amcdrill | AMC8 AMC10 AMC12 Practice

Q1

What is the smallest sum of two 3-digit numbers that can be obtained by placing each of the six digits 4, 5, 6, 7, 8, 9 in one of the six boxes in this addition problem?

通过将六个数字4、5、6、7、8、9各放置在该加法题的六个方框中，能得到的最小两位3位数之和是多少？

(A) 947 947 (B) 1037 1037 (C) 1047 1047 (D) 1056 1056 (E) 1245 1245

Q2

Which digit of .12345, when changed to 9, gives the largest number?

将小数 .12345 的哪一位数字改为9，能得到最大的数？

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

Q3

What fraction of the square is shaded?

正方形中有多少分数被涂黑？

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

Q4

Which of the following could not be the unit's digit of the square of a whole number?

下列哪一个不可能是某个整数平方的个位数字？

(A) 1 1 (B) 4 4 (C) 5 5 (D) 6 6 (E) 8 8

Q5

Which of the following is the closest to the product $(.48017)(.48017)(.48017)$?

下列哪一个最接近于乘积 $(.48017)(.48017)(.48017)$？

(A) 0.011 0.011 (B) 0.110 0.110 (C) 1.10 1.10 (D) 11.0 11.0 (E) 110 110

Q6

Which of these five numbers is the largest?

这五个数中哪个最大？

(A) $13579 + \frac{1}{2468}$ $13579 + \frac{1}{2468}$ (B) $13579 - \frac{1}{2468}$ $13579 - \frac{1}{2468}$ (C) $13579 \times \frac{1}{2468}$ $13579 \times \frac{1}{2468}$ (D) $13579 \div \frac{1}{2468}$ $13579 \div \frac{1}{2468}$ (E) $13579.2468$ $13579.2468$

Q7

When three different numbers from the set $\{-3, -2, -1, 4, 5\}$ are multiplied, the largest possible product is

从集合 $\{-3, -2, -1, 4, 5\}$ 中选取三个不同的数相乘，最大可能积是

(A) 10 10 (B) 20 20 (C) 30 30 (D) 40 40 (E) 60 60

Q8

A dress originally priced at $80 was put on sale at 25% off. If 10% tax was added to the sale price, then the total selling price of the dress was

一件原价 80 美元的连衣裙打 25% 折销售。销售价上再加 10% 税，总售价是

(A) $45 $45 (B) $52 $52 (C) $54 $54 (D) $66 $66 (E) $68 $68

Q9

The fifteen scores in Mr. Freeman's class were: 89, 72, 54, 97, 77, 92, 85, 74, 75, 63, 84, 78, 71, 80, 90. In Mr. Freeman's class, what percent of the students received a grade of C?

弗里曼先生班上的 15 个成绩是：89, 72, 54, 97, 77, 92, 85, 74, 75, 63, 84, 78, 71, 80, 90。在弗里曼先生班上，有百分之多少的学生获得 C 等级？

(A) 20% 20% (B) 25% 25% (C) 30% 30% (D) 33 1/3% 33 1/3% (E) 40% 40%

Q10

On this monthly calendar, the date behind one of the letters is added to the date behind C. If this sum equals the sum of the dates behind A and B, then the letter is

在这个月历上，其中一个字母后面的日期加上 C 后面的日期，其和等于 A 和 B 后面日期的和，则该字母是

(A) P P (B) Q Q (C) R R (D) S S (E) T T

Q11

The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is

这个立方体的各个面上的数字是连续的整数。三对相对面的两个数字之和相等。这个立方体上六个数字的总和是

(A) 75 75 (B) 76 76 (C) 78 78 (D) 80 80 (E) 81 81

Q12

There are twenty-four 4-digit whole numbers that use each of the four digits 2, 4, 5, and 7 exactly once. Listed in numerical order from smallest to largest, the number in the 17th position in the list is

有二十四个4位数的整数，它们恰好各使用一次数字2、4、5和7。从最小到最大按数值顺序排列，列表中第17个位置的数是

(A) 4527 4527 (B) 5724 5724 (C) 5742 5742 (D) 7245 7245 (E) 7542 7542

Q13

One proposal for new postage rates for a letter was 30¢ for the first ounce and 22¢ for each additional ounce (or fraction of an ounce). The postage for a letter weighing 4.5 ounces was

一封信的新邮资方案是首盎司30美分，每额外盎司（或零头）22美分。重4.5盎司的信的邮资是

(A) 96¢ 96 美分 (B) $1.07 $1.07 (C) $1.18 $1.18 (D) $1.20 $1.20 (E) $1.40 $1.40

Q14

A bag contains only blue balls and green balls. There are 6 blue balls. If the probability of drawing a blue ball at random from this bag is $\frac{1}{4}$, then the number of green balls in the bag is

