2019年AMC10真题PDF下载(B卷)
1. Alicia had two containers. The first was 5 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 full of water. What is the ratio of the volume of the smaller container to the volume of the larger container?
Alicia有两个容器,第一个里面的水是56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34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. In a high school with 500 students, 40% of the seniors play a musical instrument, while 30% of the non-seniors do not play a musical instrument. In all, 46.8% of the students do not play a musical instrument. How many non-seniors play a musical instrument?
在一所有500名学生的高中,40%的高三学生会演奏乐器,而30%的非高三学生不会演奏乐器。整体而言,46.8%的学生不会演奏乐器。有多少非高三学生会演奏乐器?
(A) 66
(B) 154
(C) 186
(D) 220
(E) 266
4. All lines with equation ax + by = c such that a, b, c form an arithmetic progression pass through a common point. What are the coordinates of that point?
a,b,c是等差列的,且方程ax + by = c表示的直线都通过一公共点。那个点的坐标是什么?
(A) (−1, 2)
(B) (0, 1)
(C) (1, −2)
(D) (1, 0)
(E) (1, 2)
5. Triangle ABC lies in the first quadrant. Points A, B and C are reflected across the line y = x to points Af, Bf and Cf, respectively. Assume that none of the vertices of the triangle lie on the line y = x. Which of the following statements is not always true?
三角形ABC位于第一象限。点A,B和C沿直线y = x反射分别得到点Af,Bf和Cf。假设三角形的顶点都不在y = x这条在线。以下哪个陈述不是一定正确?
(A) Triangle Af BfCf lies in the first quadrant. 三角形Af BfCf在第一象限。
(B) Triangle ABC and Af BfCf have the same area. 三角形ABC和 Af BfCf 的面积相同。
(C) The slope of line AAf is −1. 直线AAf的斜率是−1。
(D) The slopes of lines AAf and CCf are the same. 直AAf和CCf 的斜率相同。
(E) Lines AB and Af Bf are perpendicular to each other. 直线AB和 Af Bf互相垂直。
6. 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的各个数位上的数字之和是多少?
(A) 2
(B) 5
(C) 10
(D) 12
(E) 15
7. Each piece of candy in a shop 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 least possible value of n?
商店里每一块糖的售价都是整数分钱。Casper有足够的钱购买12红色糖果,14绿色糖果,15色糖果,或者n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
8. The figure below shows a square and four equilateral triangles, with each triangle having a side lying on a side of the square, such that each triangle has side length 2 and the third vertices of the triangles meet at the center of the square. The region inside the square but outside the triangles is shaded. What is the area of the shaded region?
下图显示了正方形和四个等边三角形,每个三角形有一条边在正方形的一条边上,使得每个三角形的边长为2,并且各三角形的第三顶点在正方形的中心相交。在正方形内但在三角形外的区域用阴影表示。问阴影区域的面积是多少?
余下真题省略!
你可能还关注