2015 AMC amc8 真题 答案 详解

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中英双语真题

2015 AMC8
Problem 1
How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.)
要覆盖长12英尺、宽9英尺的长方形地板，需要多少平方码的地毯？（1码等于3英尺）
(A) 12 (B) 36 (C) 108 (D) 324 (E) 972

Problem 2
Point ( O ) is the center of the regular octagon ( ABCDEFGH ), and ( X ) is the midpoint of the side ( AB ). What fraction of the area of the octagon is shaded?
点 ( O ) 是正八边形 ( ABCDEFGH ) 的中心，( X ) 是边 ( AB ) 的中点，问在整个八边形面积中，图中阴影部分面积所占的比例是多少？
(A) ( \frac{11}{32} ) (B) ( \frac{3}{8} ) (C) ( \frac{13}{32} ) (D) ( \frac{7}{16} ) (E) ( \frac{15}{32} )

Problem 3
Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of 10 miles per hour. Jack walks to the pool at a constant speed of 4 miles per hour. How many minutes before Jack does Jill arrive?
Jack 和 Jill 要去距离他们家 1 英里的游泳池游泳。他们同时从家出发。Jill 以每小时 10 英里的速度骑自行车去泳池，Jack 以每小时 4 英里的速度步行过去。那么 Jill 比 Jack 早到多少分钟？
(A) 5 (B) 6 (C) 8 (D) 9 (E) 10

英文真题

Compiled on: January 1, 2021 AMC8 2015 Problems Page 27 of 109 Q1. How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.) A) 12 B) 36 C) 108 D) 324 E) 972 Q2. Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side AB. What fraction of the area of the octagon is shaded? A) ( \frac{11}{32} ) B) ( \frac{3}{8} ) C) ( \frac{13}{32} ) D) ( \frac{7}{16} ) E) ( \frac{15}{32} ) Q3. Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of 10 miles per hour. Jack walks to the pool at a constant speed of 4 miles per hour. How many minutes before Jack does Jill arrive? A) 5 B) 6 C) 8 D) 9 E) 10 Q4. The Dragonvale Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible? A) 2 B) 4 C) 5 D) 6 E) 12 Q5. Billy's basketball team scored the following points over the course of the first 11 games of the season: 42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73 If his team scores 40 in the 12th game, which of the following statistics will show an increase? A) range B) median C) mean D) mode E) mid-range Q6. In △ABC, AB = BC = 29, and AC = 42. What is the area of △ABC? A) 100 B) 420 C) 500 D) 609 E) 701 Q7. Each of two boxes contains three chips numbered 1, 2, 3. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even? A) ( \frac{1}{9} ) B) ( \frac{2}{9} ) C) ( \frac{4}{9} ) D) ( \frac{1}{2} ) E) ( \frac{5}{9} ) Q8. What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19? A) 24 B) 29 C) 43 D) 48 E) 57

真题文字详解(英文)

Problem 1 Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.)
(A) 12 (B) 36 (C) 108 (D) 324 (E) 972

Solution 1 We need $12 \cdot 9$ square feet of carpet to cover the floor. Since there are 9 square feet in a square yard, we divide this by 9 to get (A) 12 square yards.
Solution 2 Since there are 3 feet in a yard, we divide 9 by 3 to get 3 yards, and 12 by 3 to get 4 yards. To find the area of the carpet, we then multiply these two values together to get $3 \cdot 4 = $ (A) 12 square yards.

Problem 2 Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side AB. What fraction of the area of the octagon is shaded?
(A) $\frac{11}{32}$ (B) $\frac{3}{8}$ (C) $\frac{13}{32}$ (D) $\frac{7}{16}$ (E) $\frac{15}{32}$

Solutions Solution 1 Since octagon ABCDEFGH is a regular octagon, it is split into 8 equal parts, such as triangles △ABO, △BCO, △CDO, etc. These parts, since they are all equal, are $\frac{1}{8}$ of the octagon each. The shaded region consists of 3 of these equal parts plus half of another, so the fraction of the octagon that is shaded is $\frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{16} = $ (D) $\frac{7}{16}$ .
Solution 2

真题文字详解(中英双语)

Problem 1 Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.) Onkon 想要用他最喜欢的红色地毯铺满他的房间地板。一个长 12 英尺、宽 9 英尺的长方形地板需要多少平方码的红色地毯？（1 码等于 3 英尺。） (A) 12 (B) 36 (C) 108 (D) 324 (E) 972 Solution 1 We need 12 · 9 square feet of carpet to cover the floor. Since there are 9 square feet in a square yard, we divide this by 9 to get (A) 12 square yards. 我们需要 12 · 9 平方英尺的地毯来铺满地板。由于 1 平方码等于 9 平方英尺，我们将这个数字除以 9，得到 (A) 12 平方码。 Solution 2 Since there are 3 feet in a yard, we divide 9 by 3 to get 3 yards, and 12 by 3 to get 4 yards. To find the area of the carpet, we then multiply these two values together to get 3 · 4 = (A) 12 square yards. 由于 1 码等于 3 英尺，我们将 9 除以 3 得到 3 码，将 12 除以 3 得到 4 码。为了找到地毯的面积，我们将这两个值相乘，得到 3 · 4 = (A) 12 平方码。 Problem 2 Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side AB. What fraction of the area of the octagon is shaded? 点 O 是正八边形 ABCDEFGH 的中心，点 X 是边 AB 的中点。阴影部分的面积占八边形面积的多少？ (A) (\frac{11}{32}) (B) (\frac{3}{8}) (C) (\frac{13}{32}) (D) (\frac{7}{16}) (E) (\frac{15}{32})

Solutions Solution 1