem 3

The following problem is from both the 2010 AMC 12B #3 and 2010 AMC 10B #8, so both problems redirect to this page. A ticket to a school play cost $x$ dollars, where $x$ is a whole number. A group of 9th graders buys tickets costing a total of $48$, and a group of 10th graders buys tickets costing a total of $64$. How many values for $x$ are possible?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Solution We find the greatest common factor of $48$ and $64$ to be $16$. The number of factors of $16$ is $5$ which is the answer (E).

真题文字详解(中英双语)

Problem 1 The following problem is from both the 2010 AMC 12B #1 and 2010 AMC 10B #2, so both problems redirect to this page. 以下问题来自2010年AMC 12B #1和2010年AMC 10B #2，因此这两个问题都重定向到该页面。 Makarla attended two meetings during her 9-hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings? Makarla 在她9小时的工作日里参加了两次会议。第一次会议持续了45分钟，第二次会议的时间是第一次的两倍。她参加会议的时间占她工作日的百分之多少？ (A) 15 (B) 20 (C) 25 (D) 30 (E) 35 Solution The total number of minutes in her 9-hour work day is 9 × 60 = 540. The total amount of time spend in meetings in minutes is 45 + 45 × 2 = 135. The answer is then \frac{135}{540} = 25% or (C). 她9小时的工作日总共有9 × 60 = 540分钟。她在会议中花费的总时间是45 + 45 × 2 = 135分钟。因此答案是\frac{135}{540} = 25%或(C)。 Problem 2 Problem 2 A big L is formed as shown. What is its area? 如下图所示，一个大L被形成。它的面积是多少？ (A) 22 (B) 24 (C) 26 (D) 28 (E) 30 Solution We find the area of the big rectangle to be 8 × 5 = 40, and the area of the smaller rectangle to be (8 - 2) × (5 - 2) = 18. The answer is then 40 - 18 = 22 (A). 我们求出大矩形的面积为8 × 5 = 40，小矩形的面积为(8-2) × (5-2) = 18。答案是40 - 18 = 22(A)。 See also