amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Jamie counted the number of edges of a cube, Jimmy counted the number of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?

Jamie数了一个立方体的边数，Jimmy数了顶点数，Judy数了面数。然后他们把这三个数相加。最终的和是多少？

(A) 12 12 (B) 16 16 (C) 20 20 (D) 22 22 (E) 26 26

Q2

Which of the following numbers has the smallest prime factor?

下列哪个数的质因数最小？

(A) 55 55 (B) 57 57 (C) 58 58 (D) 59 59 (E) 61 61

Q3

A burger at Ricky C’s weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?

Ricky C’s的一份汉堡重120克，其中30克是填充物。汉堡中非填充物的百分比是多少？

(A) 60% 60% (B) 65% 65% (C) 70% 70% (D) 75% 75% (E) 90% 90%

Q4

A group of children riding on bicycles and tricycles rode past Billy Bob’s house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?

一群孩子骑着自行车和三轮车经过Billy Bob的房子。Billy Bob数到7个孩子和19个轮子。有多少辆三轮车？

(A) 2 2 (B) 4 4 (C) 5 5 (D) 6 6 (E) 7 7

Q5

If 20% of a number is 12, what is 30% of the same number?

一个数的20%是12，该数的30%是多少？

(A) 15 15 (B) 18 18 (C) 20 20 (D) 24 24 (E) 30 30

Q6

Given the areas of the three squares in the figure, what is the area of the interior triangle?

给定图中三个正方形的面积，内部三角形的面积是多少？

(A) 13 13 (B) 30 30 (C) 60 60 (D) 300 300 (E) 1800 1800

Q7

Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny’s average and Blake’s average on these four tests?

Blake 和 Jenny 各参加了四次满分 100 分的测试。Blake 的四次测试平均分是 78 分。Jenny 在第一次测试比 Blake 高 10 分，第二次比他低 10 分，第三次和第四次各比他高 20 分。这四次测试中，Jenny 的平均分与 Blake 的平均分的差是多少？

(A) 10 10 (B) 15 15 (C) 20 20 (D) 25 25 (E) 40 40

Q8

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown. Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?

问题 8、9 和 10 使用伴随段落和图中的数据。烘焙义卖四位朋友 Art、Roger、Paul 和 Trisha 烤饼干，所有饼干厚度相同。饼干形状不同，如图所示。谁从一批曲奇面团中分到的曲奇最少？

(A) Art Art (B) Paul Paul (C) Roger Roger (D) Trisha Trisha (E) There is a tie for fewest. 并列最少。

Q9

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown. Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Art’s cookies sell for 60¢ each. To earn the same amount from a single batch, how much should one of Roger’s cookies cost?

四位朋友——Art、Roger、Paul 和 Trisha——烤曲奇，而且所有曲奇的厚度都相同。曲奇的形状不同，如图所示。每个人使用相同数量的面团，Art 恰好做了 12 块曲奇。 Art 的饼干每个卖 60 美分。要从一批饼干中赚取相同金额，Roger 的一个饼干应该卖多少钱？

(A) 18¢ 18美分 (B) 25¢ 25美分 (C) 40¢ 40美分 (D) 75¢ 75美分 (E) 90¢ 90美分

Q10

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown. Each friend uses the same amount of dough, and Art makes exactly 12 cookies. How many cookies will be in one batch of Trisha’s cookies?

四位朋友——Art、Roger、Paul 和 Trisha——烤曲奇，而且所有曲奇的厚度都相同。曲奇的形状不同，如图所示。每个人使用相同数量的面团，Art 恰好做了 12 块曲奇。一批 Trisha 的饼干有多少个？

(A) 10 10 (B) 12 12 (C) 16 16 (D) 18 18 (E) 24 24

Q11

Business is a little slow at Lou’s Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday’s prices by 10%. Over the weekend, Lou advertises the sale: “Ten percent off the listed price. Sale starts Monday.” How much does a pair of shoes cost on Monday that cost $40 on Thursday?

Lou’s Fine Shoes 的生意有点清淡，所以 Lou 决定搞促销。周五，Lou 将周四的所有价格提高 10%。周末，Lou 广告促销：“标价九折。促销从周一开始。”一双周四价格为 $40 的鞋子，周一多少钱？

(A) $36 $36 (B) $39.60 $39.60 (C) $40 $40 (D) $40.40 $40.40 (E) $44 $44

Q12

When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by 6?

当一个公平的六面骰子掷在桌面上时，底面看不到。五个可见面上的数字乘积能被 6 整除的概率是多少？

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

Q13

Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?

14 个白色小立方体组合成右图所示的图形。图形的整个表面（包括底部）被涂成红色。然后图形被拆分成单个小立方体。有多少个单个小立方体正好有四个红色面？

(A) 4 4 (B) 6 6 (C) 8 8 (D) 10 10 (E) 12 12

Q14

In this addition problem, each letter stands for a different digit. If T = 7 and the letter O represents an even number, what is the only possible value for W?

