2012 AMC amc12a 真题 答案 详解

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中英双语真题

2012 AMC12A

Problem 1
A bug crawls along a number line, starting at -2. It crawls to -6, then turns around and crawls to 5. How many units does the bug crawl altogether?
(A) 9 (B) 11 (C) 13 (D) 14 (E) 15

Problem 2
Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?
(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

Problem 3
A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold n grams of clay. What is n?
(A) 120 (B) 160 (C) 200 (D) 240 (E) 280

英文真题

2012 AMC 12A Problems

Problem 1
A bug crawls along a number line, starting at -2. It crawls to -6, then turns around and crawls to 5. How many units does the bug crawl altogether?
(A) 9 (B) 11 (C) 13 (D) 14 (E) 15

Problem 2
Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?
(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

Problem 3
A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold n grams of clay. What is n?
(A) 120 (B) 160 (C) 200 (D) 240 (E) 280

Problem 4
In a bag of marbles, (\frac{3}{5}) of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number of blue marbles stays the same, what fraction of the marbles will be red?
(A) (\frac{2}{5}) (B) (\frac{3}{7}) (C) (\frac{4}{7}) (D) (\frac{3}{5}) (E) (\frac{4}{5})

Problem 5
A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?
(A) 8 (B) 16 (C) 25 (D) 64 (E) 96

Problem 6
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

Problem 7
Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
(A) 5 (B) 6 (C) 8 (D) 10 (E) 12

Problem 8
An iterative average of the numbers 1, 2, 3, 4, and 5 is computed in the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure?
(A) (\frac{31}{16}) (B) 2 (C) (\frac{17}{8}) (D) 3 (E) (\frac{65}{16})

Problem 9
A year is a leap year if and only if the year number is divisible by 400 (such as 2000) or is divisible by 4 but not by 100 (such as 2012). The 200th anniversary of the birth of novelist Charles Dickens was celebrated on February 7, 2012, a Tuesday. On what day of the week was Dickens born?

真题文字详解(英文)

Problem 1 The following problem is from both the 2012 AMC 12A #1 and 2012 AMC 10A #3, so both problems redirect to this page. A bug crawls along a number line, starting at -2. It crawls to -6, then turns around and crawls to 5. How many units does the bug crawl altogether?
(A) 9 (B) 11 (C) 13 (D) 14 (E) 15

Solution Crawling from -2 to -6 takes it a distance of 4 units. Crawling from -6 to 5 takes it a distance of 11 units. Add 4 and 11 to get (E) 15.

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Problem 2 The following problem is from both the 2012 AMC 12A #2 and 2012 AMC 10A #1, so both problems redirect to this page. Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?
(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

Solution 1 Cagney can frost one in 20 seconds, and Lacey can frost one in 30 seconds. Working together, they can frost one in ( \frac{20 \cdot 30}{20 + 30} = \frac{600}{50} = 12) seconds. In 300 seconds (5 minutes), they can frost (D) 25 cupcakes.

Solution 2 In 300 seconds (5 minutes), Cagney will frost ( \frac{300}{20} = 15 ) cupcakes, and Lacey will frost ( \frac{300}{30} = 10 ) cupcakes. Therefore, working together they will frost ( 15 + 10 = \textbf{(D)}\ 25 ) cupcakes.

Solution 3 Since Cagney frosts 3 cupcakes a minute, and Lacey frosts 2 cupcakes a minute, they together frost ( 3 + 2 = 5 ) cupcakes a minute. Therefore, in 5 minutes, they frost ( 5 \times 5 = 25 \Rightarrow \textbf{(D)} ).

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Problem 3 A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold n grams of clay. What is n?
(A) 120 (B) 160 (C) 200 (D) 240 (E) 280

真题文字详解(中英双语)

Problem 1 The following problem is from both the 2012 AMC 12A #1 and 2012 AMC 10A #3, so both problems redirect to this page. 以下题目来自2012年AMC 12A #1和2012年AMC 10A #3，因此这两个题目都重定向到这个页面。 A bug crawls along a number line, starting at -2. It crawls to -6, then turns around and crawls to 5. How many units does the bug crawl altogether? 一只虫子沿着数轴爬行，从-2开始。它爬到-6，然后转身爬到5。虫子总共爬了多少单位？ (A) 9 (B) 11 (C) 13 (D) 14 (E) 15 Solution Crawling from -2 to -6 takes it a distance of 4 units. Crawling from -6 to 5 takes it a distance of 11 units. Add 4 and 11 to get (E) 15. Problem 2 The following problem is from both the 2012 AMC 12A #2 and 2012 AMC 10A #1, so both problems redirect to this page. Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes? (A) 10 (B) 15 (C) 20 (D) 25 (E) 30 Solution 1 Cagney can frost one in 20 seconds, and Lacey can frost one in 30 seconds. Working together, they can frost one in \frac{20\cdot30}{20+30}=\frac{600}{50}=12 seconds. In 300 seconds (5 minutes), they can frost (D) 25 cupcakes. Solution 2 In 300 seconds (5 minutes), Cagney will frost \frac{300}{20}=15 cupcakes, and Lacey will frost \frac{300}{30}=10 cupcakes. Therefore, working together they will frost 15 + 10 = (D) 25 cupcakes. Solution 3 Since Cagney frosts 3 cupcakes a minute, and Lacey frosts 2 cupcakes a minute, they together frost 3 + 2 = 5 cupcakes a minute. Therefore, in 5 minutes, they frost 5 × 5 = 25 → (D) Problem 3 A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold n grams of clay. What is n?