amcdrill | AMC8 AMC10 AMC12 Practice

Q1

How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.)

需要多少平方码的地毯来覆盖一个长12英尺、宽9英尺的矩形地板？（1码=3英尺。）

(A) 12 12 (B) 36 36 (C) 108 108 (D) 324 324 (E) 972 972

Q2

Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of side AB. What fraction of the area of the octagon is shaded?

点O是正八边形ABCDEFGH的中心，X是边AB的中点。阴影部分占八边形面积的几分之几？

(A) $\frac{11}{32}$ $\frac{11}{32}$ (B) $\frac{3}{8}$ $\frac{3}{8}$ (C) $\frac{13}{32}$ $\frac{13}{32}$ (D) $\frac{7}{16}$ $\frac{7}{16}$ (E) $\frac{15}{32}$ $\frac{15}{32}$

Q3

Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of 10 miles per hour. Jack walks to the pool at a constant speed of 4 miles per hour. How many minutes before Jack does Jill arrive?

杰克和吉尔要去离家一英里的游泳池游泳。他们同时出发。吉尔骑自行车以10英里/时的恒定速度去游泳池。杰克以4英里/时的恒定速度步行去游泳池。吉尔比杰克早多少分钟到达？

(A) 5 5 (B) 6 6 (C) 8 8 (D) 9 9 (E) 10 10

Q4

The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?

Centerville中学的象棋队由两名男孩和三名女孩组成。摄影师想为当地报纸拍摄团队照片。她决定让他们坐成一排，两端各坐一名男孩，中间坐三名女孩。有多少种这样的排列方式？

(A) 2 2 (B) 4 4 (C) 5 5 (D) 6 6 (E) 12 12

Q5

Billy's basketball team scored the following points over the course of the first 11 games of the season: 42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73. If his team scores 40 in the 12th game, which of the following statistics will show an increase?

比利的篮球队在前11场比赛中得分如下：42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73。如果第12场比赛得分40，以下哪项统计量会增加？

(A) range 极差 (B) median 中位数 (C) mean 平均数 (D) mode 众数 (E) mid-range 中程数

Q6

In $\triangle ABC$, $AB = BC = 29$, and $AC = 42$. What is the area of $\triangle ABC$?

在 $\triangle ABC$ 中，$AB = BC = 29$，$AC = 42$。$\triangle ABC$ 的面积是多少？

(A) 100 100 (B) 420 420 (C) 500 500 (D) 609 609 (E) 701 701

Q7

Each of two boxes contains three chips numbered 1, 2, 3. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?

有两个盒子，每个盒子里有编号为 1、2、3 的三个筹码。从每个盒子随机抽取一个筹码，将两个筹码上的数字相乘。它们的乘积为偶数的概率是多少？

(A) $\frac{1}{9}$ $\frac{1}{9}$ (B) $\frac{2}{9}$ $\frac{2}{9}$ (C) $\frac{4}{9}$ $\frac{4}{9}$ (D) $\frac{1}{2}$ $\frac{1}{2}$ (E) $\frac{5}{9}$ $\frac{5}{9}$

Q8

What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19?

有一个边长为 5 和边长为 19 的三角形，其周长的上确界（大于该周长的最小整数）是多少？

(A) 24 24 (B) 29 29 (C) 43 43 (D) 48 48 (E) 57 57

Q9

On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 20 days?

Janabel 第一天工作卖了 1 个小部件。第二天卖了 3 个。第三天卖了 5 个，此后每天比前一天多卖 2 个小部件。工作 20 天后，Janabel 总共卖了多少个小部件？

(A) 39 39 (B) 40 40 (C) 210 210 (D) 400 400 (E) 401 401

Q10

How many integers between 1000 and 9999 have four distinct digits?

1000 到 9999 之间有多少个四位数具有四个不同数字？

(A) 3024 3024 (B) 4536 4536 (C) 5040 5040 (D) 6480 6480 (E) 6561 6561

Q11

In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "AMCS"?

