本文格式为Word版，下载可任意编辑2022年AMC12真题及答案 2022 AMC12 A Problem 1 What is the value of ? Solution Problem 2 For what value of does ? Solution Problem 3 The remainder can be defined for all real numbers and with by where What is the value of ? denotes the greatest integer less than or equal to . Solution Problem 4 The mean, median, and mode of the data values to . What is the value of ? Solution Problem 5 Goldbach's conjecture states that every even integer greater than 2 can be written as the sum of two prime numbers (for example, ). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of? are all equal Solution Problem 6 A triangular array of coins has coin in the first row, coins in the second row, coins in the third row, and so on up to coins in the th row. What is the sum of the digits of ? Solution Problem 7 Which of these describes the graph of ? Solution Problem 8 What is the area of the shaded region of the given rectangle? Solution Problem 9 The five small shaded squares inside this unit square are congruent and have disjoint interiors. The midpoint of each side of the middle square coincides with one of the vertices of the other four small squares as shown. The common side length is integers. What is ? , where and are positive Solution Problem 10 Five friends sat in a movie theater in a row containing seats, numbered to from left to right. (The directions \seats.) During the movie Ada went to the lobby to get some popcorn. When she returned, she found that Bea had moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada been sitting before she got up? Solution Problem 11 Each of the students in a certain summer camp can either sing, dance, or act. Some students have more than one talent, but no student has all three talents. There are students who cannot sing, students who cannot dance, and students who cannot act. How many students have two of these talents? Solution Problem 12 In , , , and and bisects . Point lies on intersect at . What is the ratio : ? . Point , and lies on bisects , . The bisectors Solution Problem 13 Let be a positive multiple of . One red ball and green balls are arranged in a line in random order. Let be the probability that at least of the green balls are on the same and that approaches as ? grows large. side of the red ball. Observe that What is the sum of the digits of the least value of such that Solution Problem 14 Each vertex of a cube is to be labeled with an integer from through , with each integer being used once, in such a way that the sum of the four numbers on the vertices of a face is the same for each face. Arrangements that can be obtained from each other through rotations of the cube are considered to be the same. How many different arrangements are possible? Solution Problem 15 Circles with centers and , having radii and , respectively, lie on the same side of line and are tangent to at and , respectively, with between and . The circle with center is externally tangent to each of the other two circles. What is the area of triangle ? Solution Problem 16 The graphs of and are plotted on the same set of axes. How many points in the plane with positive -coordinates lie on two or more of the graphs? Solution Problem 17 Let be a square. Let and and be the centers, respectively, of equilateral each exterior to the square. What is the ratio ? triangles with bases of the area of square to the area of square Solution Problem 18 For some positive integer the number has positive integer divisors, including and the number How many positive integer divisors does the number have? Solution Problem 19 Jerry starts at on the real number line. He tosses a fair coin times. When he gets heads, he moves unit in the positive direction; when he gets tails, he moves unit in the negative direction. The probability that he reaches at some time during this process is where and are relatively prime positive integers. What is ) (For example, he succeeds if his sequence of tosses is — 7 —。