1986 年 AMC 8 真题（P版）

1

\(1861\) 年七月，印度乞拉朋齐降雨 \(366\) 英寸。那个月平均每小时降雨多少英寸？

A\(\dfrac{366}{31 \times 24}\) B\(\dfrac{366 \times 31}{24}\) C\(\dfrac{366 \times 24}{31}\) D\(\dfrac{31 \times 24}{366}\) E\(366 \times 31 \times 24\)

English

In July \(1861,\) \(366\) inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month?

(A) \(\dfrac{366}{31 \times 24}\)(B) \(\dfrac{366 \times 31}{24}\)(C) \(\dfrac{366 \times 24}{31}\)(D) \(\dfrac{31 \times 24}{366}\)(E) \(366 \times 31 \times 24\)

2

下列哪个数的倒数最大？

A\(\dfrac13\) B\(\dfrac25\) C\(1\) D\(5\) E\(1986\)

English

Which of the following numbers has the largest reciprocal?

(A) \(\dfrac13\)(B) \(\dfrac25\)(C) \(1\)(D) \(5\)(E) \(1986\)

3

从集合 \(\{7, 25, -1, 12, -3\}\) 中选三个不同的数相加，可能得到的最小和是

A\(-3\) B\(-1\) C\(3\) D\(5\) E\(21\)

English

The smallest sum one could get by adding three different numbers from the set \(\{7, 25, -1, 12, -3\}\) is

(A) \(-3\)(B) \(-1\)(C) \(3\)(D) \(5\)(E) \(21\)

4

乘积 \((1.8)(40.3 + 0.07)\) 最接近

A\(7\) B\(42\) C\(74\) D\(84\) E\(737\)

English

The product \((1.8)(40.3 + 0.07)\) is closest to

(A) \(7\)(B) \(42\)(C) \(74\)(D) \(84\)(E) \(737\)

5

一场比赛从某天中午开始，\(1000\) 分钟后结束。比赛在什么时间结束？

A晚上 \(10\!:\!00\) B午夜 C凌晨 \(2\!:\!30\) D凌晨 \(4\!:\!40\) E早上 \(6\!:\!40\)

English

A contest began at noon one day and ended \(1000\) minutes later. At what time did the contest end?

(A) \(10\!:\!00\) p.m.(B) midnight(C) \(2\!:\!30\) a.m.(D) \(4\!:\!40\) a.m.(E) \(6\!:\!40\) a.m.

6

下列表达式的值是多少？

\[\frac{2}{1 - \frac{2}{3}}\]

A\(-3\) B\(-\dfrac43\) C\(\dfrac23\) D\(2\) E\(6\)

English

What is the value of the following expression?

\[\frac{2}{1 - \frac{2}{3}}\]

(A) \(-3\)(B) \(-\dfrac43\)(C) \(\dfrac23\)(D) \(2\)(E) \(6\)

7

\(\sqrt{8}\) 和 \(\sqrt{80}\) 之间有多少个整数？

A\(5\) B\(6\) C\(7\) D\(8\) E\(9\)

English

How many whole numbers are between \(\sqrt{8}\) and \(\sqrt{80}?\)

(A) \(5\)(B) \(6\)(C) \(7\)(D) \(8\)(E) \(9\)

8

在所示乘法中，\(B\) 表示一个数字。\(B\) 的值是多少？

\[\begin{array}{r} B2 \\ \times\, 7B \\ \hline 6396 \end{array}\]

A\(3\) B\(5\) C\(6\) D\(7\) E\(8\)

English

In the multiplication shown, \(B\) represents a digit. What is the value of \(B?\)

\[\begin{array}{r} B2 \\ \times\, 7B \\ \hline 6396 \end{array}\]

(A) \(3\)(B) \(5\)(C) \(6\)(D) \(7\)(E) \(8\)

9

只沿图示路径和方向，从 \(M\) 到 \(N\) 有多少条不同路线？

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

English

Using only the paths and the directions shown, how many different routes are there from \(M\) to \(N?\)

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

10

一幅宽 \(3\) 英尺的画挂在一面宽 \(19\) 英尺的墙正中央。画最近的一边距离墙端多少英尺？

A\(1\dfrac12\) B\(8\) C\(9\dfrac12\) D\(16\) E\(22\)

English

A picture \(3\) feet across is hung in the center of a wall that is \(19\) feet wide. How many feet from the end of the wall is the nearest edge of the picture?

