amcdrill | AMC8 AMC10 AMC12 Practice

Q1

$\frac{1}{10} + \frac{9}{100} + \frac{9}{1000} + \frac{7}{10000} =$

(A) 0.0026 0.0026 (B) 0.0197 0.0197 (C) 0.1997 0.1997 (D) 0.26 0.26 (E) 1.997 1.997

Q2

Ahn chooses a two-digit number, subtracts it from 200, and doubles the result. What is the largest number Ahn can get?

Ahn 选择一个两位数，从 200 中减去它，然后将结果加倍。Ahn 能得到的最大数是多少？

(A) 200 200 (B) 202 202 (C) 220 220 (D) 380 380 (E) 398 398

Q3

Which of the following numbers is the largest?

下列哪个数最大？

(A) 0.97 0.97 (B) 0.979 0.979 (C) 0.9709 0.9709 (D) 0.907 0.907 (E) 0.9089 0.9089

Q4

Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, which of the following number of words would be appropriate length for her speech?

Julie 正在为她的班级准备演讲。她的演讲必须持续在半小时到四分之三小时之间。理想的演讲速度是每分钟 150 词。如果 Julie 以理想速度演讲，下列哪个词数适合她的演讲长度？

(A) 2250 2250 (B) 3000 3000 (C) 4200 4200 (D) 4350 4350 (E) 5650 5650

Q5

There are many two-digit multiples of 7, but only two of the multiples have a digit sum of 10. The sum of these two multiples of 7 is

有许多两位数的 7 的倍数，但只有两个倍数的数字和为 10。这两个 7 的倍数的和是

(A) 119 119 (B) 126 126 (C) 140 140 (D) 175 175 (E) 189 189

Q6

In the number 74982.1035 the value of the place occupied by the digit 9 is how many times as great as the value of the place occupied by the digit 3?

在数字 74982.1035 中，数字 9 所在位置的值是数字 3 所在位置的值的多少倍？

(A) 1,000 1,000 (B) 10,000 10,000 (C) 100,000 100,000 (D) 1,000,000 1,000,000 (E) 10,000,000 10,000,000

Q7

The area of the smallest square that will contain a circle of radius 4 is

能容纳半径为 4 的圆的最小正方形的面积是

(A) 8 8 (B) 16 16 (C) 32 32 (D) 64 64 (E) 128 128

Q8

Walter gets up at 6:30 am, catches the school bus at 7:30 am, has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours additional time at school. He takes the bus that arrives at 4:00 pm. How many minutes has he spent on the bus?

沃尔特早上 6:30 起床，7:30 坐校车，上午有 6 节课每节 50 分钟，午餐 30 分钟，学校还有 2 小时额外时间。他坐的校车下午 4:00 到家。他总共在校车上花了多少分钟？

(A) 30 30 (B) 60 60 (C) 75 75 (D) 90 90 (E) 120 120

Q9

Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back?

三个学生，名字不同，排成一列单队。从前到后按字母顺序排列的概率是多少？

(A) $\frac{1}{12}$ $\frac{1}{12}$ (B) $\frac{1}{9}$ $\frac{1}{9}$ (C) $\frac{1}{6}$ $\frac{1}{6}$ (D) $\frac{1}{3}$ $\frac{1}{3}$ (E) $\frac{2}{3}$ $\frac{2}{3}$

Q10

What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.

这个正方形区域中有多少分数被涂黑？条纹宽度相等，且图形按比例绘制。

(A) $\frac{5}{12}$ $\frac{5}{12}$ (B) $\frac{1}{2}$ $\frac{1}{2}$ (C) $\frac{7}{12}$ $\frac{7}{12}$ (D) $\frac{2}{3}$ $\frac{2}{3}$ (E) $\frac{5}{6}$ $\frac{5}{6}$

Q11

Let $d(N)$ mean the number of positive divisors of $N$. For example, $d(3) = 2$. Find the value of picture.

设 $d(N)$ 表示 $N$ 的正因数个数。例如，$d(3)=2$。求图中表达式的值。

(A) 6 6 (B) 8 8 (C) 12 12 (D) 16 16 (E) 24 24

Q12

$\angle 1 + \angle 2 = 180^\circ$ $\angle 3 = \angle 4$ Find $\angle 4$ (figure with angles 40° and 70° shown).

$\angle1+\angle2=180^\circ$ $\angle3=\angle4$ 求 $\angle4$（图中标有 $40^\circ$ 和 $70^\circ$）。

(A) 20° 20° (B) 25° 25° (C) 30° 30° (D) 35° 35° (E) 40° 40°

Q13

Three bags of jelly beans contain 26, 28, and 30 beans. The ratios of yellow beans to all beans in each of these bags are 50%, 25%, and 20%, respectively. All three bags of candy are dumped into one bowl. Which of the following is closest to the ratio of yellow jelly beans to all beans in the bowl?

三个果冻豆袋子分别含 26、28 和 30 颗豆子。各袋中黄色豆子与总豆子的比例分别为 50%、25% 和 20%。将三个袋子全部倒入一个碗中。碗中黄色果冻豆与总豆子的比例最接近以下哪一项？

(A) 31% 31% (B) 32% 32% (C) 33% 33% (D) 35% 35% (E) 95% 95%

Q14

There is a set of five positive integers whose average (mean) is 5, whose median is 5, and whose only mode is 8. What is the difference between the largest and smallest integers in the set?

