2023年数学竞赛AMC8真题C卷（含答案）.docx

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1、Junior DivisionQuestions 1 to 10 are worth 3 marks each.1-10 题，每题 3 分1. Kurt paved his courtyard in the pattern shown. How many 11 pavers are in his courtyard?Kurt 将庭院铺上图中的瓷砖。庭院中一共有多少块 11 的瓷砖？（A）28（B）30（C）32（D）34（）362. Which of the following expressions has the smallest value?以下哪个算式的值最小？（A）3+2（B）3-2

2、（C）32（D）32（E）323. The numbers on the top corners of these five playing cards add to 21. What is the number on the hidden card?右图中五张扑克牌左上角的数字之和为 21，被遮住的扑克牌上的数字是多少？（A）2（）3（C）5（D）7（）94. What is the value of x in this diagram?图中 x 的值为？（）50（B）60（C）70（D）80（E）1005. These two clocks show opening and closing

3、 times of my local Marine Discovery Centre. For how long is it open each day?这两个时钟分别显示了海洋探索中心的开放和关闭时间。这个中心每天会开放多长时间？（A）5 hours and 40 minutes5 小时 40 分钟（B）6 hours and 20 minutes6 小时 20 分钟（C）6 hours and 40 minutes6 小时 40 分钟（D）7 hours and 20 minutes7 小时 20 分钟（E）7 hours and 40 minutes7 小时 40 分钟6. What i

4、s the value of2 + 3 + 4 等于多少？7 + 8 + 92 + 3 + 4 ?7 + 8 + 9（A） 1（B） 2（C） 3（D） 4（E） 1678927. How many 25cm25cm squares fit in a 50cm1m rectangle?有多少个 25cm25cm 的正方形可以完全放入 50cm1m 的长方形？（A）1（B）2（C）4（D）6（E）88. This graph shows the water stored in my rainwater tank last May.What was the increase in water in

5、 the tank between the 10th and the 30th of May?如图所示，今年 5 月份水箱中存储的水量情况。5 月 10 日到 30 日之间水箱中的水量增加了多少？（A）32kL（B）37kL（C）40kL（D）42kL（E）43kL9. The sum of the ages of Ali, Bey and Cam is 32 years. What will be the sum of their ages in 3 years time?Ali、Bey 和 Cam 三个人的年龄之和为 32 岁。请问 3 年后他们的年龄之和是多少？（A）33years 33

6、 岁（B）35 years 35 岁（C）38 years 38 岁（D）41 years 41 岁（E）96 years 96 岁10. A parallelogram PQRS has an area of 60 cm2 and side PQ of length 10 cm. Which length is 6cm?如图所示，平行四边形 PQRS 的面积为 60cm2，边 PQ 的长度为 10cm。请问哪条线段的长度是 6cm？（A）RQ（B）RS（C）QT（D）PT（E）QSQuestions 11 to 20 are worth 4 marks each.11-20 题，每题 4 分

7、11. Mei can travel to her grandmas house by a direct route, or by a scenic route that is 5 km longer. When she travels by the scenic route, and comes directly home, the round trip is 35 km. How long is the direct route?小梅可以选择一条直达路线或者选择一条风景优美的路线去奶奶家，风景优美的路线比直达路线长 5km，如果她选择风景优美的路线去奶奶家并选择直达路线回家，来回路程一共为

8、35 km。请问直达路线有多远？（A）5km（B）12.5km（C）15km（D）20km（E）22.5km12. In the game of Nurdle, players try to guess a three-digit number. After each guess, the digits are marked with one of the following three symbols: if the digit is correct and in the right place if the digit is correct, but is not yet in the r

9、ight place if the digit is not in the three-digit number at all.Mikes guesses so far are shown.How many different three-digit numbers fit the clues he has so far?在 Nurdle 游戏中，玩家需要猜测一个三位数。每次猜测后，猜测的三位数的各位数字会用以下三种符号中的一种表示： 表示这个数字正确且位置正确 表示这个数字正确，但是位置错误 表示这个数字不在这个三位数中目前 Mike 的猜测在图中。有多少个不同的三位数符合目前已有的线索？（

10、A）5（B）6（C）7（D）8（E）913. In this triangle, the number in the centre of each side is the sum of the two numbers at the ends of the sides.What is the sum of the three numbers at the ends of the sides?如图所示，三角形中，每条边中间的数字是两端数字之和。这三条边两端的三个数字之和是多少？（）46（B）52（）59（D）64（E）6814. A fuel tank is 40% empty. Then 40

