2023年数学竞赛AMC8真题B卷(含答案).docx

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1、Upper Primary DivisionQuestions 1 to 10 are worth 3 marks each.1-10 题,每题 3 分1. This shape is made from 7 squares, each 1 cm by 1 cm. What is its perimeter?如图所示,图形由 7 个边长为 1cm 的正方形组成。请问这个图形的总周长是多少?(A)7cm(B)12cm(C)14cm(D)16cm(E)28cm2. There are five shapes here. How many are quadrilaterals?以下五个图形中,请问有

2、多少个是四边形?(A)1(B)2(C)3(D)4(E)53. In a board game, Nik rolls three standard dice, one at a time. He needs his three rolls to add to 12. His first two dice rolls are 5 and 3. What does he need his third roll to be?一个棋盘游戏中,小尼投掷三枚标准的骰子,每次掷出一枚。如果他需要三次掷出的点数之和为 12,并且在前两次掷出的骰子的点数分别是 5 和 3,请问小尼第三次需要掷出的点数是多少?()

3、2(B)3(C)4(D)5(E)64. In this diagram, how many of the small squares need to be shaded for the large rectangle to be one-quarter shaded?如果要使得图中阴影面积占大长方形面积的四分之一,那么一共需要给多少个小正方形涂上阴影?(A)2(B)3(C)4(D)6(E)125. Petra left for school at 8:51 am. She got to school at 9:09 am. How long did it take Petra to get t

4、o school?小潘在上午 8:51 出发去学校并于上午 9:09 到达学校。请问小潘去学校花了多长时间?(A)9 minutes 9 分钟(B)10 minutes 10 分钟(C)18 minutes 18 分钟(D)42 minutes 42 分钟(E)1 hour 1 小时6. Which letter marks where 25 is on this number line?请问一下哪个字母代表下方数轴上数字 25 的位置?7. This bottle holds 4 glasses of water.一个瓶子可以容纳 4 杯水。Which one of the followin

5、g holds the most water?以下哪个选项能装最多的水?8. Two pizzas are shared equally between 3 students. What fraction of a whole pizza does each student get?如果将两个披萨平均分给 3 个学生。那么每一个学生可以得到一整个披萨的几分之几?(A) 1(B) 1(C) 1(D) 3(E) 3234249. A piece of card is cut out and labelled as shown in the diagram. It is folded along t

6、he dotted lines to make a box without a top. Which letter is on the bottom of the box?如果将一张卡片裁剪成如图所示的形状,并标记上字母,然后将卡片沿着虚线折叠成一个没有顶部的盒子。那么位于盒子底部的字母是?(A)(B)(C)C(D)D(E)E10. Doughnuts come in bags of 3 and boxes of 8. I bought exactly 25 doughnuts for my party. What do I get when I add the number of boxes

7、 I bought and the number of bags I bought?甜甜圈以每袋 3 个和每盒 8 个两种方式进行出售。如果我为聚会恰好购买了 25 个甜甜圈, 并将所购买的甜甜圈的盒数和袋数相加,那么盒数与袋数之和是?()4(B)5(C)6(D)7(E)8Questions 11 to 20 are worth 4 marks each.11-20 题,每题 4 分11. This line graph shows the temperature each hour during a day.以下折线图显示了一天中各个小时的温度。Roughly for how long wa

8、s the temperature above 20C?那么温度高于 20大约有多长时间?(A)7 hours 7 小时 (B)8 hours 8 小时 (C)9 hours 9 小时(D)10 hours 10 小时 (E)11 hours 11 小时 12. VIV takes her three children, HANNAH, OTTO and IZZI, out shopping. Each is wearing a t- shirt with their name on the front in capital letters. When they stand in front

9、of the shop mirror, which names appear the same in the reflection as on the shirts?VIV 带着她的三个孩子 HANNAH, OTTO 和 IZZI 去购物。每一个孩子的 T 恤都印有自己的名字,并且名字用大写字母印在 T 恤正面。当他们站在商店镜子面前时,哪些名字在镜子中看到的图像与衬衫上的名字图像相同?(A)VIV and TTOVIV 和 OTTO(B)V, OTTO and IZZIVIV、OTTO 和 IZZI(C)V, HANNAH and IZZIVIV、HANNAH 和 IZZI(D)HANNAH

10、 and OTTOHANNAH 和 OTTO(E)All four of them 四个名字都相同13. This regular hexagon has angles of 120 and the square has angles of 90. What is the angle z in the diagram?如图所示,正六边形的内角度数为 120,正方形的内角度数为 90。那么图中角 x的度数是多少?(A)90(B)120(C)135(D)150(E)18014. Syeds mother had some money to share with her family. She ga

