amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Margie bought 3 apples at a cost of 50 cents per apple. She paid with a 5-dollar bill. How much change did Margie receive?

Margie 买了 3 个苹果，每个苹果 50 美分。她用一张 5 美元钞票支付。她收到了多少找零？

(A) $1.50 $1.50 (B) $2.00 $2.00 (C) $2.50 $2.50 (D) $3.00 $3.00 (E) $3.50 $3.50

Q2

Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Whose garden is larger in area?

Karl 的矩形菜园是 20 英尺乘 45 英尺，Makenna 的菜园是 25 英尺乘 40 英尺。谁的菜园面积更大？

(A) Karl's garden is larger by 100 square feet. 卡尔的菜园大100平方英尺。 (B) Karl's garden is larger by 25 square feet. 卡尔的菜园大25平方英尺。 (C) The gardens are the same size. 两个菜园面积相同。 (D) Makenna's garden is larger by 25 square feet. 梅肯纳的菜园大25平方英尺。 (E) Makenna's garden is larger by 100 square feet. 梅肯纳的菜园大100平方英尺。

Q3

Extend the square pattern of 8 black and 17 white square tiles by attaching a border of black tiles around the square. What is the ratio of black tiles to white tiles in the extended pattern?

将由 8 个黑色和 17 个白色方形瓷砖组成的正方形图案扩展，在正方形周围附加一层黑色瓷砖边框。扩展图案中黑色瓷砖与白色瓷砖的比率为多少？

(A) 8 : 17 8 : 17 (B) 25 : 49 25 : 49 (C) 36 : 25 36 : 25 (D) 32 : 17 32 : 17 (E) 36 : 17 36 : 17

Q4

Here is a list of the numbers of fish that Tyler caught in nine outings last summer: 2, 0, 1, 3, 0, 3, 3, 1, 2. Which statement about the mean, mode, and median of these numbers is true?

以下是 Tyler 去年夏天九次出游捕鱼的数量列表：2, 0, 1, 3, 0, 3, 3, 1, 2。关于这些数字的均值、众数和中位数的哪个陈述是正确的？

(A) median < mean < mode 中位数 < 均值 < 众数 (B) mean < mode < median 均值 < 众数 < 中位数 (C) mean < median < mode 均值 < 中位数 < 众数 (D) median < mode < mean 中位数 < 众数 < 均值 (E) mode < median < mean 众数 < 中位数 < 均值

Q5

What time was it 2011 minutes after the beginning of January 1, 2011?

从 2011 年 1 月 1 日开始后 2011 分钟是什么时间？

(A) January 1 at 9:31PM 1月1日晚上9:31 (B) January 1 at 11:51PM 1月1日晚上11:51 (C) January 2 at 3:11AM 1月2日凌晨3:11 (D) January 2 at 9:31AM 1月2日上午9:31 (E) January 2 at 6:01PM 1月2日晚上6:01

Q6

In a town of 351 adults, every adult owns a car, a motorcycle, or both. If 331 adults own cars, and 45 adults own motorcycles, how many of the car owners do not own a motorcycle?

一个城镇有351名成人，每位成人都拥有汽车、摩托车或两者皆有。如果有331名成人拥有汽车，45名成人拥有摩托车，那么有多少汽车拥有者不拥有摩托车？

(A) 20 20 (B) 25 25 (C) 45 45 (D) 306 306 (E) 351 351

Q7

Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially shaded. What percent of the total area is partially shaded?

以下四个全等的大正方形每个都被细分为全等的三角形或矩形的组合，并部分涂阴影。部分涂阴影的区域占总面积的百分之多少？

(A) $12\frac{1}{2}$ $12\frac{1}{2}$ (B) 20 20 (C) 25 25 (D) $33\frac{1}{3}$ $33\frac{1}{3}$ (E) $37\frac{1}{2}$ $37\frac{1}{2}$

Q8

Bag A contains three chips labeled 1, 3, and 5. Bag B contains three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?

袋A包含三个标签为1、3和5的筹码。袋B包含三个标签为2、4和6的筹码。如果从每个袋中抽取一个筹码，两筹码上数字之和可能有多少种不同的值？

(A) 4 4 (B) 5 5 (C) 6 6 (D) 7 7 (E) 9 9

Q9

Carmen takes a long bike ride on a hilly highway. The graph indicates the miles traveled during the time of her ride. What is Carmen's average speed for her entire ride in miles per hour?

卡门在丘陵公路上进行了一次长途骑行。图表显示了她骑行时间的里程数。卡门整个骑行的平均速度是多少英里每小时？

(A) 2 2 (B) 2.5 2.5 (C) 4 4 (D) 4.5 4.5 (E) 5 5

Q10

The taxi fare in Gotham City is $2.40 for the first 1/2 mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?

哥谭市的出租车费，第一半英里2.40美元，此后每额外0.1英里0.20美元。你计划给司机2美元小费。用10美元能乘坐多少英里？

(A) 3.0 3.0 (B) 3.25 3.25 (C) 3.3 3.3 (D) 3.5 3.5 (E) 3.75 3.75

Q11

The graph below shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?