在这个加法题中，每个字母代表一个不同的数字。若 T = 7 且字母 O 代表一个偶数，则 W 的唯一可能值是多少？

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

Q15

A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?

一个由单位立方体构成的图形。每个立方体至少与另一个立方体共享一面。建造一个具有所示正面和侧视图的最少需要多少个立方体？

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

Q16

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver’s seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?

Ali、Bonnie、Carlo 和 Dianna 要一起开车去附近的游乐园。他们使用的汽车有四个座位：一个驾驶座、一个前排乘客座和两个后排座位。只有 Bonnie 和 Carlo 会开车。有多少种可能的座位安排？

(A) 2 2 (B) 4 4 (C) 6 6 (D) 12 12 (E) 24 24

Q17

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim’s siblings? [table: Child Eye Hair Benjamin Blue Black; Jim Brown Blond; Nadeen Brown Black; Austin Blue Blond; Tevyn Blue Black; Sue Blue Blond]

下面列出的六个孩子来自两个每家三个兄弟姐妹的家庭。每个孩子有蓝眼睛或棕色眼睛，以及黑头发或金头发。同一家庭的孩子至少有一个这些特征相同。Jim 的兄弟姐妹是哪两个孩子？[表格：Child Eye Hair Benjamin 蓝黑；Jim 棕金；Nadeen 棕黑；Austin 蓝金；Tevyn 蓝黑；Sue 蓝金]

(A) Nadeen and Austin Nadeen和Austin (B) Benjamin and Sue Benjamin和Sue (C) Benjamin and Austin Benjamin和Austin (D) Nadeen and Tevyn Nadeen和Tevyn (E) Austin and Sue Austin和Sue

Q18

Each of the twenty dots on the graph below represents one of Sarah’s classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah’s party?

下图中有二十个点，每个点代表 Sarah 的一位同学。朋友之间的同学用线段连接。Sarah 的生日派对只邀请以下人员：她所有的朋友以及所有与她的朋友至少有一个朋友的同学。有多少位同学不会被邀请到 Sarah 的派对？

(A) 1 1 (B) 4 4 (C) 5 5 (D) 6 6 (E) 7 7

Q19

How many integers between 1000 and 2000 have all three of the numbers 15, 20 and 25 as factors?

1000 到 2000 之间有多少个整数同时被 15、20 和 25 整除？

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

Q20

What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?

4:20 a.m. 时钟指针形成的锐角是多少度？

(A) 0° 0° (B) 5° 5° (C) 8° 8° (D) 10° 10° (E) 12° 12°

Q21

The area of trapezoid ABCD is 164 cm$^2$. The altitude is 8 cm, AB is 10 cm, and CD is 17 cm. What is BC, in centimeters? [figure]

梯形ABCD的面积是164 cm$^2$。高是8 cm，AB是10 cm，CD是17 cm。BC的长是多少厘米？[figure]

(A) 9 9 (B) 10 10 (C) 12 12 (D) 15 15 (E) 20 20

Q22

The following figures are composed of squares and circles. Which figure has a shaded region with largest area?

以下图形由正方形和圆组成。哪个图形的阴影区域面积最大？

(A) A only 仅A (B) B only 仅B (C) C only 仅C (D) both A and B A和B (E) all are equal 全等

Q23

In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares. If the pattern is continued, where would the cat and mouse be after the 247th move?

在下面的图案中，猫顺时针通过四个正方形的四个位置，鼠标逆时针通过四个正方形的八个外部边段。如果图案继续，247步后猫和鼠标在哪里？

(A)

(B)

(C)

(D)

(E)

Q24

A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship’s distance from Island X as it moves along its course?

一艘船从点A到点B沿以岛X为圆心的半圆路径行驶。然后从B到C沿直线路径行驶。以下哪个图像最好显示了船沿航线移动时与岛X的距离？

(A)

(B)

(C)

(D)

(E)

Q25

In the figure, the area of square WXYZ is 25 cm$^2$. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In △ABC, AB = AC, and when △ABC is folded over side BC, point A coincides with O, the center of square WXYZ. What is the area of △ABC, in square centimeters? [figure]

图中正方形WXYZ的面积是25 cm$^2$。四个小正方形的边长为1 cm，与大正方形的边平行或重合。在△ABC中，AB = AC，当沿BC折叠△ABC时，点A与O（WXYZ正方形中心）重合。求△ABC的面积（平方厘米）？[figure]

(A) \frac{15}{4} \frac{15}{4} (B) \frac{21}{4} \frac{21}{4} (C) \frac{27}{4} \frac{27}{4} (D) \frac{21}{2} \frac{21}{2} (E) \frac{27}{2} \frac{27}{2}

AMC8 2003