2023年数学竞赛AMC8真题D卷（含答案）.docx

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1、Intermediate DivisionQuestions 1 to 10 are worth 3 marks each.1-10 题，每题 3 分1. A 40-minute lesson started at 10:50 am. Exactly half-way through the lesson the fire alarm went off. At what time did the fire alarm go off?一节时长为 40 分钟的课程从上午 10:50 开始上课。当课程正好进行到一半时，火警报警器响了， 那么火警报警器响起的时间是？（A）10:30am（B）11:00

2、am（C）11:10am（D）11:20am（E）11:30am2. Two rectangles have a vertex in common, as shown. What is the size of the angle marked xbetween them?如下方图片，两个长方形共用一个顶点。那么这两个长方形之间标记为 x角的度数是多少？（A）10（B）20（C）30（D）40（E）503. What is the value of2 + 3 + 4 ?7 + 8 + 92 + 3 + 4 的值是多少？7 + 8 + 9（A） 1（B） 2（C） 3（D） 4（E） 167892

3、4. How many 25cm25cm squares fit in a 50cm1m rectangle?有多少个边长为 25cm 的正方形可以完全放入宽 50cm 长 1m 的长方形？（A）1（B）2（C）4（D）6（E）85. Which one of these is equal to 57953? 57953 的结果是？（A）321（B）4321（C）54321（D）654321（E）76543216. A parallelogram PQRS has an area of 60 cm2 and side PQ of length 10 cm.Which length is 6cm

4、?如下图，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）QS7. Mei can travel to her grandmas house by a direct route, or by a scenic route that is 5km longer. When she travels by the scenic route, and comes directly home, the round trip is 35 km. How long is the direct route?梅

5、想要去奶奶家，可以选择一条直达路线或者选择一条风景优美的路线，风景优美的路线比直达的路线要长 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 35 km。那么直达路线有多远？（A）5km（B）12.5km（C）15km（D）20km（E）22.5km8. What is the value of(20 )2 )3 ?请问(20 )2 )3 的值是多少？（A）1（B）12（C）32（D）64（E）2569. What must 0.05 be divided by to get 50?请问 0.05 除以以下哪个数字才能得到 50？（A）1000（B）100（C）0.

6、1（D）0.001（E）0.000110. In the right-angled triangle ABC shown, what is the value of y?如图所示，一个直角三角形 ABC，那么 y 的值是多少？（A）45（B）48（C）54（D）60（E）72Questions 11 to 20 are worth 4 marks each.11-20 题，每题 4 分11. The number 11 can be written as the sum of three positive whole numbers in many ways. In how many ways

7、 can this be done where the numbers are different and in increasing order?数字 11 可以用多种方式表示为三个正整数之和。那么共有多少种方式可以将 11 表示为三个以升序方式排列的不同数字之和？（A）3（B）4（C）5（D）6（E）712. A two-digit number is reversed then added to itself. The answer cannot be一个两位数，将它颠倒后再加上它本身。那么相加后的结果不可能是下列哪一项？（A）55（B）110（C）132（D）154（E）18613.

8、Amy designed this rectangular flag for her fleet of yachts. What fraction of the flag is shaded?如图所示，艾米为游艇舰队设计了一面长方形旗帜。那么在图中阴影部分的面积占这面旗帜总面积的几分之几？（A） （B） （C） （D）（E）14. What is the largest possible whole-number value of the expression where a, b, c, d, e, fare the numbers 1, 2, 3, 4, 5 and 6 in some o

9、rder?如果 a、b、c、d、e、f 分别表示以某种顺序排列的数字 1、2、3、4、5 和 6，请问表达式a b + c - e 的最大可能整数值是？df（A）30（B）31（C）32（D）33（E）3415. Four children named, from youngest to oldest, Abdul, Bipin, Cai and Denise have ages which are equally spaced apart. Abdul and Bipins ages add to 18, whilst Cai and Denises ages add to 34. How

10、old is Denise?四个小孩按照年龄从小到大的排列顺序分别是阿卜杜勒、比平、蔡和丹尼斯，前后两个小孩的年龄之差都相等。阿卜杜勒和比平的年龄之和为 18，蔡和丹尼斯的年龄之和为 34。那么丹尼斯的年龄是？（A）14（B）16（C）18（D）19（E）2016. The country of Exponentia uses six-digit telephone numbers. At the moment, this is plenty, since there are only 1000 phone numbers in use. However, increasing populat