在数学乐园这个小国，所有汽车车牌都有四个符号。第一个必须是元音（A、E、I、O 或 U），第二和第三个必须是21个非元音字母中的两个不同字母，第四个必须是数字（0 到 9）。如果这些符号是按照这些条件随机选择的，那么车牌显示“AMCS”的概率是多少？

(A) $\frac{1}{22,050}$ $\frac{1}{22050}$ (B) $\frac{1}{21,000}$ $\frac{1}{21000}$ (C) $\frac{1}{10,500}$ $\frac{1}{10500}$ (D) $\frac{1}{2,100}$ $\frac{1}{2100}$ (E) $\frac{1}{1,050}$ $\frac{1}{1050}$

Q12

How many pairs of parallel edges, such as $\overline{AB}$ and $\overline{GH}$ or $\overline{EH}$ and $\overline{FG}$, does a cube have?

一个立方体有多少对平行边，例如 $\overline{AB}$ 和 $\overline{GH}$ 或 $\overline{EH}$ 和 $\overline{FG}$？

(A) 6 6 (B) 12 12 (C) 18 18 (D) 24 24 (E) 36 36

Q13

How many subsets of two elements can be removed from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$ so that the mean (average) of the nine remaining numbers is 6?

从集合 $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$ 中移除多少个两元素子集，使得剩余九个数的平均数（均值）为6？

(A) 1 1 (B) 2 2 (C) 3 3 (D) 5 5 (E) 6 6

Q14

Which of the following integers cannot be written as the sum of four consecutive odd integers?

以下哪个整数不能表示为四个连续奇整数的和？

(A) 16 16 (B) 40 40 (C) 72 72 (D) 100 100 (E) 200 200

Q15

At Euler Middle School, 198 students voted on two issues in a school referendum with the following results: 149 voted in favor of the first issue and 119 voted in favor of the second issue. If there were exactly 29 students who voted against both issues, how many students voted in favor of both issues?

在欧拉中学，有198名学生在学校公投中对两个议题进行了投票，结果如下：149人赞成第一个议题，119人赞成第二个议题。如果恰好有29名学生反对两个议题，那么有多少名学生赞成两个议题？

(A) 49 49 (B) 70 70 (C) 79 79 (D) 99 99 (E) 149 149

Q16

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\frac{1}{5}$ of all the ninth graders are paired with $\frac{2}{3}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

在中学导师计划中，一些六年级学生与九年级学生配对成为伙伴。没有九年级学生被分配超过一个六年级伙伴。如果所有九年级学生的 $\frac{1}{5}$ 与所有六年级学生的 $\frac{2}{3}$ 配对，那么六年级和九年级学生总数中有多少分数的人有伙伴？

(A) $\frac{2}{15}$ $\frac{2}{15}$ (B) $\frac{4}{11}$ $\frac{4}{11}$ (C) $\frac{11}{30}$ $\frac{11}{30}$ (D) $\frac{3}{8}$ $\frac{3}{8}$ (E) $\frac{11}{15}$ $\frac{11}{15}$

Q17

Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?

杰里米的父亲在高峰期交通中开车送他上学用20分钟。有一天没有交通，所以父亲可以比平时快18英里每小时，并在12分钟内送他到学校。到学校有多远（英里）？

(A) 4 4 (B) 6 6 (C) 8 8 (D) 9 9 (E) 12 12

Q18

Each row and each column in this 5 × 5 array is an arithmetic sequence with five terms. What is the value of X?

这个5×5阵列中，每行和每列都是一个五项等差数列。X的值是多少？

(A) 21 21 (B) 31 31 (C) 36 36 (D) 40 40 (E) 42 42

Q19

A triangle with vertices at A = (1, 3), B = (5, 1), and C = (4, 4) is plotted on a 6 × 5 grid. What fraction of the grid is covered by the triangle?

