amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?

安娜阿姨42岁。凯特琳比布里安娜小5岁，布里安娜的年龄是安娜阿姨年龄的一半。凯特琳多大？

(A) 15 15 (B) 16 16 (C) 17 17 (D) 21 21 (E) 37 37

Q2

Which of these numbers is less than its reciprocal?

以下哪个数小于它的倒数？

(A) -2 -2 (B) -1 -1 (C) 0 0 (D) 1 1 (E) 2 2

Q3

How many whole numbers lie in the interval between $\frac{5}{3}$ and $2\pi$?

区间$\frac{5}{3}$和$2\pi$之间有多少个整数？

(A) 2 2 (B) 3 3 (C) 4 4 (D) 5 5 (E) infinitely many 无数个

Q4

In 1960 only 5% of the working adults in Carlin City worked at home. By 1970 the "at-home" work force had increased to 8%. In 1980 there were approximately 15% working at home, and in 1990 there were 30%. The graph that best illustrates this is:

1960年，卡林市仅有5%的在职成人居家工作。到1970年，居家劳动力增加到8%。1980年约为15%，1990年为30%。最能说明这一情况的图表是：

(A)

(B)

(C)

(D)

(E)

Q5

Each principal of Lincoln High School serves exactly one 3-year term. What is the maximum number of principals this school could have during an 8-year period?

林肯高中的每个校长任期正好3年。8年内该校最多可能有多少位校长？

(A) 2 2 (B) 3 3 (C) 4 4 (D) 5 5 (E) 8 8

Q6

Figure ABCD is a square. Inside this square three smaller squares are drawn with side lengths as labeled. The area of the shaded L-shaped region is

图 ABCD 是一个正方形。在这个正方形内画了三个较小的正方形，边长如图所示。阴影 L 形区域的面积是

(A) 7 7 (B) 10 10 (C) 12.5 12.5 (D) 14 14 (E) 15 15

Q7

What is the minimum possible product of three different numbers of the set $\{-8, -6, -4, 0, 3, 5, 7\}$?

集合 $\{-8, -6, -4, 0, 3, 5, 7\}$ 中三个不同数的乘积的最小可能是多少？

(A) -336 -336 (B) -280 -280 (C) -210 -210 (D) -192 -192 (E) 0 0

Q8

Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is

三个骰子如图所示堆叠。十八个面中七个可见，留下十一个隐藏的面（背面、底面、之间）。在这个视图中不可见的点数总数是

(A) 21 21 (B) 22 22 (C) 31 31 (D) 41 41 (E) 53 53

Q9

Three-digit powers of 2 and 5 are used in this cross-number puzzle. What is the only possible digit for the outlined square? ACROSS 2. $2^m$ DOWN 1. $5^n$

这个填字谜中使用三位数的 2 和 5 的幂。虚线方框的唯一可能数字是？ ACROSS 2. $2^m$ DOWN 1. $5^n$

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

Q10

Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?

Ara 和 Shea 曾经身高相同。此后 Shea 长高了 20%，而 Ara 长高了 Shea 英寸数的一半。Shea 现在 60 英寸高。Ara 现在多高（英寸）？

(A) 48 48 (B) 51 51 (C) 52 52 (D) 54 54 (E) 55 55

Q11

The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property?

数字 64 具有能被其个位数整除的性质。在 10 到 50 之间，有多少个整数具有这种性质？

(A) 15 15 (B) 16 16 (C) 17 17 (D) 18 18 (E) 20 20

Q12

A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?

一座长 100 英尺、高 7 英尺的砌块墙将使用高 1 英尺、长 2 英尺或 1 英尺的砌块建造（砌块不得切割）。砌块的垂直接缝必须如图所示错开，且墙两端必须平整。建造这座墙需要的最小砌块数是多少？

(A) 344 344 (B) 347 347 (C) 350 350 (D) 353 353 (E) 356 356

Q13

In triangle CAT, we have $\angle ACT = \angle ATC$ and $\angle CAT = 36^\circ$. If $\overline{TR}$ bisects $\angle ATC$, then $\angle CRT =$

在三角形 CAT 中，$\\angle ACT = \\angle ATC$ 且 $\\angle CAT = 36^\circ$。如果 $\\overline{TR}$ 平分 $\\angle ATC$，则 $\\angle CRT =$

(A) 16° 16° (B) 51° 51° (C) 72° 72° (D) 90° 90° (E) 108° 108°

Q14

What is the units digit of $19^{19} + 99^{99}$?

$19^{19} + 99^{99}$ 的个位数是多少？

(A) 0 0 (B) 1 1 (C) 2 2 (D) 8 8 (E) 9 9

Q15

Triangle ABC, ADE, and EFG are all equilateral. Points D and G are midpoints of AC and AE, respectively. If AB = 4, what is the perimeter of figure ABCDEFG?

