2021AMC8考题及答案

2024年1月22日发(作者：北京101数学试卷)

2021 AMC 8 考题及答案

Problem 1

Which of the following values is largest?

Problem 2

Alicia, Brenda, and Colby were the candidates in a recent election for

student president. The pie chart below shows how the votes were

distributed among the three candidates. If Brenda received 36 votes,

then how many votes were cast all together?

Problem 3

What is the value of the expression ?

Problem 4

When 0.000315 is multiplied by 7,928,564 the product is closest to

which of the following?

Problem 5

What is the value of the expression

?

Problem 6

If the degree measures of the angles of a triangle are in the ratio

, what is the degree measure of the largest angle of the

triangle?

Problem 7

Let be a 6-digit positive integer, such as 247247, whose first

three digits are the same as its last three digits taken in the same

order. Which of the following numbers must also be a factor of ?

Problem 8

Malcolm wants to visit Isabella after school today and knows the

street where she lives but doesn\'t know her house number. She tells

him, \"My house number has two digits, and exactly three of the

following four statements about it are true.\"

(1) It is prime.

(2) It is even.

(3) It is divisible by 7.

(4) One of its digits is 9.

This information allows Malcolm to determine Isabella\'s house number.

What is its units digit?

Problem 9

All of Marcy\'s marbles are blue, red, green, or yellow. One third of

her marbles are blue, one fourth of them are red, and six of them are

green. What is the smallest number of yellow marbles that Marcy could

have?

Problem 10

A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards

are selected randomly without replacement from the box. What is the

probability that 4 is the largest value selected?

Problem 11

A square-shaped floor is covered with congruent square tiles. If the

total number of tiles that lie on the two diagonals is 37, how many

tiles cover the floor?

Problem 12

The smallest positive integer greater than 1 that leaves a remainder

of 1 when divided by 4, 5, and 6 lies between which of the following

pairs of numbers?

Problem 13

Peter, Emma, and Kyler played chess with each other. Peter won 4

games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler

lost 3 games, how many games did he win?

Problem 14

Chloe and Zoe are both students in Ms. Demeanor\'s math class. Last

night they each solved half of the problems in their homework

assignment alone and then solved the other half together. Chloe had

correct answers to only

overall

of the problems she solved alone, but

of her answers were correct. Zoe had correct answers to

of the problems she solved alone. What was Zoe\'s overall

percentage of correct answers?

Problem 15

In the arrangement of letters and numerals below, by how many

different paths can one spell AMC8? Beginning at the A in the middle,

a path allows only moves from one letter to an adjacent (above,

below, left, or right, but not diagonal) letter. One example of such

a path is traced in the picture.

Problem 16

In the figure below, choose point on so that and

? have equal perimeters. What is the area of

Problem 17

Starting with some gold coins and some empty treasure chests, I tried

to put 9 gold coins in each treasure chest, but that left 2 treasure

chests empty. So instead I put 6 gold coins in each treasure chest,

but then I had 3 gold coins left over. How many gold coins did I

have?

Problem 18

In the non-convex quadrilateral

right angle, , ,

shown below,

, and .

is a

What is the area of quadrilateral ?

Problem 19

For any positive integer

the integers through

is a factor of the sum

, the notation

?

denotes the product of

. What is the largest integer for which

Problem 20

An integer between

all distinct?

and , inclusive, is chosen at random.

What is the probability that it is an odd integer whose digits are

Problem 21

Suppose , , and are nonzero real numbers, and . What

are the possible value(s) for ?

Problem 22

In the right triangle , , , and angle is a

right angle. A semicircle is inscribed in the triangle as shown. What

is the radius of the semicircle?

Problem 23

Each day for four days, Linda traveled for one hour at a speed that

resulted in her traveling one mile in an integer number of minutes.

Each day after the first, her speed decreased so that the number of

minutes to travel one mile increased by 5 minutes over the preceding

day. Each of the four days, her distance traveled was also an integer

number of miles. What was the total number of miles for the four

trips?

Problem 24

Mrs. Sanders has three grandchildren, who call her regularly. One

calls her every three days, one calls her every four days, and one

calls her every five days. All three called her on December 31, 2021.

On how many days during the next year did she not receive a phone

call from any of her grandchildren?

Problem 25

In the figure shown,

and

and are line segments each of length 2,

are each one-sixth of a circle . Arcs and

with radius 2. What is the area of the region shown?

2021 AMC 8 Answer Key

1.

A

2.

E

3.

C

4.

D

5.

B

6.

D

7.

A

8.

D

9.

D

10.

C

11.

C

12.

D

13.

B

14.

C

15.

D

16.

D

17.

C

18.

B

19.

D

20.

B

21.

A

22.

D

23.

C

24.

D

25.

B