2007 AMC amc12b 真题 答案 详解

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英文真题

2007 AMC 12B Problems

Problem 1

Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?

(A) 678 (B) 768 (C) 786 (D) 867 (E) 876

Problem 2

A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his parents' SUV and averaged only 20 miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?

(A)22 (B)24 (C)25 (D)26 (E)28

Problem 3

The point ( O ) is the center of the circle circumscribed about triangle ( ABC ), with ( \angle BOC = 120^\circ ) and ( \angle AOB = 140^\circ ), as shown. What is the degree measure of ( \angle ABC )?

(A)35 (B)40 (C)45 (D)50 (E)60

Problem 4

At Frank's Fruit Market, 3 bananas cost as much as 2 apples, and 6 apples cost as much as 4 oranges. How many oranges cost as much as 18 bananas?

(A)6 (B)8 (C)9 (D)12 (E)18

Problem 5

The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each problem left unanswered. After looking over the 25 problems, Sarah has decided to attempt the first 22 and leave the last 3 unanswered. How many of the first 22 problems must she solve correctly in order to score at least 100 points?

(A)13 (B)14 (C)15 (D)16 (E)17

Problem 6

Triangle ( ABC ) has side lengths ( AB = 5 ), ( BC = 6 ), and ( AC = 7 ). Two bugs start simultaneously from ( A ) and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point ( D ). What is ( BD )?

(A)1 (B)2 (C)3 (D)4 (E)5

Problem 7

All sides of the convex pentagon ( ABCDE ) are of equal length, and ( \angle A = \angle B = 90^\circ ). What is the degree measure of ( \angle E )?

(A)90 (B)108 (C)120 (D)144 (E)150

Problem 8

Tom's age is ( T ) years, which is also the sum of the ages of his three children. His age ( N ) years ago was twice the sum of their ages then. What is ( T/N )?

(A)2 (B)3 (C)4 (D)5 (E)6

Problem 9

A function ( f ) has the property that ( f(3x-1)=x^2+x+1 ) for all real numbers ( x ). What is ( f(5) )?

(A)7 (B)13 (C)31 (D)111 (E)211

真题文字详解(英文)

Problem 1 The following problem is from both the 2007 AMC 12B #1 and 2007 AMC 10B #1, so both problems redirect to this page. Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted? (A) 678 (B) 768 (C) 786 (D) 867 (E) 876 Solution There are four walls in each bedroom (she can't paint floors or ceilings). Therefore, we calculate the number of square feet of walls there is in one bedroom: 2 · (12 · 8 + 10 · 8) - 60 = 2 · 176 - 60 = 292 We have three bedrooms, so she must paint 292 · 3 = (E) 876 square feet of walls. Problem 2 The following problem is from both the 2007 AMC 12B #2 and 2007 AMC 10B #3, so both problems redirect to this page. A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his parents' SUV and averaged only 20 miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip? (A) 22 (B) 24 (C) 25 (D) 26 (E) 28 Solution 1 The trip was 240 miles long and took 120/30 + 120/20 = 4 + 6 = 10 gallons. Therefore, the average mileage was 240/10 = (B) 24 Solution 2 Alternatively, we can use the harmonic mean to get 2/(1/20 + 1/30) = 2/((1/12) = (B) 24 Problem 3 The point O is the center of the circle circumscribed about triangle ABC, with ∠BOC = 120° and ∠AOB = 140°, as shown. What is the degree measure of ∠ABC?

真题文字详解(中英双语)

Problem 1 The following problem is from both the 2007 AMC 12B #1 and 2007 AMC 10B #1, so both problems redirect to this page. Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?
(A) 678 (B) 768 (C) 786 (D) 867 (E) 876 Solution There are four walls in each bedroom (she can't paint floors or ceilings). Therefore, we calculate the number of square feet of walls there is in one bedroom:
2 · (12 · 8 + 10 · 8) - 60 = 2 · 176 - 60 = 292 We have three bedrooms, so she must paint 292 · 3 = (E) 876 square feet of walls. Problem 2 The following problem is from both the 2007 AMC 12B #2 and 2007 AMC 10B #3, so both problems redirect to this page. A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his parents' SUV and averaged only 20 miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?
(A) 22 (B) 24 (C) 25 (D) 26 (E) 28 Solution 1 The trip was 240 miles long and took 120/30 + 120/20 = 4 + 6 = 10 gallons. Therefore, the average mileage was 240/10 = (B) 24 Solution 2 Alternatively, we can use the harmonic mean to get 2/(1/20 + 1/30) = 2/(1/12) = (B) 24 Problem 3 The point O is the center of the circle circumscribed about triangle ABC, with ∠BOC = 120° and ∠AOB = 140°, as shown. What is the degree measure of ∠ABC?