What is
(E)
6@2 中文：定义 a @ b=ab-b2 ，a # b=a + b - ab2。求 的值。 6#2 3. An aquarium has a rectangular base that measures 100cm by 40cm and has a height of 50cm. It is filled with water to a height of 40cm. A brick with a rectangular base that measures 40cm by 20cm and a height of 10cm is placed in the aquarium. By how many centimeters does that water rise? (A) 0.5 (B) 1 (C) 1.5 (D) 2 (E)2.5 中文：一个养鱼缸有 100cm×40cm 的底，高为 50cm。它装满水到 40cm 的高度。把一 个底为 40cm×20cm，高为 10cm 的砖块放在这个养鱼缸里。鱼缸里的水上升了多少厘 米？ 4. The larger of two consecutive odd integers is three times the smaller. What is their sum? (A) 4 (B) 8 (C) 12 (D) 16 (E) 20 中文：2 个连续的奇整数中较大的数是较小的数的 3 倍。它们的和是多少？ 5. A school store sells 7 pencils and 8 notebooks for $4.15. It also sells 5 pencils and 3 notebooks for $1.77. How much do 16 pencils and 10 notebooks cost? (A) $4.76 (B) $5.84 (C) $6.00 (D) $6.16 (E) $6.32 中文：在一个学校商店花 4.15 美元可以买到 7 支铅笔和 8 个笔记本，花 1.77 美元可以 买到 5 个铅笔和 3 个笔记本。问 16 支铅笔和 10 个笔记本需要多少钱？ 6. At Euclid High School, the number of students taking the AMC10 was 60 in 2002, 66 in 2003, 70 in 2004, 76 in 2005, and 78 in 2006, and is 85 in 2007. Between what two consecutive years was there the largest percentage increase? (A) 2002 and 2003 (B) 2003 and 2004 (C) 2004 and 20and 125 =5 . What is ab? (E) 60
b a-3
b
a-3
和 125 =5 ，问 ab 的值是多少？
10. The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is 20, the father is 48 years old, and the average age of the mother and children is 16. How many children are in the family? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 中文：Dunbar 一家的家庭成员包括爸爸，妈妈和几个孩子。他们的平均年龄是 20 岁， 其中爸爸 48 岁，妈妈和几个孩子的平均年龄是 16 岁。问家中有多少个孩子？ 11. The numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. What is this common sum? (A) 14 (B) 16 (C) 18 (D) 20 (E) 24 中文：数字 1 到 8 被放在立方体的 8 个顶点上。使每面上的四个顶点代表的数字和相 同。问每面上的四个顶点的数字和是多少？ 12. Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourists are possible?
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8th AMC 10 A
2007
(D) 2005 and 2006 (E) 2006 and 2007 中文：在 Euclid 高中，2002 年参加 AMC10 的学生有 60 人，2003 年有 66 人，2004 年 有 70 人，2005 年有 76 人，2006 年有 78 人，2007 年有 85 人。在相邻的哪两年中人数 增长的百分率最大？ 7. Last year Mr. John Q. Public received an inheritance. He paid 20% in federal taxes on the inheritance, and paid 10% of what he had left in state taxes. He paid a total of $10,500 for both taxes. How many dollars was the inheritance? (A) 30,000 (B) 32,500 (C) 35,000 (D) 37,500 (E) 40,000 中文：去年 Mr. John Q. Public 收到了一笔遗产。其中 20%用于交联邦税，剩下钱中的 10%用于交州税。交这两种税款一共需要 10,500 美元。问这笔遗产共多少美元？ 8. Triangles ABC and ADC are isosceles with AB=AC and AD=DC. Point D is inside △ABC, ∠ABC=40°, and ∠ADC=140°. What is the degree measure of ∠BAD? (A) 20 (B) 30 (C) 40 (D) 50 (E) 60 中文：△ABC 和△ADC 是等腰三角形且 AB=AC，AD=DC。点 D 在△ABC 内，∠ ABC=40°, ∠ADC=140°。问∠BAD 的度数是多少？ 9. Real numbers a and b satisfy the equations 3 =81 (A)－60 (B)－17 (C) 9 (D) 12 中文：实数 a 和实数 b 满足等式 3 =81
(A) 32
(B) 22+12 2
(C) 16+16 3
(D) 48
(E) 36+16 2
中文：如图所示，四个半径是 1 的圆分别与正方形的两边相切且与一个半径是 2 的圆 外切，这个正方形的面积是多少？ 16. Integers a, b, c, and d, not necessarily distinct, are chosen independently and at random
8th AMC 10 A 8th AMC 10 A
2007 2007
1. One ticket to a show costs $20 at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickets using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan? (A) 2 (B) 5 (C) 10 (D) 15 (E) 20 中文：一张展览票全价为 20 美元。Susan 用优惠券买 4 张票打七五折。Pam 用优惠券 买 5 张票打七折。Pam 比 Susan 多花了多少美元？ 2. Define a@b=ab - b2 and a#b=a + b - ab2. 1 (A)－ 2 1 (B)－ 4 (C) 1 8 (D) 1 4 6@2 ? 6#2 1 2
中文：Yan 站在他家和运动场之间，要到运动场。他可以直接走路到运动场，或他走路 回 家再沿原路径骑自行车到运动场。骑自行车的速率是走路速率的 7 倍，两种方法所花 的时间都相同。问 Yan 站的位置到他家的距离与到运动场的距离之比值是多少？ 14. A triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3. What is the area of the triangle? (A) 8.64 (B) 12 (C) 5π (D) 17.28 (E) 18 中文：一个三角形的外接圆半径是 3，且其三边长之比是 3:4:5。问此三角形的面积是 多 少？ 15. Four circles of radius 1 are each tangent to two sides of a square and externally tangent to a circle of radius 2, as shown. What is the area of the square?