AMC8竞赛试题英文版汇总.docx

1、AMC8竞赛试题英文版汇总Problem 1Aunt Anna isyears old. Caitlin isyears younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? 安妮今年42岁，凯琳比柏娜小五岁，而柏娜的年龄是安妮的一半。试问凯琳今年几岁？Problem 2Which of these numbers is less than its reciprocal? 下列那一个数小于它的倒数？Problem 3How many whole numbers lie in the

2、interval betweenand有多少个整数介于5/3和2之间？Problem 4Inonlyof the working adults in Carlin City worked at home. Bythe at-home work force increased to. Inthere were approximatelyworking at home, and inthere were. The graph that best illustrates this is在卡林市，1960年只有5%的成年工作者在家工作，至1970年在家工作人数增加到8%，1960年大约有15%的人在家

3、工作，而在1990年则有30%。试问下面那一个图是这种情形的最佳说明Problem 5Each principal of Lincoln High School serves exactly one-year term. What is the maximum number of principals this school could have during an-year period? 林肯中学每一位校长都洽服务一次三年任期，则在8年期间林肯中学最多有几位校长？Problem 6Figureis a square. Inside this square three smaller squ

4、ares are drawn with the side lengths as labeled. The area of the shaded L-shaped region is右图ABCD是正方形。此正方形内有3个较小的正方形，它们的边长如图中所标示，则L行黑影区域的面积为多少？Problem 7What is the minimum possible product of three different numbers of the set? 从-8，-6，-4，0，3，5，7中任取三个不同数做乘积，则最小的乘积是Problem 8Three dice with faces number

5、ed 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is 每面标有1至6点的三颗骰子推成一串，如右图所示，其中可见七个面，而十一个面是看不到的(背面、底面，之间的面)，试问看不见的面其点数总和是Problem 9Three-digit powers of 2 and 5 are used

6、in thiscross-numberpuzzle. What is the only possible digit for the outlined square? 填数游戏：右方格子中横的三个格子内(自左至右)填入三位数，此三位数可表为2m(m为正整数)，纵的三个格子内(自上至下)填入三位数，此三位数可表为5n(n为正整数)；试问，粗黑的格子内只能出现那一个数字？Problem 10Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grow half as many inc

7、hes as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now? Ara和Shea两人的身高本来相同。如今Shea又长高20%，而Ara只长高Shea所长高的一半。Shea现在的身高是60吋，则Ara现在的身高是多少吋？Problem 11The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property? 整数64具有

8、可被它的个位数字所整除的性质。试问在10和50之间有多少个整数具有这种性质？Problem 12A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the

9、 ends. What is the smallest number of blocks needed to build this wall? 欲建一道长100呎高七呎的砖墙，能够使用的砖块有两种：1呎高2呎长或1呎高1呎长(但砖块不能切割)。垂直连接砖块必须如图所示交错间隔，且墙的两端必须推砌平整。试问至少需要多少砖块才能建成此道墙？Problem 13In triangle, we haveand. Ifbisects, then 已知CAT中，ACT=ATC，且CAT=36，若TR平分ATC时，则CRT=Problem 14What is the units digit of?的个位数字

10、是什么数？Problem 15Triangles, andare all equilateral. Pointsandare midpoints ofand, respectively. If, what is the perimeter of figure? 如图，ABC，ADE及EFG都是等边三角形，D及G分别为AC及AE的中点。若AB=4时，图形ABCDEFG外围的周长是多少？Problem 16In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the len

11、gth 25 times or walk its perimeter 10 times. What is the area of Mateens backyard in square meters? 马丁为了在他家的长方形后院走一公里(1000公尺)，他必须在后院的长边走25趟或绕着后院的周边走10圈，试问马丁家后院的面积是多少平方公尺？Problem 17The operationis defined for all nonzero numbers by. Determine. 设，表任意两个不等于零的数，我们定义运算如下：=2/则(12) 31(23)= Problem 18Conside

12、r these two geoboard quadrilaterals. Which of the following statements is true? 考虑右图方格板中的两个四边形，下列哪一个叙述是正确的？ 四边形I的面积大于四边形II的面积 四边形I的面积小于四边形II的面积 这两个四边形有相同的面积及相同的周长 这两个四边形有相同的面积，但I的周长大于II的周长 这两个四边形有相同的面积，但I的周长小于II的周长Problem 19Three circular arcs of radius 5 units bound the region shown. Arcsandare qua

13、rter-circles, and arcis a semicircle. What is the area, in square units, of the region? 半径为5单位的三个圆弧围成如右图所示的区域，其中AB弧与AD弧是四分之一圆弧，而BCD弧是一个半圆弧，则此区域的面积是多少平方单位？Problem 20You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $, with at least one coin of each typ

14、e. How many dimes must you have? 设有九个硬币，一分的、五分的、十分的和二十五分的硬币，且每种硬币至少有一个。若这九个硬币总值是1.02美元，则十分硬币必须有几个？Problem 21Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is设甲投掷一个一元硬币，乙投掷两个一元硬币，则乙投掷出现正面的个数和甲投掷出现正面的个数相同时的机率是多少？Problem

15、 22A cube has edge length 2. Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to

16、设有边长都是2的正立方体。假定在它顶上的面在黏上一个边长都是1的小正立方体，小正方体的一个面完全贴紧在大正立方体顶上的面上。试问新立体的表面积(侧面、顶面、顶上侧面、底面等)比原正立方体的表面积增加的百分比最接近于下面那一个数？Problem 23There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If the average of all seven numbers is, then the nu

17、mber common to both sets of four numbers is设有排成一列的七个数，前四个数(由最左边算起)的平均数是5，后四个数的平均数是8。假定全部七个数的平均数是6 4/7时，则前、后两组四个数中重叠的数是下列何者？Problem 24Ifand, then 如图，A=20，AFG=AGF，则B+D=？Problem 25The area of rectangleis 72. If pointand the midpoints ofandare joined to form a triangle, the area of that triangle is 如图，长方形ABCD的面积是72。由点A和BC及CD的中点连接成一个三角形，则此三角形的面积是多少？