2026 AMC8 #1 · Algebra · ★
What is the value of the following expression?
以下表达式的值是多少？
正确答案：A · 分值：1
用同分类同星级进入练习 →题库列表
优先读取 Supabase 真题库；若未配置则自动回退到本地样例数据。
2026 AMC8 #2 · Algebra · ★★
In the array shown below, three 3s are surrounded by 2s, which are in turn surrounded by a border of 1s. What is the sum of the numbers in the array?
在下面的数组中，三个数字 3 被数字 2 包围，而这些 2 又被一圈 1 包围。该数组中所有数字之和是多少？
正确答案：C · 分值：1
用同分类同星级进入练习 →2026 AMC8 #3 · Geometry · ★★
Haruki has 24 centimeters of wire. He cuts the wire and bends it into the following shapes, one at a time:
- A regular hexagon with side length 5 cm
- A square of area 36 cm²
- A right triangle whose legs are 6 and 8 cm long
Which of the shapes can Haruki make?
Haruki 有 24 厘米长的铁丝。他剪断铁丝并把它弯成以下形状，一次做一个：
- 边长为 5 cm 的正六边形 - 面积为 36 cm² 的正方形 - 两条直角边分别为 6 cm 和 8 cm 的直角三角形
Haruki 能做出哪些形状？
正确答案：D · 分值：1
用同分类同星级进入练习 →2026 AMC8 #4 · Algebra · ★
Brynn's savings decreased by 20% in July, then increased by 50% in August. Brynn's savings are now what percent of the original amount?
Brynn 的存款在七月减少了 20%，然后在八月增加了 50%。现在她的存款是原始金额的百分之多少？
正确答案：E · 分值：1
用同分类同星级进入练习 →2026 AMC8 #5 · Algebra · ★
Casey went on a road trip that covered 100 miles, stopping only for a lunch break along the way. The trip took 3 hours in total and her average speed while driving was 40 miles per hour. In minutes, how long was the lunch break?
Casey 进行了一次总路程为 100 英里的公路旅行，途中只停了一次吃午饭。整个旅程耗时 3 小时，她开车时的平均速度为每小时 40 英里。请问她的午餐休息了多长时间（以分钟计）？
正确答案：B · 分值：1
用同分类同星级进入练习 →2026 AMC8 #6 · Geometry · ★★
Peter lives near a rectangular field that is filled with blackberry bushes. The field is 10 meters long and 8 meters wide, and Peter can reach any blackberries that are within 1 meter of an edge of the field. The portion of the field he can reach is shaded in the figure below. What fraction of the area of the field can Peter reach?
Peter 住在一块长方形黑莓地附近。这块地长 10 米，宽 8 米。他能够采摘到距离地块边缘 1 米范围内的所有黑莓。下图中阴影部分表示他能到达的区域。他能到达的区域占整块地面积的几分之几？
正确答案：E · 分值：1
用同分类同星级进入练习 →2026 AMC8 #7 · Algebra · ★★
Mika would like to estimate how far she can ride a new model of electric bike on a fully charged battery. She completed two trips totaling 40 miles. The first trip used 1/2 of the total battery power, while the second trip used 3/10 of the total battery power. How many miles can this electric bike go on a fully charged battery?
Mika 想估算她新买的电动自行车充满电后最多能骑行多远。她完成了两次行程，总共骑行了 40 英里。第一次行程消耗了总电量的 1/2，第二次行程消耗了总电量的 3/10。这辆电动自行车充满电后最多能骑行多少英里？
正确答案：C · 分值：1
用同分类同星级进入练习 →2026 AMC8 #8 · Number Theory · ★★
A poll asked a number of people if they liked solving mathematics problems. Exactly 74% answered "yes." What is the fewest possible number of people who could have been asked the question?
一项民意调查询问若干人是否喜欢解数学题。恰好有 74% 的人回答“是”。最少可能有多少人接受了这项调查？
正确答案：D · 分值：1
用同分类同星级进入练习 →2026 AMC8 #9 · Algebra · ★★
What is the value of this expression?
以下表达式的值是多少？
正确答案：B · 分值：1
用同分类同星级进入练习 →2026 AMC8 #10 · Counting, Probability & Statistics · ★★
Five runners completed the grueling Xmarathon: Luke, Melina, Nico, Olympia, and Pedro.Nico finished 11 minutes behind Pedro.Olympia finished 2 minutes ahead of Melina, but 3 minutes behind Pedro.Olympia finished 6 minutes ahead of Luke.
Which runner finished fourth?