有一个五个正整数的集合，其平均数（均值）为 5，中位数为 5，且唯一众数为 8。求该集合中最大整数与最小整数之差。

(A) 3 3 (B) 5 5 (C) 6 6 (D) 7 7 (E) 8 8

Q15

Each side of the large square in the figure is trisected. The corners of an inscribed square are at these trisection points, as shown. The ratio of the area of the inscribed square to the area of the large square is

图中大正方形的每条边被三分等分。内接正方形的顶点位于这些三分点上，如图所示。内接正方形面积与大正方形面积之比为

(A) $\frac{\sqrt{3}}{3}$ $\frac{\sqrt{3}}{3}$ (B) $\frac{5}{9}$ $\frac{5}{9}$ (C) $\frac{2}{3}$ $\frac{2}{3}$ (D) $\frac{\sqrt{5}}{3}$ $\frac{\sqrt{5}}{3}$ (E) $\frac{7}{9}$ $\frac{7}{9}$

Q16

Penni Precisely buys $100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A, B, and C are the final value of the stock, then

Penni Precisely 在三家公司：Alabama Almonds、Boston Beans 和 California Cauliflower 各购买了价值 $100 的股票。一年后，AA 上涨 20%，BB 下跌 25%，CC 不变。第二年，AA 较前一年下跌 20%，BB 较前一年上涨 25%，CC 不变。如果 A、B 和 C 是股票的最终价值，则

(A) $A = B = C$ $A = B = C$ (B) $A = B < C$ $A = B < C$ (C) $C < B = A$ $C < B = A$ (D) $A < B < C$ $A < B < C$ (E) $B < A < C$ $B < A < C$

Q17

A cube has eight vertices (corners) and twelve edges. A segment, such as x, which joins two vertices not joined by an edge is called a diagonal. Segment y is also a diagonal. How many diagonals does a cube have?

一个立方体有八个顶点（角）和十二条边。连接两个不相邻顶点的线段（如 x）称为对角线。线段 y 也是对角线。立方体有几个对角线？

(A) 6 6 (B) 8 8 (C) 12 12 (D) 14 14 (E) 16 16

Q18

At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for $5. This week they are on sale at 5 boxes for $4. The percent decrease in the price per box during the sale was closest to

上周杂货店，小盒面巾纸的价格是 4 盒 $5。本周特价 5 盒 $4。每盒价格在促销期间的百分比降幅最接近

(A) 30% 30% (B) 35% 35% (C) 40% 40% (D) 45% 45% (E) 65% 65%

Q19

If the product $\frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdot \frac{6}{5} \cdot \frac{7}{6} = 9$, what is the sum of a and b?

如果乘积 $\frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdot \frac{6}{5} \cdot \frac{7}{6} = 9$，a 和 b 的和是多少？

(A) 11 11 (B) 13 13 (C) 17 17 (D) 35 35 (E) 37 37

Q20

A pair of 8-sided dice have sides numbered 1 through 8. Each side has the same probability of landing face up. The probability that the product of the two numbers on the sides that land face-up exceeds 36 is

一对 8 面骰子，面编号 1 到 8。每面朝上的概率相同。两个朝上面数字的乘积超过 36 的概率是

(A) $\frac{5}{32}$ $\frac{5}{32}$ (B) $\frac{11}{64}$ $\frac{11}{64}$ (C) $\frac{3}{16}$ $\frac{3}{16}$ (D) $\frac{1}{4}$ $\frac{1}{4}$ (E) $\frac{1}{2}$ $\frac{1}{2}$

Q21

Each corner cube is removed from this 3 cm × 3 cm × 3 cm cube. The surface area of the remaining figure is

从这个 $3\ cm \times 3\ cm \times 3\ cm$ 的正方体中移除了每个角上的小正方体。剩余图形的表面积是

(A) 19 sq.cm 19 平方厘米 (B) 24 sq.cm 24 平方厘米 (C) 30 sq.cm 30 平方厘米 (D) 54 sq.cm 54 平方厘米 (E) 72 sq.cm 72 平方厘米

Q22

A two-inch cube (2 × 2 × 2) of silver weighs 3 pounds and is worth $200. How much is a three-inch cube of silver worth?

一个 2 英寸的银立方体（$2 \times 2 \times 2$）重 3 磅，价值 200 美元。一个 3 英寸的银立方体价值多少？

(A) $300 $300 (B) $375 $375 (C) $450 $450 (D) $560 $560 (E) $675 $675

Q23

There are positive integers that have these properties: I. The sum of the squares of their digits is 50, and II. Each digit is larger than the one on its left. The product of the digits of the largest integer with both properties is

存在具有以下性质的正整数：I. 其各位数字平方和为 50，且 II. 每位数字都大于其左边的数字。具有两者性质的最大整数的各位数字乘积是

(A) 7 7 (B) 25 25 (C) 36 36 (D) 48 48 (E) 60 60

Q24

Diameter ACE is divided at C in the ratio 2 : 3. The two semicircles, ABC and CDE, divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region is

直径 ACE 在 C 点按 2 : 3 的比例分割。两个半圆 ABC 和 CDE 将圆形区域分成上部（阴影）区域和下部区域。上部区域面积与下部区域面积的比值为

(A) 2:3 2:3 (B) 1:1 1:1 (C) 3:2 3:2 (D) 9:4 9:4 (E) 5:2 5:2

Q25

All of the even numbers from 2 to 98 inclusive, except those ending in 0, are multiplied together. What is the rightmost digit (the units digit) of the product?

将从 2 到 98（包含）的所有偶数相乘，但排除那些末位为 0 的数。乘积的最右边数字（个位数）是多少？

(A) 0 0 (B) 2 2 (C) 4 4 (D) 6 6 (E) 8 8

AMC8 1997