2019年AMC12真题PDF下载-B卷
1. Alicia had two containers. The first was 5/6 full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was 3/4 full of water. What is the ratio of the volume of the first container to the volume of the second container?
Alicia 有两个容器。 第一个里面的水是5/6满的，第二个是空的。 她将第一个容器中的所有水倒入第二个容器中，此时第二个容器中的水是3/4满的。较小容器的容积与较大容器的容积之比是多少?
A.5/8
B.4/5
C.7/8
D.9/10
E.11/12
2.Consider the statement, "If n is not prime, then n − 2 is prime." Which of the following values of n is a counterexample to this statement?
考虑论断：“如果n不是质数，那么n−2就是质数。” 以下的哪个n值是此论断的反例?
(A)11 (B)15 (C)19 (D)21 (E)27
3. Which one of the following rigid transformations (isometries) maps the line segment AB onto the line segment A'B' so that the image of A(−2,1) is A'(2,−1) and the image of B(−1,4) is B'(1,−4)?
下列哪个刚性变换(等距变换)把线段AB映像到线段A'B'，并且使得A(−2,1)的映像是A'(2,−1)，B(−1,4)的映像是B'(1,−4)?
(A) reflection in the y-axis 关于y轴的反射
(B) counterclockwise rotation around the origin by 90°绕原点逆时针旋转90°
(C) translation by 3 units to the right and 5 units down向右平移 3 个单位再向下平移5 个单位
(D) reflection in the x -axis 关于 x 轴的反射
(E) clockwise rotation about the origin by 180°绕原点顺时针旋转180°
4. A positive integer n satisfies the equation (n +1)!+ (n + 2)!= 440·n!. What is the sum of the digits of n ?
正整数n 满足等式(n +1)!+ (n + 2)!= 440·n!.n的数字总和是多少?
(A)2 (B)5 (C)10 (D)12 (E)15
5. Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or n pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of n ?
商店里每一块糖的售价都是整分钱。 Casper 有足够的钱购买12 块红色糖果，14块绿色糖果，15 块蓝色糖果，或者n 块紫色糖果。一块紫色糖果售价20 美分。n 的最小可能价值是多少?
(A)18 (B)21 (C)24 (D)25 (E)28
6. In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of VABC is 50 units and the area of □ABC is 100 square units?
在给定的平面中，点A和B相距10个单位。平面上有多少个点 C， 使得VABC的周长是50单位，VABC的面积是100 平方单位?
(A)0 (B)2 (C)4 (D)8 (E)infinitely many
7. What is the sum of all real numbers x for which the median of the numbers 4,6,8,17, and x is equal to the mean of those five numbers?
实数x 满足4，6，8，17 和x 的中位数等于这五个数的平均值，问所有这样的实数x 的总和是多少?
A.-
B.0
C.5
D.15/4
E.35/4
余下真题省略！
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