11、ion and phone usage means that the number of phone numbers needs to double each year. Approximately how many years will it take for Exponentia to run out of phone numbers?E 国使用六位数的电话号码。这在目前已经够用，因为这个国家只有 1000 个电话号码在使用。然而，由于人口和电话使用量不断增加，所需要的电话号码的数量每年都需要翻倍。那么 E 国大约需要多少年可以用完所有的电话号码？（A）5（B）10（C）20（D）30（E

12、）4017. A 15cm15cm square of origami paper is dark blue on top and pale yellow underneath. The top-left corner is folded down so that a crease is made from the top-right corner to a point xcm above the bottom- left corner.Once folded, the visible regions of yellow and blue paper have equal areas. Wha

13、t is the value15cm ofx?一张边长为 15cm 的正方形手工折纸，正面是深蓝色，背面是淡黄色。将纸张的左上角向下折， 使折痕从右上角延伸到离左下角 xcm 的位置。如图所示，折好后，可见区域中淡黄色和深蓝色纸张的面积相等。那么 x 的值是？3（A）5（B）6 2（C） 33（D）6（E） 4218. In this equation, the coefficient of y has been hidden, but we know that it is a positive integer, 1 or more.The equation has at least one

14、solution where x and y are positive integers.How many different values are possible for the hidden coefficient?在下面的方程中，y 的系数被遮住了，已知这个系数是一个大于等于 1 的正整数。2x+y=25并且这个方程至少有一个解，其中 x 和 y 的值都是正整数。那么被遮住的 y 的系数可能有多少个不同的值？（A）10（B）12（C）13（D）24（E）2519. Farmer Smith had a square property that he extended by buying

15、 a smaller square of land, creating the property shown.The new square of land increased the total perimeter of the property by 10%.By what percentage did the area of the property increase?农民史密斯拥有一块正方形的土地，于是他又购买了一块较小的正方形土地拓宽了原有的土地。新买的正方形土地使得他拥有的土地的总周长增加了 10%。那么土地的面积增加了百分之多少？（A）2（B）4（C）6（D）8（E）1020. I

16、 hear that dogs age 7 dog years every year. My dog Ruby was born on my ninth birthday. Four years from now, on our birthday, Rubys age in dog years will be exactly four times my age in normal years. How old am I now?据说，人的一岁相当于狗龄的 7 岁。我的狗茹比是在我九岁生日时出生的。并且再过四年我们过生日时，茹比的狗龄将恰好是我年龄的四倍。那么我现在的年龄是？（A）10（B）12

17、（C）13（D）15（E）17Questions 21 to 25 are worth 5 marks each.21-25 题，每题 5 分21. An ancient beast guards a 2km2km square building on an otherwise featureless plain.A 4 km-long unbreakable chain connects the beast to the outside wall of the building, as shown in the diagram. Neither the beast nor the chain

18、 can cross into the area occupied by the building.What is the area that the beast can access, in square kilometres?一只古兽守卫着荒原上一座边长为 2km 的方形建筑。一条长度为 4km 的锁链将古兽守卫与方形建筑物外面的墙连在了一起。古兽和锁链都不能进入建筑物占据的区域。请问古兽可以活动的区域的面积是多少平方千米？（A）9（B）10（C）11（D）12（E）1322. I have four numbers. When I add 3 to the first number, s

19、ubtract 3 from the second number, multiply the third number by 3 and divide the fourth number by 3, my four answers are all equal.My original 4 numbers added to 32. What is the sum of the largest two of these?我一共有四个数字。将第一个数字加上 3，第二个数字减去 3，第三个数字乘以 3，第四个数字除以 3，并且这四个算式最后得到的四个结果都相等。已知原来的四个数字之和为 32，那么原来的

20、四个数字中最大的两个数字之和是？（A）24（B）25（C）26（D）27（E）2823. These two rectangular prisms have the same surface area. Both x and y are integers less than 10.What is x + y ?如图所示，这两个长方体的表面积相等，其中 x 和 y 都是小于 10 的整数。那么 x + y 的结果是多少？（A）5（B）7（C）11（D）12（E）1324. Sometimes a three-digit number is an exact multiple of its dig

