2025年AMC8国际数学竞赛（八年级及以下学生）

2025AMC8 1.The eight-pointed star,shown in the figure below,is a popular quilting pattern.What percent of the entire 4-by-4 grid is covered by the star? 下图所示的八角星是一种流行的绗缝图案。整个4×4的网格中有百分之多少被星星覆盖？ (A)40 (B)50 (C)60 (D)75 (E)80 2.The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers. 下表显示了古埃及象形文字，这些象形文字被用来表示不同的数字。 100,000 10.000 1.000 100 10 For example,the number 32 was represented by nnn.What number was represented by the following combination of hieroglyphs? 例如，数字32由∩∩∩表示。以下象形文字组合代表了哪个数字？ (A)1,423 B)10.423 (C)14.023 (D)14.203 (E)14,230 3.Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the game.When Annika and 3 of her friends play Buffalo Shuffle-0,each player is dealt 15 cards.Suppose 2 more friends join the next game.How many cards will be dealt to each player? Buffalo Shuffle-o是一种纸牌游戏，在游戏开始时所有牌都会平均分发给所有玩家。当Annika 和她的3个朋友玩Buffalo Shuffle--o时，每个玩家发到15张牌。假设下一次游戏有2个更 多的朋友加入，那么每个玩家将会分到多少张牌？ (A)8 (B)9 (C)10 (D)11 (E)12 4.Lucius is counting backward by 7s.His first three numbers are 100,93,and 86.What is his 10th number? 卢修斯正在以7为间隔倒数。他的前三个数字是100、93和86。他的第十个数字是什么？ (A)30 (B)37(C)42 D)44(E)47 5.Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory (labeled F)and drives to location A,then B,then C,before returning to F. What is the shortest distance,in blocks,she can drive to complete the route? 贝蒂驾驶一辆卡车在下图所示的街区地图中递送包裹。贝蒂从工厂（标记为F)开始，然后开 车到位置A,接着是B,然后是C,最后返回到F。她完成路线的最短距离是多少个街区？ A I block B I block (A)20 (B)22 (C)21 D)26 (E)28 6.Sekou writes the numbers 15,16,17,18,19.After he erases one of the numbers,the sum of the remaining four numbers is a multiple of 4.Which number did he erase? Skou写下了数字15,16,17,18,19。在他擦掉其中一个数字之后，剩下的四个数字之和是4 的倍数。他擦掉了哪个数字？ (A)15 (B)16 (C17 (D)18 (E)19 7.On the most recent exam in Prof.Xochi's class, 5 students earned a score of at least 95%, 13 students earned a score of at least 90%, 27 students earned a score of at least 85%,and 50 students earned a score of at least 80%. How many students earned a score of at least 80%and less than 90%? 在Xochi教授最近的一次考试中， 5名学生获得了至少95%的分数， 13名学生获得了至少90%的分数， 27名学生获得了至少85%的分数， 50名学生获得了至少80%的分数。 有多少学生获得了至少80%但不到90%的成绩？ (A)8 (B)14 (C)22 (D)37 (E)45 8.Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right,which has an area of 18 square centimeters.What was the volume of the cube in cubic centimeters? 以赛亚沿着纸板立方体的一些边缘切割，形成了右侧显示的平面形状，其面积为18平方厘米。 立方体的体积是多少立方厘米？ (A)3V3 B)6 (C)9 (D)6V3 (E)9V5 9.Ningli looks at the 6 pairs of numbers directly across from each other on a clock.She takes the average of each pair of numbers.What is the average of the resulting 6 numbers? 宁莉看着钟面上直接相对的6对数字。她取每对数字的平均值。这6个数字的平均值是多少？ 12 (A)5 (B)6.5 (C)8 D)9.5 (E)12 10.In the figure below,ABCD is a rectangle with sides of length AB=5 inches and AD=3 inches. Rectangle ABCD is rotated 90'clockwise around the midpoint of side DC to give a second rectangle.What is the total area,in square inches,covered by the two overlapping rectangles? 在下图中，ABCD是一个矩形，边长AB=5英寸，AD-3英寸。矩形ABCD绕边DC的中点顺 时针旋转90度，形成第二个矩形。两个重叠矩形覆盖的总面积是多少平方英寸？ A B (A)21 (B)22.25 (C)23 (D)23.75 (E)25 11.A tetromino consists of four squares connected along their edges.There are five possible tetromino shapes,I,O.L,T,and S,shown below,which can be rotated or flipped over.Three tetrominoes are used to completely cover a 3 x 1 rectangle.At least one of the tiles is an S tile.What are the other two tiles? 一个四格骨牌由四个沿着边缘相连的正方形组成。有五种可能的四格骨牌形状，分别是I、O、 L、T和S,如下所示，它们可以旋转或翻转。三个四格骨牌可以完全覆盖一个3×4的矩形。 至少有一片是S形，另外两个是什么形？ (A)I and L (B)I andT (C)L and L (D)L and S (E)O and T 12.The region shown below consists of 24 squares,each with side length I centimeter.What is the area,in square centimeters,of the largest circle that can fit inside the region,possibly touching the boundaries? 下面显示的区域由24个边长为1厘米的正方形组成。请问，能够完全适应在该区域内的最大 圆的面积是多少平方厘米（圆可触及边界）？ (A)3π (B)4π (C)5π (D)6π (E)8π 13.Each of the even numbers 2,4,6....,50 is divided by7.The remainders are recorded.Which histogram displays the number of times each remainder occurs? 每个偶数2,4,6,50被7除后，记录下余数。哪个直方图显示了每个余数出现的次数？ 44 4 3 3 0123456 0 123456 (A) Remainder (B) Remainder 4444 4 33 0 12345 6 0 23456 (C) Remainder (D) Remainder uno 0 12 3456 () Remainder 14.A number N is inserted into the list 2,6,7,7,28.The mean is now twice as great as the median.What is N? 一个数字N被插入列表2,6,7,7,28中。现在平均数是中位数的两倍。N是多少？ (A)7 (B)14 (C)20 D)28 (E)34 15.Kei draws a 6-by-6 grid.He colors 13 of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically,forming pairs of overlapping unit squares.Let m and M equal the least and greatest possible number of gold-on-gold pairs,respectively.What is the value ofn+M? Kci画了一个6乘6的网格。他将其中的13个单位方格涂成银色，其余的涂成金色。然后Ki 将网格垂直对折，形成了重叠的单位方格对。设和M分别代表金-金对的最小和最大可能数 量。求n+M的值是多少？ (A)12 (B)14 (C)16 (D)18 (E)20 16.Five distinct integers from I to 10 are chosen,and five distinct integers from 11 to 20 are chosen. No two numbers differ by exactly 10.What is the sum of the ten chosen numbers? 从1到10中选择五个不同的整数，再从11到20中选择五个不同的整数。没有任何两个数的 差是10。这十个选定数字的总和是多少？ (A)95 (B)100 (C)105 (D)110 E)I15 17.In the land of Markovia,there are three cities:A,B,and C.There are 100 people who live in A,120 who live in B,and 160 who live in C.Everyone works in one of the three cities,and a person may work in the same city where they live.In the figure below,an arrow pointing from one city to another is labeled with the fraction of people living in the first city who work in the second city.(For exampleof the people who live inA work in B.)How many people work inA? 在马克沃亚的土地上，有三个城市：A、B和C。A城市居住着100人，B城市居住着120人， C城市居住着160人.每个人都在三个城市中的一个工作，一个人可能在他们居住的城市工作， 在下面的图中，从一个城市指向另一个城市的箭头标有居住在第一个城市中在第二个城市工作 的那部分人的分数。（例如，住在A的人中有1/4在B工作。）有多少人在A城市工作？ 1/4 /8 1/3 1/5 B 1/10 1/6 (A)55 B)60 (C)85 (D)115 (E)160 18.The circle shown below on the left has a radius of I unit.The region between the circle and the inscribed square is shaded.In the circle shown on the right,one quarter of the region between the circle and the inscribed square is shaded.The shaded regions in the two circles have the same area. What is the radius R,in units,of the circle on the right? 左边显示的圆的半径为1单位。圆与内切正方形之间的区域被涂成阴影。在右边显示的圆中， 圆与内切正方形之间区域的四分之一被涂成阴影。两个圆中阴影区域的面积相同。右边圆的半 径R是多少单位？ (A)N2(B)2(C)22(D)4(E)4V2 19.Two towns,A and B,are connected by a straight road,15 miles long.Traveling from town A to town B,the speed limit changes every 5 miles:from 25 to 40 to 20 miles per hour (mph).Two cars,one at town A and one at town B,start moving toward each other at the same time.They drive at exactly the speed limit in each portion of the road.How far from town A,in miles,will the two cars meet? 两个城镇，A和B,通过一条长15英里的直路相连。从城镇A到城镇B,每5英里速度限制 就会改变：从25英里每小时(mph)变为40英里每小时，再变为20英里每小时。两辆车， 一辆在城镇A,一辆在城镇B,同时开始向对方行驶。它们在路的每个部分都严格按照速度限 制行驶。两车将在距离城镇A多少英里处相遇？ 