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2024 AMC8 #1 · Algebra · ★
What is the ones digit of
请问下方算式的个位数是几？
222,222−22,222−2,222−222−22−2?222,222 - 22,222 - 2,222 - 222 - 22 - 2?

正确答案：B · 分值：1

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2024 AMC8 #2 · Algebra · ★
What is the value of this expression in decimal form? 4411+11044+441100\displaystyle \frac{44}{11} + \frac{110}{44} + \frac{44}{1100}
请问下列表达式的值用小数可以表示为哪一项？

正确答案：C · 分值：1

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2024 AMC8 #3 · Geometry · ★★
Four squares of side length 4, 7, 9, and 10 units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate in color white-gray-white-gray, respectively, as shown in the figure. What is the area of the visible gray region in square units?
将四个边长分别为 4、7、9、10 个单位的正方形从小到大依次排列，使得它们的左侧边和底边分别对齐。四个正方形的颜色按照白色-灰色-白色-灰色的顺序交替出现，如图所示。请问灰色可见区域的面积为多少个平方单位？

正确答案：E · 分值：1

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2024 AMC8 #4 · Number Theory · ★
When Yunji added all the integers from 1 through 9, she mistakenly left out a number. Her incorrect sum turned out to be a square number. Which number did Yunji leave out?
Yunji 将 1到 9之间的所有整数相加时，漏加了一个数字，得到的错误结果是一个平方数。请问Yunji 漏加的是哪个数字？

正确答案：E · 分值：1

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2024 AMC8 #5 · Counting, Probability & Statistics · ★★
Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of 6. Which of the following integers cannot be the sum of the two numbers?
Aaliyah投掷两枚标准的六面殷子。她发现掷出的两个点数之积是6的倍数，请问下列哪个整数不可能是这两个点数之和？

正确答案：B · 分值：1

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2024 AMC8 #6 · Geometry · ★★
Sergei skated around an ice rink, gliding along different paths. The gray lines in the figures below show four of the paths labeled P, Q, R, and S. What is the sorted order of the four paths from shortest to longest?
Sergei在滑冰场沿着不同路径滑冰。下图中的灰色线条表示4条不同路径，分别标记为P、Q、R、S。请问这4条路径从短到长的正确排列顺序是什么？

正确答案：D · 分值：1

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2024 AMC8 #7 · Geometry · ★★
AA3×73 \times 7 rectangle is covered without overlap by 3 shapes of tiles: 2×22 \times 2, 1×41\times4, and 1×11\times1, shown below. What is the minimum possible number of 1×11\times1 tiles used?
一个3×7的矩形被下方3种规格分别为2×2、1×4和1×1的瓷砖所覆盖，且各瓷砖之间互不重叠。请问最少可能会用到多少个1×1的瓷砖？

正确答案：E · 分值：1

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2024 AMC8 #8 · Counting, Probability & Statistics · ★★
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
周一那天，Taye有2美元。每天，他要么获得3美元，要么拥有的金额变成前一天的两倍。请问三天后，也就是周四，Taye 拥有的金额可能有多少种不同的结果?

正确答案：D · 分值：1

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2024 AMC8 #9 · Algebra · ★★
All of the marbles in Maria's collection are red, green, or blue. Maria has half as many red marbles as green marbles and twice as many blue marbles as green marbles. Which of the following could be the total number of marbles in Maria's collection?
Maria收藏有红色、绿色、蓝色三种颜色的大理石，其中红色大理石的数量是绿色大理石数量的一半，蓝色大理石数量是绿色大理石数量的两倍。请问Maria收藏的大理石总数可能是多少？

正确答案：E · 分值：1

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2024 AMC8 #10 · Algebra · ★
In January 1980, the Mauna Loa Observatory recorded carbon dioxide (CO₂) levels of 338 ppm (parts per million).
Over the years, the average CO₂ reading has increased by about 1.515 ppm per year.
What is the expected CO₂ level in January 2030, in ppm? Round your answer to the nearest integer.
1980年1月，莫纳罗亚天文台记录的二氧化碳浓度为338ppm（百万分之一)。近年来，二氧化碳浓度平均每年增加约1.515ppm。请问2030年1月的二氧化碳浓度预计为多少ppm？将答案四舍五入到最接近的整数。

正确答案：B · 分值：1

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2024 AMC8 #11 · Geometry · ★★★
The coordinates of △ABC are A(5, 7), B(11, 7), and C(3, y), with y > 7.
The area of △ABC is 12.
What is the value of y?
△ABC 的顶点坐标分别为 A(5,7)、B(11,7)和 C(3,y)，其中 y>7。已知△ABC 的面积为12，请问y的值为多少？