11、ve one-quarter of her money to Syed.Then she gave one-third of what was left to Ahmed. Then she gave one-half of what was left to Raiyan. She was left with $15, which she kept for herself.How much money did Syeds mother have to start with?小赛的妈妈要分一些钱给家人。她把四分之一的钱给了小赛,把剩下的钱的三分之一给了小艾,然后她再把剩下的钱的一半给了小莱, 最

12、后还剩下 15 美元。请问小赛的妈妈最开始有多少钱?(A)$30(B)$45(C)$60(D)$90(E)$12015. The rectangle shown has a side length of 9 cm. It is divided into 3 identical rectangles as shown. What is the area, in square centimetres, of the original rectangle?在下侧的图片中,一个边长为 9cm 的长方形被分成三个相同的小长方形。请问原来的大长方形的面积是多少?()45(B)50(C)52(D)54(E)

13、6316. This diagram shows a rectangle with a perimeter of 30cm. It has been divided by 2 lines into 4 small rectangles. Three of the small rectangles have the perimeters shown. What is the perimeter of fourth small rectangle?在下侧的图中,一个周长为 30cm 的大长方形被两条直线分成 4 个小长方形,其中三个小长方形的周长已标注出来。那么第四个小长方形的周长是多?()10c

14、m(B)12cm(C)14cm(D)16cm(E)18cm17. There are 10 questions in a test. Each correct answer scores 5 points, each wrong answer loses 3 points, and if a question is left blank it scores 0 points.Tycho did this test and scored 27 points. How many questions did Tycho leave blank?一场测试中一共有 10 道题目,答对一题得 5 分,答错

15、一题扣 3 分,不答得 0 分。迪谷参加了这场测试,并且他的最终得分为 27 分。请问迪谷一共有多少道题目是空着的?()1(B)2(C)3(D)4(E)518. Estelle is making decorations shaped like the 8-pointed star shown. She folds a square of paper to make a triangle with 8 layers as shown. 小爱正在制作八角星形状的装饰品。如图所示,她将一张正方形纸张,折叠成有 8 层的三角形。How could she cut the triangle so th

16、at the unfolded shape is the star?请问小爱如何裁剪这个三角形,才能使得展开后的形状是八角星形?19. Earlier this year Ben said, Next year I will turn 13, but 2 days ago I was 10. Bens birthday is今年早些时候,本说:“到明年我就 13 岁了,但是在两天前我才 10 岁。” 那么本的生日是在几月几日?(A) 1st January 1 月 1 日(B) 2nd January 1 月 2 日(C) 29th December 12 月 29 日(D) 30th Dec

17、ember 12 月 30 日(E) 31st December 12 月 31 日20. Peyton, Luka and Dan have 180 stickers in total. Peyton has half as many stickers as Luka. Dan has three times as many as Luka.How many stickers does Peyton have?佩顿、卢卡和丹一共有 180 张贴纸。佩顿的贴纸数是卢卡的一半,同时丹的贴纸数是卢卡的三倍。那么佩顿一共有几张贴纸?(A)20(B)24(E)54(C)30(D)40Questions

18、 21 to 25 are worth 5 marks each.21-25 题,每题 5 分21. Mrs Graaf invents a game for her students to practise arithmetic. They roll two 10-sided dice to pick two random numbers. Starting at one of the numbers, they keep adding the other number until they reach a 3-digit number.Ian rolls a 5 and an 8. If

19、he chooses to start with 5 and then add 8 again and again, his list is 5, 13, 21, 93, 101. If he chooses to start with 8 and add 5, his list is 8, 13, 18, 98, 103.On Naras turn, she makes a list that ends with 107.What pair of numbers could she have rolled?格拉芙女士为她的学生设计了一个练习计算的游戏。如图所示,学生们投掷两枚 10 面骰子得

20、到两个随机数,然后选择其中一个数开始,反复加上另一个数,直到得出一个三位数为止。伊恩掷出了一个 5 和一个 8。当他选择从 5 开始,然后反复加上 8,得到的数列是 5,13, 21,93,101。当他选择从 8 开始,反复加上 5,得到的数列是 8,13,18,98,103。在娜拉的回合中,她得到的数列以 107 结束。那么她可能掷出了哪一对数字?(A)4 and 84 和 8(B)5 and 75 和 7(C)3 and 43 和 4(D)6 and 96 和 9(E)3 and 83 和 822. At a school concert, the tickets cost $20 per

21、 adult and $2 per child. The total paid by the 100 people who attended was $920. How many were children?在一场学校音乐会上,一张成人票是 20 美元,一张儿童票是 2 美元。参加音乐会的 100 人支付的总金额是 920 美元。那么这 100 人中有多少名是儿童?(A) between 25 and 35 在 25 名至 35 名之间(B) between 35 and 45 在 35 名至 45 名之间(C) between 45 and 55 在 45 名至 55 名之间(D) betw

