2025 AMC amc8 真题 答案 详解

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中英双语真题

2025 MAA AMC 8

Problem 1.

Lucius is counting backward by 7s. His first three numbers are 100, 93, and 86. What is his 9th number?

Lucius 按每次倒数 7 的方式数数。他的前三个数是 100、93 和 86。问他数的第 9 个数是多少？

(A) 30
(B) 37
(C) 42
(D) 44
(E) 47

Problem 2.

The eight-point star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4-by-4 grid is covered by the star?

如下图所示的八角星是流行的拼布图案。问这颗星覆盖了整个 4×4 网格的百分之多少？

(A) 40
(B) 50
(C) 60
(D) 75
(E) 80

Problem 3.

100,000	10,000	1,000	100	10	1

The table above shows the ancient Egyptian hieroglyphs that were used to represent

英文真题

2025 AMC 8 Problems

Problem 1

The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4\times 4$ grid is covered by the star?

(A) 40 (B) 50 (C) 60 (D) 75 (E) 80

Problem 2

The table below shows the Ancient Egyptian hieroglyphs that were used to represent different numbers.

For example, the number 32 was represented by the hieroglyphs . What number is represented by the following combination of hieroglyphs?

(A) 1,423 (B) 10,423 (C) 14,023 (D) 14,203 (E) 14,230

Problem 3

Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the game. When Annika and 3 of her friends play Buffalo Shuffle-o, each player is dealt 15 cards. Suppose 2 more friends join the next game. How many cards will be dealt to each player?

(A) 8 (B) 9 (C) 10 (D) 11 (E) 12

Problem 4

Lucius is counting backward by 7's. His first three numbers are 100, 93, and 86. What is his 10th number?

(A) 30 (B) 37 (C) 42 (D) 44 (E) 47

Problem 5

Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory (labeled F) and drives to location A, then B, then C, before returning to F. What is the shortest distance, in blocks, she can drive to complete the route?

真题文字详解(英文)

Problem 1 The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4\times 4$ grid is covered by the star?
(A) 40 (B) 50 (C) 60 (D) 75 (E) 80

Solution 1 Each of the unshaded triangles has base length 2 and height 1, so they all have area $\frac{2\cdot 1}{2}=1$. Each of the unshaded unit squares has area 1. The area of the shaded region is equal to the area of the entire grid minus the area of the unshaded region, or $4^2-4\cdot 1-4\cdot 1=8$. The star is then $\frac{8}{16}=\frac{1}{2}=\frac{50}{100}$, or (B) 50 percent of the entire grid. ~cxsmi

Solution 2 There are 16 total squares in the diagram and each square has 2 triangles whose areas are half the area of a unit square. Thus, the total number of triangles in the diagram is $4^2\cdot 2=32$ triangles. There are 16 shaded triangles in the diagram, so the area of the star is $\frac{16}{32}=\frac{1}{2}=\frac{50}{100}$, or (B) 50 percent. ~Pi_in_da_box

Solution 3 There are 4 squares that are entirely shaded and 4 squares that have no shading. The rest of the squares are half-half. Therefore the shaded region is (B) 50 percent of the grid.

Solution 4 Note that we can move one triangle from each of the four cells in the middle to each of the four corners. This will leave every cell in the grid with one triangle each, and each triangle has an area of half the area of each cell. Thus, our answer must equal to $\frac12$, and so our answer is (B) 50. ~derekwang2048

Solution 5

真题文字详解(中英双语)

Problem 1 The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4\times 4$ grid is covered by the star? 下图所示，八角星是一个流行的quilting图案。这个星形占整个$4\times 4$网格的百分之多少？
(A) 40 (B) 50 (C) 60 (D) 75 (E) 80

Solution 1 Each of the unshaded triangles has base length 2 and height 1, so they all have area $\frac{2\cdot1}{2}=1$. Each of the unshaded unit squares has area 1. The area of the shaded region is equal to the area of the entire grid minus the area of the unshaded region, or $4^2-4\cdot1-4\cdot1=8$. The star is then $\frac{8}{16}=\frac12=\frac{50}{100}$, or (B) 50 percent of the entire grid. ~cxsmi 每个未着色的三角形都有2的底边长度和1的高度，所以它们都有$\frac{2\cdot1}{2}=1$的面积。每个未着色的单位正方形都有1的面积。着色区域的面积等于整个网格的面积减去未着色区域的面积，即$4^2-4\cdot1-4\cdot1=8$。然后星形是$\frac{8}{16}=\frac12=\frac{50}{100}$，即(B) 50百分比之整个网格。~cxsmi

Solution 2 There are 16 total squares in the diagram and each square has 2 triangles whose areas are half the area of a unit square. Thus, the total number of triangles in the diagram is $4^2\cdot2=32$ triangles. There are 16 shaded triangles in the diagram, so the area of the star is $\frac{16}{32}=\frac12=\frac{50}{100}$, or (B) 50 percent. ~Pi_in_da_box 图中共有16个正方形，每个正方形有2个三角形，这些三角形的面积是单位正方形面积的一半。因此，图中三角形的总数是$4^2\cdot2=32$个。图中还有16个阴影三角形，所以星形的面积是$\frac{16}{32}=\frac12=\frac{50}{100}$，即(B) 50百分比。~Pi_in_da_box

Solution 3