正确答案：D · 分值：1

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2024 AMC8 #12 · Algebra · ★★★
Rohan keeps a total of 90 guppies in 4 fish tanks. • There is 1 more guppy in the 2nd tank than in the 1st tank. • There are 2 more guppies in the 3rd tank than in the 2nd tank. • There are 3 more guppies in the 4th tank than in the 3rd tank.
How many guppies are in the 4th tank?
Rohan 的 4 个鱼缸中一共有 90 条孔雀鱼。
• 第二个鱼缸比第一个鱼缸多 1 条孔雀鱼。 • 第三个鱼缸比第二个鱼缸多 2 条孔雀鱼。 • 第四个鱼缸比第三个鱼缸多 3 条孔雀鱼。
请问第四个鱼缸中有多少条孔雀鱼？

正确答案：E · 分值：1

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2024 AMC8 #13 · Counting, Probability & Statistics · ★★★
Buzz Bunny is hopping up and down a set of stairs, one step at a time.
In how many ways can Buzz Bunny start on the ground, make a sequence of 6 hops, and end up back on the ground?
(For example, one sequence of hops is up-up-down-down-up-down.)
小兔子Buzz在台阶上跳上跳下，每次跳一个台阶。Buzz从地面开始跳跃，连续跳跃6次。请问Buzz有几种方式，最后可以跳回地面？ （例如其中一种方式为上-上-下下-上-下。）

正确答案：B · 分值：1

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2024 AMC8 #14 · Counting, Probability & Statistics · ★★★
The one-way routes connecting towns A, M, C, X, Y, and Z are shown in the figure below (not drawn to scale).
The distances in kilometers along each route are marked.
Traveling along these routes, what is the shortest distance from A to Z in kilometers?
如图所示，A、M、C、X、Y、Z几座小镇之间通过单行道相连。图中标明了每条单行道的长度，单位为千米。请问沿单行道从A行驶到Z的最短距离为多少千米？（图形未按比例绘制）

正确答案：A · 分值：1

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2024 AMC8 #15 · Number Theory · ★★★
Let the letters F, L, Y, B, U, and G represent distinct digits.
Suppose F‾ L‾ Y‾ F‾ L‾ Y‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} is the greatest six-digit number that satisfies the following equation:
8⋅F‾ L‾ Y‾ F‾ L‾ Y‾=B‾ U‾ G‾ B‾ U‾ G‾8 \cdot \underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} = \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}\,\underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}
What is the value of F‾ L‾ Y‾+B‾ U‾ G‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} + \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}?
用 F、L、Y、B、U、G 表示不同数字。
若 F‾ L‾ Y‾ F‾ L‾ Y‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} 为满足下列等式的最大六位数：
8⋅F‾ L‾ Y‾ F‾ L‾ Y‾=B‾ U‾ G‾ B‾ U‾ G‾8 \cdot \underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} = \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}\,\underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}
求 F‾ L‾ Y‾+B‾ U‾ G‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} + \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}} 的值。

正确答案：C · 分值：1

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2024 AMC8 #16 · Counting, Probability & Statistics · ★★★
Minh enters the numbers 1 through 81 into the cells of a 9 × 9 grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by 3?
Minh按照某种顺序将数字1到81填入一个9×9的网格中，并计算出每行每列的数字之积。请问至少有多少行和列的乘积可以被3整除？

正确答案：D · 分值：1

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2024 AMC8 #17 · Counting, Probability & Statistics · ★★★
A chess king is said to attack all the squares one step away from it, horizontally, vertically, or diagonally. For instance, a king on the center square of a 3 × 3 grid attacks all 8 other squares, as shown below. Suppose a white king and a black king are placed on different squares of a 3 × 3 grid so that they do not attack each other. In how many ways can this be done?
在国际象棋中，"国王"可以进攻横向、纵向或对角线方向上所有距离一步的棋格。如下图所示，在一个3×3棋盘中，位于中心位置的"国王"可以进攻其他8个棋格。假设要在一个3×3棋盘的不同方格中放入一枚白色"国王"和一枚黑色"国王"，请问有多少种放置方式可以使得这两个"国王"不会互相进攻？

正确答案：E · 分值：1

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2024 AMC8 #18 · Geometry · ★★★
Three concentric circles centered at O have radii of 1, 2, and 3. Points B and C lie on the largest circle. The region between the two smaller circles is shaded, as is the portion of the region between the two larger circles bounded by central angle ∠BOC, as shown in the figure below. Suppose the shaded and unshaded regions are equal in area. What is the measure of ∠BOC in degrees?
以点 O 为圆心的三个同心圆的半径分别为 1、2、3。点 B 和点 C 位于最大圆上。两个较小圆之间的区域被涂上阴影，两个较大圆之间且位于圆心角 ∠BOC 内的区域也被涂上阴影，如图所示。若阴影区域与非阴影区域面积相等，请问 ∠BOC 的度数是多少？