下图显示了Asha（黑条）和Sasha（灰条）在一周内每天学习的时间（分钟数）。平均每天Sasha比Asha多学习了多少分钟？

(A) 6 6 (B) 8 8 (C) 9 9 (D) 10 10 (E) 12 12

Q12

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?

Angie、Bridget、Carlos和Diego随机围坐在一张方桌旁，每边一人。Angie和Carlos坐在对面的概率是多少？

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

Q13

Two congruent squares, ABCD and PQRS, have side length 15. They overlap to form the 15 by 25 rectangle AQRD shown. What percent of the area of rectangle AQRD is shaded?

有两个边长为15的相符正方形ABCD和PQRS，它们重叠形成如图所示的15×25矩形AQRD。矩形AQRD面积中有多少百分比是阴影部分？

(A) 15 15 (B) 18 18 (C) 20 20 (D) 24 24 (E) 25 25

Q14

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5 : 4. There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4 : 5. The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?

Colfax中学的学生有270人，男孩与女孩比例为5:4。Winthrop中学的学生有180人，男孩与女孩比例为4:5。两校举办舞会，所有学生都参加。舞会上女孩占学生总数的几分之几？

(A) $\frac{7}{18}$ $\frac{7}{18}$ (B) $\frac{7}{15}$ $\frac{7}{15}$ (C) $\frac{22}{45}$ $\frac{22}{45}$ (D) $\frac{1}{2}$ $\frac{1}{2}$ (E) $\frac{23}{45}$ $\frac{23}{45}$

Q15

How many digits are in the product $4^5 \cdot 5^{10}$?

$4^5 \cdot 5^{10}$的乘积有几位数？

(A) 8 8 (B) 9 9 (C) 10 10 (D) 11 11 (E) 15 15

Q16

Let $A$ be the area of a triangle with sides of length 25, 25, and 30. Let $B$ be the area of a triangle with sides of length 25, 25, and 40. What is the relationship between $A$ and $B$?

设$A$为边长分别为25、25和30的三角形的面积。设$B$为边长分别为25、25和40的三角形的面积。$A$和$B$之间是什么关系？

(A) $A = \frac{9}{16}B$ $A = \frac{9}{16}B$ (B) $A = \frac{3}{4}B$ $A = \frac{3}{4}B$ (C) $A = B$ $A = B$ (D) $A = \frac{4}{3}B$ $A = \frac{4}{3}B$ (E) $A = \frac{16}{9}B$ $A = \frac{16}{9}B$

Q17

Let $w, x, y, z$ be whole numbers. If $2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$, then what does $2w + 3x + 5y + 7z$ equal?

设$w, x, y, z$为整数。若$2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$，则$2w + 3x + 5y + 7z$等于多少？

(A) 21 21 (B) 25 25 (C) 27 27 (D) 35 35 (E) 56 56

Q18

A fair six-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?

一个公平的六面骰子掷两次。第一骰子显示的数字大于等于第二骰子显示的数字的概率是多少？

(A) $\frac{1}{6}$ $\frac{1}{6}$ (B) $\frac{5}{12}$ $\frac{5}{12}$ (C) $\frac{1}{2}$ $\frac{1}{2}$ (D) $\frac{7}{12}$ $\frac{7}{12}$ (E) $\frac{5}{6}$ $\frac{5}{6}$

Q19

How many rectangles are in this figure?

这个图形中有多少个矩形？

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

Q20

Quadrilateral ABCD is a trapezoid, AD = 15, AB = 50, BC = 20, and the altitude is 12. What is the area of the trapezoid?

四边形ABCD是一个梯形，AD = 15，AB = 50，BC = 20，高为12。梯形的面积是多少？

(A) 600 600 (B) 650 650 (C) 700 700 (D) 750 750 (E) 800 800

Q21

Students guess that Norb’s age is 24, 28, 30, 32, 36, 38, 41, 44, 47, and 49. Norb says, “At least half of you guessed too low, two of you are off by one and my age is a prime number.” How old is Norb?

学生们猜测Norb的年龄是24、28、30、32、36、38、41、44、47和49。Norb说：“至少有一半人猜得太低，你们中有两人差了一岁，我的年龄是一个质数。”Norb多大年龄？

(A) 29 29 (B) 31 31 (C) 37 37 (D) 43 43 (E) 48 48

Q22

What is the tens digit of $7^{2011}$?

$7^{2011}$的十位数字是多少？

(A) 0 0 (B) 1 1 (C) 3 3 (D) 4 4 (E) 7 7

Q23

How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?

有多少个四位正整数具有四个不同数字，开头数字不为零，该整数是5的倍数，且5是其中最大的数字？

(A) 24 24 (B) 48 48 (C) 60 60 (D) 84 84 (E) 108 108

Q24

In how many ways can 10,001 be written as the sum of two primes?

10001可以用两个质数之和表示多少种方式？

(A) 0 0 (B) 1 1 (C) 2 2 (D) 3 3 (E) 4 4

Q25

A circle with radius 1 is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle’s shaded area to the shaded area between the two squares?

一个半径为1的圆内接于一个正方形，并外接于另一个正方形，如图所示。圆的阴影面积与两个正方形之间阴影面积的比值最接近于哪个分数？

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

AMC8 2011