tceic.com
学霸学习网 这下你爽了
赞助商链接
当前位置:首页 >> 英语考试 >>

2011AMC10美国数学竞赛B卷


2011AMC10 美国数学竞赛 B 卷

2011 AMC10 美国数学竞赛 B 卷 1. What is (A) -1
2 + 4 + 6 1+ 3 + 5 ? ? 1+ 3 + 5 2 + 4 + 6 5 7 (C) (B) 36 12

(D)

147 60

(E)

43 3

2. Josanna’s test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise here test average at least 3 pints with her next test. What is the minimum test score she would need to accomplish this goal? (A) 80 (B) 82 (C) 85 (D) 90 (E) 95

3. At a store, when a length is reported as x inches that means the length is at least x-0.5 inches and at most x+0.5 inches. Suppose the dimensions of a rectangular tile are reported as 2 inches by 3 inches. In square inches, what is the minimum area for the rectangle? (A) 3.75 (B) 4.5 (C) 5 (D) 6 (E) 8.75

4. LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip, it turned out that LeRoy had paid A dollars and Bernardo had paid B dollars, where A<B. How many dollars must LeRoy give to Bernardo so that they share she costs equally? (A)
A+ B 2

(B)

A? B 2

(C)

B?A 2

(D) B ? A

(E) A + B

- 1 -

2011AMC10 美国数学竞赛 B 卷

5. In multiplying two positive integers a and b, Ron reversed the digits of the two-digit number a. His erroneous product was 161. What is the correct value of the product of a and b? (A) 116 (B) 161 (C) 204 (D) 214 (E) 224

6. On Halloween Casper ate 1/3 of his candies and then gave 2 candies to his brother. The next day he ate 1/3 of his remaining candies and then gave 4 candies to his sister. On the third day he ate his final 8 candies. How many candies did Casper have at the beginning? (A) 30 (B) 39 (C) 48 (D) 57 (E) 66

7. The sum of two angles of a triangle is 6/5 of a right angle, and one of these two angles is 30°larger than the other. What is the degree measure of the largest angle in the triangle? (A) 69 (B) 72 (C) 90 (D) 1024 (E) 108

8. At a certain beach if it is at least 80℉and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded about the weather conditions on June 10? (A) The temperature was cooler than 80℉ and it was not sunny. (B) The temperature was cooler than 80℉ or it was not sunny. (C) If the temperature was at least 80℉, then it was sunny.

- 2 -

2011AMC10 美国数学竞赛 B 卷

(D) If the temperature was cooler than 80℉, then is was sunny. (E) If the temperature was cooler than 80℉, then it was not sunny.

9. The area of △EBD is one third of the area of 3-4-5 △ABC. Segment DE is perpendicular to segment AB. What is BD? (A)
4 3

(B)

3

(C)

9 4

(D)

4 3 3

(E)

5 2

10. Consider the set of numbers {1, 10, 102, 103……1010}. The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer? (A) 1 (B) 9 (C) 10 (D) 11 (E) 101

11. There are 52 people in a room. What is the largest value of n such that the statement “At least n people in this room have birthdays falling in the same month” is always true? (A) 2 (B) 3 (C) 4 (D) 5 (E) 12

12. Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The track has a width of 6 meters, and it takes her 36 seconds longer to walk around the outside edge of the track than around the inside edge. What is Keiko’s speed in meters per second?

- 3 -

2011AMC10 美国数学竞赛 B 卷

(A)

π
3

(B)

2π 3

(C) π

(D)

4π 3

(E)

5π 3

13. Two real numbers are selected independently at random from the interval [-20, 10]. What is the probability that the product of those numbers is greater than zero? (A)
1 9

(B)

1 3

(C)

4 9

(D)

5 9

(E)

2 3

14. A rectangular parking lot has a diagonal of 25 meters and an area of 168 square meters. In meters, what is the perimeter of the parking lot? (A) 52 (B) 58 (C) 62 (D) 68 (E) 70

15. Let @ denote the “averaged with” operation: a @ b = distributive laws hold for all numbers x, y, and z? I. II. III.
x @( y + z ) = ( x @ y ) @( x @ z ) x @( y + z ) = ( x + y ) @( x + z ) x @( y@z ) = ( x @ y ) @( x @ z )

a +b . Which of the following 2

(A) I only

(B) II only

(C) III only

(D) I and III only (E) II and III only

16. A dart board is a regular octagon divided into regions as shown. Suppose that a dart thrown at the board is equally likely to land anywhere on the board. What is probability that the dart lands within the center square? (A)
2 ?1 2

(B)

1 4

(C)

2? 2 2

- 4 -

2011AMC10 美国数学竞赛 B 卷

(D)

2 4

(E) 2 ? 2

17. In the given circle, the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4:5. What is the degree measure of angle BCD? (A) 120 (D) 135 (B) 125 (E) 140
D C A

(C) 130
E B

18. Rectangle ABCD has AB=6 and BC=3. Point M is chosen on side AB so that ∠AMD=∠CMD. What is the degree measure of ∠AMD? (A) 15 (B) 30 (C) 45 (D) 60 (E) 75

19. What is the product of all the roots of the equation (A) -64 (B) -24 (C) -9 (D) 24 (E) 576

5 x + 8 = x 2 ? 16 ?