正确答案：A · 分值：1

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2024 AMC8 #19 · Counting, Probability & Statistics · ★★★
Jordan owns 15 pairs of sneakers.
Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top.
The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction?
Jordan 有 15 双运动鞋。其中 35\displaystyle \frac{3}{5} 的鞋是红色，其余为白色；其中 23\displaystyle \frac{2}{3} 的鞋是高帮，其余为低帮。红色高帮运动鞋的数量占全部鞋数的一个分数。这个分数的最小可能值是多少？

正确答案：C · 分值：1

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2024 AMC8 #20 · Geometry · ★★★
Any three vertices of the cube PQRSTUVW, shown in the figure below, can be connected to form a triangle.
For example, vertices P, Q, and R can be connected to form an isosceles △PQR.
How many of these triangles are equilateral and contain P as a vertex?
如图所示，立方体PQRSTUVW上任意三个顶点相连可以构成一个三角形（例如，顶点P,Q，R相连可以构成一个等腰三角形△PQR）。请问在上述三角形中， 有多少个是以P为一个顶点的等边三角形？

正确答案：D · 分值：1

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2024 AMC8 #21 · Algebra · ★★★
A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow when in the sun. Initially, the ratio of green to yellow frogs was 3:1. Then 3 green frogs moved to the sunny side and 5 yellow frogs moved to the shady side. Now the ratio is 4:1. What is the difference between the number of green frogs and the number of yellow frogs now?
一群青蛙（号称青蛙军团）生活在树上。它们在树荫中呈绿色，在阳光下又变成黄色。刚开始，绿色青蛙和黄色青蛙的数量之比是3：1。随后，3只绿色青蛙跳到阳光下，5只黄色青蛙跳到树荫下，此时数量之比变成4：1。请问现在绿色青蛙和黄色青蛙的数量相差多少？

正确答案：E · 分值：1

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2024 AMC8 #22 · Geometry · ★★★★
A roll of tape is 4 inches in diameter and is wrapped around a ring that is 2 inches in diameter. A cross section of the tape is shown in the figure below. The tape is 0.015 inches thick. If the tape is completely unrolled, approximately how long would it be? Round your answer to the nearest 100 inches.
下图为一卷胶带的横截面。胶带直径为4英寸，其中包裹着一个直径为2英寸的圆环。胶带厚度为0.015英寸。请问这卷胶带全部展开大约有多少英寸？请将答案四舍五入到最接近的百位数。

正确答案：B · 分值：1

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2024 AMC8 #23 · Geometry · ★★★★★
Rodrigo has a very large piece of graph paper. First he draws a line segment connecting point (0, 4) to point (2, 0) and colors the 4 cells whose interiors intersect the segment, as shown below. Next Rodrigo draws a line segment connecting point (2000, 3000) to point (5000, 8000). Again he colors the cells whose interiors intersect the segment. How many cells will he color this time?
Rodrigo有一张非常大的方格纸。他先画了一条线段连接点（O,4)和点（2,0），然后为内部与该线段相交的4个方格上色，如图所示。紧接着Rodrigo又画了一条线段连接点(2000,3000）和点（5000,8000)，并为内部与该线段相交的方格上色。 请问这次Rodrigo要给多少个方格上色？

正确答案：C · 分值：1

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2024 AMC8 #24 · Geometry · ★★★★
Jean made a piece of stained glass art in the shape of two mountains, as shown in the figure below.
One mountain peak is 8 feet high and the other peak is 12 feet high. Each peak forms a 90° angle, and the straight sides of the mountains form 45° angles with the ground.
The artwork has an area of 183 square feet. The sides of the mountains meet at an intersection point near the center of the artwork, h feet above the ground.
What is the value of h?
Jean制作了一件两座山形状的彩色玻璃艺术品，如下图所示。一座山峰高8英尺，另一座山峰高12英尺。每座山的顶部都形成一个90°的角，两座山的直边都与地面形成一个45°的夹角。这件艺术品的面积为183平方英尺。两座山的另一边在艺术品中心附近的位置相交，相交点距离地面h英尺。请问h的值是多少？

正确答案：B · 分值：1

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2024 AMC8 #25 · Counting, Probability & Statistics · ★★★★
A small airplane has 4 rows of seats with 3 seats in each row. Eight passengers have boarded the plane and are distributed randomly among the seats. A married couple is next to board. What is the probability there will be 2 adjacent seats in the same row for the couple?
一架小型飞机有4排座位，每排3个座位。目前已有8位乘客随机入座。接下来一对夫妻登机。这对夫妻能坐到同一排且相邻两个座位的概率是多少？

正确答案：C · 分值：1

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