(A) \(1\dfrac12\)(B) \(8\)(C) \(9\dfrac12\)(D) \(16\)(E) \(22\)

11

如果 \(A * B\) 表示 \(\dfrac{A + B}{2}\)，那么 \((3 * 5) * 8\) 等于

A\(6\) B\(8\) C\(12\) D\(16\) E\(30\)

English

If \(A * B\) means \(\dfrac{A + B}{2},\) then \((3 * 5) * 8\) is

(A) \(6\)(B) \(8\)(C) \(12\)(D) \(16\)(E) \(30\)

12

图表显示了一个数学班 \(30\) 名学生在最近两次测验中的成绩分布。例如，正好有一名学生在测验 \(1\) 中得“D”，在测验 \(2\) 中得“C”（圈出的格子）。有百分之多少的学生两次测验得到了相同成绩？

A\(12\%\) B\(25\%\) C\(33\dfrac13\%\) D\(40\%\) E\(50\%\)

English

The table shown displays the grade distribution of the \(30\) students in a mathematics class on the last two tests. For example, exactly one student received a ‘D’ on Test \(1\) and a ‘C’ on Test \(2\) (the circled entry). What percent of the students received the same grade on both tests?

(A) \(12\%\)(B) \(25\%\)(C) \(33\dfrac13\%\)(D) \(40\%\)(E) \(50\%\)

13

图中多边形的周长是

A\(14\) B\(20\) C\(28\) D\(48\) E无法由给定信息确定

English

The perimeter of the polygon shown is

(A) \(14\)(B) \(20\)(C) \(28\)(D) \(48\)(E) cannot be determined from the information given

14

如果 \(200 \le a \le 400\) 且 \(600 \le b \le 1200\)，那么商 \(\dfrac{b}{a}\) 的最大值是

A\(\dfrac32\) B\(3\) C\(6\) D\(300\) E\(600\)

English

If \(200 \le a \le 400\) and \(600 \le b \le 1200,\) then the largest value of the quotient \(\dfrac{b}{a}\) is

(A) \(\dfrac32\)(B) \(3\)(C) \(6\)(D) \(300\)(E) \(600\)

15

阿贾克斯折扣店的促销价比原价低 \(50\%\)。周六在促销价基础上再打 \(20\%\) 折扣。一件原价 \(\$180\) 的外套周六价格是多少？

A\(\$54\) B\(\$72\) C\(\$90\) D\(\$108\) E\(\$110\)

English

Sale prices at the Ajax Outlet Store are \(50\%\) below original prices. On Saturdays an additional discount of \(20\%\) off the sale price is given. What is the Saturday price of a coat whose original price is \(\$180?\)

(A) \(\$54\)(B) \(\$72\)(C) \(\$90\)(D) \(\$108\)(E) \(\$110\)

16

一幅条形图显示了一家快餐连锁店在每个季节卖出的汉堡数量。但是，表示冬季销量的条形被一块污迹遮住了。如果这家连锁店全年汉堡销量中正好有 \(25\%\) 是秋季卖出的，那么冬季卖出多少百万个汉堡？

A\(2.5\) B\(3\) C\(3.5\) D\(4\) E\(4.5\)

English

A bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If exactly \(25\%\) of the chain’s hamburgers are sold in the fall, how many million hamburgers are sold in the winter?

(A) \(2.5\)(B) \(3\)(C) \(3.5\)(D) \(4\)(E) \(4.5\)

17

设 \(o\) 是一个奇整数，\(n\) 是任意整数。关于整数 \(o^2 + no\)，下列哪项总为真？

A它总是奇数 B它总是偶数 C只有当 \(n\) 为偶数时它才是偶数 D只有当 \(n\) 为奇数时它才是奇数 E只有当 \(n\) 为偶数时它才是奇数

English

Let \(o\) be an odd whole number and let \(n\) be any whole number. Which of the following statements about the whole number \(o^2 + no\) is always true?

(A) it is always odd(B) it is always even(C) it is even only if \(n\) is even(D) it is odd only if \(n\) is odd(E) it is odd only if \(n\) is even

18

一个矩形牧场要用一段 \(100\) 米石墙作为第四边，只在另外三边围栅栏。栅栏上每隔 \(12\) 米立一个柱子，包括栅栏与石墙相接处的两个柱子。围出一个 \(36\) 米乘 \(60\) 米的区域，最少需要多少根柱子？

A\(11\) B\(12\) C\(13\) D\(14\) E\(16\)

English

A rectangular grazing area is to be fenced off on three sides using part of a \(100\) meter rock wall as the fourth side. Fence posts are to be placed every \(12\) meters along the fence, including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area \(36\) m by \(60\) m?

