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2023 AMC8 #2 · Geometry · ★★
A square piece of paper is folded twice into four equal quarters, as shown below, then cut along the dashed line. When unfolded, the paper will match which of the following figures?
如下图所示，将一张正方形纸对折两次，变成四等分，然后沿虚线裁剪。问这张纸展开后会是下面哪个图形？

正确答案：E · 分值：1

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2023 AMC8 #3 · Algebra · ★
Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation:
(wind chill)=(air temperature)−0.7×(wind speed)(\text{wind chill}) = (\text{air temperature}) - 0.7 \times (\text{wind speed})
where temperature is measured in degrees Fahrenheit (∘F^{\circ}\mathrm{F}) and wind speed is measured in miles per hour (mph). Suppose the air temperature is 36∘F36^{\circ}\mathrm{F} and the wind speed is 18 mph. Which of the following is closest to the approximate wind chill?
风寒指数衡量人们在室外受风时感受到的寒冷程度。可用下面的关系式较好地估算风寒指数：
(风寒指数)=(气温)−0.7×(风速)\text{(风寒指数)} = \text{(气温)} - 0.7 \times \text{(风速)}
其中气温以华氏度（∘F^{\circ}\mathrm{F}）计量，风速以英里每小时（mph）计量。设气温为 36∘F36^{\circ}\mathrm{F}，风速为 18 mph。下列哪一项最接近此时的风寒指数？

正确答案：B · 分值：1

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2023 AMC8 #4 · Number Theory · ★★
The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below. Consider the four numbers that will appear in the shaded squares, on the same diagonal as the number 7. How many of these four numbers are prime?
在正方形方格表上，数 1 到 49 从中心开始，按螺旋式方式排列。前面几个数已经填入到下面的方格表中。考虑与数 7 出现在同一个对角线上的阴影方格中的四个数。问这四个数中有几个质数？

正确答案：D · 分值：1

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2023 AMC8 #5 · Algebra · ★
A lake contains 250 trout, along with a variety of other fish. When a marine biologist catches and releases a sample of 180 fish from the lake, 30 are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?
湖里有 250 条鳟鱼，以及其他一些鱼类。当一位海洋生物学家从湖中捕获并释放 180 条鱼的样本时，他发现其中 30 条鱼是鳟鱼。假设在样本中鳟鱼所占的比例和湖里鳟鱼在全部鱼类中所占的比例相同。问湖里有多少条鱼？

正确答案：B · 分值：1

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2023 AMC8 #6 · Algebra · ★★
The digits 2, 0, 2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the expression?
将数字2，0，2，3填入下面的表达式中，每个方框内填一个数字．问表达式的最大可能值是多少?

正确答案：C · 分值：1

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2023 AMC8 #7 · Geometry · ★★
A rectangle, with sides parallel to the x-axis and y-axis, has opposite vertices at (15, 3) and (16, 5). A line is drawn through A(0,0) and B(3,1). Another line is drawn through C(0,10) and D(2,9). How many points on the rectangle lie on at least one of the two lines?
有一个矩形，它的边平行于 x 轴和 y轴，两个相对的顶点分别是（15，3）与（16，5）。过点 A(0,0) 与 B(3,1) 作一条直线，再过点 C(0,10) 与 D(2,9) 作另一条直线。问矩形的边界上有多少个点落在两条直线中至少一条上？

正确答案：B · 分值：1

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2023 AMC8 #8 · Counting, Probability & Statistics · ★★
Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three players exactly twice. Shown below are the win-loss records for the players. The numbers 1 and 0 represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo’s win-loss record?
Lola，Lolo，Tiya，Tiyo参加一场乒乓球锦标赛．每名选手与其他三名选手中的每个人比赛恰好两次. 下面显示的是选手的胜负记录. 数字1和0分别代表赢或输. 例如Lola一共赢了五场比赛，第四场比赛输了. 问Tiyo的胜负记录是怎样的?

