2018年AMC8考题和答案解析(20210313165905)

1、2017 AMC 8 考题及答案Problem 1Which of the followi ng values is largest?A)2+0 + l + 7(B) 2x0 +1 + 7(C)2 + 0xl + 7(D) 2 + 04-1x7(E) 2x0x1 xProblem 2Alicia, Bren da, and Colby were the can didates in a rece nt electio n for stude nt preside nt. The pie chart below shows how the votes were distributed among

2、 the three can didates. If Brenda received 36 votes, the n how many votes were cast all together?Alicia45%Brenda 、30%(A) 70(B) 84(C) 100(D) 106(E) 120Problem 3What is the value of the expressi on I ?(A) 4(B) 4“(C) 8(D) 8v(E) 16Problem 4When 0.000315 is multiplied by 7,928,564 the product is closest

3、to which of the follow ing?(A) 210(B) 240(C) 2100(D) 2400(E) 24000Problem 51 2 3 4 5 (b 7 8What is the value of the expression 1 + 2 + 3 + 4 + 5 + G + 7 +(A) 1020(T3) 1120(C) 1220(D) 2240(E) 3360Problem 6If the degree measures of the angles of a triangle are in the ratio3:3:4, what is the degree mea

4、sure of the largest an gle of thetrian gle?(A) 18(B) 36(C) 60(D) 72(E) 90Problem 7Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the followi ng nu mbers must also be a factor ofZ?(A) 11(B) 19(C) 10

5、1(D) 111(E) 1111Problem 8Malcolm wants to visit Isabella after school today and knows the street where she lives but does nt know her house nu mber. She tells him, My house nu mber has two digits, and exactly three of the follow ing four stateme nts about it are true.(1) It is prime.(2) It is eve n.

6、(3) It is divisible by 7.(4) One of its digits is 9.This information allows Malcolm to determine Isabellas house number.What is its units digit?(A) 4(B) 6(C) 7(D) 8(E) 9Problem 9All of Marcys marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and

7、six of them are gree n. What is the smallest nu mber of yellow marbles that Marcy could have?(A) 1(B) 2(C) 3(D) 4(E) 5Problem 10A box contains five cards, nu mbered 1,2, 3, 4, and 5. Three cards are selected ran domly without replaceme nt from the box. What is the probability that 4 is the largest v

8、alue selected?Problem 11A square-shaped floor is covered with con grue nt square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?(A) 148(B) 324(C) 361(D) 1296(E) 1369Problem 12The smallest positive in teger greater tha n 1 that leaves a rema in

9、 der of 1 whe n divided by 4, 5, and 6 lies betwee n which of the follow ing pairs of nu mbers?(A) 2 and 19(B) 20 and 39(C) 40 and 59(D) 60 and 79(E) 80 and 124Problem 13Peter, Emma, and Kyler played chess with each other. Peter won 4games and lost 2 games. Emma won 3 games and lost 3 games. If Kyle

10、r lost 3 games, how many games did he win?(A) 0(B) 1(C) 2(D) 3(E) 4Problem 14Chloe and Zoe are both stude nts in Ms. Demea nors math class. Lastni ght they each solved half of the problems in their homeworkassig nmen t al one and the n solved the other half together. Chloe had correct answers to onl

11、y80% of the problems she solved alone, butoverall 88% of her answers were correct. Zoe had correct answers to 90% of the problems she solved alone. What was Zoes overall perce ntage of correct an swers?(A) 89(B) 92(C) 93(D) 96(E) 98Problem 15In the arrangement of letters and numerals below, by how m

12、anydiffere nt paths can one spell AMC8? Beg inning at the A in the middle, a path allows only moves from one letter to an adjace nt (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.8C88CA/C8CMAMCSCMC88C8(A) 8(B) 9(C) 12(D) 24(E) 36Problem 1

13、6In the figure below, choose point D on HC so that ACD and ABD have equal perimeters. What is the area ofABD?33125(A) -(B) -(C) 2(D) (E)-Problem 17Start ing with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty.

14、 So in stead I put 6 gold coins in each treasure chest, but the n I had 3 gold coins left over. How many gold coins did I have?(A) 9(B) 27(C) 15(D) 63(E) 81Problem 18In the non-con vex quadrilateral.;.Sshown below,is aright an gle,._, -| I, ?, and -: :, .DWhat is the area of quadrilateralABCD?(A) 12

15、(B) 24(C) 26(D) 30(E) 36Problem 19For any positive integerAl, the notation M denotes the product ofthe integers1 through AL What is the largest integernfor which 5n isa factor of the sum 98! + 99! + 100! ?(A) 23(B) 24(C) 25(D) 26(E) 27Problem 20An integer between1000 and 9999, inclusive, is chosen a

16、t random.What is the probability that it is an odd integer whose digits are alldisti net?145610779(A) (B) (C) (D) (E)752254002525Problem 21Suppose Q, b, and c are non zero real nu mbers, andG + 方 + E = 0.a b c abcWhat are the possible value(s) for11?(A) 0(B) 1 and - 1(C) 2 and -2(D) 0,2, and -2(E) 0

17、,1, and -Problem 22In the right triangleABC, AC 12, DC = 5, and angle C is a rightan gle. A semicircle is in scribed in the tria ngle as show n. What is the radius of the semicircle?Problem 23Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an

18、 integer number of minutes. Each day after the first, her speed decreased so that the nu mber of minu tes to travel one mile in creased by 5 minu tes over the preced ing day. Each of the four days, her dista nee traveled was also an in teger nu mber of miles. What was the total nu mber of miles for the four trips?(A) 10(B) 15(C) 25(D) 50(E) 82Problem 24 Mrs. San ders has three gran dchildre n, who call her regularly. One calls her every three days,