五名选手完成了艰苦的 X 马拉松比赛：Luke、Melina、Nico、Olympia 和 Pedro。已知：Nico 比 Pedro 晚了 11 分钟；Olympia 比 Melina 早 2 分钟，但比 Pedro 晚 3 分钟；Olympia 比 Luke 早 6 分钟。
谁是第四名？
正确答案：A · 分值：1
用同分类同星级进入练习 →2026 AMC8 #11 · Geometry · ★★★
Squares of side length 1, 1, 2, 3, and 5 are arranged to form the rectangle shown below. A curve is drawn by inscribing a quarter circle in each square and joining the quarter circles in order, from shortest to longest. What is the length of the curve?
边长分别为 1、1、2、3 和 5 的正方形被排列成如下所示的矩形。在每个正方形内画一个四分之一圆，并按从小到大的顺序将这些四分之一圆连接起来形成一条曲线。这条曲线的长度是多少？
正确答案：B · 分值：1
用同分类同星级进入练习 →2026 AMC8 #12 · Algebra · ★★★
In the figure below, each circle will be filled with a digit from 1 to 6. Each digit must appear exactly once. The sum of the digits in neighboring circles is shown in the box between them. What digit must be placed in the top circle?
下图中的每个圆圈需填入 1 到 6 中的一个数字，且每个数字恰好使用一次。相邻两个圆圈中的数字之和标在它们之间的方框中。顶部圆圈中必须填入哪个数字？
正确答案：D · 分值：1
用同分类同星级进入练习 →2026 AMC8 #13 · Geometry · ★★★
The figure below shows a tiling of 1×1 unit squares. Each row of unit squares is shifted horizontally by half a unit relative to the row above it. A shaded square is drawn on top of the tiling. Each vertex of the shaded square is a vertex of one of the unit squares. In square units, what is the area of the shaded square?
下图展示了一种由 1×1 单位正方形组成的铺砖图案。每一行相对于上一行水平偏移半个单位。图中还有一个覆盖在铺砖上的阴影正方形，其每个顶点都是某个单位正方形的顶点。这个阴影正方形的面积是多少（单位：平方单位）？
正确答案：A · 分值：1
用同分类同星级进入练习 →2026 AMC8 #14 · Algebra · ★★★
Jami picked three equally spaced integer numbers on the number line. The sum of the first and the second numbers is 40, while the sum of the second and third numbers is 60. What is the sum of all three numbers?
Jami 在数轴上选取了三个等间距的整数。第一个数与第二个数之和为 40，第二个数与第三个数之和为 60。这三个数的总和是多少？
正确答案：B · 分值：1
用同分类同星级进入练习 →2026 AMC8 #15 · Geometry · ★★★
Elijah has a large collection of identical wooden cubes which are white on 4 faces and gray on 2 faces that share an edge. He glues some cubes together face-to-face. The figure below shows 2 cubes being glued together, leaving 3 gray faces visible. What is the fewest number of cubes that he could glue together to ensure that no gray faces are visible, no matter how he rotates the figure?
Elijah 有很多相同的木制小立方体，每个立方体有 4 个白色面和 2 个灰色面，且这两个灰色面共享一条棱。他将一些立方体面对面粘在一起。下图展示了两个立方体粘合后，露出 3 个灰色面的情形。他至少需要粘合多少个小立方体，才能确保无论怎样旋转整个图形，都看不到任何灰色面？
正确答案：A · 分值：1
用同分类同星级进入练习 →2026 AMC8 #16 · Number Theory · ★★★
Consider all positive four-digit integers consisting of only even digits. What fraction of these integers are divisible by 4?
考虑所有由偶数数字组成的四位正整数。其中有多少比例的数能被 4 整除？
正确答案：D · 分值：1
用同分类同星级进入练习 →2026 AMC8 #17 · Counting, Probability & Statistics · ★★★
Four students are seated in a row. They chat with the people sitting next to them, then rearrange themselves so that they are no longer seated next to any of the same people. How many rearrangements are possible?
四名学生坐在一排。他们先和相邻的人聊天，然后重新排列座位，使得每个人都不再与之前相邻的人坐在一起。有多少种这样的重新排列方式？
正确答案：A · 分值：1
用同分类同星级进入练习 →2026 AMC8 #18 · Number Theory · ★★★
In how many ways can 60 be written as the sum of two or more consecutive odd positive integers that are arranged in increasing order?
有多少种方式可以将 60 表示为两个或更多个连续奇正整数（按递增顺序排列）的和？
正确答案：B · 分值：1
用同分类同星级进入练习 →2026 AMC8 #19 · Algebra · ★★★
Miguel is walking with his dog, Luna. When they reach the entrance to a park, Miguel throws a ball straight ahead and continues to walk at a steady pace. Luna sprints toward the ball, which stops by a tree. As soon as the dog reaches the ball, she brings it back to Miguel. Luna runs 5 times faster than Miguel walks. What fraction of the distance from the entrance to the tree will Miguel have walked when Luna returns the ball to him?
