2023年美国AMC8五～六年级数学联赛（中英双语版本）

MAAAMC MAA American Mathematics Competitions 38th Annual AMC 8 Tuesday,January 17.2023 through Monday.January 23,2023 NSTRUCTIONS|說明I说明 1.DO NOT TURN TO THE NEXT PAGE UNTIL YOUR COMPETITION MANAGER TELLS YOU TO BEGIN. 在未收到篮考老師周考指示前，麟不要那開此封面。 在未收到监考老师开考指示前，请不要短开此封面： 2.This is a 25-question multiple-choice competition.For each question,only one answer choice is comect. 這是一套包括25道遭择题的荆赋，每道题目只有一阀正答案。 这是一套包括25道选择题的测试，每道题目只有一个正确答案。 3.Mark your answer to each problem on the answer sheet with a pencil.Check blackened answers for accuracy and erase errors completely.Only answers that are properly marked on the answer sheet will be scored. 請將每道题日的答案用铅筆標柱在答题卡上。詩注意检查炫高的黑色長方 塊的撑雅性，用橡皮完全擦掉给阅的答案。只有恰盆標注在答题卡上的答 案才合被部分。 请将每道题目的答案用铅笔标注在答题卡上，请注意检查涂写的黑色长方 块的准确性，用橡皮完全擦掉错误的答案。只有恰当标注在答题卡上的答 案才会被评分， weritly prumnkarme wre mul owd he pubikatio repod5t增ormemalen of the problm,r情htett af thb cnm由nmt客he periad whe市 n的rre女知甲e向时4nk#件e代D影aael种ot选fdhe Erdiaul aa toe dormg them perinl le a viclabeo r catatuiswn pks n25 ahemaicl Amod重MnAa 4.SCORING:You will receive I point for each correct answer,0 points for each problem left unanswered,and 0 points for each incorrect answer. 干分：每道题目答對得1分，不答得0分，答错得0分。 评分：每道题目答对得1分，不答得0分，答错得0分。 5.Only blank scratch paper,rulers,and erasers are allowed as aids.Prohibited materials include calulators,smartwatches,phones,computing devices, compasses,protractors,and graph paper.No problems on the competition will require the use of a calculator. 只隆使用空白的草稿气、空白的坐桥绕、尺子、圆规和橡皮作A韩助工 具。不允許的器具包括针算器，餐能手镀、手機和計算設循。测试中沒有 任何間题必须要使用卧算器。 只能使用空白的草稿纸、空白的坐标纸、尺子、图规和檬皮作为辅助工 具。不允许的器具包括计算器、智能手表、手机和计算设备。测试中投有 任何问题必须要使用计算器。 6.Figures are not necessarily drawn to scale. 置形不一定按比例龄要。 图形不一定按比例绘制。 7.Before beginning the competition.make sure to write the Competition Code "AMC8".your name and Competition ID with your signature on the answer sheet,especially to bubble in the 9-digit Competition ID completely! 在周始慧賽之前，靖隧保已将簸賽代两“AMC8”,姓名和准考證赋填高在 答题卡上並簽名，特别是9位准考證藏的每位数字已经控好相座的黑色長 方境。 在开始宽赛之前，请确保已将党赛代码“AMC8”,姓名和准考证号填写在 答题卡上并签名，特别是9位准考证号的每位数学已经涂好相应的黑色长 方块。 8.You will have 40 minutes to complete the test once your competition manager tells you to begin. 監考老晒宣布脚始後，你將有40分缠的時閩完成测献。 监考老师宣布开始后，你将有40分钟的时间完成测试 9.All the problems are written in English.Traditional Chinese and Simplified Chinese.In case of any discrepancy between these versions,the English version shall prevail. 所有的周题问特以爽文、繁體中文和简酸中文表述，如果避些版本之周存 在差翼，以英文版本华。 所有的问题问时以英文、繁体中文和简体中文表述。如果这些版本之间存 在差异，以英文版本为准。 2023 MAA AMC 8 1.What is the value of below expression? 下面表道无的伍是多少 下面表达式的值是多少？ (8×4+2)-(8+4×2) (A)0 (B6 (C10 (D)18 (E)24 2.A square piece of paper is folded twice into four equal quarters,as shown below,then cut along the dashed line.When unfolded,the paper will match which of the following figures? 