2024年4月11日发(作者：好用的初一数学试卷推荐)

*欧阳光明*创编 2021.03.07

2011AMC10美国数学竞赛A卷

欧阳光明（2021.03.07）

1. A cell phone plan costs $20 each month, plus 5¢ per text message sent,

plus 10¢ for each minute used over 30 hours. In January Michelle sent

100 text messages and talked for 30.5 hours. How much did she have to

pay?

(A) $24.00(B) $24.50(C) $25.50(D) $28.00(E) $30.00

2. A small bottle of shampoo can hold 35 milliliters of shampoo,

Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine

wants to buy the minimum number of small bottles necessary to

completely fill a large bottle. How many bottles must she buy?

(A) 11(B) 12(C) 13(D) 14(E) 15

3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the

average of a, b, and c. What is {{1 1 0} [0 1] 0}?

(A)(B)(C)(D)(E)

4. Let X and Y be the following sums of arithmetic sequences:

X= 10 + 12 + 14 + …+ 100.

Y= 12 + 14 + 16 + …+ 102.

What is the value of ?

(A) 92(B) 98(C) 100(D) 102(E) 112

5. At an elementary school, the students in third grade, fourth grade, and

fifth grade run an average of 12, 15, and 10 minutes per day, respectively.

*欧阳光明*创编 2021.03.07

*欧阳光明*创编 2021.03.07

There are twice as many third graders as fourth graders, and twice as

many fourth graders as fifth graders. What is the average number of

minutes run per day by these students?

(A) 12(B) (C) (D) 13 (E) 14

6. Set A has 20 elements, and set B has 15 elements. What is the smallest

possible number of elements in A∪B, the union of A and B?

(A) 5(B) 15(C) 20(D) 35 (E) 300

7. Which of the following equations does NOT have a solution?

(A)

(D)

(B)

(E)

(C)

8. Last summer 30% of the birds living on TownLake were geese, 25%

were swans, 10% were herons, and 35% were ducks. What percent of the

birds that were not swans were geese?

(A) 20(B) 30(C) 40(D) 50(E) 60

9. A rectangular region is bounded by the graphs of the equations y=a,

y=-b, x=-c, and x=d, where a, b, c, and d are all positive numbers. Which

of the following represents the area of this region?

(A) ac + ad + bc + bd(B) ac – ad + bc – bd(C) ac + ad – bc – bd

(D) –ac –ad + bc + bd(E) ac – ad – bc + bd

10. A majority of the 20 students in Ms. Deameanor’s class bought

pencils at the school bookstore. Each of these students bought the same

number of pencils, and this number was greater than 1. The cost of a

pencil in cents was greater than the number of pencils each student

*欧阳光明*创编 2021.03.07


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