25 mph 40 mph 20 mph 5mi 5mi 5mi (A)7.75 (B)8 (C)8.25 (D)8.5 (E)8.75 20.Sarika,Dev,and Rajiv are sharing a large block of cheese.They take turns cutting off half of what remains and eating it:first Sarika eats half of the cheese,then Dev eats half of the remaining half, then Rajiv eats half of what remains,then back to Sarika,and so on.They stop when the cheese is too small to see.About what fraction of the original block of cheese does Sarika eat in total? 萨丽卡、德夫和拉吉夫正在分享一大块奶酪。他们轮流切下剩余的一半并吃掉：首先萨丽卡吃 掉一半的奶酪，然后德夫吃掉剩下的一半的一半，接着拉吉夫吃掉剩下的，然后又轮到萨丽卡， 如此循环。当奶酪小到看不见时他们停止。萨丽卡总共吃掉了原始奶酪的多少分数？ 3 7 E) 21.The Konigsberg School has assigned grades I through 7 to pods A through G,one grade per pod. Some of the pods are connected by walkways,as shown in the figure below.The school noticed that each pair of connected pods has been assigned grades differing by 2or more grade levels.(For example,grades I and 2 will not be in pods directly connected by a walkway.)What is the sum of the grade levels assigned to pods C.E,and F? 柯尼斯堡学校将1至7年级分配给A至G舱，每个舱一个年级。如下图所示，部分吊舱通过 通道相连。学校注意到，每一对相连的豆荚都被分配了两个或两个以上的等级。（例如，1年 级和2年级将不会在由人行道直接连接的吊舱中。)C、E、F三个舱的年级等级之和是多少？ B D (A)12 (B)13 (C)14 (D)15 (E)16 22.A classroom has a row of 35 coat hooks.Paulina likes coats to be equally spaced,so that there is the same number of empty hooks before the first coat,after the last coat,and between every coat and the next one.Suppose there is at least I coat and at least I empty hook.How many different numbers of coats can satisfy Paulina's pattern? 一个教室有一排35个衣帽钩。Paulina希望大农之间以及大衣与两端之间都等距离地分布，这 样在第一件大衣之前、最后一件大衣之后以及每件大衣之间都有相同数量的空钩子。假设至少 有一件大衣和至少一个空钩子。有多少种不同的大衣数量能满足Paulina的模式？ (A)2 (B)4 (C)5 (D)7 (E)9 23.How many four-digit numbers have all three of the following properties? (1)The tens digit and ones digit are both 9. (II)The number is I less than a perfect square. (III)The number is the product of exactly two prime numbers. 有多少个四位数同时具有以下三个属性？ ①十位数和个位数都是9。 )这个数比一个完全平方数少1。 )这个数是恰好两个质数的乘积。 (A)0 (B)1 (C)2 (D)3 (E)4 24.In trapezoid ABCD,angles B and C measure 60 and AB=DC.The side lengths are all positive integers and the perimeter of ABCD is 30 units.How many non-congruent trapezoids satisfy ail of these conditions？ 在梯形ABCD中，角B和角C的度数分别为60度，且AB=DC。边长都是正整数，ABCD的 周长为30个单位。满足所有这些条件的非全等梯形有多少个？ D G0° 60 B (A)0 (B)1 (C)2 (D)3 (E)4 25.Makayla finds all the possible ways to draw a path in a 5 x 5 diamond-shaped grid.Each path starts at the bottom of the grid and ends at the top,always moving one unit northeast or northwest. She computes the area of the region between each path and the right side of the grid.Two examples are shown in the figures below.What is the sum of the areas determined by all possible paths? Makayla找到了在一个5X5钻石形网格中绘制路径的所有可能方式。每条路径从网格底部开 始，结束于顶部，总是向东北或西北方向移动一个单位。她计算了每条路径与网格右侧之间的 区域面积。下面的图中展示了两个示例。所有可能路径确定的区域面积之和是多少？ area =11 area 13 (A)2520 (B)3150 (C)3840 (D)4730 (E)5050 2025年AMC8真题解析 1.答案【B】 解析：最终问占格子的百分之多少，使用割补法会发现阴影部分是占了8个格子，一共有 16个格子，那么就应该是8+16=0.5=50%. 2.答案【B】 解析：根据题目要求来，10000+400+20+3=10423 3.答案【c】 解析：A和她的三个朋友，首先是有4个人在玩，所以一共有60张牌，那么又来2个朋友， 说明一共有6人，所以每人数量=60+6=10. 4.答案【B】 解析：求第10项，就是求末项，用末项公式：an=a1+n-1)×d=100+(10-1)×(-7)=37.特别注意 的是明确公差是-7：也可以直接枚举，后面数比前面数小7，递减的等差数列，可以直接列 出第10个数 5.答案【c】 解析：明确题目要求，从F点出发走回F点，每一次都是直角，最短距离因此需要明确每 一次起始位置与目标位置不走回头路，画出最短距离，最终就是求长7，宽5的长方形周 长.（长+宽）×2=24.： 题目简单，可以直接数出最短距离就是24. 6.答案【c】 解析：分别计算15,16,17,18,19除以4的余数可以得到3,0,1,2,3，他们的和除 以4的余数是3+0+1+2+3=1，那么应该删除17，剩下的数的和就是4的倍数了. 7.答案【D】 解析：80%-90%之间的学生的数量应该是80%以上的减去90%以上的，即为50-13=37. 8.答案【A】 解析：每个正方形的面积是18÷6=3，那么边长就是√3，所以体积就是3v. 9.答案【B】 解析：分析题意容易得到所有的平均数即为所有数的平均数，注意到1-12是等差数列，平 均数就是(1+12)÷2=6.5. 10.答案【D】 解析：分别补全左下角和右上角，根据对称性可以得到三个正方形，边长分别为5.5,2.5 和0.5，那么所有面积为5.52-2.52-0.52=(5.5+2.5)*(5.5-2.5)-0.25=23.75.