21、it sum:For instance, the digit sum of 102 is 1+0+2=3 and 102=334. If a three-digit number is k times the sum of its digits, what is the smallest possible integer value of k?有时一个三位数的值是它的各位数字之和的整数倍。例如，102 这个数字的的各位数字之和是1+0+2=3，且 102=334。如果一个三位数是它的各位数字之和的 k 倍，那么整数 k 的最小可能值是多少？（）9（）10（C）11（D）12（E）1325. S

22、ix identical equilateral triangles of side length 2 are drawn outside a regular hexagon of side length 1, defining a larger hexagon as shown.What is the ratio of the area of the larger hexagon to the area of the smaller hexagon?如下图，在边长为 1 的正六边形外侧画上六个相同的边长为 2 的等边三角形，从而出现了一个更大的六边形。那么大六边形的面积与小六边形的面积之比是

23、多少？（A）5:1（B）6:1（C）7:1（D）8:1（E）9:1 For questions 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 3

24、0 题占 10 分。26. Sena was arranging her collection of postage stamps into groups when a cat jumped onto them and scattered the stamps. All she can remember is that when she put them into groups of 2, 3, 4, 5 or 6 she always had 1 stamp left over. When she placed them into groups of 7 there were none le

25、ft over.What is the minimum number of stamps Sena could have had in her collection?瑟娜正在将她收集到的邮票分组，这时一只猫跳到邮票上面弄乱了邮票。瑟娜只记得之前她将邮票以 2 张、3 张、4 张、5 张或者 6 张分为一组时，总会剩下 1 张邮票，但将邮票分成 7 张一组时，不会剩下邮票。那么瑟娜至少收集了多少张邮票？27. A square ABCD is inscribed in a right-angled triangle EFG as shown.The length of EG is 4 units

26、and the length of EF is 3 units.As a fraction in simplest form, the side-length of the square isa . Whatbis the value ofa + b ?如下图，正方形 ABCD 内接于一个直角三角形 EFG 中。EG 的长度为 4，同时 EF 的长度为 3。正方形的边长可以表示为最简分式 a 。那么 a + b 的结果是？b28. The elves have to choose who will go the annual magic conference. They sit in a ci

27、rcle and the chief elf Elvin starts counting round the circle, starting with himself.Every second elf counted drops out of the circle and the counting continues until Elvin drops out. All those left in the circle go to the conference.This year, there are 1000 elves in the circle. How many will go to

28、 the conference?小精灵们需要选出精灵去参加一年一度的魔法盛会。于是所有精灵围成一个圆圈坐下，精灵首领艾尔文从自己开始沿着圆圈数数，每数到第二个的精灵离开圆圈，直到艾尔文离开圆圈时， 停止数数。所有留在圆圈中的精灵都能够参加盛会。今年，一共有 1000 只精灵围成一个圆圈坐下。那么最后会有多少只精灵将参加盛会？29. Two wheels are fixed to an axle as shown. Due to their different sizes, the two wheels trace two concentric circles when rolled on le

29、vel ground.In centimetres, what is the radius of the circle traced on the ground by the larger wheel?如下图，有两个车轮固定在一个车轴上。当车轮在水平地面滚动时，由于车轮的尺寸不同，这两个车轮会划出两个同心圆。请问大车轮在地面上划过的圆的半径是多少？30. A tromino is a shape made from three squares traced on gridlines. A 23 grid can be tiled by trominoes in exactly three wa

30、ys, as shown.We count two tilings that are reflections of each other as different. Similarly, two tilings that are rotations of each other are counted as different.In how many different ways can a 36 grid be tiled by trominoes?三格骨牌是在网格线上绘制三个正方形组成的形状。如下图，一个 23 网格恰好可以通过三种方式用三格骨牌平铺而成。我们将两个对称的平铺方式也算作是两个不同的方式。同样，旋转后相同的平铺方式也看作是不同的方式。那么一共有多少种不同的方式能够用三格骨牌平铺构成 36 的网格？澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer1C11C21E2E12E22D3C13E23A4E14B24C5C15D25C6D16B263017C17A27978A18B28629D19B2937510C20E30170