(A) \(11\)(B) \(12\)(C) \(13\)(D) \(14\)(E) \(16\)

19

旅行开始时，里程表读数为 \(56{,}200\) 英里。司机给油箱加满了 \(6\) 加仑汽油。旅途中，当里程表读数为 \(56{,}560\) 时，司机又给油箱加了 \(12\) 加仑汽油。旅行结束时，司机又加了 \(20\) 加仑汽油；此时里程表读数为 \(57{,}060\)。按最接近的十分之一计算，整段旅行中汽车平均每加仑行驶多少英里？

A\(22.5\) B\(22.6\) C\(24.0\) D\(26.9\) E\(27.5\)

English

At the beginning of a trip, the mileage odometer read \(56{,}200\) miles. The driver filled the gas tank with \(6\) gallons of gasoline. During the trip, the driver filled the tank again with \(12\) gallons of gasoline when the odometer read \(56{,}560.\) At the end of the trip, the driver filled the tank again with \(20\) gallons of gasoline; the odometer read \(57{,}060.\) To the nearest tenth, what was the car’s average miles-per-gallon for the entire trip?

(A) \(22.5\)(B) \(22.6\)(C) \(24.0\)(D) \(26.9\)(E) \(27.5\)

20

表达式

\[\frac{(304)^5}{(29.7)(399)^4}\]

的值最接近

A\(0.003\) B\(0.03\) C\(0.3\) D\(3\) E\(30\)

English

The value of the expression

\[\frac{(304)^5}{(29.7)(399)^4}\]

is closest to

(A) \(0.003\)(B) \(0.03\)(C) \(0.3\)(D) \(3\)(E) \(30\)

21

在所示 T 形图中，分别把八个带字母的相同正方形中的一个与四个阴影正方形放在一起。所得图形中有多少个可以折成一个没有顶盖的立方体盒子？

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

English

Suppose one of the eight lettered identical squares is included with the four shaded squares in the T-shaped figure shown. How many of the resulting figures can be folded into a topless cubical box?

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

22

艾伦、贝丝、卡洛斯和戴安娜正在讨论本评分期数学课可能得到的成绩。艾伦说：“如果我得 A，那么贝丝会得 A。”贝丝说：“如果我得 A，那么卡洛斯会得 A。”卡洛斯说：“如果我得 A，那么戴安娜会得 A。”这些话都是真的，但只有两名学生得了 A。哪两名学生得了 A？

A艾伦、贝丝 B贝丝、卡洛斯 C卡洛斯、戴安娜 D艾伦、戴安娜 E贝丝、戴安娜

English

Alan, Beth, Carlos, and Diana were discussing their possible grades in mathematics class this grading period. Alan said, “If I get an A, then Beth will get an A.” Beth said, “If I get an A, then Carlos will get an A.” Carlos said, “If I get an A, then Diana will get an A.” All of these statements were true, but only two of the students received an A. Which two received A’s?

(A) Alan, Beth(B) Beth, Carlos(C) Carlos, Diana(D) Alan, Diana(E) Beth, Diana

23

大圆的直径是 \(AC\)。两个小圆的圆心在 \(AC\) 上，并且在大圆圆心 \(O\) 处相切。如果每个小圆半径为 \(1\)，阴影区域面积与一个小圆面积之比是多少？

A在 \(\dfrac12\) 和 \(1\) 之间 B\(1\) C在 \(1\) 和 \(\dfrac32\) 之间 D在 \(\dfrac32\) 和 \(2\) 之间 E无法由给定信息确定

English

The large circle has diameter \(AC.\) The two small circles have their centers on \(AC\) and just touch at \(O,\) the center of the large circle. If each small circle has radius \(1,\) what is the value of the ratio of the area of the shaded region to the area of one of the small circles?

(A) between \(\dfrac12\) and \(1\)(B) \(1\)(C) between \(1\) and \(\dfrac32\)(D) between \(\dfrac32\) and \(2\)(E) cannot be determined from the information given

24

金氏初中的 \(600\) 名学生午餐时被平均分成三组。每组在不同时间吃午餐。电脑随机把每名学生分到三组之一。三个朋友艾尔、鲍勃和卡罗尔被分到同一午餐组的概率大约是

A\(\dfrac{1}{27}\) B\(\dfrac19\) C\(\dfrac18\) D\(\dfrac16\) E\(\dfrac13\)

English

The \(600\) students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of the three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately

(A) \(\dfrac{1}{27}\)(B) \(\dfrac19\)(C) \(\dfrac18\)(D) \(\dfrac16\)(E) \(\dfrac13\)

25

下列哪一组整数的平均数最大？

A\(1\) 到 \(101\) 之间的 \(2\) 的倍数 B\(1\) 到 \(101\) 之间的 \(3\) 的倍数 C\(1\) 到 \(101\) 之间的 \(4\) 的倍数 D\(1\) 到 \(101\) 之间的 \(5\) 的倍数 E\(1\) 到 \(101\) 之间的 \(6\) 的倍数

English

Which of the following sets of whole numbers has the largest average?

(A) multiples of \(2\) between \(1\) and \(101\)(B) multiples of \(3\) between \(1\) and \(101\)(C) multiples of \(4\) between \(1\) and \(101\)(D) multiples of \(5\) between \(1\) and \(101\)(E) multiples of \(6\) between \(1\) and \(101\)