Miguel 带着他的狗 Luna 散步。当他们走到公园入口时，Miguel 向前扔出一个球并继续匀速行走。Luna 冲向球，球停在一棵树旁。Luna 一拿到球就立刻跑回 Miguel 身边。Luna 的奔跑速度是 Miguel 步行速度的 5 倍。当 Luna 把球送回给 Miguel 时，Miguel 已经走了从入口到树这段距离的几分之几？
正确答案：D · 分值：1
用同分类同星级进入练习 →2026 AMC8 #20 · Counting, Probability & Statistics · ★★★
The land of Catania uses gold coins and silver coins. Gold coins are 1 mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 8 mm tall using any arrangement of gold and silver coins, assuming order matters?
Catania 国使用金币和银币。金币厚 1 毫米，银币厚 3 毫米。Taylor 想用任意数量和顺序的金币与银币堆叠出一个总高为 8 毫米的硬币堆（顺序不同视为不同方式）。共有多少种堆法？
正确答案：D · 分值：1
用同分类同星级进入练习 →2026 AMC8 #21 · Counting, Probability & Statistics · ★★★
Charlotte the spider is walking along a web shaped like a 5-pointed star, shown in the figure below. The web has 5 outer points and 5 inner points. Each time Charlotte reaches a point, she randomly chooses a neighboring point and moves to that point. Charlotte starts at one of the outer points and makes 3 moves (re-visiting points is allowed). What is the probability she is now at one of the outer points of the star?
Charlotte 是一只蜘蛛，她在一张形如五角星的网上爬行（如下图所示）。这张网有 5 个外顶点和 5 个内顶点。每次 Charlotte 到达一个顶点时，会随机选择一个相邻顶点并移动过去（允许重复访问）。她从一个外顶点出发，共移动 3 次。此时她位于外顶点的概率是多少？
正确答案：B · 分值：1
用同分类同星级进入练习 →2026 AMC8 #22 · Counting, Probability & Statistics · ★★★★★
The integers from 1 to 25 are arbitrarily separated into five groups of 5 numbers each. The median of each group is identified. Let M equal the median of the five medians. What is the least possible value of M?
将 1 到 25 的整数任意分成五组，每组 5 个数。找出每组的中位数，再求这五个中位数的中位数 M。M 的最小可能值是多少？
正确答案：A · 分值：1
用同分类同星级进入练习 →2026 AMC8 #23 · Geometry · ★★★★
Lakshmi has 5 round coins of diameter 4 centimeters. She arranges the coins in 2 rows on a table top, as shown below, and wraps an elastic band tightly around them. In centimeters, what will be the length of the band?
Lakshmi 有 5 枚直径为 4 厘米的圆形硬币。她将这些硬币按如下方式在桌面上排成两行，并用一根橡皮筋紧紧围住它们。橡皮筋的长度是多少厘米？
正确答案：C · 分值：1
用同分类同星级进入练习 →2026 AMC8 #24 · Number Theory · ★★★★
The notation n! (read " factorial") is defined as the product of the first positive integers. (For example, .) Define the superfactorial of a positive number, denoted by , to be the product of the first factorials. (For example, .) How many factors of 7 appear in the prime factorization of , the superfactorial of 51?
记号 n!（读作" 阶乘"）定义为前 个正整数的乘积（例如 ）。定义超阶乘 为前 个阶乘的乘积（例如 ）。在 的质因数分解中，因子 7 出现了多少次？
正确答案：E · 分值：1
用同分类同星级进入练习 →2026 AMC8 #25 · Geometry · ★★★★
In an equiangular hexagon, all interior angles measure 120°. An example of such a hexagon with side lengths 2, 3, 1, 3, 2, and 2 is shown below, inscribed in equilateral triangle ABC. Consider all equiangular hexagons with positive integer side lengths that can be inscribed in △ABC, with all six vertices on the sides of the triangle. What is the total number of such hexagons? Hexagons that differ only by a rotation or a reflection are considered the same.
在一个等角六边形中，所有内角均为 120°。下图展示了一个边长依次为 2、3、1、3、2、2 的例子，它内接于一个等边三角形 ABC 中。考虑所有边长为正整数、且六个顶点都在 △ABC 三边上的等角六边形。若两个六边形仅通过旋转或反射重合，则视为相同。这样的六边形共有多少个？
正确答案：E · 分值：1
用同分类同星级进入练习 →