正确答案：A · 分值：1

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2023 AMC8 #9 · Counting, Probability & Statistics · ★
Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she skis along a trail. In total, how many seconds does she spend at an elevation between 4 and 7 meters?
正在山上滑雪下图显示了她沿着小径滑雪时以山脚为基准的海拔高度 (单位为米)．问她在4米到7米之间的高度共停留了多少秒？

正确答案：B · 分值：1

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2023 AMC8 #10 · Algebra · ★★
Harold made a plum pie to take on a picnic. He was able to eat only 14\displaystyle \frac{1}{4} of the pie, and he left the rest for his friends. A moose came by and ate 13\displaystyle \frac{1}{3} of what Harold left behind. After that, a porcupine ate 13\displaystyle \frac{1}{3} of what the moose left behind. How much of the original pie still remained after the porcupine left?
Harold 做了一个李子派带去野餐。他只吃了这个派的 14\displaystyle \frac{1}{4}，剩下的留给他的朋友们。一只驼鹿经过，吃掉了 Harold 剩下的 13\displaystyle \frac{1}{3}。在那之后，一只豪猪吃掉了驼鹿剩下的派的 13\displaystyle \frac{1}{3}。问豪猪走后，原来的派还剩下多少？

正确答案：D · 分值：1

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2023 AMC8 #11 · Algebra · ★★★
NASA's Perseverance Rover was launched on July 30, 2020. After traveling 292,526,838292{,}526{,}838 miles, it landed on Mars in Jezero Crater about 6.5 months later. Which of the following is closest to the Rover's average interplanetary speed in miles per hour?
美国国家航空航天局（NASA）的「毅力号」火星车于 2020 年 7 月 30 日发射。它在飞行了 292,526,838 英里后，于大约 6.5 个月后着陆在火星的耶泽罗陨石坑。以下哪一个选项最接近毅力号在星际航行中的平均速度（英里每小时）？

正确答案：C · 分值：1

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2023 AMC8 #12 · Geometry · ★★★
The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What fraction of the interior of the large white circle is shaded?
如图所示，在一个大的白色圆圈内部有许多较小的白色和灰色圆圈．问灰色部分在大的白色圆圈内部所占的比例是多少？

正确答案：B · 分值：1

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2023 AMC8 #13 · Algebra · ★★★
Along the route of a bicycle race, 7 water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also 2 repair stations evenly spaced between the start and finish lines. The 3rd water station is located 2 miles after the 1st repair station. How long is the race in miles?
如下图所示，在自行车比赛路线的起点和终点之间均匀分布着7个饮用水补给站. 另外，在起点和终点之间还均匀分布着2个维修站.第三个饮用水补给站在第一个维修站后2英里处：问比赛的全程是多少英里？

正确答案：D · 分值：1

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2023 AMC8 #14 · Number Theory · ★★★
Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas would like to cover the package with a large number of stamps. Suppose he has a collection of 5-cent, 10-cent, and 25-cent stamps, with exactly 20 of each type. What is the greatest number of stamps Nicolas can use to make exactly $7.10 in postage?
(Note: The amount $7.10 corresponds to 7 dollars and 10 cents. One dollar is worth 100 cents.)
Nicolas计划将一个包裹寄给爱好集邮的朋友Anton．为了支付邮资，Nicolas准备在包裹上贴大量的邮票．假设他有5美分，10美分，25美分的邮票，每种邮票恰好各有20张. Nicolas最多可以使用多少张邮票来恰好支付$7.10的邮资？ (注意：金额$7.10是指7美元10美分, 1美元是100美分.)

正确答案：E · 分值：1

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2023 AMC8 #15 · Algebra · ★★★
Viswam walks half a mile to get to school each day. His route consists of 10 city blocks of equal length and he takes 1 minute to walk each block. Today, after walking 5 blocks, Viswam discovers he has to make a detour, walking 3 blocks of equal length instead of 1 block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk in order to get to school at his usual time?
Viswam 每天要步行半英里去上学，他上学的路线由 10 个等长的街区组成，每走 1 个街区需要一分钟。今天，在走了 5 个街区后，Viswam 发现他必须绕路：要走 3 个等长的街区而不是 1 个街区才能到达下一个交叉路口。从他绕行开始，Viswam 必须以每小时多少英里的速度步行，才能像平常一样准时到校？

正确答案：B · 分值：1

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2023 AMC8 #16 · Algebra · ★★★
The letters P\text{P}, Q\text{Q}, and R\text{R} are entered into a 20×2020\times 20 table according to the pattern shown below. How many P\text{P}'s, Q\text{Q}'s, and R\text{R}'s will appear in the completed table?
将字母 P\text{P}、Q\text{Q}、R\text{R} 按下图所示的规律填入 20×2020\times 20 的方格表中。问在完成的表中，各会出现多少个 P\text{P}、多少个Q\text{Q}、多少个R\text{R}？

