amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?

Rachelle 用 3 磅肉做 8 个汉堡给家人。她需要多少磅肉来为社区野餐做 24 个汉堡？

(A) 6 6 (B) $6\frac{2}{3}$ $6\frac{2}{3}$ (C) $7\frac{1}{2}$ $7\frac{1}{2}$ (D) 8 8 (E) 9 9

Q2

In the county of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?

在 East Westmore 县，统计学家估计每 8 小时出生一个婴儿，每天死亡一人。每年 East Westmore 人口增加多少人？（四舍五入到百位）

(A) 600 600 (B) 700 700 (C) 800 800 (D) 900 900 (E) 1000 1000

Q3

On February 13 The Oshkosh Northwestern listed the length of daylight as 10 hours and 24 minutes, the sunrise as 6:57 AM, and the sunset as 8:15 PM. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?

2 月 13 日，Oshkosh Northwestern 报上说白天长度为 10 小时 24 分钟，日出为上午 6:57，日落为晚上 8:15。白天长度和日出时间正确，但日落时间错了。太阳真正何时落下？

(A) 5:10 PM 下午 5:10 (B) 5:21 PM 下午 5:21 (C) 5:41 PM 下午 5:41 (D) 5:57 PM 下午 5:57 (E) 6:03 PM 下午 6:03

Q4

Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?

Peter 一家晚餐点了 12 片比萨。Peter 吃了一片，并与弟弟 Paul 平分另一片。Peter 吃了比萨的几分之几？

(A) $\frac{1}{24}$ $\frac{1}{24}$ (B) $\frac{1}{12}$ $\frac{1}{12}$ (C) $\frac{1}{8}$ $\frac{1}{8}$ (D) $\frac{1}{6}$ $\frac{1}{6}$ (E) $\frac{1}{4}$ $\frac{1}{4}$

Q5

In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is $X$, in centimeters?

在图中，所有角都是直角，边长以厘米为单位给出。注意图未按比例绘制。$X$ 是多少厘米？

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

Q6

A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?

一张矩形照片放置在一个四周边框宽度为2英寸的相框中。照片的高度为8英寸，宽度为10英寸。边框的面积是多少平方英寸？

(A) 36 36 (B) 40 40 (C) 64 64 (D) 72 72 (E) 88 88

Q7

Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of at least 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized that she could still reach her goal. What is the lowest possible score she could have made on the third test?

伊莎贝拉在数学课上必须参加四次满分100分的测试。她的目标是测试平均分至少95分。她前两次测试分数分别是97和91。在看到第三次测试分数后，她意识到自己仍然能达到目标。她第三次测试的最低可能分数是多少？

(A) 90 90 (B) 92 92 (C) 95 95 (D) 96 96 (E) 97 97

Q8

A shop advertises that everything is “half price in today’s sale.” In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage discount off the original price?

一家商店宣传“今日特卖一切商品半价”。此外，一张优惠券在特卖价基础上再打8折。使用优惠券，今天的价格相对于原价是多少折扣百分比？

(A) 10 10 (B) 33 33 (C) 40 40 (D) 60 60 (E) 70 70

Q9

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

沃思堡动物园有一些两腿鸟类和一些四腿哺乳动物。玛吉一次参观时数到200个头和522条腿。玛吉数到的动物中有多少是两腿鸟类？

(A) 61 61 (B) 122 122 (C) 139 139 (D) 150 150 (E) 161 161

Q10

How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?

使用数字2012的四个数字，有多少个大于1000的四位数？

(A) 6 6 (B) 7 7 (C) 8 8 (D) 9 9 (E) 12 12

Q11

The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, $x$ are all equal. What is the value of $x$?

正整数 3, 4, 5, 6, 6, 7, $x$ 的均值、中位数和唯一众数都相等。$x$ 的值为多少？

(A) 5 5 (B) 6 6 (C) 7 7 (D) 11 11 (E) 12 12

Q12

What is the units digit of $13^{2012}$?

$13^{2012}$ 的个位数是多少？

(A) 1 1 (B) 3 3 (C) 5 5 (D) 7 7 (E) 9 9

Q13

Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43. Sharona bought some of the same pencils and paid $1.87. How many more pencils did Sharona buy than Jamar?

贾马尔在学校书店买了一些每支超过一美分的铅笔，共支付 $1.43。莎罗娜买了一些同样的铅笔，支付 $1.87。莎罗娜比贾马尔多买了多少支铅笔？

(A) 2 2 (B) 3 3 (C) 4 4 (D) 5 5 (E) 6 6

Q14

In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?

在 BIG N 中学足球联盟中，每支队伍与其他每支队伍正好比赛一次。2012 赛季总共进行了 21 场联盟比赛，BIG N 联盟有多少支队伍？

(A) 6 6 (B) 7 7 (C) 8 8 (D) 9 9 (E) 10 10

Q15

The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?

