amcdrill | AMC8 AMC10 AMC12 Practice

Question 1

AMC8 2026 · Q1

What is the value of the following expression? $1+2-3+4+5-6+7+8-9+10+11-12$

以下表达式的值是多少？ $1+2-3+4+5-6+7+8-9+10+11-12$

(A) 18 18 (B) 21 21 (C) 24 24 (D) 27 27 (E) 30 30

Question 2

AMC8 2026 · Q3

Haruki has a piece of wire that is $24$ centimeters long. He wants to bend it to form each of the following shapes, one at a time: A regular hexagon with side length $5$ cm. A square with area $36 \hspace{3pt} \text{cm}^2$. A right triangle whose legs are $6$ and $8$ cm long. Which of the shapes can Haruki make?

春树有一段长为 $24$ 厘米的铁丝。他想将它弯成下列每一种形状，依次折成：边长为 $5$ 厘米的正六边形。面积为 $36 \hspace{3pt} \text{cm}^2$ 的正方形。两条直角边分别为 $6$ 厘米和 $8$ 厘米的直角三角形。春树能做出哪几种形状？

(A) \text{Triangle only} \hspace{3pt} \text{Triangle only} \\ (B) \text{Hexagon and square only} \hspace{3pt} \text{Hexagon and square only} \\ (C) \text{Hexagon and triangle only} \hspace{3pt} \text{Hexagon and triangle only} \\ (D) \text{Square and triangle only} \hspace{3pt} \text{Square and triangle only} \\ (E) \text{Hexagon, triangle, and square} \hspace{3pt} \text{Hexagon, triangle, and square}

Question 3

AMC8 2026 · Q6

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?

彼得住在一个长方形的田地附近，田地里长满了黑莓灌木。田地长10米，宽8米，彼得可以够得着离田地边缘1米以内的任何黑莓。田地中彼得能够够到的部分在下面的图中阴影部分所示。彼得能够够到的田地面积占田地总面积的几分之几？

(A) \frac{1}{6} \frac{1}{6} (B) \frac{1}{4} \frac{1}{4} (C) \frac{1}{3} \frac{1}{3} (D) \frac{3}{8} \frac{3}{8} (E) \frac{2}{5} \frac{2}{5}

Question 4

AMC8 2026 · Q9

What is the value of this expression? \[\frac{\sqrt{16\sqrt{81}}}{\sqrt{81\sqrt{16}}}\]

这个表达式的值是多少？ \[ \frac{\sqrt{16\sqrt{81}}}{\sqrt{81\sqrt{16}}} \]

(A) \hspace{3pt} \frac{4}{9} \hspace{19pt} \hspace{3pt} \frac{4}{9} \hspace{19pt} (B) \hspace{3pt} \frac{2}{3} \hspace{19pt} \hspace{3pt} \frac{2}{3} \hspace{19pt} (C) \hspace{3pt} 1 \hspace{19pt} \hspace{3pt} 1 \hspace{19pt} (D) \hspace{3pt} \frac{3}{2} \hspace{19pt} \hspace{3pt} \frac{3}{2} \hspace{19pt} (E) \hspace{3pt} \frac{9}{4} \hspace{3pt} \frac{9}{4}

Question 5

AMC8 2026 · Q14

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在线上选择了三个等间距的整数。第一个和第二个数的和是40，而第二个和第三个数的和是60。三个数的总和是多少？

(A) 70 70 (B) 75 75 (C) 80 80 (D) 85 85 (E) 90 90

Question 6

AMC8 2026 · Q15

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 有一大批相同的木制立方体，这些立方体有 4 个面为白色，2 个面为灰色，且这两个灰色面共用一条边。他将一些立方体面与面地粘在一起。下图显示了两个立方体被粘在一起，露出了 3 个灰色面。要确保无论如何旋转图形，都看不到灰色面，他最少需要粘多少个立方体？

(A) 4 4 (B) 6 6 (C) 8 8 (D) 9 9 (E) 27 27

Question 7

AMC8 2026 · Q16

Consider all positive four-digit integers consisting of only even digits. What fraction of these integers are divisible by $4$?

考虑所有只由偶数组成的正四位数。这些整数中有多少比例是能被 $4$ 整除的？

(A) \frac{1}{4} \frac{1}{4} (B) \frac{2}{5} \frac{2}{5} (C) \frac{1}{2} \frac{1}{2} (D) \frac{3}{5} \frac{3}{5} (E) \frac{3}{4} \frac{3}{4}

Question 8

AMC8 2026 · Q18

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?

有多少种方法可以将 $60$ 写成两个或两个以上递增排列的连续奇正整数的和？

(A) 1 1 (B) 2 2 (C) 3 3 (D) 4 4 (E) 5 5

Question 9

AMC8 2026 · Q21

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?

蜘蛛Charlotte在一个形状如下图所示的五角星形网线上行走。该网有5个外部顶点和5个内部顶点。每次Charlotte到达一个顶点时，都会随机选择一个相邻的顶点移动过去。Charlotte从一个外部顶点开始，进行3次移动（允许重复访问顶点）。她现在在五角星的某个外部顶点的概率是多少？

(A) \frac{1}{5} \frac{1}{5} (B) \frac{1}{4} \frac{1}{4} (C) \frac{2}{5} \frac{2}{5} (D) \frac{1}{2} \frac{1}{2} (E) \frac{3}{5} \frac{3}{5}

Question 10

AMC8 2026 · Q23

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 $5$ 个直径为 $4$ 厘米的圆形硬币。她将硬币如图所示，摆成两排放在桌面上，并用橡皮筋紧紧地围绕它们。橡皮筋的长度是多少厘米？

(A) 2\pi + 20 2\pi + 20 (B) \frac{5}{2}\pi + 20 \frac{5}{2}\pi + 20 (C) 4\pi + 20 4\pi + 20 (D) \frac{9}{2}\pi + 20 \frac{9}{2}\pi + 20 (E) 9\pi + 20 9\pi + 20

Diagnostic - AMC8