2018AMC10B試題及答案

1、2018 AMC 10B ProblemsProblem 1Kate bakes a 20-inch by 18-ineb pan of corn bread. The corn bread is cut irrto pieces thai measure 2 inches by 2 inches How many pieces of cornbread does the pan contafn?(A) 90(B) 1 (MJ (C) 180(D) 200(E) 360Problemi 2Sam drove 96 miles in 90 minutes. Hisbpted during the

2、 rirAt 30 (Tiiriutes was 60mph (miles per hour), and Ms average speed during The second 30 mrnutes was 65 nriph. What was his average speed, in mph, during th。last 30 nninutes?(A) 64(B) 65(C) 66(D) 67(E) 68Problem 3In the expression (x) + (>)each blank is to be Piled in with one o'the digiis

3、1,2, 3. or 4* v/jth each digit being used once* How many different values csr be obtained?(A) 2(B) 3(C) 4(D) 6(E) 24Problem 4A three-dimensional rectangular box wth dimensions X, and Zhas faces whose surface srsas are 24, 24. 4& 48, 72, and 72 square units. What is X -1 Y k Z?(A) 18(B) 22(C) 24(

4、D) 30(E) 36Saint its hiProblem 5How many subsets of 2t 3、4, 5t 6,7,8,9 cortain at least one prime number?(A) 128(B) 1S2 (C) 224(D) 240(E) 256Problem 6A box contains 5 chips, numbered h 2 3, 45 and 5. Chips are drawn randomly one at a time without replacement untikhe sum of the values drawn exceeds 4

5、. What is the probabilhy tha： 3 draws are required?號(hào)T1播強(qiáng)1,13)話肓O -fi功尊 (El -Problem 7In the figure below, N congruent semicircles are drawn aong a dfameter of a large semicircle, with their diameters covering the diameter of the large semicircle with no overlap. Let. 1 be :he ccmbed area o* th 巳 sma

6、 I semicircles and £? be the area (/ the region inside the large semicircle but outsfde the small semicircles. The ratio >1 i B Is 1:18* What is TV?(A) 1«罰応on(B)17(C) 18(D) W (E) 36ProblemSnra makes a staircase out of tootbpicKs as shown:This Is a 3-step staircase and uses 18 toothpicks

7、, How many steps would be in a staircase that used 180 toothpicks?(U)21(E) 30Problemi 9The taces of each of 7 standard dice are label&d with the integers from 1 to 6. Let p be the probability that when all 7 dice are rolled* the sum of the numbers on the top faces Is 10- What other sum occurs wi

8、th the same probability p?(A) 13(B) 26(C) 32(D) 39(E) 42Sa nr 伽Problem 10tn the rectangular paral elepiped shown, AB 一 3, Z3C7 = lr and CG = 2. Point M is the midpoint of EG, What is the volume of the rectangular pyramid with base BCHE and apex M?& MAA AMC5American Mathematics Competition(E)1(A)

9、 1(B) bProblem 11Which of the following expressions is never a prime number when 歲 is 自 prime number?(A)戸帶汕(R)於半M (G)於爛vn)聲嚨(E) p2 A©6Problem 12Line segment J/? is a diameter of a circle with AIJ = 24. Point Ct not equal to .1 or ft lies on the circle. As point C moves arouncf the circle, the c

10、entroid (center of mass) of traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by :his curve?(A) 25(B) 38(C) 50(D) 63(E) 75Problem 13How many of the first 2018 numbers in the sequence 101,100L 10001, 100001 are divisible by 101?(A) 2

11、53(B) 504(C) 505(D) 5U6(E) 1009SolutionProblem 14A list of 2()IS positive integers has a unique mode, which occurs exactly 10 times. What is the lea&t number of distinet values that can occur in the list?(A) 202(B)223(C) 224(D) 225(E)234Problem 15A closed box with a square base is to be wrapped

12、with a square sheet of wrapping paper The box Is c 會(huì) ntered on the wrapping paper with the vertices of the base lying omthe midlines of the square sheet of paper, as shown in the figure on the left. The four comers of the wrapping paper are to be folded up over the sides and brought together to meet

13、 at the center of the top of the boxt point ,1 in the figure on the right, The box has base length ?rand heig 卜 t h. What ig thm area erf th 它 sheet wrapping paper?2018 AMC 10B Problems(A) 2(w + A)2(B)仙牛研(C)+ 4wh (D) 2w2(E) w2/i£SolutionProblem 16Let (iita2).is be a strict!/1ncreasing sequence

14、of positive integers such that引 + S 4*+20 IB 處咔What Is the remaincfer when aj + a J + +。蕩耶 is divided by 6?(A)0(B)1(C)2(D)3(E)4SolutT onProblem 17In rectangle PQRSt PQ = 8 and QR = & Points A and B ie on PQt points C and D lie on QR, poFnts E and Flie on 麗.and points G and H Ne on SP so thatAP =

15、 BQ < 4 and 岀 E convex octagon ABODEFGil is equilateraL The length of a side of this octagon can be expressed in the farm k + mVnt where k. niA snd n are integers and n is ncn divisible by the square o, any prime. What is fe + 門r+ n?(A) 1(B)7(C)21(D) «2(E) 106SoliutieMnProblem IBThree young

16、brot-erAsister pairs from different families need to take a trip In 呑 van. These six children will occupy the second 用 nd third rows rn lhe van, each of which Jias three seats. To avoid disruptions, siblings may not sit right next to each o'ber in the same row, and no child may sit directlv in f

17、ront of his or her skiing How mainy seating arrangements are possible for this trip?(A) 60(B) 72(C) 92(D) 9S (E) 120Sc!ufl£MnProblem 19Joey and Chloe and their daughter Zoe all have the same birthday, Joey is T year older than Chloe, and Zoe is exactly 1 year old today Today is the first of the

18、 9 birthdays on whiert CrioeHs age will be an integral multiple of Zoe's age. What will be the sum oT the two digits of Joey's age the next time h 誼 age Is a multiple of Zoe's age?(A) 7(B)8(C)9(D)1(E)11Problem 201 andA functlon / is defined recursively by /(I) = /(2)/(n) = /(n- l)-/(n-2)

19、+nfor all integers n > 3. What is f (2018)?(A) 2016(B) 20L7(C) 2018(D) 2019(E) 2020SsjlwtkmProblem 21Mary chose an even 4digit number n. She wrote down all the dMsors of n in increasing n order from left to right: l,2t< n. At some moment Mary wrote 323 as a divisor of 仏JuWhat is the smallest p

20、ossible value of the next divisor written to the right of 323?(A) 324(B) 330(C) 340(D) 361(E) 646駅 lutkmProblem 22Real numbers xand y are chosen independently and uniformly at random from the interval 0.1 Which of the foltowing numbers is closest to the probability that y, and 1 are the side lengths of an obtuse triangle?(A) 0J1(B) 0,25(C) 0.29(D) 0,50(E) 0.79Soluti onProblenn 23How many ordered pairs («,