20. Rhombus ABCD has side length 2 and ∠B=120°. Region R consists of all points inside the rhombus that are closer to vertex B than any of the other three vertices. What is the area of R? (A)
3 3

(B)

3 3

(C)

2 3 3

(D) 1 +

3 3

(E) 2

21. Brian writes down four integers w>x>y>z whose sum is 44. The pairwise positive

- 5 -

2011AMC10 美国数学竞赛 B 卷

differences of these numbers are 1, 3, 4, 5, 6, and 9. What is the sum of the possible values for w? (A) 16 (B) 31 (C) 48 (D) 62 (E) 93

22. A pyramid has a square base with sides of length land has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that one face is on the base of the pyramid and its opposite face has all its edges on the lateral faces of the pyramid. What is the volume of this cube? (A) 5 2 ? 7 (B) 7 ? 4 3 (C)
2 2 27

(D)

2 9

(E)

3 9

23. What is the hundreds digit of 20112011 ? (A) 1 (B) 4 (C) 5 (D) 6 (E) 9

24. A lattice point in an xy-coordinate system in any point (x, y) where both x and y are integers. The graph of y = mx + 2 passes through no lattice point with 0 < x ≤ 100 for all m such that (A)
51 101 1 < m < a . What is the maximum possible value of a? 2 50 51 52 13 (B) (C) (D) (E) 99 100 101 25

25. Let T1 be a triangle with sides 2011, 2012, and 2013 for n ≥ 1 , if Tn=△ABC and D, E, and F are the points of tangency of the incircle of △ABC to the sides AB, BC and AC, respectively, then Tn+1 is a triangle with side lengths AD, BE, and CF, if it exists. What is the perimeter of the last triangle in the sequence (Tn)? - 6 -

2011AMC10 美国数学竞赛 B 卷
1509 8 1509 32 1509 64 1509 128 1509 256

(A)

(B)

(C)

(D)

(E)

- 7 -


赞助商链接
推荐相关:

2011AMC10美国数学竞赛A卷 中文翻译及答案

2011AMC10美国数学竞赛A卷 中文翻译及答案_学科竞赛_高中教育_教育专区。2011AMC...某个矩形是由 y=a, y=-b, x=-c, 与 x=d,的圆形所围成的,其中 a,...


2011AMC10美国数学竞赛A卷

X ? (A) 92 (B) 98 (C) 100 (D) 102 (E) 112 - 1 - 2011AMC10 美国数学竞赛 A 卷 5. At an elementary school, the students in third grade...


2008 AMC10美国数学竞赛B卷

2011AMC10美国数学竞赛A卷 7页 1财富值 2009 AMC10美国数学竞赛B卷... 7页 1财富值如要投诉违规内容,请到百度文库投诉中心;如要提出功能问题或意见建议,请点击...


2000到2012年AMC10美国数学竞赛

2000到2012年AMC10美国数学竞赛_高三数学_数学_高中...(A) 2 (B) 4 (C) 6 (D) 8 (E) 10 11...(A) 2011 (B) 2012 (C) 2013 (D) 2015 (E...


2010AMC10美国数学竞赛A卷

2010AMC10美国数学竞赛A卷_数学_初中教育_教育专区。2010AMC10 美国数学竞赛 A...2010AMC10美国数学竞赛B... 2011AMC10美国数学竞赛A... 2011AMC10美国数学竞赛...


2010-2015年AMC 10A和B竞赛真题及答案(英文版)_图文

2010-2015年AMC 10A和B竞赛真题及答案(英文版)_学科竞赛_高中教育_教育专区。...2011年AMC8竞赛真题(英文... 7页 1下载券 AMC 美国数学竞赛 2002 ... 16...


AMC10美国数学竞赛真题2009B卷

AMC10美国数学竞赛真题2009B卷 - Problem 1 Each morning of her five-day workweek, Jane bought either a 50-ce...


2012美国数学竞赛AMC10B答案详解

高中一年级美国数学竞赛... 9页 1下载券 2012年-AMC10-A卷 6页 免费 美国数学邀请赛2007AMC1... 6页 免费 2011AMC10美国数学竞赛B... 7页 1下载券©...


AMC10美国数学竞赛真题2003B卷

AMC10美国数学竞赛真题2003B卷 - Problem 1 Which of the following is the same as Solution Problem 2 Al get...


2000-2012美国AMC10中文版试题及答案

2000到2012年AMC10美国数学竞赛 2000-2012美国AMC10...(A) 3 (B) 6 (C) 9 (D) 17 (E) 20 。...(A) 2011 (B) 2012 (C) 2013 (D) 2015 (E...

网站首页 | 网站地图
All rights reserved Powered by 学霸学习网 www.tceic.com
copyright ©right 2010-2021。
文档资料库内容来自网络,如有侵犯请联系客服。zhit325@126.com