2018年AMC12真题PDF下载（A卷）
1.A large urn contains 100 balls, of which 36% are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be 72%? (No red balls are to be removed.)
A.28
B.32
C.36
D.50
E.64
2.While exploring a cave, Carl comes across a collection of 5-pound rocks worth $14 each, 4-pound rocks worth $11 each, and 1-pound rocks worth $2 each. There are at least 20 of each size. He can carry at most 18 pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?
A.48
B.49
C.50
D.51
E.52
3.How many ways can a student schedule 3 mathematics courses -- algebra,geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)
A.3
B.6
C.12
D.18
E.24
4.Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then
remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Let d be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of ?
A.(0,4)
B.(4,5)
C.(4,6)
D.(5,6)
E.(5,∞）
5.What is the sum of all possible values of k for which the polynomials x2-3x+2 and x2-5x+k have a root in common?
A.3
B.4
C.5
D.6
E.10
6.For positive integers m and n such that m+10
A.20
B.21
C.22
D.23
E.24
7.For how many (not necessarily positive) integer values of n is the value of 400▪(2/5)n an integer?
A.3
B.4
C.6
D.8
E.9
8.All of the triangles in the diagram below are similar to iscoceles triangle ABC,in which AB=AC. Each of the 7 smallest triangles has area 1,and △ABC has area 40. What is the area of trapezoid DBCE?
A.16
B.18
C.20
D.22
E.24
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