2023年数学竞赛AMC8真题E卷（含答案）.docx

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1、Senior DivisionQuestions 1 to 10 are worth 3 marks each.1-10 题，每题 3 分1. What is the value of 2023-3202? 2023-3202 的值为哪个选项？（A）-1221（B）-1179（C）1179（D）1221（E）52252. A parallelogram PQRS has an area of 60 cm2 and side PQ of length 10 cm. Which length is 6cm?下图中的平行四边形 PQRS 的面积为 60cm2，边 PQ 的长度为 10cm。哪条线段的

2、长度是 6cm？（A）RQ（B）RS（C）QT（D）PT（E）QS3. Which one of these is equal to 57953? 57953 的值等于以下哪项？（）321（B）4321（C）54321（D）654321 （E）76543214. What is the difference between 25 and 52? 25 和 52 相差多少？（）0（B）1（C）3（D）5（E）75. What is the value of the angle in the diagram?如图所示，角 的度数是多少？（A）100（B）110（C）120（D）130（E）1406

3、. The shaded square is inscribed in the larger square as shown.What is the ratio of shaded to unshaded area in the diagram?下图中阴影正方形内接于较大的正方形中。阴影部分的面积与非阴影部分的面积之比是多少？（A）5:4（B）25:24（C）3:2（D）7:4（E）12:77. Jemmy multiplies together all the integers from 1 to 18. What are the last three digits of the resul

4、t?杰米将 1 到 18 之间的所有整数相乘。得到结果的最后三位数字是什么？（A）000（B）020（）200（D）080（E）8008. A fuel tank is 40% empty. Then 40 litres of fuel is removed. The tank is now 40% full. How many litres are in a full tank?一个油箱中 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？（A）40（B）100（）160（D）200（E）4009. The volume V of a sphere of ra

5、dius r is given byV = 4 p r3 .3For a sphere of volume V=100cm3, which of the following is closest to the radius?半径为 r 的球体体积为 V，体积公式为V = 4 p r3 。3一个体积为 V=100cm3 的球体，哪项最接近它的半径？（A）2.9cm（B）3.5cm（C）5cm（D）5.8cm（E）10cm10. If I add 3 consecutive odd integers, I get a total of 9m+3. The largest of these 3 in

6、tegers is如果将 3 个连续的奇数相加，和是 9m+3。这 3 个奇数中最大的数是哪一个？（A）3m-3（B）3m-1（C）3m（D）3m+1（E）3m+3Questions 11 to 20 are worth 4 marks each.11-20 题，每题 4 分2411. The value of (+ 54 )2 is24请问(+ 54 )2 等于？（）140（B）150（C）160（D）170（E）18012. In a group of 6 people there are 3 pairs of twins. How many 3-member committees can

7、 be chosen that do not contain any pair of twins?一个 6 人组中有 3 对双胞胎，请问一共可以选出多少个不包含任何一对双胞胎的 3 人小组？（A）0（B）8（C）12（D）24（E）4813. Assuming a b 0 , the expression can be written as假设 a b 0 ，表达式可以表示为（A）b - a ab（B）b + a ab（C）ab b + a（D）a2 - b2 a - b（E） a - b14. A bag contains red and yellow balls such that the

8、 ratio red:yellow is 5:7. Then 10 balls of each colour are removed and the ratio changes to 5:8.How many balls were originally in the bag?袋子里装有红球和黄球，红球与黄球的数量之比为 5:7。从袋子里取出 10 个黄球和 10 个红球后，红球和黄球的数量之比变为 5:8请问袋子里原先一共有多少个球？（A）48（B）60（C）72（D）84（E）9615. In the solution to this number puzzle, whenever ther

9、e are three numbers in a straight line, the middle number is the sum of the other two.What is the value of x?要解出右侧的数字谜题，要求位于一条直线上的三个数字中，中间的数字是其余两个数字之和。x 的值是多少？（A） 1 (a + b + c)（B） 1 (b - a - c)（C） 1 (a + b - c)222（D） 1 (a - b + c)（E） 1 (b + c - a)2216. If f (x) = 5 + x and g (x) = 7 - x , then f ( g