如下图所乐，将一廉正方形纸對折雨次，受成四等分，然爱海虚缘裁，同 述蒸峡展開棱合是下面偶园形？ 知下旧所示，将一猴正方形纸时新两次，变成四等分，然后活虚线载期。问 这球旅展开后会是下面哪个图形？ (A (B C (D) 1 2023 MAA AMC 8 3.Wind chill is a measure of how cold people feel when expased to wind out- side.A good estimate for wind chill can be found using this calculation (wind chill)"(air temperature)-0.7 x (wind speed) where temperature is measured in degrees Fahrenheit(F)and wind speed is measured in mules per hour (mph)Suppose the air temperature is 36F and the wind speed is 18 mph.Which of the following is closest to the approximate wind chill? 风★指粒是封人们暴露在堂外风中诗寒冷感凭的度量，通道下面的计算可 以背風寒指数纹出很好的结计： (風寒指教)=（氧遥）-07×（成递） 其中温度以華氏度（℉）马单位，压连以英里每小時(mph)为军位.餐规 襄浸為36F,风连為18mph,两以下察侧莲项最接近風来指教 风寒指数是对人们暴常在室外风中时寒冷感凳的度量，通过下面的计算可 以对风寒指数做出很好的结计： (风寒福数)■（气）-07×（风健） 其中度以华氏度(F)为单位，风逢以英里每小时(mph)为单位。氧设 气温为36℉，风违为18mph,网以下哪个进项最接近风寒指餐？ A)18 B)23 ©28 D)32 (E35 2 2023 MAA AMC 8 4.The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center.The first few numbers have been entered into the grid below.Consider the four numbers that will appear in the shaded squares,on the same diagonal as the number 7.How many of these four numbers are prime? 在正才形方格表上，数1到49批中心候始，按螺旋式方式排到。前面隐但 教己蝶填入写下面的方格表中，考感电教7出现在同一售背角擦上的隆影 方格中的四個数，同这四佃数中有残但贫数？ 在正方形方格表上，数1到49从中心开始，按棵疑式方式排列，精面几个 数巴经填入到下面的方格表中，考恋与数7出现在同一个对角载上的朋彩 方格中的四个数，问这四个数中有几个质数？ 43 (A)0 (B01 (○2 D)3 4 3 2023 MAA AMC 8 5.A lake contains 250 trout,along with a variety of other fish.When a marine biologist catches and releases a sample of 180 fish from the lake,30 are identified as trout.Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake.How many fish are there in the lake? 潮里有250修鲜兔，以及其他一委色须。常一住海洋生斯學家批期中捕覆 益释效180修兔的爆未聘，他任现其中30修，角是舞兔，就设在爆本中雄龟 新佔的比明和湖里鲜童在全部竟中所估的比例相同。同翔里有多少锋鱼？ 淘里有250承每鱼，以及吴他一些鱼类，台一住海洋生物学家从期中捕被 异释放10希兔的样本时。他发观其中30条童是郴灸，氧设在样本中蜂鱼 所占的比例和湖里蝉灸在全童类中所占的比创相周。问期里有多少条鱼？ A)1250 (B)1500(C1750 D)1800 (回2000 6.The digits 2,0,2,and 3 are placed in the expression below,one digit per box.What is the maximum possible value of the expression? 排数字2.0.2.3，入下面的表道式中，每但方担内填一四数字，两表造 式的最七可能值是多少： 将数学2,0,2,3填入下面的表达式中，每个方框内填一个数字。网表达 式的装大可能值是多少？ A)0 B)8 (C☐9 D)16 (回18 4 2023 MAA AMC 8 7.A rectangle,with sides parallel to the x-axis and yaxis,has opposite ver tices located at (15.3)and (16.5).A line is drawn through points A(0 0) and B(3,1).Another line is drawn through points C(0.10)and D(2.9). How many points on the rectangle lie on at least one of the two lines? 有一信矩形。它的逢平行势×轴和物，而图相野的顶贴是(15,3)和（门65） 通通點A(0,0)B3,1)繪装一修直線，通通點C(0,10)和D(29)婚裂另 一修直像。同矩形的逢界」有多少回贴位势雨修意棉中的至少修上？ 有一个矩形，它的边平行于x轴和y轴，两个柯对的通点是(15,3)和，16,5) 通过点A(0,0)和(3.1)龄制一帝直线通边点C(0,10)和D(2)龄制芳 一条直线问矩形的边界上有多少个点位于两条直线中的至山一条上？ D 2343679121341516 (A)0 B)1C2 (D)3 )4 5 2023 MAA AMC 8 8.Lola,Lolo,Tiva,and Tiyo participated in a ping pong tournament.Each player competed against each of the other three playersexactlv twice.Shown below are the win-loss records for the plavers.The numbers 1 and 0 rep- resent a win or loss,respectively.For example,Lola won five matches and lost the fourth match.What was Tiy s win-loss record? Lola,L0b,Dva,Tyo家加一場乒年球锌棒赛，每名退手典其他三名遥手 中的年個人比赛格好雨次。下面照示的是涯手的麟角记锋。数字1和0分 期代表或或物。例如L0a一共赢了五场比套，第四墙比赛棉了.两刀v0的 醇负记锋是怎樣的？ Lolh,Loo,Tya,Ty0参加一场乒兵球绵标赛，每名选手与其他三名选手 中的每个人比赛诊好两次，下面显示的是选手的胜真记录。数字1和0分 别代衣高或输.例如L0l归一兴赢了五场比赛，第四语比赛愉了，问Ty四的 雅负记兼是怎样的？ Player Result Lola 111011 Lolo 101010 Tiya 010100 Ty022222n (A)090101B)001001(gD10000(D)010101(E011000 6 2023 MAA AMC 8 9.Malaika is skiing on a mountain.The graph below shows her elevation,in meters,above the base of the mountain as she skis along a tratl.In total, how many seconds does she spend at anelevation between 4 and 7 meters? Maka正在山上滑雪.下围颜示了地浴若小很滑雪特以山种為基浪的海 报高度：章位為米》。同她在4来到1朱之的高度共停留了多少秒？ Maka正在上滑雪，下图显示了地沿着小径滑雪时以山种为基准的海 规高度（单住为来》。同地在4来到7来之间的高度共停留了多少秒？ 14 12 10 2 46810121416 Time (seconds) elevation|海技高度I海核高度，mcer|米1来 ime|时周|时间，s0cond,秒，秒 (A)6 (B8 (Q10 (D)12 目14 7 2023 MAA AMC 8 10.Harold made a plum pie to take on a picnic.He was able to eat only of the ple,and he left the rest for his friends.A moose came by and ate ofwhat Harold lef behind.After that.a porcupine ateof what the moose left behind.How much of the original pie still remained after the porcupine left? 1 Hold微了一侧李子浪去野茶，地只吃拌了造朝滚的4？业把制下的液留 ，1 热了她的翻友们，一线轮能经遇並吃排了aod制下的装为了在那之後， 一凭案绪吃了陀晓制下的谦的了·同幸储走後，原来的派瑾料下多少？ 1 Harold做了一个李于源去野餐.他只吃梓T这个滚的了并把制下的液留 给了艳的朋友们.一只驼晓经过并吃掉了Harold刺下的浪的了在那之后， 一只豪信吃了驼魔制下的派的} 问豪霜走后，原来的源还剩下多少？ 11.NASA's Perseverance Rover was launched on July 30,2020.After travel- ing 292.526,838 miles,it landed on Mars in Jezero Crater about 6.5 months later.Which of the following is closest to the Rover's average interplane- tary speed in miles per hour? 美器圈家杭空状天局的就力授遵者或火置探测器补2020年7月30日倍朝. 在最行了292,526,838英里陵，於大的6.5但月战登改犬星，降幕在那泽厘 风石坑拟英里每小骑秀单住，以下婚但退项最耧近：力爱避者就的平均 星坠行说逢度？ 夫国国家杭空杭天局的餐力漫游考号文星探测器于2020年7月30日发射 在飞行了292,526838装里后，于大约6.5个月后受陆大星，降落在那泽罗 风石抗.以装里叠小时为肇住，以下哪个选项最楼近瓮力爱等者号的平均 星际行进速虎2 (A)6,000B)12.000C60.000D)120,000(E600.000 8 2023 MAA AMC 8 12.The figure below shows a large white circle with a number of smaller white and shaded circles in its interior.What fraction of the interior of the large white circle is shaded? 如图所示，在一但大的向色置图内部有井多校小的白色和友色面图，問灰 色邦分在大的白色国图内部所估的比创是多少？ 如图所示，在一个大的白色圈内部有计多校小的白色和灰色画周，问灰 色部分在大的白色围周内部所占的比朝是多少 2023 MAA AMC 8 13.Along the route of a bicycle race,7 water stations are evenly spaced be- tween the start and finish lines,as shown in the figure below.There are also 2 repair stations evenly spaced between the start and finish lines.The 3rd water station is located 2 miles after the 1st repair statian.How long is the race in miles? 如下圈所示，在自行单比赛路榨的起斯和婷贴之司均匀分作著7信欣用水 褙龄站，另外，在起贴和醉贴之同遥均匀分作著2四维修站，第三幅饮用 水精给站在第一细维修站後2英里震。