一个袋子里只有蓝球和绿球。有6个蓝球。从袋中随机抽取一个蓝球的概率是$\frac{1}{4}$，则袋子里的绿球数是

(A) 12 12 (B) 18 18 (C) 24 24 (D) 30 30 (E) 36 36

Q15

The area of this figure is 100 cm². Its perimeter is

这个图形的面积是100 cm²。其周长是

(A) 20 cm 20 cm (B) 25 cm 25 cm (C) 30 cm 30 cm (D) 40 cm 40 cm (E) 50 cm 50 cm

Q16

1990 - 1980 + 1970 - 1960 + \dots - 20 + 10 =

(A) -990 -990 (B) -10 -10 (C) 990 990 (D) 1000 1000 (E) 1990 1990

Q17

A straight concrete sidewalk is to be 3 feet wide, 60 feet long and 3 inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?

一条直线混凝土人行道宽 3 英尺，长 60 英尺，厚 3 英寸。承包商需要订购多少立方码混凝土，如果混凝土必须以整数量的立方码订购？

(A) 2 2 (B) 5 5 (C) 12 12 (D) 20 20 (E) more than 20 超过 20

Q18

Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?

一个长方体每个角都被切掉。图中展示了八个切口中的两个。新图形有多少条边？

(A) 24 24 (B) 30 30 (C) 36 36 (D) 42 42 (E) 48 48

Q19

There are 120 seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?

一排有 120 个座位。必须占用多少个座位，才能使下一个坐下的人必须坐在某人旁边？（最少）

(A) 30 30 (B) 40 40 (C) 41 41 (D) 60 60 (E) 119 119

Q20

The annual incomes of 1,000 families range from \$8200 to \$98,000. In error, the largest income was entered on the computer as $980,000. The difference between the mean of the incorrect data and the mean of the actual data is

1000 个家庭的年收入从 8200 美元到 98,000 美元。由于输入错误，最高收入在计算机上被输入为 980,000 美元。不正确数据平均数与实际数据平均数的差值为

(A) $882 $882 (B) $980 $980 (C) $1078 $1078 (D) $482,000 $482,000 (E) $882,000 $882,000

Q21

A list of 8 numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the first number if the last three are shown: \[ ? , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , 16 , 64 , 1024 \] what is the first number?

一个由8个数组成的列表，从给定的两个数开始形成。列表中的每个新数是前两个数的乘积。如果最后三个数已知： \[? , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , \underline{\hspace{1cm}} , 16 , 64 , 1024\] 求第一个数。

(A) \frac{1}{64} \frac{1}{64} (B) \frac{1}{4} \frac{1}{4} (C) 1 1 (D) 2 2 (E) 4 4

Q22

Several students are seated at a large circular table. They pass around a bag containing 100 pieces of candy. Each person receives the bag, takes one piece of candy and then passes the bag to the next person. If Chris takes the first and the last piece of candy, then the number of students at the table could be

几个学生围坐在一张大圆桌旁。他们传着一个装有100块糖果的袋子。每人拿到袋子时，取一块糖果，然后传给下一个。克里斯拿了第一块和最后一块糖果，则桌旁学生人数可能是

(A) 10 10 (B) 11 11 (C) 19 19 (D) 20 20 (E) 25 25

Q23

The graph relates the distance traveled [in miles] to the time elapsed [in hours] on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?

该图表示实验飞机一次飞行中行驶距离[英里]与经过时间[小时]的关系。在哪一小时该飞机的平均速度最大？

(A) first (0-1) 第一 (0-1) (B) second (1-2) 第二 (1-2) (C) third (2-3) 第三 (2-3) (D) ninth (8-9) 第九 (8-9) (E) last (11-12) 最后一 (11-12)

Q24

Three $\triangle$ and a $\diamond$ will balance nine $\bullet$'s. One $\triangle$ will balance a $\diamond$ and a $\bullet$. How many $\bullet$'s will balance the two $\diamond$'s in this balance?

三个 $\triangle$ 和一个 $\diamond$ 可以平衡九个 $\bullet$。一个 $\triangle$ 可以平衡一个 $\diamond$ 和一个 $\bullet$。在这个天平中，两个 $\diamond$ 可以平衡多少个 $\bullet$？

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

Q25

How many difference patterns can be made by shading exactly two of the nine squares? Patterns that can be matched by flips and/or turns are not considered different.

在九个方格中恰好涂黑两个，能形成多少种不同的图案？可以通过翻转和/或旋转匹配的图案不视为不同。

(A) 3 3 (B) 6 6 (C) 8 8 (D) 12 12 (E) 18 18

AMC8 1990