10、 ( x) - g ( f ( x)equals如果 f (x) = 5 + x , g (x) = 7 - x ,则 f ( g ( x) - g ( f ( x) 等于?（A）10 - x（B）7（C） x + 2（D）10（E） 2x - 217. The hypotenuse of a right-angled triangle has length 6cm. The perimeter of the triangle is 14 cm.What is the area of the triangle in square centimetres? 一个直角三角形的斜边长度为 6cm，周

11、长为 14cm。这个三角形的面积是多少平方厘米？（A）7（B）12（C）14（D）21（E）24318. I have two identical dice, each with faces 1, 1 ,2, 1 , 123and.2312I roll both dice and multiply the two numbers rolled, then simplify my answer. What is the probability that this product is rational?3131,我有两枚相同的骰子，每枚骰子的六面标记为1,2和3 。2抛掷这两枚骰子并将得到的点数

12、相乘并化简结果。得到的积为有理数的概率是多少？（A） 1（B） 1（C） 1（D） 5（E） 7962181819. How many distinct pairs(x, y) satisfyx2 + y2 y ?如果 x 和 y 均为正整数、且 x y ，有多少个不同的数对(x, y) 满足x2 + y2 50 ?（）15（B）13（C）11（D）9（E）820. A 15cm20cm rectangle is cut into two triangles. One triangle is rotated and placed on top of the other triangle as

13、shown to form a concave pentagon.What is the perimeter of the pentagon?将一个 15cm20cm 的长方形剪成两个三角形。旋转其中一个三角形并放在另一个三角形上方，形成一个凹五边形，如下图。这个五边形的周长等于？（A）80cm（B）84cm（C）93cm（D）96cm（E）105cmQuestions 21 to 25 are worth 5 marks each.21-25 题，每题 5 分21. I have four numbers. When I add 3 to the first number, subtract

14、 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?我有四个数字。我把第一个数字加上 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，得到的四个结果都相等。原来的四个数字之和为32，原来的四个数字中最大的两个数字之和是多少？（A）

15、24（B）25（C）26（D）27（E）2822. Antonio walked 11.5 km to his cousin Marias house.At first he walked uphill, then along a flat part of the road and the final part was downhill. The trip took 2 hours 54 minutes. The next day his walk back home took 3 hours 6 minutes. Antonio walks uphill at a constant spee

16、d of 3 km/h, on the flat at 4 km/h and downhill at 5 km/h.What is the length, in kilometres, of the flat part of the road?安多尼奥步行到表妹玛丽亚家，全程 11.5km。一开始他要爬坡，然后沿着一段平路行走，最后一段是下坡，整个过程花费了 2 小时 54 分钟。第二天他沿原路返回，花费了 3 小时 6 分钟。安东尼奥以 3km/h 的速度匀速爬坡，以4km/h 的速度匀速在平路上行走，以5km/h 的速度匀速下坡。全程中平路的长度是多少公里？（A）4（B）4.5（C）5（D

17、）5.5（E）623. I think of two positive integers and call their sum S and their product P. Which one of the following could not be the value of S+P?我想到两个正整数，它们之和可以用 S 表示，它们之积可以用 P 表示。哪项不可能是 S+P的值？（A）84（B）86（C）88（D）90（E）9224. A solid regular tetrahedron has 4 faces, each an equilateral triangle. It is su

18、spended in the entomology laboratory. There are two food sources on the tetrahedron, one at a vertex V and theother at X, the centre of the opposite face. When a geodesic grub is placed anywhere upon the tetrahedron, it instinctively crawls along the shortest possible path over the surface to the cl

19、osest food source.What fraction of the surface area is closer to V than to X, in terms of paths along the surface?一个实心正四面体有四个面，每个面都为等边三角形。将它悬挂在昆虫学实验室中。正四面体上放了两处食物，一处位于顶点 V 处，另一处位于相对面的中心 X 处。将一只幼虫放置在正四面体上的任意位置时，幼虫本能地沿着表面上最短的路径爬行到离自己最近的食物处。根据幼虫沿表面爬行的路径，距离 V 比 X 更近的表面积占正四面体表面积的比例是多少？（A） 1（B） 1（C） 1（D）