同比零的全程是多少英里？ 如下因所示，在角行车比赛路线的起点和终点之间均匀分布着7个饮用水 补给站。芳外，在起点和终点之间还均句分有着2个维修站.第三个软用 水补给鸡在第一个维修站后2英里处。问比零的全程是多少莞里？ 44.044 tart|起给|起给，finish1终结I终结，water|水I术 A)8 B)16 (924 (D)48 (包96 10 2023 MAA AMC 8 14.Nicolas is planning to send a package to his friend Anton,who is a stamp collector.To pay for the postage,Nicolas would like to cover the package with a large number of stamps.Suppose he has a collection of 5-cent,10- cent,and 25-cent stamps,with exactly 20 of each type.What is the greatest number of stamps Nicolas can use to make exactly $7.10 in postage? (Note:The amount $7.10 corresponds to7 dollars and 10 cents.One dollar is worth 100 cents.) Nicolas叶封得一国包表寄给爱好集部的朋友Anton,為了支付部青.Nico 1山5非倩在包襄上贴大量的部票。假授他有5美分，10美分，25美分的部 票，每佳部票拾好各有20張，Ni心ola最多可以使可多少颈部票来恰好支 付57.10的解资9 (往意：金新37,10是指7美元10美分，1美元是100美分.》 Nicolas计划将一个包表专给爱好集的初友Anton,为了支行年资，Nco l5位备在包裹上贴大量的邮票.但设他有5美分，10美分，25美分的邮 票，每种师票拾好各有20保.Nicolas最多可以使周多少张邮最来恰好是 付s7.10的邮贵2 《注意：金题s7,10是指7美元10美分，1美元是100美分，》 (A)45 (846 (C51 D)54 E)55 11 2023 MAA AMC 8 15.Viswam walks half a mile to get to school each day.His route consists of 10 city blocks of equal length and he takes one minute to walk each blok. Today,after walking 5 blocks,Viswam discovers that he has to make a detour,walking 3 blocks of equal length instead of I block to reach the next comner.From the time he starts his detour,at what speed,in miles per hour,must Viswam walk in order to arrive at school at his usual time? 5wm每天委步行半英里去上挚。他上學的路棉由10個等表的城市街篮 组成，每走一個街是需要一分维.今天，在是了5佃街但後，swm景现 他必领城格，委走3四等最的衡照而不是】细斯照才能到连下一创交义路 口，搅他城行阳始，iswm必類以每小时多少英里的连度多行才能在真平 特网操的转可到速學校？ Vm每天要步行半英里去上学，他上学的路残由1切个等长的城市街区 红成，每走一个街区需要一分钟.今天，在走了5个街区后，Vwm发现 他必频绕路，要走3个等长的街区而不是】个街区才能门达下一水文义路 口。从他晓行开始，5wam必须以每小时多少英里的逢度步行才能在与平 时网样的时同到逃学校？ School school|释校1学靓 (A)4 B)4.2(C4.5D)48 (回5 12 2023 MAA AMC 8 16.The letters P,Q,and R are entered into a 20 x 20 table according to the pat- tern shown pelow.How many Ps,Qs,and Rs will appear in the completed table? 字华P,Q,R接如下圈斯示的规律填入到20×20的方移表中，同镇好的 方格表中将出现多少但P、多少如Q和多少信R? 宇母P,Q,R按如下图所示纳规律填入到20×20的方格泰中，问填好的 方格友中将出见多少个P多少个Q和多少人R? QR P Q R P Q RP Q R P RP Q (A)132Ps.134Q5,134Rs (B)33Ps,133Q5,134Rs (☐133P%,134Qs,133Rs (D)134Pg,132h.134Rs (E134Ps,133Qs,133Rs 13 2023 MAA AMC 8 17.A regularoctmhedron has eight equilateral triangle faces with four faces meet- ing at each vertex.Jun will make the r'gular octahedron shown on the right by folding the piece of paper shown on the left.Which numbered face will end up to the right of O? 正入面世有入朝面，都是等邊三角形，在每偶顶粘咸有四相面相交，Ju把 左逢的纸月新成了右逢的正入面性，两出观在Q的右逢的那鳕面上的数是 烧？ 正入面体有入个面，都是等边三角形，在每个项点处有四个面和交J加把 左边的纸片新咸了右边的正入面体，问出现在口的右边的那个面上的数是 几2 A)1 B)2 C☐3 D)4 (E5 18.Greta Grasshopper sits on a long line of lily pads in a pond.From any lily pad,Greta can jump 5 pads to the right or 3 pads to the left.What is the fewest number ot jumps Greta must make to reach the lil pad located 2023 pads to the right of her starting position? 