11、litres of fuel is removed. The tank is now 40% full. How many litres are in a full tank?一个油箱的 40%是空的，取出 40 升油后，油箱的 40%是满的。这个油箱可以装满多少升油？（）40（B）100（C）160（D）200（E）40015. The game Tutu uses 4 standard dice with opposite faces adding to 7. The dice are rolled and randomly arranged into a 22 block.A block

12、s score is the sum of the 4 numbers showing on top plus the sum of the 8 numbers showing around the outside.What is the largest possible score for the block shown?游戏 Tutu 会用到 4 枚标准骰子，每枚骰子相对面的点数之和都为 7。投掷骰子并将骰子随机排列成 22 组合方块。组合方块的得分是顶面显示的 4 个点数与四周显示的 8 个点数之和。对于图中的组合方块，得分的最大可能值为？（A）44（B）46（C）48（D）50（E）5

13、216. The five clocks below are all showing the wrong time. One clock is 3 minutes away from the correct time and another is 7 minutes away.Which clock is closest to the correct time?这五个时钟显示的时间都是错误的。其中一个与正确时间相差 3 分钟，另一个时钟与正确时间相差 7 分钟。哪个时钟最接近正确时间？17. I wrote a list of all multiples of 7 between 1 and

14、500. Then I looked at the last digit of each number in my list.Which digit appeared most often as the last digit?我列出了 1 到 500 之间 7 的所有倍数，观察数列中每个数的最后一位数。哪项是最后一位数中出现频率最高的数字？（A）1（B）3（C）7（D）9（E）None of（A）-（D）, because there is no single last digit that appears most often以上均不正确，因为最后一位数中没有出现频率最高的数字18. Amy

15、 designed this rectangular flag for her fleet of yachts. What fraction of the flag is shaded? Amy 为游艇舰队设计了长方形旗帜。阴影部分的面积占旗帜总面积的几分之几？（A） （B） （C） （D） （E） 19. To unlock a security door, Daniyal enters a code on the keypad shown. To make it easy to remember:l the code has 10 digitsl the code uses every d

16、igit exactly oncel the code steps from button to button only if the two buttons touchl the code is as large as possible.What are the last 3 digits in Daniyals code?为了打开一扇安全门，Daniyal 在如图所示的键盘上输入一串密码。为了方便记忆：l 这个密码由 10 个数字组成l 这个密码使用每个数字恰好一次l 这个密码只能从一个按键上的数字到另一个相邻按键上的数字l 这个密码的数值尽可能大密码的最后 3 个数字是多少？（A）0（B

17、）1（C）2（D）6（E）720. Jake had 3 times as many gold balloons as blue balloons, and no other colours. Then some blew away, leaving him with 5 times as many blue balloons as gold balloons.What is the smallest number of balloons that Jake could have started with?Jake 的金色气球数量是蓝色气球的 3 倍，且没有其他颜色的气球。有一些气球被吹走了，

18、剩下的气球中，蓝色气球是金色气球的 5 倍。请Jake 刚开始最少有多少个气球？（A）15（B）20（C）24（D）30（E）100Questions 21 to 25 are worth 5 marks each.21-25 题，每题 5 分21. Li attempted to multiply a single-digit number by 36, but he accidentally multiplied by 63 instead. His answer was 189 larger than the correct answer.What was the correct ans

19、wer to the multiplication?小李尝试将一个一位数乘以 36，但他不小心将这个一位数乘以了63。结果比正确结果大189。这个乘法计算的正确结果是多少？（A）180（B）189（C）216（D）252（E）28822. The numbers from 1 to 12 are to be placed on the vertices of the 5 interconnected squares in this diagram. The sum of the 4 vertices of any of the 5 squares is a constant. What is

20、this constant? 把数字 1 到 12 放置在右图中 5 个相互连接的正方形的顶点上。每个正方形的 4 个顶点上的数字之和都是一个常数。这个常数是多少？（A）26（B）28（C）30（D）32（E）3423. Ann is running round her favourite running course at a steady pace of 5 minutes per kilometre. She passes a marker which she knows is one-quarter of the way round. One minute and 40seconds