20、2（E） 34323425. Three spheres of radius 2 sit on a flat surface touching one another. A smaller sphere sits on the same surface, in the middle and touching all three of the bigger spheres. What is its radius?（D）（C）（B）三个半径为 2 的球体放在平面上且彼此相切。将一个更小的球体放在同一平面上，位于三个大球体中间且相切于这三个大球体。请问这个小球体的半径是多少?（E）（A） For q

21、uestions 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. How many ways can you se

22、lect four distinct equally spaced numbers from the set 1, 40 ?从集合1, 40 中选出4个不同的数字，要求前后数字之差相同，一共有多少种选择方式？27. Digits a, b and c are chosen and then two six-digit numbers are formed, M with digits abcabcand N with digits ababab. The ratio M:N is 55:54. What is the 3-digit number abc?选出数字a、b 和c，构成两个六位数M

23、 和N，M 的各位数字为abcabc，N 的各位数字为ababab。已知 M:N 等于 55:54，三位数 abc 是多少？28. Two wheels are fixed to an axle as shown. Due to their different sizes, the two wheels trace two concentric circles when rolled on level ground.In centimetres, what is the radius of the circle traced on the ground by the larger wheel?

24、下图中两个车轮固定在一个车轴上。车轮在水平地面滚动时，由于其尺寸不同，这两个车轮会划出两个同心圆。大车轮在地面上划过的圆的半径是多少厘米？29. Martin the gardener has 3 new vegetable beds, near the kitchen, laundry and shed. Each year he will plant one bed with tomatoes, one with beans, and one with carrots. He needs a schedule for planting that goes for 8 summers.To

25、balance the disease risk and soil nutrients, his schedule must follow these rules：l A bed that has tomatoes one summer cant have tomatoes next summer or the one after.l Carrots cant be in a bed that had beans last summer.In how many ways can he schedule his vegetable planting for these 8 summers?园丁马

26、丁有 3 块新菜地，分别靠近厨房、洗衣房和仓库。每年他会在 3 块菜地上分别种植番茄、豆荚和胡萝卜。他需要制定一个历时 8 个夏季的种植计划。为了平衡虫害风险和土壤养分，这个计划必须遵循以下规则：l 如果菜地在一个夏季种植了番茄，接下来的一个夏季或者再后一个夏季就不能再种植番茄。l 上个夏季种植豆荚的菜地，不能种植胡萝卜。他一共有多少种方式安排这 8 个夏季的蔬菜种植？30. A percussionist is practising patterns within an 11-beat bar of music. To visualise this, she arranges 11 dots

27、 around a circle, with black dots representing a drum hit. She reads this pattern of dots clockwise, starting at the top.Her patterns have at least one black dot, no two adjacent black dots and two patterns only count asthe same if they are the same in every detail, including where the pattern start

28、s in the circle and the direction it is read.For instance, patterns A and B below are two of her patterns, and they count as different, even though B can be thought of as A starting on a different beat.Pattern C is not one of her patterns, since it has two adjacent black dots. How many drumming patt

29、erns like this are possible?一名打击乐手正在练习 11 拍乐曲小节中的节奏模式。为了使得练习过程更清晰，她在一个圆圈上排列了 11 个点，其中黑点表示击鼓。她从最上面的点开始，顺时针读取这些点的节奏模式。她的节奏模式中至少有一个黑点，且任意两个黑点不相邻。只有当两个节奏模式的每个细节都相同，包括起始位置和读取方向，这两个节奏模式才被视为相同的模式。例如，下面的 A 和 B 是两种节奏模式，它们被视为不同的模式，尽管 B 可以看作是 A 从不同的节拍开始的节奏模式。图 C 不属于她的节奏模式，因为它有两个相邻的黑点。这样的击鼓模式可能有多少种？澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer澳AMCMiddle PrimaryAnswer1B11B21D2D12B22A3C13C23C4E14C24B5A15D25E6B16D262477A17A271858D18E283759A19B2933010E20B30198