林好Geta坐在池墙更一排長長的连装上，找任何哈连爱出货，Geta都 可以向右乘5匈莱片或者向左跳3但菜片.附Gea最少跳多少次才能到 连位外地起始位置右侧的第2023片峰连菜上2 蜂娃Greta坐在也墙更一排长长的啡篷叶上，从任何暗篷叶出发，Gta都 可以向右5个叶片或者向左脆3个叶片，问G由最少貌多少次才能到 达位于她起始位置右匐的第2023片硬篷叶上？ (AU405 B)407 (☐409 D)411 日413 14 2023 MAA AMC 8 19.An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below.The side length of the inner triangle is the side length of the larger triangle.What is the ratio of the area of one trapezoid to the area of the inner triangle? 如圈所示，一倒等连三角琴在芳一偶更大的等提三角形内都，它门之同的 图城可以分成三偶全等的祸形，内部三角形的提长是大三痛形逢长的，阿 一偶梯形的面精典内部三庙形的而衡之比是多少？ 知国所示，一个等边三角形在另一个更大的等边三角形内饰，它们之间的 区越可以分成三个全等的球形，内部三角形的边长是大三角形边长的了·问 一个梯形的面积与内部三角形的面积之比是多少？ ()1:3()3:8(Q5:12D)7:16回4：9 20.Two integers are inserted into the list 3.3.8,11.28 to double its range.The mode and median remain unchanged.What is the maximum possible sum of the two additional numbers? 将两信整数加入数排列表3,3.8,11，阳使得它的经差加得，而尿数和中 住数保林不燮，两所添加的两僧数之和的量大可能值是多少？ 持两个整数加入数据列表3,3,8,11,28使得它的规差加偏，而众数和中 住数供持不变。问所添加的两个数之和的最大可能值是多少？ (56 (B团57 (C58 D)60 E61 15 2023 MAA AMC 8 21.Alina writes the numbers 1.2.....9 on separate cards,one number per card.She wishes to divide the cards into 3 groups of 3 cards so that the sum of the numbers in each group will be the same.In how manv ways can this be done? Aina将数1,2，，9窝在不同的卡片上，每装卡片上有一画数。地希望 将卡片分成3组，每姐3張卡片，传得每组中的备数之和相同，同有多少 種是棵的分组方法？ A1ia将数1,2，，，9写在不同的卡片上，舞张卡片上有一个数，她希望 精卡片分盛3植，每组3张卡片，使母每如中的各数之和知同.问有多少 种这料的分性方法？ A)0 B)1 (C 2 D)3 (国4 22.In a seqnence of positive integers.each term after the second is the product of the previous two terms.The sixth term in the sequence is 4000.What is the first term? 在一国正整数教列中，第二项之禳的海一项都是前面雨项的农積。数列中 的第六项是00.两第一项是多少？ 在一个正整章数列中，第二项之后的每一项都是前面两项的乘松，数列中 的第六境是4000，问第一项麦多少？ A)1 B)2 (○4 D)5 (E10 16 2023 MAA AMC 8 23.Each square in a 3 x 3 grid is randomly filled with one of the 4 eray-and- white tiles snown below on the left.What is the probability that the tiling will contain a large gray diamond in one of the smaller 2 x 2 grids7 An example of such a tiling is on the right. 将3×3方格表中的每倡小方格髓媛的周知下圈左所示的4细灰向复色 方挑：一丧入，有一四大灰色菱影将出现在某细2×2子方格表中的规率是 多少？一僧越根的镶畏方食的例子如下园右侧所帝， 将3×3方格泰中的每个小方格固机的周物下图左倒所示的4个灰白双色 方块之一款入，有一个大灰色菱形将出现在某个2×2子方格泰中的既率是 多少？一个这样的镶丧方案的例子如下因右侧所示， (A)1024 (82死 1 C 17 2023 MAA AMC 8 24.Isosceles triangle ABC has equal side lengths AB and BC.In the figures below,segments are drawn parallel to AC so that the shaded portions of AABC have the same area.The heights of the two unshaded portions are 11 and 5 units,respectively.What is the height hof AABC? 在等腰三角形ABC中，逢AB和B配的最度桶￥.在下圈中，由平行势AC 的線段利成的△ABC中的雨细信影部分具有相网的面積.雨個空白部分的 高鹿分刷%11和5.阴△ABC的高h是多少？ 在等糖三角形ABC中，边AB和BC的长度相等.在下因调中，由平行于AC 的植段移成的△A6C中的两个阴影部分其有和网的面积。两个空白年分的 高度分别为11和5.问△ABC的高h是多少？ 11 A )146B)14.8(C15D)15.2(回154 18