三角形 ABC、ADE 和 EFG 均为等边三角形。点 D 和 G 分别是 AC 和 AE 的中点。若 AB = 4，则图形 ABCDEFG 的周长是多少？

(A) 12 12 (B) 13 13 (C) 15 15 (D) 18 18 (E) 21 21

Q16

In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?

为了让Mateen在他的矩形后院走一公里（1000米），他必须沿着长度走25次，或者沿着周长走10次。Mateen的后院面积有多少平方米？

(A) 40 40 (B) 200 200 (C) 400 400 (D) 500 500 (E) 1000 1000

Q17

The operation $\otimes$ is defined for all nonzero numbers by $a \otimes b = \frac{a^2}{b}$. Determine $[[(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]]$.

操作$\otimes$对于所有非零数定义为$a\otimes b=\frac{a^2}{b}$。求$[[(1\otimes 2)\otimes 3]-[1\otimes(2\otimes 3)]]$的值。

(A) $-\frac{2}{3}$ $-\frac{2}{3}$ (B) $-\frac{1}{4}$ $-\frac{1}{4}$ (C) 0 0 (D) $\frac{1}{4}$ $\frac{1}{4}$ (E) $\frac{2}{3}$ $\frac{2}{3}$

Q18

Consider these two geoboard quadrilaterals. Which of the following statements is true?

考虑这两个地理板上的四边形。以下哪个陈述是正确的？

(A) The area of quadrilateral I is more than the area of quadrilateral II. 四边形I的面积大于四边形II的面积。 (B) The area of quadrilateral I is less than the area of quadrilateral II. 四边形I的面积小于四边形II的面积。 (C) The quadrilaterals have the same area and the same perimeter. 两个四边形面积和周长相同。 (D) The quadrilaterals have the same area, but the perimeter of I is more than the perimeter of II. 两个四边形面积相同，但I的周长大于II的周长。 (E) The quadrilaterals have the same area, but the perimeter of I is less than the perimeter of II. 两个四边形面积相同，但I的周长小于II的周长。

Q19

Three circular arcs of radius 5 units bound the region shown. Arcs AB and AD are quarter-circles, and arc BCD is a semi-circle. What is the area, in square units, of the region?

三个半径为5单位的圆弧包围了所示区域。弧AB和AD是四分之一圆，弧BCD是半圆。该区域面积有多少平方单位？

(A) 25 25 (B) $10 + 5\pi$ $10 + 5\pi$ (C) 50 50 (D) $50 + 5\pi$ $50 + 5\pi$ (E) $25\pi$ $25\pi$

Q20

You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02$, with at least one coin of each type. How many dimes must you have?

你有九枚硬币：便士、镍币、角币和25分币，总价值1.02美元，且至少有一种每种类型。必须有多少个角币？

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

Q21

Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is

惠子抛一枚硬币，以法莲抛两枚硬币。以法莲得到与惠子相同数量正面的概率是

(A) $\frac{1}{4}$ $\frac{1}{4}$ (B) $\frac{3}{8}$ $\frac{3}{8}$ (C) $\frac{1}{2}$ $\frac{1}{2}$ (D) $\frac{2}{3}$ $\frac{2}{3}$ (E) $\frac{3}{4}$ $\frac{3}{4}$

Q22

A cube has edge length 2. Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to:

一个边长为2的立方体。我们将一个边长为1的立方体粘在大立方体的顶部，使其一个面完全贴在大立方体顶面上。从原立方体到新形成的固体的表面积（侧面、顶部和底部）的百分比增加最接近：

(A) 10 10 (B) 15 15 (C) 17 17 (D) 21 21 (E) 25 25

Q23

There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If the average of all seven numbers is $6\frac{4}{7}$, then the number common to both sets of four numbers is

有一列七个数。前四个数的平均数是5，后四个数的平均数是8。如果全部七个数的平均数是$6\frac{4}{7}$，则两个四数集合共有的那个数是

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

Q24

If $\angle A = 20^\circ$ and $\angle AFG = \angle AGF$, then $\angle B + \angle D =$

若$\angle A = 20^\circ$且$\angle AFG = \angle AGF$，则$\angle B + \angle D =$

(A) 48° 48° (B) 60° 60° (C) 72° 72° (D) 80° 80° (E) 90° 90°

Q25

The area of rectangle ABCD is 72. If point A and the mid-points of $\overline{BC}$ and $\overline{CD}$ are joined to form a triangle, the area of that triangle is

矩形ABCD的面积是72。若将点A与BC和CD的中点连接形成一个三角形，则该三角形的面积是

(A) 21 21 (B) 27 27 (C) 30 30 (D) 36 36 (E) 40 40

AMC8 2000