大于 2 的最小数，除以 3、4、5 或 6 余数均为 2，它位于什么数之间？

(A) 40 and 50 40 和 50 (B) 51 and 55 51 和 55 (C) 56 and 60 56 和 60 (D) 61 and 65 61 和 65 (E) 66 and 99 66 和 99

Q16

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?

将数字0、1、2、3、4、5、6、7、8、9各使用一次，组成两个五位数，使得它们的和尽可能大。以下哪一个可能是其中一个数？

(A) 76531 76531 (B) 86724 86724 (C) 87431 87431 (D) 96240 96240 (E) 97403 97403

Q17

A square with an integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?

一个边长为整数的正方形被切成10个边长均为整数的小正方形，其中至少8个面积为1。原正方形边长的最小可能值是多少？

(A) 3 3 (B) 4 4 (C) 5 5 (D) 6 6 (E) 7 7

Q18

What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?

最小的既非质数又非平方数，且没有小于50的质因数的正整数是多少？

(A) 3127 3127 (B) 3133 3133 (C) 3137 3137 (D) 3139 3139 (E) 3149 3149

Q19

In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?

一个装有红、绿、蓝三色小圆珠的罐子，除了6颗是红的，其余都是红的；除了8颗是绿的，其余都是绿的；除了4颗是蓝的，其余都是蓝的。罐子里共有多少颗小圆珠？

(A) 6 6 (B) 8 8 (C) 9 9 (D) 10 10 (E) 18 18

Q20

What is the correct ordering of the three numbers $\frac{5}{19}$, $\frac{7}{21}$, and $\frac{9}{23}$, in increasing order?

下列三个分数 $\frac{5}{19}$、$\frac{7}{21}$、$\frac{9}{23}$ 由小到大的正确顺序是？

(A) $\frac{9}{23} < \frac{7}{21} < \frac{5}{19}$ $\frac{9}{23} < \frac{7}{21} < \frac{5}{19}$ (B) $\frac{5}{19} < \frac{7}{21} < \frac{9}{23}$ $\frac{5}{19} < \frac{7}{21} < \frac{9}{23}$ (C) $\frac{9}{23} < \frac{5}{19} < \frac{7}{21}$ $\frac{9}{23} < \frac{5}{19} < \frac{7}{21}$ (D) $\frac{5}{19} < \frac{9}{23} < \frac{7}{21}$ $\frac{5}{19} < \frac{9}{23} < \frac{7}{21}$ (E) $\frac{7}{21} < \frac{5}{19} < \frac{9}{23}$ $\frac{7}{21} < \frac{5}{19} < \frac{9}{23}$

Q21

Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?

Marla有一个边长为10英尺的大白色立方体。她还有足够覆盖300平方英尺的绿色油漆。Marla使用所有油漆在每个面上创建一个白色的正方形，中心位置，四周有绿色边框。其中一个白色正方形的面积是多少平方英尺？

(A) $5\sqrt{2}$ $5\sqrt{2}$ (B) 10 10 (C) $10\sqrt{2}$ $10\sqrt{2}$ (D) 50 50 (E) $50\sqrt{2}$ $50\sqrt{2}$

Q22

Let $R$ be a set of nine distinct integers. Six of the elements of the set are 2, 3, 4, 6, 9, and 14. What is the number of possible values of the median of $R$?

令$R$是一个包含九个不同整数的集合。其中六个元素是2、3、4、6、9和14。$R$的中位数的可能值有多少个？

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

Q23

An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?

一个等边三角形和一个正六边形具有相同的周长。如果三角形的面积是4，则六边形的面积是多少？

(A) 4 4 (B) 5 5 (C) 6 6 (D) $4\sqrt{3}$ $4\sqrt{3}$ (E) $6\sqrt{3}$ $6\sqrt{3}$

Q24

A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?

一个半径为2的圆被切成四个全等的弧。这四个弧连接形成图示的星形图形。星形图形的面积与原圆面积的比率为多少？

(A) $\frac{4-\pi}{\pi}$ $\frac{4-\pi}{\pi}$ (B) $\frac{1}{\pi}$ $\frac{1}{\pi}$ (C) $\frac{\sqrt{2}}{\pi}$ $\frac{\sqrt{2}}{\pi}$ (D) $\frac{\pi-1}{\pi}$ $\frac{\pi-1}{\pi}$ (E) $\frac{3}{\pi}$ $\frac{3}{\pi}$

Q25

A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length $a$ and the other of length $b$. What is the value of $ab$?

一个面积为4的正方形内接于一个面积为5的正方形，小正方形的每个顶点位于大正方形的一条边上。小正方形的一个顶点将大正方形的一条边分成两段，长分别为$a$和$b$。$ab$的值是多少？

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

AMC8 2012