一个顶点在 A = (1, 3)、B = (5, 1) 和 C = (4, 4) 的三角形绘制在6×5网格上。三角形覆盖网格的几分之几？

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

Q20

Ralph went to the store and bought 12 pairs of socks for a total of \$24. Some of the socks he bought cost \$1 a pair, some of the socks he bought cost \$3 a pair, and some of the socks he bought cost \$4 a pair. If he bought at least one pair of each type, how many pairs of \$1 socks did Ralph buy?

拉尔夫去商店买了12双袜子，总共24美元。他买的一些袜子每双1美元，一些每双3美元，一些每双4美元。如果他至少买了每种各一双，拉尔夫买了多少双1美元的袜子？

(A) 4 4 (B) 5 5 (C) 6 6 (D) 7 7 (E) 8 8

Q21

In the given figure hexagon ABCDEF is equiangular, ABJI and FEHG are squares with areas 18 and 32 respectively, △JBK is equilateral and FE = BC. What is the area of △KBC?

在给定的图形中，六边形ABCDEF是等角的，ABJI和FEHG是面积分别为18和32的正方形，△JBK是等边三角形，且FE = BC。△KBC的面积是多少？

(A) $6\sqrt{2}$ $6\sqrt{2}$ (B) 9 9 (C) 12 12 (D) $9\sqrt{2}$ $9\sqrt{2}$ (E) 32 32

Q22

On June 1, a group of students is standing in rows, with 15 students in each row. On June 2, the same group is standing with all of the students in one long row. On June 3, the same group is standing with just one student in each row. On June 4, the same group is standing with 6 students in each row. This process continues through June 12 with a different number of students per row each day. However, on June 13, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?

6月1日，一群学生排成每行15人的行。6月2日，同一群学生排成一行长行。6月3日，同一群学生排成每行仅一人。6月4日，同一群学生排成每行6人。此过程持续到6月12日，每天每行学生数不同。然而，6月13日，他们找不到新的组织方式。该群学生的最小可能人数是多少？

(A) 21 21 (B) 30 30 (C) 60 60 (D) 90 90 (E) 1080 1080

Q23

Tom has twelve slips of paper which he wants to put into five cups labeled A, B, C, D, E. He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from A to E. The numbers on the papers are 2, 2, 2, 2.5, 2.5, 3, 3, 3, 3, 3.5, 4, and 4.5. If a slip with 2 goes into cup E and a slip with 3 goes into cup B, then the slip with 3.5 must go into what cup?

Tom有十二张纸条，他想放入标有A、B、C、D、E的五个杯子中。他希望每个杯子中纸条数字之和为整数。而且，他希望这五个整数从A到E连续递增。纸条上的数字是2、2、2、2.5、2.5、3、3、3、3、3.5、4和4.5。如果一张2的纸条放入杯子E，一张3的纸条放入杯子B，那么3.5的纸条必须放入哪个杯子？

(A) A A (B) B B (C) C C (D) D D (E) E E

Q24

A baseball league consists of two four-team divisions. Each team plays every other team in its division N games. Each team plays every team in the other division M games with N > 2M and M > 4. Each team plays a 76 game schedule. How many games does a team play within its own division?

一个棒球联盟由两个四队分组成。每个队与其分内其他队各打N场比赛。每个队与另一分的所有队各打M场比赛，其中N > 2M且M > 4。每个队打76场比赛的赛程。一个队在其本分内打多少场比赛？

(A) 36 36 (B) 48 48 (C) 54 54 (D) 60 60 (E) 72 72

Q25

One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?

从这个5英寸正方形的四个角上切下1英寸正方形。能放入剩余空间的最大正方形的面积（平方英寸）是多少？

(A) 9 9 (B) $12\frac{1}{2}$ $12\frac{1}{2}$ (C) 15 15 (D) $15\frac{1}{2}$ $15\frac{1}{2}$ (E) 17 17

AMC8 2015