21、later, she passes another marker which is one-third of the way round. How long will it take her to run the whole course?安正在绕着她最喜欢的跑道以 5 分钟/公里匀速前进，她经过了一个标记牌，表示跑道的四分之一。一分钟四十秒后，她经过了另一个标记牌，表示跑道的三分之一。跑完整个跑道需要多长时间？（A） 18 minutes 18 分钟（B） 20 minutes 20 分钟（C） 20 minutes and 40 seconds 20 分钟 40 秒（D） 22 minut

22、es and 30 seconds 22 分钟 30 秒（E） 24 minutes 24 分钟24. Jaz unlocked a secret level in the game Numbercraft. She entered a 6-digit code where the sum of the first three digits equals the sum of the last three digits. Further, she gained a bonus, since her code had four 7s in a row.For instance, she coul

23、d have entered 077770.How many different codes could she have entered to get the secret level and the bonus?杰解锁了Numbercraft 游戏的一个秘密等级。她输入了一个六位数密码，其中前三位数字之和等于后三位数字之和。因为她的密码中有四个连续的数字 7，她还得到了额外奖励。例如，她输入的密码可能是 077770。为了解锁秘密等级和获得奖励，她可以输入多少个不同的密码？（）10（B）18（）20（D）27（E）6425. Two identical dice have faces la

24、belled A, C, H, M, S and T.The diagram shows what they look like when placed in front of a mirror, but the reflection of the second dice has been left blank.What does the reflection of the second dice look like?两枚相同骰子的六个面上分别标记有 A、C、H、M、S 和T。下图中将它们放在镜子前呈现的图像，但第二枚骰子的图像是空白的。下列哪项是第二枚骰子在镜子中的图像？For questi

25、ons 26 to 30, colour in the bubbles on the answer sheet to record whole-number answers from 0 to 999. Questions 26 to 30 are worth 6, 7, 8, 9 and 10 marks respectively.26 题至 30 题的答案为 0 至 999 的整数，请正确填涂在答题卡上。第 26 题占 6 分，第 27 题占 7 分，第 28 题占 8 分，第 29 题占 9 分，第 30 题占 10 分。26. I start with a number, multip

26、ly it by 10, and then subtract a multiple of 9 that is less than 100. My answer is 5347. What number did I start with?我先将某个数字乘以 10，减去一个小于 100 的 9 的倍数，最终结果是 5347。起始数字是多少？27. Amelia noticed that the names of three friends, Mei, Emma and Liam, were all made fromletters of Amelia. She chose different va

27、lues from 0 to 9 for each of A, E, I, LM + E + I = E + M + M + A = L + I + A + Mand M so thatWhat is the largest possible value of A + M + E + L + I + A ?阿梅莉亚注意到三个朋友梅、艾玛和莉安姆的名字都是由“Amelia”中的字母组成的。她给A、E、I、L 和 M 中的每个字母选定了从 0 到 9 之间不同的值，使得M + E + I = E + M + M + A = L + I + A + M A + M + E + L + I + A 的

28、最大可能值为？28. There are three sets of three parallel lines in a plane. Lines in different sets are not parallel, and every pair of non-parallel lines intersect. The diagram shows one way to do this, but for other arrangements the number of points of intersection varies.Find the largest possible number

29、of intersection points and the smallest possible number of intersection points, then multiply these two numbers.一个平面上有三组平行线，每组各三条平行线。不同组中的线是不平行的，每对非平行线会相交。图中显示了一种可能的方式，但对于其他排列方式，交点的数量各不相同。交点数量的最大可能值和最小可能值之积是多少?29. A two-digit number has the property that when it is divided by the sum of its digits t

30、he result is 4 with remainder 3. What is the sum of all two-digit numbers with this property?一个两位数具有这些性质：当这个两位数除以它的各位数字之和时，商为 4，余数为 3。具有这个性质的所有两位数之和是多少？30. Donna likes all numbers that are not divisible by 3 and Sandra likes all numbers that have no digits divisible by 3. How many four-digit numbers are there that both Donna and Sandra like?多娜喜欢不能被 3 整除的所有数字，桑德拉喜欢各个数位上的数字都不能被 3 整除的所有数字。有多少个四位数是多娜和桑德拉都喜欢的数字？澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer1A11C21D2B12C22A3A13D23B4A14D24C5B15B25E6C16B265417E17C27348A18E283519D19A2916410D20B30810