AMC10B试题及答案

1、Problem 1Kate bakes a 20-inch by 18-incb pan of corn bread. The cornbread is cut into pieces t hai messune 2 inches by 2 inches. How many pieces of combEd does the pan contain?(A) 90(B) 1W (C) 180(D) 200(E) 360Problem 2SafTi drove 96 tnies in 90 niinutes. His average speed during the firt 30 (Tiiriu

2、tes was GO mph (miles per hour), and his average speed during the second 30 minutes was 65 mph, What was his average spesd in mphr during the last 30 nninutes?(A) 64(B) 65(C) 66(D) 67(E) 68Problem 3In the expression (x) + (x) each blank is to bE nlled 'n with one c/the digiis 1,2, 3* or 4* v/ith

3、 each digit being used once* How many different values ccr be obtained?(A) 2(B) 3(C) 4(D) 6(E) 24帥 utkmProblem 4A three-dlmenslanal rectangular box wth dimensions X, and Z has faces wnose surface areas are 24, 24, 48, 48, 72, and 72 square units. What 海 X + F + 刀？(A) 18(B) 22(C) 24(D) 30(E) 36Salnii

4、cifiProblem 5How many subsets Of 2? 3, 4? 5,6,7,8,9 cortain at least one prime rumber?(A) 128(B) 1S2(C) 224(D) 240(E) 256Problem 6A box cor tains 5 chips, numbered 1, 2t 3, 4. and 5. Chips are drawn rjndurnly one at a time without replacement until the sum of the values drawn exceeds 4. What is the

5、probability that 3 draws are required? *(B)C) ；(D) Z (E) 7炳IP5<Problem 7In the figure below, N congruent semicfrcles are drawn along a diameter of a large semicircle, with their diameters covering the diameter of the large semicirGle w th no overlap. Let A be :he ccrnb ned area o* th巳 sma I semic

6、ircles and B be the rea of the region Inside the large sari汜iirl旦 but outsfde the small semicircles. The ratfo >4 f B is 1:18. What is TV?(A) 16(B) 17旣皿onProblem 8Sara makRS a staircase out of toothpicks as shown:How man/ steps would be in a staircaseThis is o 3-sto staircase ard 18 toc:noick&

7、;.that used 18® tGOthpioks?(A) J©阿H(©)'S4! 3WProblem 9The taces of each of 7 standard dice are label&d with the in:egers from 1 to 6. Let p be the probability that when all 7 ci汜巳 are rolled, the sum of the numbers on the top faces is 10. What other sum occurs with the same pr

8、obability p?(A) 13(B) 2G (C) 32(D) 39(E)號伽m2 Point aI is the base BCHE andProblem 10In the rectangular parallelepiped shown, AB 3, fiC = lt and CG midpoint of 卜G What is the volume of the rectangular pyramid with apex A/?塔-龜切.3gy .(A)l(B)|(q>|(D)|(助足Problem 11Which of the folkswi门g expressions is

9、 never a prime rtimber when p is a prime number?(A) + M (B) j +24(C)p2+3B (II)(E)沪+ 96Problem 12Line segmen: AI3 is a diameter of a circle with A/? 24. Point not equal to A or B lies on the circle. As point C moves around the circle, 1he centroid (center of mass) of AABC traces out a closed curve mi

10、ssing two points. To the nearest positive integer, what is the area of the region bounded by this curve?(A) 25(B) 38(C) 50(D) 63(E) 75SolutfanProblem 13How many of :he first 2018 numbers In the sequence 101,1001,10001,1000C1, are divisible by 101?(A) 253(B) 504(C) 505(D) 50G(E) 1009SolutionProblem 1

11、4A list of 2018 positive ntegers has a unique mode, which occurs exactly 10 times. What Is the least number of distinct values that can occur in the list?(A) 202(B) 223(C) 224(D) 225(E) 234Sal uttonProblem 15A closed box witn a square base 胆 to be wrapped with a square sheet of wrapping paper. The b

12、ox is centered on the wrapping paper with the vertices of the base lying on the midlines of the square sheet of paper, as shown in the figure on the left. The four corners of the wrapp ng paper are to be folded up over the sides and brought together to meet at the center of the top of the box, point

13、 A in the figure on the right The box has base length w and height h. What is the area of the sheet oi wrapping paper?(A) 2(矽 + Kf (B)帥 £ 处 (C) 2w2 + 4wh(D) 2沪(E) w2hProblem 16Let ,桃厕诃 be a strictly Increasing sequence of positive integers such that如 + 如 + * * 丰 flaoia 2018aoiB,What is the rema

14、inder when 囲 + 曲 + + is divided by 6?(A) 0(B) 1(C) 2(D) B (E) 4丽m伽Problem 17In rectangle PQRS、PQ = 8 and QR = 6. Points A and B Ife on PQt points C and D lie on QE points E and ?' lie on HS, and points G and H lie on SP so that AP = BQ < 4 and the convex octagon A13GDEFGH fs equi ateraL The l

15、ength of a side of this octagon can be expressed Tn the farm A： + my/nt where kt th. and 7i are integers 自nd n is not divisible by the squars of any prime. What 13 fc + m + n?(A) 1(B) 7(C) 21(D) 92(E) 106Problem 18Three young brother-sister pairs from different Emilies need to tak a trip in a van. T

16、hese six children will occupy the second and third rows in the van: each of which has three_n avoic disrhptions, s blings may not 吋t right next tn other In the same row, and no child may sit directly in front of bis or nor aibling. How many seating arrangemerts are possible for this trip?(A) 60(B) 7

17、2(C) 92(D) 96(E) 120帥 ar:fc)nProblem 19Joey and Chloe and their daughter Zoe all have the same birthday Joey is 1 year older than Chloe, Hnd Zoe Is exactly 1 year old loday. Today Is the first of the 9 birthdays on wnich Ch oe's age wil be an integral mu tiple of Zoe's age. What will be the

18、sum of the two digits of Joey's age the next time his age is a multiple of Zoes age?(A) 7(B) 8(C) 9(D) 10(E) 11Problem 20A function f is defined recursively by /(l) = /(2) = 1 and/(n) = J(n L) f(n - 2) +n for all Integers n > 3. What is J(2018)?(A) 2016(B) 2017(C) 2018(D) 20L9(E) 2020Problem

19、21Mary chose an even 4-digit number n. She wrote down all the divisors of n In Increaslrgnorder trom left to right L 2,At some moment Mary wrote 323 as a divisor of n.What is the smallest possible valu已 of the next diviso' v/ri:ten to the right of 323?(A) 324(B) 330(C) 340(D) 361(B) 646SolutionP

20、roblem 22Real numbers 不 and y are chosen independently and uniformly at random from the inten/al 0,1, Which of the following numbers is closest to the probability that x, / and 1 are tlie Side lengths of an obtuse triancle?(A) 0.21(B) 0.25<C) 0.29(D) 0.50(E) 0.7SProblem 23How many ordered pairs (u, b) of positTve inlegers satisfy the equationa >6 + 63 20 -km(arb) + 12 - gcd(<z, fr),wher