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
random翻译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. 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) (B) (C)
(D) (E)
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 a
rea 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 bought, and the total cost of all the pencils was $17.71. What was the cost of a pencil in cents?
(A) 7(B) 11(C) 17(D) 23  (E) 77
11. Square EFGH has one vertex on each side of square ABCD. Point E is on AB with AE=7·EB. What is the ratio of the area of EFGH to the area of ABCD?
(A)(B)(C)(D)(E)
12. The players on a basketball team made some three-point shots, some two-point shots, some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team’s total score was 61 points. How many free throws did they make?
(A) 13(B) 14(C) 15(D) 16(E) 17
13. How many even integers are there between 200 and 700 whose digits are all different and come from the set {1, 2, 5, 7, 8, 9}?
(A) 12(B)20(C)72(D) 120 (E) 200
14. A pair of standard 6-sided fair dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle’s circumference?
(A)(B)(C)(D)(E)
15. Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first 40 miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of 0.02 gallons per mile. On the whole trip he averaged 55 miles per gallon. How long was the trip in miles?
(A) 140(B) 240(C) 440(D) 640(E) 840
16. Which of the following in equal to ?
(A)(B)(C)(D)(E)
17. In the eight-term sequence A, B, C, D, E, F, G, H, the value of C is 5 and the sum of any three consecutive terms is 30. What is A + H?
(A) 17(B) 18(C) 25(D) 26  (E) 43
18. Circles A, B, and C each have radius 1. Circles A and B share one point of tangency. Circle C has a point of tangency with the midpoint of AB. What is the area inside Circle C
but outside Circle A and Circle B?

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