22、een 55 and 65 在 55 名至 65 名之间(E) between 65 and 75 在 65 名至 75 名之间23. Meena has a standard dice, with each pair of opposite faces adding to 7. At first, the three faces she can see add to 6, as shown.She holds the dice between a pair of opposite faces and rotates it 180, keeping these opposite faces f

23、acing the same direction. She puts the dice back down and adds up the three faces she can now see. What is the smallest possible total she could get?米娜有一枚形制标准骰子,相对的面上的点数之和为 7。在下侧的图片中,她现在可以看到的三个面的点数之和是 6。现在她抓住骰子上一对相对的面,将其旋转 180,保持相对面的方向不变。然后将骰子放下,并将能看到的三个面的点数相加。那么最后得到的和的最小可能值是?()6(B)8(C)10(D)12(E)142

24、4. I have 4 whole numbers that add up to 98.If I were to add 6 to the first number, subtract 6 from the second number, multiply the third number by 6 and divide the fourth number by 6, the four answers would all be the same.What is the sum of the largest two of my original four numbers?如果我有四个整数,并且它们

25、的和为 98。如果将第一个数字加上 6,第二个数字减去 6,第三个数字乘以 6,第四个数字除以 6,最终这四个算式得到的四个结果都相等。那么最初的四个数字中,最大的两个数字之和是多少?()72(B)86(C)88(D)90(E)9425. When I ride my bike at 20 kilometres per hour, each wheel turns at 2 revolutions per second. When I ride 1 kilometre, how many revolutions does each wheel make?当我以每小时 20 公里的速度骑自行车时

26、,每个车轮每秒转 2 圈。当我骑行 1 公里时,请问每个车轮转了多少圈?()40(B)240(C)320(D)360(E)420For 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

27、 分,第 28 题占 8 分,第 29 题占 9 分,第 30 题占 10 分。,26. In this puzzle,and represent different nonzero digits.What is the three-digit number?如图所示,在这个谜题中,、和分别表示不同的非零数字。那么三位数是多少?27. Li attempted to multiply a single-digit number by 36, but he accidentally multiplied by 63 instead. His answer was 189 larger than

28、the correct answer.What was the correct answer to the multiplication?小李尝试将一个一位数乘以 36,但他在粗心之下将这个一位数乘以了 63,最终得到的结果比原本应该得到的正确结果大 189。请问这个乘法计算的正确结果是?28. Using 9 out of the 10 possible digits Safia writes 3 numbers, each between 100 and 999. She adds her 3 numbers together. What is the smallest possible

29、sum?萨菲亚从 10 个可能的一位数中选出 9 个一位数,组成 3 个数,每个数都介于 100 到 999 之间。将这 3 个数相加,请问得到的最小可能值是多少?29. Yifan has a construction set consisting of red, blue and yellow rods. All rods of the same colour are the same length, but differently coloured rods are different lengths. She wants to make quadrilaterals using the

30、se rods.一帆有一个含有红色、蓝色和黄色小棒的组装套件。颜色相同的小棒长度相同,颜色不同的小棒长度也不同。她想用这些小棒拼成四边形。l When she uses two red, one blue and one yellow rod, the perimeter of the quadrilateral is 36 cm.l When she uses two blue, one red and one yellow rod, the perimeter is 35 cm.l When she uses two yellow, one blue and one red rod, th

31、e perimeter is 33 cm.l 使用两根红色、一根蓝色和一根黄色小棒拼成的四边形周长是 36 cm。l 使用两根蓝色、一根红色和一根黄色小棒拼成的四边形周长为 35 cm。l 使用两根黄色,一根蓝色和一根红色小棒拼成的四边形周长为 33 cm。What number do you get when you multiply the lengths of one red rod, one blue rod and one yellow rod?现在将一根红色、一根蓝色和一根黄色小棒的长度相乘,请问最后的结果是?30. Janus is making patterns using s

32、quare tiles. Each pattern is made by copying the previous pattern, then adding a tile to every grid square that shares an edge with the copied pattern.杰纳斯正在用正方形的瓷砖制作图案。每个图案的制作方式都是先复制上一个图案,再将与复制的图案共用一条边的每个方格都中再添加一块瓷砖。His last pattern is the largest one that can be made with fewer than 1000 tiles. How many tiles are in this last pattern?他制作的最后一个图案是使用少于 1000 块瓷砖可以制作出来的最大图案。那么最后一个图案用了几块瓷砖?澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer1D11E21E2B12A22D3C13D23C4B14C24D5C15D25D6D16E262857A17C272528D18B287119B19E2963010B20A30925

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