경시 · AMC 대비 · 4단계 중 4

AMC 10 2021B 문제 25개

문제마다 원리부터 푸는 풀이와 처음 풀 수 있는 학년(CCSS 기준)이 있습니다.

AMC 10 2021B #1 7학년부터 arithmetic
How many integer values of x satisfy |x|<3π?
AMC 10 2021B #2 8학년부터 arithmetic
What is the value of √((3-2√3)²)+√((3+2√3)²)?
AMC 10 2021B #3 6학년부터 arithmetic
In an after-school program for juniors and seniors, there is a debate team with an equal number of students from each cl…
AMC 10 2021B #4 4학년부터 counting
At a math contest, 57 students are wearing blue shirts, and another 75 students are wearing yellow shirts. The 132 stude…
AMC 10 2021B #5 5학년부터 arithmetic
The ages of Jonie's four cousins are distinct single-digit positive integers. Two of the cousins' ages multiplied togeth…
AMC 10 2021B #6 6학년부터 rate-ratio
Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is 84, and the a…
AMC 10 2021B #7 7학년부터 geometry-2d
In a plane, four circles with radii 1,3,5, and 7 are tangent to line ell at the same point A, but they may be on either…
AMC 10 2021B #8 5학년부터 geometry-2d
Mr. Zhou places all the integers from 1 to 225 into a 15 by 15 grid. He places 1 in the middle square (eighth row and ei…
AMC 10 2021B #9 8학년부터 geometry-2d
The point P(a,b) in the xy-plane is first rotated counterclockwise by 90° around the point (1,5) and then reflected abou…
AMC 10 2021B #10 8학년부터 geometry-3d
An inverted cone with base radius 12 cm and height 18 cm is full of water. The water is poured into a tall cylinder whos…
AMC 10 2021B #11 6학년부터 geometry-2d
Grandma has just finished baking a large rectangular pan of brownies. She is planning to make rectangular pieces of equa…
AMC 10 2021B #12 6학년부터 number-theory
Let N = 34 · 34 · 63 · 270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N?
AMC 10 2021B #13 6학년부터 arithmetic
Let n be a positive integer and d be a digit such that the value of the numeral 32d in base n equals 263, and the value…
AMC 10 2021B #14 8학년부터 geometry-2d
Three equally spaced parallel lines intersect a circle, creating three chords of lengths 38,38, and 34. What is the dist…
AMC 10 2021B #15 8학년부터 algebra
The real number x satisfies the equation x+1/x = √5. What is the value of x¹¹-7x⁷+x³?
AMC 10 2021B #16 4학년부터 number-theory
Call a positive integer an uphill integer if every digit is strictly greater than the previous digit. For example, 1357,…
AMC 10 2021B #17 2학년부터 arithmetic
Ravon, Oscar, Aditi, Tyrone, and Kim play a card game. Each person is given 2 cards out of a set of 10 cards numbered 1,…
AMC 10 2021B #18 7학년부터 probability
A fair 6-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appe…
AMC 10 2021B #19 6학년부터 algebra
Suppose that S is a finite set of positive integers. If the greatest integer in S is removed from S, then the average va…
AMC 10 2021B #20 8학년부터 geometry-2d
The figure is constructed from 11 line segments, each of which has length 2. The area of pentagon ABCDE can be written a…
AMC 10 2021B #21 8학년부터 geometry-2d
A square piece of paper has side length 1 and vertices A,B,C, and D in that order. As shown in the figure, the paper is…
AMC 10 2021B #22 7학년부터 probability
Ang, Ben, and Jasmin each have 5 blocks, colored red, blue, yellow, white, and green; and there are 5 empty boxes. Each…
AMC 10 2021B #23 8학년부터 geometry-2d
A square with side length 8 is colored white except for 4 black isosceles right triangular regions with legs of length 2…
AMC 10 2021B #24 7학년부터 arithmetic
Arjun and Beth play a game in which they take turns removing one brick or two adjacent bricks from one "wall" among a se…
AMC 10 2021B #25 8학년부터 number-theory
Let S be the set of lattice points in the coordinate plane, both of whose coordinates are integers between 1 and 30, inc…

가족의 부모 대시보드는 sensimlab.com에 있습니다.