正确答案：C · 分值：1

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2023 AMC8 #17 · Geometry · ★★★
A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regular octahedron shown on the right by folding the piece of paper shown on the left. Which numbered face will end up to the right of QQ?
正八面体有八个面，都是等边三角形，在每个顶点处有四个面相交。如图所示，Jun 把左边的纸片折成了右边的正八面体。问出现在 Q 的右边的那个面上的数是几？

正确答案：A · 分值：1

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2023 AMC8 #18 · Number Theory · ★★★
Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump 5 pads to the right or 3 pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located 2023 pads to the right of her starting position?
蚱锰Greta坐在池塘里一排长长的睡莲叶上：从任何睡莲叶出发，Greta都可以向右跳5个叶片或者向左跳3个叶片. 问Greta最少跳多少次才能到达位于她起始位置右侧的第2023片睡莲叶上？

正确答案：D · 分值：1

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2023 AMC8 #19 · Geometry · ★★★
An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below. The side length of the inner triangle is 23\displaystyle \frac{2}{3} the side length of the larger triangle. What is the ratio of the area of one trapezoid to the area of the inner triangle?
如图所示，一个等边三角形在另一个更大的等边三角形内部，它们之间的区域可以分成三个全等的梯形．内部三角形的边长是大三角形边长的23\displaystyle \frac{2}{3}，问一个梯形的面积与内部三角形的面积之比是多少？

正确答案：C · 分值：1

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2023 AMC8 #20 · Counting, Probability & Statistics · ★★★
Two integers are inserted into the list 3, 3, 8, 11, 28 to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?
将两个整数加入数据列表3，3，8，11，28使得它的极差加倍，而众数和中位数保持不变．问所添加的两个数之和的最大可能值是多少？

正确答案：D · 分值：1

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2023 AMC8 #21 · Counting, Probability & Statistics · ★★★★
Alina writes the numbers 1,2,…,91, 2, \dots, 9 on separate cards, one number per card. She wishes to divide the cards into 3 groups of 3 cards so that the sum of the numbers in each group will be the same. In how many ways can this be done?
Alina将数1,2,…,91, 2, \dots, 9写在不同的卡片上，每张卡片上有一个数.她希望将卡片分成3组，每组3张卡片，使得每组中的各数之和相同. 问有多少种这样的分组方法?

正确答案：C · 分值：1

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2023 AMC8 #22 · Number Theory · ★★★★
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is 4000. What is the first term?
在一个正整数数列中，第二项之后的每一项都是前面两项的乘积. 数列中的第六项是4000. 问第一项是多少?

正确答案：D · 分值：1

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2023 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Each square in a 3×33\times 3 grid is randomly filled with one of the 4 gray and white tiles shown below on the right. What is the probability that the tiling will contain a large gray diamond in one of the smaller 2×22\times 2 grids? Below is an example of such a tiling.
将3×3方格表中的每个小方格随机的用如下图左侧所示的4个灰白双色方块之一嵌入，有一个大灰色菱形将出现在某个2×2子方格表中的概率是多少？一个这样的镶嵌方案的例子如下图右侧所示，

正确答案：C · 分值：1

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2023 AMC8 #24 · Geometry · ★★★★
Isosceles triangle ABCABC has equal side lengths ABAB and BCBC. In the figures below, segments are drawn parallel to AC‾\overline{AC} so that the shaded portions of △ABC\triangle ABC have the same area. The heights of the two unshaded portions are 11 and 5 units, respectively. What is the height hh of △ABC\triangle ABC?
在等腰三角形ABC中，边AB和BC的长度相等．在下图中，由平行于AC的线段形成的△ABC中的两个阴影部分具有相同的面积. 两个空白部分的高度分别为 11和5. 问△ABC的高h是多少?

正确答案：A · 分值：1

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2023 AMC8 #25 · Algebra · ★★★★
Fifteen integers a1,a2,…,a15a_1, a_2, \dots, a_{15} are arranged in order on a number line. The integers are equally spaced and have the property that
1≤a1≤10,13≤a2≤20,and241≤a15≤250.1 \le a_1 \le 10,\quad 13 \le a_2 \le 20,\quad \text{and}\quad 241 \le a_{15} \le 250.
What is the sum of the digits of a14a_{14}?
十五个整数 a1,a2,…,a15a_1,a_2,\dots,a_{15}依次排列在数轴上．这些整数呈等距排列，并且具有以下特性
1≤a1≤10,13≤a2≤20,241≤a15≤250.1 \le a_1 \le 10,\quad 13 \le a_2 \le 20,\quad 241 \le a_{15} \le 250.
问 a14a_{14} 的各位数字之和是多少？

正确答案：A · 分值：1

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